Daily Papers

Exploration bonuses in reinforcement learning guide long-horizon exploration by defining custom intrinsic objectives. Several exploration objectives like count-based bonuses, pseudo-counts, and state-entropy maximization are non-stationary and hence are difficult to optimize for the agent. While this issue is generally known, it is usually omitted and solutions remain under-explored. The key contribution of our work lies in transforming the original non-stationary rewards into stationary rewards through an augmented state representation. For this purpose, we introduce the Stationary Objectives For Exploration (SOFE) framework. SOFE requires identifying sufficient statistics for different exploration bonuses and finding an efficient encoding of these statistics to use as input to a deep network. SOFE is based on proposing state augmentations that expand the state space but hold the promise of simplifying the optimization of the agent's objective. We show that SOFE improves the performance of several exploration objectives, including count-based bonuses, pseudo-counts, and state-entropy maximization. Moreover, SOFE outperforms prior methods that attempt to stabilize the optimization of intrinsic objectives. We demonstrate the efficacy of SOFE in hard-exploration problems, including sparse-reward tasks, pixel-based observations, 3D navigation, and procedurally generated environments.

Complex numerical time series analysis often demands multi-step reasoning capabilities beyond current models' reach. Tasks like medical diagnosis and weather forecasting require sequential reasoning processes - including counterfactual analysis, logical deduction, knowledge application, and multi-modal contextual integration - that existing time series models cannot explicitly perform. While recent research has shown large language models (LLMs) can achieve sophisticated Chain-of-Thought (CoT) reasoning through reinforcement learning (RL), these advances have primarily focused on mathematical and coding domains, with LLMs still demonstrating poor performance on time series tasks. We introduce Chain Of thought for Understanding Numerical Time Series (COUNTS), the first framework that trains LLMs to perform CoT reasoning across diverse time series tasks using RL with verifiable rewards. Our approach employs a Residual Vector-Quantized VAE to create high-fidelity discrete tokens that seamlessly integrate into a pre-trained LLM's vocabulary. COUNTS undergoes a two-stage training process: first, supervised fine-tuning on time series analysis tasks to master our novel representations, followed by Group Relative Policy Optimization training on verifiable problems using prompting strategies that encourage explicit reasoning steps before producing final answers. Our experiments demonstrate that this RL-driven approach with intermediate CoT reasoning significantly enhances LLM performance across various time series analysis tasks, opening new possibilities for complex temporal data reasoning.

Despite progress in video understanding, current MLLMs struggle with counting tasks. Existing benchmarks are limited by short videos, close-set queries, lack of clue annotations, and weak multimodal coverage. In this paper, we introduce CG-AV-Counting, a manually-annotated clue-grounded counting benchmark with 1,027 multimodal questions and 5,845 annotated clues over 497 long videos. It supports both black-box and white-box evaluation, serving as a comprehensive testbed for both end-to-end and reasoning-based counting. To explore ways to improve model's counting capability, we propose AV-Reasoner, a model trained with GRPO and curriculum learning to generalize counting ability from related tasks. AV-Reasoner achieves state-of-the-art results across multiple benchmarks, demonstrating the effectiveness of reinforcement learning. However, experiments show that on out-of-domain benchmarks, reasoning in the language space fails to bring performance gains. The code and benchmark have been realeased on https://av-reasoner.github.io.

Exploration in environments which differ across episodes has received increasing attention in recent years. Current methods use some combination of global novelty bonuses, computed using the agent's entire training experience, and episodic novelty bonuses, computed using only experience from the current episode. However, the use of these two types of bonuses has been ad-hoc and poorly understood. In this work, we shed light on the behavior of these two types of bonuses through controlled experiments on easily interpretable tasks as well as challenging pixel-based settings. We find that the two types of bonuses succeed in different settings, with episodic bonuses being most effective when there is little shared structure across episodes and global bonuses being effective when more structure is shared. We develop a conceptual framework which makes this notion of shared structure precise by considering the variance of the value function across contexts, and which provides a unifying explanation of our empirical results. We furthermore find that combining the two bonuses can lead to more robust performance across different degrees of shared structure, and investigate different algorithmic choices for defining and combining global and episodic bonuses based on function approximation. This results in an algorithm which sets a new state of the art across 16 tasks from the MiniHack suite used in prior work, and also performs robustly on Habitat and Montezuma's Revenge.

We propose YOLO-Count, a differentiable open-vocabulary object counting model that tackles both general counting challenges and enables precise quantity control for text-to-image (T2I) generation. A core contribution is the 'cardinality' map, a novel regression target that accounts for variations in object size and spatial distribution. Leveraging representation alignment and a hybrid strong-weak supervision scheme, YOLO-Count bridges the gap between open-vocabulary counting and T2I generation control. Its fully differentiable architecture facilitates gradient-based optimization, enabling accurate object count estimation and fine-grained guidance for generative models. Extensive experiments demonstrate that YOLO-Count achieves state-of-the-art counting accuracy while providing robust and effective quantity control for T2I systems.

We propose a new method for count-based exploration in high-dimensional state spaces. Unlike previous work which relies on density models, we show that counts can be derived by averaging samples from the Rademacher distribution (or coin flips). This insight is used to set up a simple supervised learning objective which, when optimized, yields a state's visitation count. We show that our method is significantly more effective at deducing ground-truth visitation counts than previous work; when used as an exploration bonus for a model-free reinforcement learning algorithm, it outperforms existing approaches on most of 9 challenging exploration tasks, including the Atari game Montezuma's Revenge.

The CLIP (Contrastive Language-Image Pretraining) model has exhibited outstanding performance in recognition problems, such as zero-shot image classification and object detection. However, its ability to count remains understudied due to the inherent challenges of transforming counting--a regression task--into a recognition task. In this paper, we investigate CLIP's potential in counting, focusing specifically on estimating crowd sizes. Existing classification-based crowd-counting methods have encountered issues, including inappropriate discretization strategies, which impede the application of CLIP and result in suboptimal performance. To address these challenges, we propose the Enhanced Blockwise Classification (EBC) framework. In contrast to previous methods, EBC relies on integer-valued bins that facilitate the learning of robust decision boundaries. Within our model-agnostic EBC framework, we introduce CLIP-EBC, the first fully CLIP-based crowd-counting model capable of generating density maps. Comprehensive evaluations across diverse crowd-counting datasets demonstrate the state-of-the-art performance of our methods. Particularly, EBC can improve existing models by up to 76.9%. Moreover, our CLIP-EBC model surpasses current crowd-counting methods, achieving mean absolute errors of 55.0 and 6.3 on ShanghaiTech part A and part B datasets, respectively. The code will be made publicly available.

Mixed-motive multi-agent settings are rife with persistent free-riding because individual effort benefits all members equally, yet each member bears the full cost of their own contribution. Classical work by Holmström established that under pure self-interest, Nash equilibrium is universal shirking. While i* represents teams as composite actors, it lacks scalable computational mechanisms for analyzing how collective action problems emerge and resolve in coopetitive settings. This technical report extends computational foundations for strategic coopetition to team-level dynamics, building on companion work formalizing interdependence/complementarity (arXiv:2510.18802) and trust dynamics (arXiv:2510.24909). We develop loyalty-moderated utility functions with two mechanisms: loyalty benefit (welfare internalization plus intrinsic contribution satisfaction) and cost tolerance (reduced effort burden for loyal members). We integrate i* structural dependencies through dependency-weighted team cohesion, connecting member incentives to team-level positioning. The framework applies to both human teams (loyalty as psychological identification) and multi-agent systems (alignment coefficients and adjusted cost functions). Experimental validation across 3,125 configurations demonstrates robust loyalty effects (15.04x median effort differentiation). All six behavioral targets achieve thresholds: free-riding baseline (96.5%), loyalty monotonicity (100%), effort differentiation (100%), team size effect (100%), mechanism synergy (99.5%), and bounded outcomes (100%). Empirical validation using published Apache HTTP Server (1995-2023) case study achieves 60/60 points, reproducing contribution patterns across formation, growth, maturation, and governance phases. Statistical significance confirmed at p<0.001, Cohen's d=0.71.

The flexibility and accuracy of methods for automatically counting objects in images and videos are limited by the way the object can be specified. While existing methods allow users to describe the target object with text and visual examples, the visual examples must be manually annotated inside the image, and there is no way to specify what not to count. To address these gaps, we introduce novel capabilities that expand how the target object can be specified. Specifically, we extend the prompt to enable what not to count to be described with text and/or visual examples, introduce the concept of `pseudo-exemplars' that automate the annotation of visual examples at inference, and extend counting models to accept visual examples from both natural and synthetic external images. We also use our new counting model, CountGD++, as a vision expert agent for an LLM. Together, these contributions expand the prompt flexibility of multi-modal open-world counting and lead to significant improvements in accuracy, efficiency, and generalization across multiple datasets. Code is available at https://github.com/niki-amini-naieni/CountGDPlusPlus.

Recently, the problem of inaccurate learning targets in crowd counting draws increasing attention. Inspired by a few pioneering work, we solve this problem by trying to predict the indices of pre-defined interval bins of counts instead of the count values themselves. However, an inappropriate interval setting might make the count error contributions from different intervals extremely imbalanced, leading to inferior counting performance. Therefore, we propose a novel count interval partition criterion called Uniform Error Partition (UEP), which always keeps the expected counting error contributions equal for all intervals to minimize the prediction risk. Then to mitigate the inevitably introduced discretization errors in the count quantization process, we propose another criterion called Mean Count Proxies (MCP). The MCP criterion selects the best count proxy for each interval to represent its count value during inference, making the overall expected discretization error of an image nearly negligible. As far as we are aware, this work is the first to delve into such a classification task and ends up with a promising solution for count interval partition. Following the above two theoretically demonstrated criterions, we propose a simple yet effective model termed Uniform Error Partition Network (UEPNet), which achieves state-of-the-art performance on several challenging datasets. The codes will be available at: https://github.com/TencentYoutuResearch/CrowdCounting-UEPNet.

Class-agnostic counting (CAC) aims to estimate the number of objects in images without being restricted to predefined categories. However, while current exemplar-based CAC methods offer flexibility at inference time, they still rely heavily on labeled data for training, which limits scalability and generalization to many downstream use cases. In this paper, we introduce CountingDINO, the first training-free exemplar-based CAC framework that exploits a fully unsupervised feature extractor. Specifically, our approach employs self-supervised vision-only backbones to extract object-aware features, and it eliminates the need for annotated data throughout the entire proposed pipeline. At inference time, we extract latent object prototypes via ROI-Align from DINO features and use them as convolutional kernels to generate similarity maps. These are then transformed into density maps through a simple yet effective normalization scheme. We evaluate our approach on the FSC-147 benchmark, where we consistently outperform a baseline based on an SOTA unsupervised object detector under the same label- and training-free setting. Additionally, we achieve competitive results -- and in some cases surpass -- training-free methods that rely on supervised backbones, non-training-free unsupervised methods, as well as several fully supervised SOTA approaches. This demonstrates that label- and training-free CAC can be both scalable and effective. Code: https://lorebianchi98.github.io/CountingDINO/.

Large vision-language models (VLMs) are shown to learn rich joint image-text representations enabling high performances in relevant downstream tasks. However, they fail to showcase their quantitative understanding of objects, and they lack good counting-aware representation. This paper conducts a reproducibility study of 'Teaching CLIP to Count to Ten' (Paiss et al., 2023), which presents a method to finetune a CLIP model (Radford et al., 2021) to improve zero-shot counting accuracy in an image while maintaining the performance for zero-shot classification by introducing a counting-contrastive loss term. We improve the model's performance on a smaller subset of their training data with lower computational resources. We verify these claims by reproducing their study with our own code. The implementation can be found at https://github.com/SforAiDl/CountCLIP.

Vision--language models (VLMs) have achieved impressive performance on complex multimodal reasoning tasks, yet they still fail on simple grounding skills such as object counting. Existing evaluations mostly assess only final outputs, offering limited insight into where these failures arise inside the model. In this work, we present an empirical study of VLM counting behavior through both behavioral and mechanistic analysis. We introduce COUNTINGTRICKS, a controlled evaluation suite of simple shape-based counting cases designed to expose vulnerabilities under different patchification layouts and adversarial prompting conditions. Using attention analysis and component-wise probing, we show that count-relevant visual evidence is strongest in the modality projection stage but degrades substantially in later language layers, where models become more susceptible to text priors. Motivated by this finding, we further evaluate Modality Attention Share (MAS), a lightweight intervention that encourages a minimum budget of visual attention during answer generation. Our results suggest that counting failures in VLMs stem not only from visual perception limits, but also from the underuse of visual evidence during language-stage reasoning. Code and dataset will be released at https://github.com/leduy99/-CVPRW26-Modality-Attention-Share.

We propose the use of dilated filters to construct an aggregation module in a multicolumn convolutional neural network for perspective-free counting. Counting is a common problem in computer vision (e.g. traffic on the street or pedestrians in a crowd). Modern approaches to the counting problem involve the production of a density map via regression whose integral is equal to the number of objects in the image. However, objects in the image can occur at different scales (e.g. due to perspective effects) which can make it difficult for a learning agent to learn the proper density map. While the use of multiple columns to extract multiscale information from images has been shown before, our approach aggregates the multiscale information gathered by the multicolumn convolutional neural network to improve performance. Our experiments show that our proposed network outperforms the state-of-the-art on many benchmark datasets, and also that using our aggregation module in combination with a higher number of columns is beneficial for multiscale counting.

We introduce an exploration bonus for deep reinforcement learning methods that is easy to implement and adds minimal overhead to the computation performed. The bonus is the error of a neural network predicting features of the observations given by a fixed randomly initialized neural network. We also introduce a method to flexibly combine intrinsic and extrinsic rewards. We find that the random network distillation (RND) bonus combined with this increased flexibility enables significant progress on several hard exploration Atari games. In particular we establish state of the art performance on Montezuma's Revenge, a game famously difficult for deep reinforcement learning methods. To the best of our knowledge, this is the first method that achieves better than average human performance on this game without using demonstrations or having access to the underlying state of the game, and occasionally completes the first level.

Interestingly, LLMs yet struggle with some basic tasks that humans find trivial to handle, e.g., counting the number of character r's in the word "strawberry". There are several popular conjectures (e.g., tokenization, architecture and training data) regarding the reason for deficiency of LLMs in simple word-based counting problems, sharing the similar belief that such failure stems from model pretraining hence probably inevitable during deployment. In this paper, we carefully design multiple evaluation settings to investigate validity of prevalent conjectures. Meanwhile, we measure transferability of advanced mathematical and coding reasoning capabilities from specialized LLMs to simple counting tasks. Although specialized LLMs suffer from counting problems as well, we find conjectures about inherent deficiency of LLMs invalid and further seek opportunities to elicit knowledge and capabilities from LLMs that are beneficial to counting tasks. Compared with strategies such as finetuning and in-context learning that are commonly adopted to enhance performance on new or challenging tasks, we show that engaging reasoning is the most robust and efficient way to help LLMs better perceive tasks with more accurate responses. We hope our conjecture validation design could provide insights into the study of future critical failure modes of LLMs. Based on challenges in transferring advanced capabilities to much simpler tasks, we call for more attention to model capability acquisition and evaluation. We also highlight the importance of cultivating consciousness of "reasoning before responding" during model pretraining.

Open-world object counting remains brittle: despite rapid advances in vision-language models (VLMs), reliably counting the objects a user intends is far from solved. We argue that a central reason is that counting granularity is left implicit; users may refer to a specific identity, an attribute, an instance type, a category, or an abstract concept, yet most methods treat "what to count" as a single, category-level matching problem. In this work, we redefine open-world counting as multi-grained counting, where visual exemplars specify target appearance and fine-grained text, with optional negative prompts, specifies the intended semantic granularity across five explicit levels. Making granularity explicit, however, exposes a critical data bottleneck: existing counting datasets lack the multi-category scenes, controlled distractors, and instance-level annotations needed to verify fine-grained prompt semantics. To address this, we propose the first fully automatic data-scaling pipeline that integrates controllable 3D synthesis with consistent image editing and VLM-based filtering, and use it to construct KubriCount, the largest and most comprehensively annotated counting dataset to date, supporting both training and multi-grained evaluation. Systematic benchmarking reveals that both multimodal large language models and specialist counting models exhibit severe prompt-following failures under fine-grained distinctions. Motivated by these findings, we train HieraCount, a multi-grained counting model that jointly leverages text and visual exemplars as complementary target specifications. HieraCount substantially improves multi-grained counting accuracy and generalizes robustly to challenging real-world scenarios. The project page is available here: https://verg-avesta.github.io/KubriCount/.

We propose a novel framework for interactive class-agnostic object counting, where a human user can interactively provide feedback to improve the accuracy of a counter. Our framework consists of two main components: a user-friendly visualizer to gather feedback and an efficient mechanism to incorporate it. In each iteration, we produce a density map to show the current prediction result, and we segment it into non-overlapping regions with an easily verifiable number of objects. The user can provide feedback by selecting a region with obvious counting errors and specifying the range for the estimated number of objects within it. To improve the counting result, we develop a novel adaptation loss to force the visual counter to output the predicted count within the user-specified range. For effective and efficient adaptation, we propose a refinement module that can be used with any density-based visual counter, and only the parameters in the refinement module will be updated during adaptation. Our experiments on two challenging class-agnostic object counting benchmarks, FSCD-LVIS and FSC-147, show that our method can reduce the mean absolute error of multiple state-of-the-art visual counters by roughly 30% to 40% with minimal user input. Our project can be found at https://yifehuang97.github.io/ICACountProjectPage/.

Large vision-language models (VLMs), such as CLIP, learn rich joint image-text representations, facilitating advances in numerous downstream tasks, including zero-shot classification and text-to-image generation. Nevertheless, existing VLMs exhibit a prominent well-documented limitation - they fail to encapsulate compositional concepts such as counting. We introduce a simple yet effective method to improve the quantitative understanding of VLMs, while maintaining their overall performance on common benchmarks. Specifically, we propose a new counting-contrastive loss used to finetune a pre-trained VLM in tandem with its original objective. Our counting loss is deployed over automatically-created counterfactual examples, each consisting of an image and a caption containing an incorrect object count. For example, an image depicting three dogs is paired with the caption "Six dogs playing in the yard". Our loss encourages discrimination between the correct caption and its counterfactual variant which serves as a hard negative example. To the best of our knowledge, this work is the first to extend CLIP's capabilities to object counting. Furthermore, we introduce "CountBench" - a new image-text counting benchmark for evaluating a model's understanding of object counting. We demonstrate a significant improvement over state-of-the-art baseline models on this task. Finally, we leverage our count-aware CLIP model for image retrieval and text-conditioned image generation, demonstrating that our model can produce specific counts of objects more reliably than existing ones.

Best-of-N (BoN) sampling, a common strategy for test-time scaling of Large Language Models (LLMs), relies on reward models to select the best candidate solution from multiple generations. However, traditional reward models often assign arbitrary and inconsistent scores, limiting their effectiveness. To address this, we propose a Pairwise Reward Model (Pairwise RM) combined with a knockout tournament for BoN sampling. Instead of assigning absolute scores, given one math problem, Pairwise RM evaluates two candidate solutions' correctness simultaneously. This approach eliminates the need for arbitrary scoring and enables cross-validation of solutions through parallel comparison. In the knockout tournament, Pairwise RM conducts pairwise comparisons between candidate solutions and eliminates the incorrect ones iteratively. We construct \ourdataset, a large-scale dataset of 443K pairwise comparisons derived from NumiaMath and annotated using gemini-1.5-flash, and train the Pairwise RM via supervised fine-tuning. Experiments on MATH-500 and the Olympiad Bench demonstrate significant improvements over traditional discriminative reward models. And a 40\% to 60\% relative improvement is achieved on the top 50\% challenging problems.

Large language models have demonstrated impressive reasoning capabilities, yet they often suffer from inefficiencies due to unnecessarily verbose or redundant outputs. While many works have explored reinforcement learning (RL) to enhance reasoning abilities, most primarily focus on improving accuracy, with limited attention to reasoning efficiency. Some existing approaches introduce direct length-based rewards to encourage brevity, but this often leads to noticeable drops in accuracy. In this paper, we propose Bingo, an RL framework that advances length-based reward design to boost efficient reasoning. Bingo incorporates two key mechanisms: a significance-aware length reward, which gradually guides the model to reduce only insignificant tokens, and a dynamic length reward, which initially encourages elaborate reasoning for hard questions but decays over time to improve overall efficiency. Experiments across multiple reasoning benchmarks show that Bingo improves both accuracy and efficiency. It outperforms the vanilla reward and several other length-based reward baselines in RL, achieving a favorable trade-off between accuracy and efficiency. These results underscore the potential of training LLMs explicitly for efficient reasoning.

Existing works on visual counting primarily focus on one specific category at a time, such as people, animals, and cells. In this paper, we are interested in counting everything, that is to count objects from any category given only a few annotated instances from that category. To this end, we pose counting as a few-shot regression task. To tackle this task, we present a novel method that takes a query image together with a few exemplar objects from the query image and predicts a density map for the presence of all objects of interest in the query image. We also present a novel adaptation strategy to adapt our network to any novel visual category at test time, using only a few exemplar objects from the novel category. We also introduce a dataset of 147 object categories containing over 6000 images that are suitable for the few-shot counting task. The images are annotated with two types of annotation, dots and bounding boxes, and they can be used for developing few-shot counting models. Experiments on this dataset shows that our method outperforms several state-of-the-art object detectors and few-shot counting approaches. Our code and dataset can be found at https://github.com/cvlab-stonybrook/LearningToCountEverything.

Zero-shot object counting (ZOC) aims to enumerate objects in images using only the names of object classes during testing, without the need for manual annotations. However, a critical challenge in current ZOC methods lies in their inability to identify high-quality exemplars effectively. This deficiency hampers scalability across diverse classes and undermines the development of strong visual associations between the identified classes and image content. To this end, we propose the Visual Association-based Zero-shot Object Counting (VA-Count) framework. VA-Count consists of an Exemplar Enhancement Module (EEM) and a Noise Suppression Module (NSM) that synergistically refine the process of class exemplar identification while minimizing the consequences of incorrect object identification. The EEM utilizes advanced vision-language pretaining models to discover potential exemplars, ensuring the framework's adaptability to various classes. Meanwhile, the NSM employs contrastive learning to differentiate between optimal and suboptimal exemplar pairs, reducing the negative effects of erroneous exemplars. VA-Count demonstrates its effectiveness and scalability in zero-shot contexts with superior performance on two object counting datasets.

We utilize an offline reinforcement learning (RL) model for sequential targeted promotion in the presence of budget constraints in a real-world business environment. In our application, the mobile app aims to boost customer retention by sending cash bonuses to customers and control the costs of such cash bonuses during each time period. To achieve the multi-task goal, we propose the Budget Constrained Reinforcement Learning for Sequential Promotion (BCRLSP) framework to determine the value of cash bonuses to be sent to users. We first find out the target policy and the associated Q-values that maximizes the user retention rate using an RL model. A linear programming (LP) model is then added to satisfy the constraints of promotion costs. We solve the LP problem by maximizing the Q-values of actions learned from the RL model given the budget constraints. During deployment, we combine the offline RL model with the LP model to generate a robust policy under the budget constraints. Using both online and offline experiments, we demonstrate the efficacy of our approach by showing that BCRLSP achieves a higher long-term customer retention rate and a lower cost than various baselines. Taking advantage of the near real-time cost control method, the proposed framework can easily adapt to data with a noisy behavioral policy and/or meet flexible budget constraints.

Large language models often fail at simple counting tasks, even when the items to count are explicitly present in the prompt. We investigate whether this failure occurs because transformers do not represent counts internally, or because they cannot convert those representations into the correct output tokens. Across three model families, Pythia, Qwen3, and Mistral, ranging from 0.4B to 14B parameters, we find strong evidence for the second explanation. Linear probes recover the correct count from intermediate layers with near-perfect accuracy (R^2>0.99), showing that the information is present. However, the internal directions that encode counts are nearly orthogonal to the output-head rows for digit tokens (|cos|leq0.032). In other words, the model stores the count in a form that the digit logits do not naturally read out. We localize this failure with two interventions. Updating only the digit rows of the output head (36,864 parameters) substantially improves constrained next-token digit prediction (60.7 to 100.0% across four tasks), but it does not fix autoregressive generation. By contrast, a small LoRA intervention on attention Q/V weights (7.67M parameters) improves upstream routing and achieves 83.1% +/- 7.2% in true greedy autoregressive generation. Logit-lens measurements confirm the mechanism: the correct digit's vocabulary rank drops from 55,980 to 1, a 50,000x improvement. Additional norm, logit-lens, and cross-task analyses show that the bottleneck generalizes across character counting, addition, and list length, while remaining absent from broader multi-step reasoning benchmarks, including MMLU, GSM8K, and DROP. These results identify counting failure as a geometric readout bottleneck rather than a failure of internal representation: the model knows the count but the output pathway is geometrically misaligned with the tokens needed to express it.

Text-to-image (T2I) diffusion models have achieved strong performance in semantic alignment, yet they still struggle with generating the correct number of objects specified in prompts. Existing approaches typically incorporate auxiliary counting networks as external critics to enhance numeracy. However, since these critics must provide gradient guidance during generation, they are restricted to regression-based models that are inherently differentiable, thus excluding detector-based models with superior counting ability, whose count-via-enumeration nature is non-differentiable. To overcome this limitation, we propose Detector-to-Differentiable (D2D), a novel framework that transforms non-differentiable detection models into differentiable critics, thereby leveraging their superior counting ability to guide numeracy generation. Specifically, we design custom activation functions to convert detector logits into soft binary indicators, which are then used to optimize the noise prior at inference time with pre-trained T2I models. Our extensive experiments on SDXL-Turbo, SD-Turbo, and Pixart-DMD across four benchmarks of varying complexity (low-density, high-density, and multi-object scenarios) demonstrate consistent and substantial improvements in object counting accuracy (e.g., boosting up to 13.7% on D2D-Small, a 400-prompt, low-density benchmark), with minimal degradation in overall image quality and computational overhead.

Class-agnostic counting methods enumerate objects of an arbitrary class, providing tremendous utility in many fields. Prior works have limited usefulness as they require either a set of examples of the type to be counted or that the query image contains only a single type of object. A significant factor in these shortcomings is the lack of a dataset to properly address counting in settings with more than one kind of object present. To address these issues, we propose the first Multi-class, Class-Agnostic Counting dataset (MCAC) and A Blind Counter (ABC123), a method that can count multiple types of objects simultaneously without using examples of type during training or inference. ABC123 introduces a new paradigm where instead of requiring exemplars to guide the enumeration, examples are found after the counting stage to help a user understand the generated outputs. We show that ABC123 outperforms contemporary methods on MCAC without needing human in-the-loop annotations. We also show that this performance transfers to FSC-147, the standard class-agnostic counting dataset. MCAC is available at MCAC.active.vision and ABC123 is available at ABC123.active.vision.

We address a persistent challenge in text-to-image models: accurately generating a specified number of objects. Current models, which learn from image-text pairs, inherently struggle with counting, as training data cannot depict every possible number of objects for any given object. To solve this, we propose optimizing the generated image based on a counting loss derived from a counting model that aggregates an object\'s potential. Employing an out-of-the-box counting model is challenging for two reasons: first, the model requires a scaling hyperparameter for the potential aggregation that varies depending on the viewpoint of the objects, and second, classifier guidance techniques require modified models that operate on noisy intermediate diffusion steps. To address these challenges, we propose an iterated online training mode that improves the accuracy of inferred images while altering the text conditioning embedding and dynamically adjusting hyperparameters. Our method offers three key advantages: (i) it can consider non-derivable counting techniques based on detection models, (ii) it is a zero-shot plug-and-play solution facilitating rapid changes to the counting techniques and image generation methods, and (iii) the optimized counting token can be reused to generate accurate images without additional optimization. We evaluate the generation of various objects and show significant improvements in accuracy. The project page is available at https://ozzafar.github.io/count_token.

Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry's under-counting probability can be provably recovered from partial observations -- under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

Object counting remains fragmented across domain-specific datasets and task formulations, despite rapid progress in generalist vision models. Existing counting models are often tailored to scenarios such as crowds, vehicles, cells, crops, or remote-sensing objects, and thus struggle to generalize across categories, visual domains, object scales, and density distributions. In this paper, we study text-guided object counting across domains, where a model takes an image and a natural-language query as input and returns an instance-grounded set of target points whose cardinality gives the count. This formulation unifies category-conditioned counting with interpretable spatial localization. To support this setting, we construct CLOC, a Cross-domain Large-scale Object Counting dataset that reorganizes diverse public data sources into a unified benchmark. CLOC covers six visual domains: General Scene, Remote Sensing, Histopathology, Cellular Microscopy, Agriculture, and Microbiology, with about 220K images, 619 categories, and 15M object instances. Based on CLOC, we propose Count Anything, a generalist model for text-guided object counting. Unlike density-map-based methods, which dominate counting models, Count Anything adopts discrete instance points and performs dual-granularity instance enumeration. A Region-level Sparse Counter provides object-level anchors for large and sparse targets, while a Pixel-level Dense Counter handles small, crowded, and weakly bounded targets via dense point prediction. A point-centric supervision strategy enables learning from heterogeneous annotations, and Complementary Count Fusion combines both counters in a parameter-free manner. Extensive experiments show that Count Anything achieves strong accuracy and multi-domain generalization, outperforming existing open-world counting methods. Code is available at: https://github.com/Mengqi-Lei/count-anything.

Diffusion models has underpinned much recent advances of dataset augmentation in various computer vision tasks. However, when involving generating multi-object images as real scenarios, most existing methods either rely entirely on text condition, resulting in a deviation between the generated objects and the original data, or rely too much on the original images, resulting in a lack of diversity in the generated images, which is of limited help to downstream tasks. To mitigate both problems with one stone, we propose a prompt-free conditional diffusion framework for multi-object image augmentation. Specifically, we introduce a local-global semantic fusion strategy to extract semantics from images to replace text, and inject knowledge into the diffusion model through LoRA to alleviate the category deviation between the original model and the target dataset. In addition, we design a reward model based counting loss to assist the traditional reconstruction loss for model training. By constraining the object counts of each category instead of pixel-by-pixel constraints, bridging the quantity deviation between the generated data and the original data while improving the diversity of the generated data. Experimental results demonstrate the superiority of the proposed method over several representative state-of-the-art baselines and showcase strong downstream task gain and out-of-domain generalization capabilities. Code is available at https://github.com/00why00/PFCD{here}.

Most counting questions in visual question answering (VQA) datasets are simple and require no more than object detection. Here, we study algorithms for complex counting questions that involve relationships between objects, attribute identification, reasoning, and more. To do this, we created TallyQA, the world's largest dataset for open-ended counting. We propose a new algorithm for counting that uses relation networks with region proposals. Our method lets relation networks be efficiently used with high-resolution imagery. It yields state-of-the-art results compared to baseline and recent systems on both TallyQA and the HowMany-QA benchmark.

Large language models have achieved strong performance on medical reasoning benchmarks, yet their deployment in clinical settings demands rigorous verification to ensure factual accuracy. While reward models offer a scalable approach for reasoning trace verification, existing methods face two limitations: they produce only scalar reward values without explicit justification, and they rely on single-pass retrieval that precludes adaptive knowledge access as verification unfolds. We introduce method, an agentic framework that addresses these limitations by training medical reasoning verifiers to iteratively query external medical corpora during evaluation. Our approach combines tool-augmented verification with an iterative reinforcement learning paradigm that requires only trace-level supervision, alongside an adaptive curriculum mechanism that dynamically adjusts training data distribution. Across four medical reasoning benchmarks, method achieves substantial gains over existing methods, improving MedQA accuracy by 23.5% and MedXpertQA by 32.0% relative to the base generator in particular. Crucially, method demonstrates an 8times reduction in sampling budget requirement compared to prior reward model baselines. These findings establish that grounding verification in dynamically retrieved evidence offers a principled path toward more reliable medical reasoning systems.

Conventional Applicant Tracking Systems (ATS) tend to be inflexible keyword-matchers, and deny gifted candidates a role due to a few minor semantic mismatches. This article describes a new two-step process to design a more refined resume evaluation model based on a small language model (<600M parameters) that is finetuned using GRPO on a custom reward function. To begin with, Supervised Fine-Tuning (SFT) was used to build a solid baseline model. Second, this SFT model was also optimized with the help of Reinforcement Learning (RL) through GRPO under the guidance of a new, multi-component reward function that can holistically assess candidates beyond simple keyword matching. We indicate that the RL application presents a critical problem of reward hacking due to the initial experiments of aggressive penalties, which produces faulty, excessively negative model behaviors. We have overcome this challenge by refining the reward function repeatedly and training hyperparameters into a stable "gentle polishing process" of the reward function. Our resulting GRPO-polished model demonstrates significant real-world efficacy, achieving a final accuracy of 91% on unseen test data. The model shows a strong ability to correctly identify qualified candidates (recall of 0.85 for the 'SELECTED' class) while also showing exceptional precision (1.0), confirming its reliability. These results indicate that a properly executed, two-step fine-tuning procedure can indeed effectively refine a small language model to be able to conduct fine-tuned and human-like candidate scoring, overcoming the drawbacks of both traditional ATS and naive RL usage.

Large language models (LLMs), despite strong performance on complex mathematical problems, exhibit systematic limitations in counting tasks. This issue arises from architectural limits of transformers, where counting is performed across layers, leading to degraded precision for larger counting problems due to depth constraints. To address this limitation, we propose a simple test-time strategy inspired by System-2 cognitive processes that decomposes large counting tasks into smaller, independent sub-problems that the model can reliably solve. We evaluate this approach using observational and causal mediation analyses to understand the underlying mechanism of this System-2-like strategy. Our mechanistic analysis identifies key components: latent counts are computed and stored in the final item representations of each part, transferred to intermediate steps via dedicated attention heads, and aggregated in the final stage to produce the total count. Experimental results demonstrate that this strategy enables LLMs to surpass architectural limitations and achieve high accuracy on large-scale counting tasks. This work provides mechanistic insight into System-2 counting in LLMs and presents a generalizable approach for improving and understanding their reasoning behavior.

Text-to-video diffusion models have enabled open-ended video synthesis, but often struggle with generating the correct number of objects specified in a prompt. We introduce NUMINA , a training-free identify-then-guide framework for improved numerical alignment. NUMINA identifies prompt-layout inconsistencies by selecting discriminative self- and cross-attention heads to derive a countable latent layout. It then refines this layout conservatively and modulates cross-attention to guide regeneration. On the introduced CountBench, NUMINA improves counting accuracy by up to 7.4% on Wan2.1-1.3B, and by 4.9% and 5.5% on 5B and 14B models, respectively. Furthermore, CLIP alignment is improved while maintaining temporal consistency. These results demonstrate that structural guidance complements seed search and prompt enhancement, offering a practical path toward count-accurate text-to-video diffusion. The code is available at https://github.com/H-EmbodVis/NUMINA.

In this paper, we consider the problem of generalised visual object counting, with the goal of developing a computational model for counting the number of objects from arbitrary semantic categories, using arbitrary number of "exemplars", i.e. zero-shot or few-shot counting. To this end, we make the following four contributions: (1) We introduce a novel transformer-based architecture for generalised visual object counting, termed as Counting Transformer (CounTR), which explicitly capture the similarity between image patches or with given "exemplars" with the attention mechanism;(2) We adopt a two-stage training regime, that first pre-trains the model with self-supervised learning, and followed by supervised fine-tuning;(3) We propose a simple, scalable pipeline for synthesizing training images with a large number of instances or that from different semantic categories, explicitly forcing the model to make use of the given "exemplars";(4) We conduct thorough ablation studies on the large-scale counting benchmark, e.g. FSC-147, and demonstrate state-of-the-art performance on both zero and few-shot settings.

Diffusion models have shown remarkable progress in photorealistic image synthesis, yet they remain unreliable for generating scenes with a precise number of object instances, particularly in complex and high-density settings. We present CountLoop, a training-free framework that provides diffusion models with accurate instance control through iterative structured feedback. The approach alternates between image generation and multimodal agent evaluation, where a language-guided planner and critic assess object counts, spatial arrangements, and attribute consistency. This feedback is then used to refine layouts and guide subsequent generations. To further improve separation between objects, especially in occluded scenes, we introduce instance-driven attention masking and compositional generation techniques. Experiments on COCO Count, T2I CompBench, and two new high-instance benchmarks show that CountLoop achieves counting accuracy of up to 98% while maintaining spatial fidelity and visual quality, outperforming layout-based and gradient-guided baselines with a score of 0.97.

Long-form numerical reasoning in financial analysis aims to generate a reasoning program to calculate the correct answer for a given question. Previous work followed a retriever-generator framework, where the retriever selects key facts from a long-form document, and the generator generates a reasoning program based on retrieved facts. However, they treated all facts equally without considering the different contributions of facts with and without numbers. Meanwhile, the program consistency were ignored under supervised training, resulting in lower training accuracy and diversity. To solve these problems, we proposed APOLLO to improve the long-form numerical reasoning framework. For the retriever, we adopt a number-aware negative sampling strategy to enable the retriever to be more discriminative on key numerical facts. For the generator, we design consistency-based reinforcement learning and target program augmentation strategy based on the consistency of program execution results. Experimental results on the FinQA and ConvFinQA leaderboard verify the effectiveness of our proposed method, achieving the new state-of-the-art.

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models, which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline \'a la Math-Shepherd using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.

Large language models perform strongly on benchmarks in mathematical reasoning, coding and document analysis, suggesting a broad ability to follow instructions. However, it remains unclear whether such success reflects general logical competence, repeated application of learned procedures, or pattern matching that mimics rule execution. We investigate this question by introducing Stable Counting Capacity, an assay in which models count repeated symbols until failure. The assay removes knowledge dependencies, semantics and ambiguity from evaluation, avoids lexical and tokenization confounds, and provides a direct measure of procedural reliability beyond standard knowledge-based benchmarks. Here we show, across more than 100 model variants, that stable counting capacity remains far below advertised context limits. Model behavior is consistent neither with open-ended logic nor with stable application of a learned rule, but instead with use of a finite set of count-like internal states, analogous to counting on fingers. Once this resource is exhausted, the appearance of rule following disappears and exact execution collapses into guessing, even with additional test-time compute. These findings show that fluent performance in current language models does not guarantee general, reliable rule following.

Most crowd counting methods directly regress blockwise density maps using Mean Squared Error (MSE) losses. This practice has two key limitations: (1) it fails to account for the extreme spatial sparsity of annotations -- over 95% of 8x8 blocks are empty across standard benchmarks, so supervision signals in informative regions are diluted by the predominant zeros; (2) MSE corresponds to a Gaussian error model that poorly matches discrete, non-negative count data. To address these issues, we introduce ZIP, a scalable crowd counting framework that models blockwise counts with a Zero-Inflated Poisson likelihood: a zero-inflation term learns the probability a block is structurally empty (handling excess zeros), while the Poisson component captures expected counts when people are present (respecting discreteness). We provide a generalization analysis showing a tighter risk bound for ZIP than MSE-based losses and DMCount provided that the training resolution is moderately large. To assess the scalability of ZIP, we instantiate it on backbones spanning over 100x in parameters/compute. Experiments on ShanghaiTech A & B, UCF-QNRF, and NWPU-Crowd demonstrate that ZIP consistently surpasses state-of-the-art methods across all model scales.

Learning from preference feedback has emerged as an essential step for improving the generation quality and performance of modern language models (LMs). Despite its widespread use, the way preference-based learning is applied varies wildly, with differing data, learning algorithms, and evaluations used, making disentangling the impact of each aspect difficult. In this work, we identify four core aspects of preference-based learning: preference data, learning algorithm, reward model, and policy training prompts, systematically investigate the impact of these components on downstream model performance, and suggest a recipe for strong learning for preference feedback. Our findings indicate that all aspects are important for performance, with better preference data leading to the largest improvements, followed by the choice of learning algorithm, the use of improved reward models, and finally the use of additional unlabeled prompts for policy training. Notably, PPO outperforms DPO by up to 2.5% in math and 1.2% in general domains. High-quality preference data leads to improvements of up to 8% in instruction following and truthfulness. Despite significant gains of up to 5% in mathematical evaluation when scaling up reward models, we surprisingly observe marginal improvements in other categories. We publicly release the code used for training (https://github.com/hamishivi/EasyLM) and evaluating (https://github.com/allenai/open-instruct) our models, along with the models and datasets themselves (https://huggingface.co/collections/allenai/tulu-v25-suite-66676520fd578080e126f618).

Despite the unprecedented success of text-to-image diffusion models, controlling the number of depicted objects using text is surprisingly hard. This is important for various applications from technical documents, to children's books to illustrating cooking recipes. Generating object-correct counts is fundamentally challenging because the generative model needs to keep a sense of separate identity for every instance of the object, even if several objects look identical or overlap, and then carry out a global computation implicitly during generation. It is still unknown if such representations exist. To address count-correct generation, we first identify features within the diffusion model that can carry the object identity information. We then use them to separate and count instances of objects during the denoising process and detect over-generation and under-generation. We fix the latter by training a model that predicts both the shape and location of a missing object, based on the layout of existing ones, and show how it can be used to guide denoising with correct object count. Our approach, CountGen, does not depend on external source to determine object layout, but rather uses the prior from the diffusion model itself, creating prompt-dependent and seed-dependent layouts. Evaluated on two benchmark datasets, we find that CountGen strongly outperforms the count-accuracy of existing baselines.

Agentic multimodal models perform diverse operations on an image via code and reason over the returned view, an effective paradigm for fine-grained visual question answering. However, code operations can be useful, redundant, or misleading. Outcome-only rewards cannot precisely distinguish these cases, and existing process rewards either fail to attribute final correctness to individual tool calls, or require an external judge model. To address this, we introduce Tool-Augmented Credit Optimization (TACO), a GRPO variant for code-tool agents built on two coupled advantage channels. The first, Differential Answer-Probe Reward (DAPR), is a self-supervised, judge-free tool-contribution advantage that credits each tool call by its own effect on answering correctly. Probe tokens inserted into the model's reasoning elicit its predictions with and without the tool, and the difference in outcome reward is taken as the call's value: positive for a useful call, negative for a misleading one, and zero for one that changes nothing. This reuses the existing answer checker with no auxiliary judge, and, being a difference rather than an absolute probe score, is naturally robust to probe-hacking. The second is the outcome advantage from the final answer, distributed by Outcome-Gated Advantage Routing (OGAR): a parameter-free rule that, conditioned on the call's outcome, delivers this credit only to the responsible segments, suppressing wasted tool calls without any cost term. We train TACO through a two-stage SFT+RL pipeline. Extensive experiments across perception, reasoning, and general multimodal benchmarks show that it yields consistent accuracy gains and learns to invoke its tools only when they help.

Rule-based reasoning has been acknowledged as one of the fundamental problems in reasoning, while deviations in rule formats, types, and complexity in real-world applications pose severe challenges. Recent studies have shown that large reasoning models (LRMs) have remarkable reasoning capabilities, and their performance is substantially enhanced by reinforcement learning (RL). However, it remains an open question whether small reasoning models (SRMs) can learn rule-based reasoning effectively with robust generalization across diverse tasks and domains. To address this, we introduce Reinforced Rule-based Reasoning, a.k.a. RuleReasoner, a simple yet effective method to conduct rule-based reasoning via a wide collection of curated tasks and a novel domain-aware dynamic sampling approach. Specifically, RuleReasoner resamples each training batch by updating the sampling weights of different domains based on historical rewards. This facilitates domain augmentation and flexible online learning schedules for RL, obviating the need for pre-hoc human-engineered mix-training recipes used in existing methods. Empirical evaluations on in-distribution (ID) and out-of-distribution (OOD) benchmarks reveal that RuleReasoner outperforms frontier LRMs by a significant margin (Delta4.1% average points on eight ID tasks and Delta10.4% average points on three OOD tasks over OpenAI-o1). Notably, our approach also exhibits higher computational efficiency compared to prior dynamic sampling methods for RL.

We present a new approach for mitigating unfairness in learned classifiers. In particular, we focus on binary classification tasks over individuals from two populations, where, as our criterion for fairness, we wish to achieve similar false positive rates in both populations, and similar false negative rates in both populations. As a proof of concept, we implement our approach and empirically evaluate its ability to achieve both fairness and accuracy, using datasets from the fields of criminal risk assessment, credit, lending, and college admissions.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem.

Large language model (LLM) agents increasingly take actions (screening applicants, recommending credit, triaging patients), yet fairness for LLMs is still measured by grading answers. We introduce AgentFairBench, a cheap, reproducible, multi-domain benchmark for demographic disparity in the actions of LLM agents. Grounded in a companion framework, the Bias Conduction Framework (BCF, restated here), it spans three regulator-anchored domains: hiring, lending, and medical triage. Synthetic, demographic-neutral profiles are evaluated in counterfactual matched sets that vary only a name-coded race x gender signal (in the Bertrand Mullainathan tradition), under four agent scaffolds of increasing agency (direct, chain-of-thought, multi-agent deliberation, tool-augmented). A NumPy-only harness computes counterfactual flip rate, mean absolute score difference (MASD), action-rate disparity, and tool-invocation disparity, with bootstrap confidence intervals, paired tests, and false-discovery-rate control, for single-digit dollars per model. A live leaderboard with a held-out private split and a contamination canary admits external models by submission. Our pilot (864 decisions plus a test-retest replication) carries a methodological lesson: comparing a six-group score spread against a two-run noise difference overstates disparity by ~ 2.4X through statistic arity alone. Against an arity matched noise floor and an omnibus group test, claude haiku 4 5 shows no demographic effect above sampling noise (0 of 120 pairwise and 0 of 9 omnibus contrasts survive correction); a planted-bias test confirms the instrument detects disparity when present. The contribution is a sound, sensitive, adoption-ready instrument, the arity matched null methodology, and open artifacts to scale it. Code, data, and harness are released under open licenses, with an anonymized review artifact.

Large Language Models (LLMs) have the potential to automate reward engineering by leveraging their broad domain knowledge across various tasks. However, they often need many iterations of trial-and-error to generate effective reward functions. This process is costly because evaluating every sampled reward function requires completing the full policy optimization process for each function. In this paper, we introduce an LLM-driven reward generation framework that is able to produce state-of-the-art policies on the challenging Bi-DexHands benchmark with 20x fewer reward function samples than the prior state-of-the-art work. Our key insight is that we reduce the problem of generating task-specific rewards to the problem of coarsely estimating task progress. Our two-step solution leverages the task domain knowledge and the code synthesis abilities of LLMs to author progress functions that estimate task progress from a given state. Then, we use this notion of progress to discretize states, and generate count-based intrinsic rewards using the low-dimensional state space. We show that the combination of LLM-generated progress functions and count-based intrinsic rewards is essential for our performance gains, while alternatives such as generic hash-based counts or using progress directly as a reward function fall short.

This paper addresses the task of counting human actions of interest using sensor data from wearable devices. We propose a novel exemplar-based framework, allowing users to provide exemplars of the actions they want to count by vocalizing predefined sounds ''one'', ''two'', and ''three''. Our method first localizes temporal positions of these utterances from the audio sequence. These positions serve as the basis for identifying exemplars representing the action class of interest. A similarity map is then computed between the exemplars and the entire sensor data sequence, which is further fed into a density estimation module to generate a sequence of estimated density values. Summing these density values provides the final count. To develop and evaluate our approach, we introduce a diverse and realistic dataset consisting of real-world data from 37 subjects and 50 action categories, encompassing both sensor and audio data. The experiments on this dataset demonstrate the viability of the proposed method in counting instances of actions from new classes and subjects that were not part of the training data. On average, the discrepancy between the predicted count and the ground truth value is 7.47, significantly lower than the errors of the frequency-based and transformer-based methods. Our project, code and dataset can be found at https://github.com/cvlab-stonybrook/ExRAC.

Tool-integrated agents that interleave reasoning with API calls are promising for complex tasks, yet aligning them for high-stakes, domain-specific deployment remains challenging: existing reinforcement learning approaches rely on coarse binary rewards that cannot distinguish tool selection errors from malformed parameters. We present ToolRLA, a three-stage post-training pipeline (SFT -> GRPO -> DPO) for domain-specific tool agents. The core contribution is a fine-grained reward function with multiplicative correctness decomposition spanning four dimensions -- format validity, tool selection, parameter accuracy, and regulatory compliance -- that encodes domain priority orderings as inductive biases in the reward landscape. Deployed on a financial advisory copilot (80+ advisors, 1,200+ daily queries), ToolRLA achieves over three months: a 47% improvement in task completion rate (62%->91%), a 63% reduction in tool invocation errors (38%->14%), and a 93% reduction in regulatory violations (12%->0.8%), within sub-2-second latency. Ablation studies show the multiplicative reward design accounts for 7 percentage points of improvement over additive alternatives. Generalization is further validated on ToolBench and API-Bank.

Object counting has progressed from class-specific models, which count only known categories, to class-agnostic models that generalize to unseen categories. The next challenge is Referring Expression Counting (REC), where the goal is to count objects based on fine-grained attributes and contextual differences. Existing methods struggle with distinguishing visually similar objects that belong to the same category but correspond to different referring expressions. To address this, we propose C-REX, a novel contrastive learning framework, based on supervised contrastive learning, designed to enhance discriminative representation learning. Unlike prior works, C-REX operates entirely within the image space, avoiding the misalignment issues of image-text contrastive learning, thus providing a more stable contrastive signal. It also guarantees a significantly larger pool of negative samples, leading to improved robustness in the learned representations. Moreover, we showcase that our framework is versatile and generic enough to be applied to other similar tasks like class-agnostic counting. To support our approach, we analyze the key components of sota detection-based models and identify that detecting object centroids instead of bounding boxes is the key common factor behind their success in counting tasks. We use this insight to design a simple yet effective detection-based baseline to build upon. Our experiments show that C-REX achieves state-of-the-art results in REC, outperforming previous methods by more than 22\% in MAE and more than 10\% in RMSE, while also demonstrating strong performance in class-agnostic counting. Code is available at https://github.com/cvlab-stonybrook/c-rex.

Large vision-language models (VLMs) can recognize what happens in video but fail to count how many times. We introduce PushupBench, 446 long-form clips (avg. 36.7s) for evaluating repetition counting. The best frontier model achieves 42.1\% exact accuracy; open-source 4B models score sim6\%, matching supervised baselines. We show that accuracy alone misleads -- weaker models exploit the modal count rather than reason temporally. Fine-tuning on counting with 1k samples transfers to general video understanding: MVBench (+2.15), PerceptionTest (+1.88), TVBench (+4.54), suggesting counting is a proxy for broader temporal reasoning.PushupBench incorporated in lmms-eval (https://github.com/EvolvingLMMs-Lab/lmms-eval/pull/1262) and hosted on (pushupbench.com/)

Generations from large language models (LLMs) can be improved by sampling and scoring multiple solutions to select a final answer. Current "sample and select" methods such as self-consistency (SC) rely on majority voting to score answers. However, when tasks have many distinct and valid answers, selection by voting requires a large number of samples. This makes SC prohibitively expensive for interactive tasks that involve generating multiple actions (answers) sequentially. After establishing that majority voting fails to provide consistent gains on such tasks, we demonstrate how to increase success rates by softening the scoring criterion. We introduce Soft Self-Consistency (SOFT-SC), which replaces SC's discontinuous scoring with a continuous score computed from model likelihoods, allowing for selection even when actions are sparsely distributed. SOFT-SC improves both performance and efficiency on long-horizon interactive tasks, requiring half as many samples as SC for comparable or better performance. For a fixed number of samples, SOFT-SC leads to a 1.3% increase over SC in absolute success rate on writing bash programs, a 6.6% increase on online shopping (WebShop), and a 4.7% increase for an interactive household game (ALFWorld). Finally, we show that SOFT-SC can be applied to both open-source and black-box models.

We provide the largest compiled publicly available dictionaries of first, middle, and last names for the purpose of imputing race and ethnicity using, for example, Bayesian Improved Surname Geocoding (BISG). The dictionaries are based on the voter files of six Southern states that collect self-reported racial data upon voter registration. Our data cover a much larger scope of names than any comparable dataset, containing roughly one million first names, 1.1 million middle names, and 1.4 million surnames. Individuals are categorized into five mutually exclusive racial and ethnic groups -- White, Black, Hispanic, Asian, and Other -- and racial/ethnic counts by name are provided for every name in each dictionary. Counts can then be normalized row-wise or column-wise to obtain conditional probabilities of race given name or name given race. These conditional probabilities can then be deployed for imputation in a data analytic task for which ground truth racial and ethnic data is not available.

Class-agnostic object counting aims to count all objects in an image with respect to example boxes or class names, a.k.a few-shot and zero-shot counting. In this paper, we propose a generalized framework for both few-shot and zero-shot object counting based on detection. Our framework combines the superior advantages of two foundation models without compromising their zero-shot capability: (i) SAM to segment all possible objects as mask proposals, and (ii) CLIP to classify proposals to obtain accurate object counts. However, this strategy meets the obstacles of efficiency overhead and the small crowded objects that cannot be localized and distinguished. To address these issues, our framework, termed PseCo, follows three steps: point, segment, and count. Specifically, we first propose a class-agnostic object localization to provide accurate but least point prompts for SAM, which consequently not only reduces computation costs but also avoids missing small objects. Furthermore, we propose a generalized object classification that leverages CLIP image/text embeddings as the classifier, following a hierarchical knowledge distillation to obtain discriminative classifications among hierarchical mask proposals. Extensive experimental results on FSC-147, COCO, and LVIS demonstrate that PseCo achieves state-of-the-art performance in both few-shot/zero-shot object counting/detection. Code: https://github.com/Hzzone/PseCo

Reinforcement learning with verifiable rewards has rapidly advanced reasoning in vision--language models. However, for chest X-ray report generation, the standard rewards (i.e. exact-match accuracy and step-level processes) are incompatible because the reports consist of unordered and orthogonal findings, rather than a causal reasoning chain. We address this gap with a set-based view: each report is split into sentences and embedded by a frozen sentence transformer, yielding unordered embedding sets. We propose the use of set-to-set distances between generated and reference embeddings as continuous, permutation-invariant rewards. Across two datasets and three vision--language models (Qwen3-VL-2B/4B, Gemma3-4B), post-training with set-to-set distance based rewards via GRPO consistently outperforms supervised fine-tuning and exact-match GRPO on all headline metrics (BERTScore, RadGraph F1 and CheXbert F1 by average \%6.80, \%7.82 and \%4.45 relative improvements respectively). The same set distances also enable test-time best-of-N selection: scoring candidates by their distance to training-report embeddings outperforms random selection on our trained models as well as three closed-source LLMs (Mistral-Small, Gemini-2.5 Flash-Lite, GPT-4o-mini) with on average \%16.4 relative improvement on BERTScore. Used as a streaming signal, they support a more efficient form of test-time scaling: pruning low-scoring candidates mid-generation reduces generated tokens by over 50\% while preserving the Findings quality of full best-of-N selection. Together these results establish set-distance rewards as a unified signal for both post-training and test-time scaling in chest X-ray report generation. Our code is publicly https://anonymous.4open.science/r/Set-Distance-Rewards-CXR-BFDA{available}.

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.

Modern Text-to-SQL systems generate multiple candidate SQL queries and rank them to judge a final prediction. However, existing methods face two limitations. First, they often score functionally equivalent SQL queries inconsistently despite identical execution results. Second, ranking cannot recover when the correct SQL is absent from the candidate pool. We propose R^3-SQL, a Text-to-SQL framework that addresses both issues through unified reward for ranking and resampling. R^3-SQL first groups candidates by execution result and ranks groups for consistency. To score each group, it combines a pairwise preference across groups with a pointwise utility from the best group rank and size, capturing relative preference, consistency, and candidate quality. To improve candidate recall, R^3-SQL introduces agentic resampling, which judges the generated candidate pool and selectively resamples when the correct SQL is likely absent. R^3-SQL achieves 75.03 execution accuracy on BIRD-dev, a new state of the art among methods using models with disclosed sizes, with consistent gains across five benchmarks.

Large language models for mathematical reasoning are typically trained with outcome-based rewards, which credit only the final answer. In our experiments, we observe that this paradigm is highly susceptible to reward hacking, leading to a substantial overestimation of a model's reasoning ability. This is evidenced by a high incidence of false positives - solutions that reach the correct final answer through an unsound reasoning process. Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps - abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest a strong association between these Miracle Steps and memorization, where the model appears to recall the answer directly rather than deriving it. To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics. The generative RRM provides fine-grained, calibrated rewards (0-1) that explicitly penalize logical flaws and encourage rigorous deduction. When integrated into a reinforcement learning pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks. Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%. Our work demonstrates that rewarding the solution process is crucial for building models that are not only more accurate but also more reliable.

As large language model (LLM) agents evolve from isolated tool users into coordinated teams, reinforcement learning (RL) must optimize not only individual actions but also how work is spawned, delegated, communicated, aggregated, and stopped. This paper studies RL for LLM-based multi-agent systems through orchestration traces: temporal interaction graphs whose events include sub-agent spawning, delegation, communication, tool use, return, aggregation, and stopping decisions. Using this lens, we identify three technical axes. First, reward design spans eight families, including orchestration rewards for parallelism speedup, split correctness, and aggregation quality. Second, reward and credit signals attach to eight credit- or signal-bearing units from token to team; explicit counterfactual message-level credit remains especially sparse in our curated pool. Third, orchestration learning decomposes into five sub-decisions: when to spawn, whom to delegate to, how to communicate, how to aggregate, and when to stop. In our curated pool as of May 4, 2026, we found no explicit RL training method for the stopping decision. We connect academic methods to public industrial evidence from Kimi Agent Swarm, OpenAI Codex, and Anthropic Claude Code. The resulting scale gap is a gap between publicly reported deployment envelopes and open academic evaluation regimes, not independent verification of industrial training traces. We release the artifact at https://github.com/xxzcc/awesome-llm-mas-rl, including an 84-entry tagged paper pool, a 32-record exclusion log, scripted corpus statistics, and a minimal JSON schema for replayable orchestration traces.

Scalable oversight studies methods of training and evaluating AI systems in domains where human judgment is unreliable or expensive, such as scientific research and software engineering in complex codebases. Most work in this area has focused on methods of improving the quality of labels. Recent work by Burns et al. (2023) considers the complementary problem of training models with low-quality labels, finding that large pretrained models often have an inductive bias towards producing correct answers. In practice, however, neither label quantity nor quality is fixed: practitioners face a quantity-quality tradeoff. In this paper, we explore the microeconomics of the quantity-quality tradeoff on binary NLP classification tasks used in Burns et al. (2023). While sample-efficient learning has been studied extensively, little public research has focused on scalable elicitation: eliciting capabilities from pretrained models subject to labeling cost constraints. We find that this setting has novel dynamics caused by the tradeoff between label quantity and quality, as well as the model's existing latent capabilities. We observe three regimes of eliciting classification knowledge from pretrained models using supervised finetuning: quantity-dominant, quality-dominant, and a mixed regime involving the use of low- and high-quality data together to attain higher accuracy at a lower cost than using either alone. We explore sample-efficient elicitation methods that make use of two datasets of differing qualities, and establish a Pareto frontier of scalable elicitation methods that optimally trade off labeling cost and classifier performance. We find that the accuracy of supervised fine-tuning can be improved by up to 5 percentage points at a fixed labeling budget by adding a few-shot prompt to make use of the model's existing knowledge of the task.

We introduce the first version of KWBench (Knowledge Work Bench), a benchmark for unprompted problem recognition in large language models: can an LLM identify a professional scenario before attempting to solve it. Existing frontier benchmarks have saturated, and most knowledge-work evaluations to date reduce to extraction or task completion against a specification. KWBench targets the step before that: recognizing the governing structure of the situation from raw inputs alone. The benchmark contains 223 tasks sourced from practitioners across acquisitions, contract negotiations, clinical pharmacy, organizational politics, fraud analysis, and incentive design. Each task encodes a formal game-theoretic pattern (principal-agent conflict, signaling, mechanism design failure, strategic omission, coalitional dynamics, strategic interdependence) and carries structured ground truth recording the expert reading of the situation and the anticipated failure modes. Models receive raw data and a task prompt with no indication of problem type. Scoring is a three-tier rubric gated by a mandatory conjunctive check. Mandatory criteria encode the predicted wrong paths. We evaluate 16 models. The best model passes on 27.9% of tasks. The top two models agree on only 31.7% of their passes. Among the top 8, 44 tasks are solved by exactly one model; routing across the top 8 covers 50.7% of the benchmark, nearly double the best single model. Conditional on passing, quality scores converge (approx 83% across models); unconditional scores do not. Same models articulate the relevant game-theoretic concept correctly when asked, then fail to apply it unprompted. We release KWBench to shift how frontier models are evaluated on knowledge work, scoring them on whether they recognize the right problem from the situation alone, not only on how well they execute once the problem has been framed for them.

We introduce T-Rex, an interactive object counting model designed to first detect and then count any objects. We formulate object counting as an open-set object detection task with the integration of visual prompts. Users can specify the objects of interest by marking points or boxes on a reference image, and T-Rex then detects all objects with a similar pattern. Guided by the visual feedback from T-Rex, users can also interactively refine the counting results by prompting on missing or falsely-detected objects. T-Rex has achieved state-of-the-art performance on several class-agnostic counting benchmarks. To further exploit its potential, we established a new counting benchmark encompassing diverse scenarios and challenges. Both quantitative and qualitative results show that T-Rex possesses exceptional zero-shot counting capabilities. We also present various practical application scenarios for T-Rex, illustrating its potential in the realm of visual prompting.

Large language models (LLMs) memorize a vast amount of prior knowledge from the Internet that help them on downstream tasks but also may notoriously sway their outputs towards wrong or biased answers. In this work, we test how the knowledge about popular subjects hurt the accuracy of vision language models (VLMs) on standard, objective visual tasks of counting and identification. We find that state-of-the-art VLMs are strongly biased (e.g, unable to recognize a fourth stripe has been added to a 3-stripe Adidas logo) scoring an average of 17.05% accuracy in counting (e.g., counting stripes in an Adidas-like logo) across 7 diverse domains from animals, logos, chess, board games, optical illusions, to patterned grids. Insert text (e.g., "Adidas") describing the subject name into the counterfactual image further decreases VLM accuracy. The biases in VLMs are so strong that instructing them to double-check their results or rely exclusively on image details to answer improves counting accuracy by only +2 points, on average. Our work presents an interesting failure mode in VLMs and an automated framework for testing VLM biases. Code and data are available at: vlmsarebiased.github.io.

Diffusion probabilistic models (DPMs) have demonstrated remarkable progress in generative tasks, such as image and video synthesis. However, they still often produce hallucinated samples (hallucinations) that conflict with real-world knowledge, such as generating an implausible duplicate cup floating beside another cup. Despite their prevalence, the lack of feasible methodologies for systematically quantifying such hallucinations hinders progress in addressing this challenge and obscures potential pathways for designing next-generation generative models under factual constraints. In this work, we bridge this gap by focusing on a specific form of hallucination, which we term counting hallucination, referring to the generation of an incorrect number of instances or structured objects, such as a hand image with six fingers, despite such patterns being absent from the training data. To this end, we construct a dataset suite CountHalluSet, with well-defined counting criteria, comprising ToyShape, SimObject, and RealHand. Using these datasets, we develop a standardized evaluation protocol for quantifying counting hallucinations, and systematically examine how different sampling conditions in DPMs, including solver type, ODE solver order, sampling steps, and initial noise, affect counting hallucination levels. Furthermore, we analyze their correlation with common evaluation metrics such as FID, revealing that this widely used image quality metric fails to capture counting hallucinations consistently. This work aims to take the first step toward systematically quantifying hallucinations in diffusion models and offer new insights into the investigation of hallucination phenomena in image generation.

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend -- the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

Counterfactual prompting (i.e., perturbing a single factor and measuring output change) is widely used to evaluate things like LLM bias and CoT faithfulness. But in this work we argue that observed effects cannot be attributed to the targeted factor without accounting for baseline ``meaning-preserving'' modifications to text that establish general model sensitivity. This is because every counterfactual edit is a compound treatment that bundles the variable of interest with incidental surface-form variation; this violates treatment variation irrelevance. We observe prediction flip rates on MedQA of 14.9% when we surgically change patient gender. However, this is statistically indistinguishable from the flip rates induced by simply paraphrasing inputs (14.1%). In this case, it would therefore be unwarranted to conclude that the LLM is especially sensitive to patient gender. To account for this and robustly measure the effects of targeted interventions, we propose a framework in which we compare (via statistical testing) differences observed under target interventions to those induced by paraphrasing inputs. We then use this framework to revisit a analysis done on the MedPerturb dataset, which reported evidence of model sensitivity to patient demographics and stylistic cues. We find that these effects largely dissipate when we account for general model sensitivity, with only 5 of 120 tests reaching statistical significance. Applying the same framework to occupational biography classification, we detect clearly significant directional gender bias, showing that the framework identifies real directional effects even when they are small. We evaluate a range of metrics -- aggregate, per-sample distributional, and regression -- and find that per-sample metrics are dramatically more powerful than aggregate metrics and regression powerfully and uniquely characterizes effect direction and magnitude.

Generative reward models with parallel sampling have enabled effective test-time scaling for reasoning tasks. Current approaches employ pointwise scoring of individual solutions or pairwise comparisons. However, pointwise methods underutilize LLMs' comparative abilities, while pairwise methods scale inefficiently with larger sampling budgets. We introduce GenSelect, where the LLM uses long reasoning to select the best solution among N candidates. This leverages LLMs' comparative strengths while scaling efficiently across parallel sampling budgets. For math reasoning, we demonstrate that reasoning models, such as QwQ and DeepSeek-R1-0528, excel at GenSelect, outperforming existing scoring approaches with simple prompting.

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense rewards also offer an appealing choice for the reinforcement learning (RL) of LLMs since their fine-grained rewards have the potential to address some inherent issues of outcome rewards, such as training efficiency and credit assignment, this potential remains largely unrealized. This can be primarily attributed to the challenges of training process reward models (PRMs) online, where collecting high-quality process labels is prohibitively expensive, making them particularly vulnerable to reward hacking. To address these challenges, we propose PRIME (Process Reinforcement through IMplicit rEwards), which enables online PRM updates using only policy rollouts and outcome labels through implict process rewards. PRIME combines well with various advantage functions and forgoes the dedicated reward model training phrase that existing approaches require, substantially reducing the development overhead. We demonstrate PRIME's effectiveness on competitional math and coding. Starting from Qwen2.5-Math-7B-Base, PRIME achieves a 15.1% average improvement across several key reasoning benchmarks over the SFT model. Notably, our resulting model, Eurus-2-7B-PRIME, surpasses Qwen2.5-Math-7B-Instruct on seven reasoning benchmarks with 10% of its training data.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long and redundant reasoning even for simple questions, which substantially increases computational cost and response latency. While existing methods incorporate length rewards to GRPO to promote concise reasoning, they incur significant performance degradation. We identify the root cause: when rewards for correct but long rollouts are penalized, GRPO's group-relative advantage function can assign them negative advantages, actively discouraging valid reasoning. To overcome this, we propose Decoupled Reward Policy Optimization (DRPO), a novel framework that decouples the length-based learning signal of correct rollouts from incorrect ones. DRPO ensures that reward signals for correct rollouts are normalized solely within the positive group, shielding them from interference by negative samples. The DRPO's objective is grounded in integrating an optimized positive data distribution, which maximizes length-based rewards under a KL regularization, into a discriminative objective. We derive a closed-form solution for this distribution, enabling efficient computation of the objective and its gradients using only on-policy data and importance weighting. Of independent interest, this formulation is general and can incorporate other preference rewards of positive data beyond length. Experiments on mathematical reasoning tasks demonstrate DRPO's significant superiority over six efficient reasoning baselines. Notably, with a 1.5B model, our method achieves 77\% length reduction with only 1.1\% performance loss on simple questions like GSM8k dataset, while the follow-up baseline sacrifices 4.3\% for 68\% length reduction.

Crowd counting is an application-oriented task and its inference efficiency is crucial for real-world applications. However, most previous works relied on heavy backbone networks and required prohibitive run-time consumption, which would seriously restrict their deployment scopes and cause poor scalability. To liberate these crowd counting models, we propose a novel Structured Knowledge Transfer (SKT) framework, which fully exploits the structured knowledge of a well-trained teacher network to generate a lightweight but still highly effective student network. Specifically, it is integrated with two complementary transfer modules, including an Intra-Layer Pattern Transfer which sequentially distills the knowledge embedded in layer-wise features of the teacher network to guide feature learning of the student network and an Inter-Layer Relation Transfer which densely distills the cross-layer correlation knowledge of the teacher to regularize the student's feature evolutio Consequently, our student network can derive the layer-wise and cross-layer knowledge from the teacher network to learn compact yet effective features. Extensive evaluations on three benchmarks well demonstrate the effectiveness of our SKT for extensive crowd counting models. In particular, only using around 6% of the parameters and computation cost of original models, our distilled VGG-based models obtain at least 6.5times speed-up on an Nvidia 1080 GPU and even achieve state-of-the-art performance. Our code and models are available at {https://github.com/HCPLab-SYSU/SKT}.

Vision-Language Models (VLMs) have advanced across multimodal benchmarks but still show clear gaps in ordinal number understanding, i.e., the ability to track relative positions and generalize to large indices. We present OrdinalBench, a diagnostic benchmark that standardizes ordinal number understanding as an evaluation task for VLMs. The core task is N-th object identification, defined by a starting reference and traversal rule. Task difficulty is controlled along three axes: (i) ordinal magnitude, from small numbers to extreme cases up to 300; (ii) arrangement complexity, from single loops to maze-like paths; and (iii) object count. The benchmark provides 39,000 question-answer pairs, each annotated with a ground-truth reasoning trajectory and balanced across difficulty levels for controlled large-scale testing. Beyond answer-only evaluation, our framework requires models to generate structured stepwise traces of the counting process and provides an open evaluation toolkit that measures both final accuracy and step-level path consistency. Zero-shot evaluations of GPT-5, Gemini 2.5 Flash Lite, Qwen2.5-VL, InternVL3.5, and Molmo reveal sharp degradation under large-ordinal and complex-path conditions, highlighting weak generalization despite strong scores on standard multimodal tasks. By framing ordinal number understanding as a core target, OrdinalBench provides a reproducible benchmark and diagnostic framework for developing VLMs with stronger sequential reasoning. All data and code are available at https://ordinalbench.github.io/

Generative modeling is widely regarded as one of the most essential problems in today's AI community, with text-to-image generation having gained unprecedented real-world impacts. Among various approaches, diffusion models have achieved remarkable success and have become the de facto solution for text-to-image generation. However, despite their impressive performance, these models exhibit fundamental limitations in adhering to numerical constraints in user instructions, frequently generating images with an incorrect number of objects. While several prior works have mentioned this issue, a comprehensive and rigorous evaluation of this limitation remains lacking. To address this gap, we introduce T2ICountBench, a novel benchmark designed to rigorously evaluate the counting ability of state-of-the-art text-to-image diffusion models. Our benchmark encompasses a diverse set of generative models, including both open-source and private systems. It explicitly isolates counting performance from other capabilities, provides structured difficulty levels, and incorporates human evaluations to ensure high reliability. Extensive evaluations with T2ICountBench reveal that all state-of-the-art diffusion models fail to generate the correct number of objects, with accuracy dropping significantly as the number of objects increases. Additionally, an exploratory study on prompt refinement demonstrates that such simple interventions generally do not improve counting accuracy. Our findings highlight the inherent challenges in numerical understanding within diffusion models and point to promising directions for future improvements.

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC^0, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies have established the upper limits of counting ability in Transformer-based expert models (i.e., models specifically trained for counting tasks), these findings do not directly extend to general-purpose LLMs due to differences in reasoning mechanisms. Recent work has highlighted how Chain of Thought (CoT) reasoning can help alleviate some of the architectural limitations of Transformers in counting tasks. However, little attention has been paid to the role of tokenization in these models. Unlike expert models that often use character-level tokenization, LLMs typically rely on byte-level (BPE) tokenizers, which fundamentally alters the way reasoning is processed. Our work investigates the impact of tokenization on the counting abilities of LLMs, uncovering substantial performance variations based on input tokenization differences. We provide both theoretical and experimental analyses, offering insights into how tokenization choices can undermine models' theoretical computability, thereby inspiring the design of new tokenization methods to enhance reasoning in LLMs.

Punishment as a mechanism for promoting cooperation has been studied extensively for more than two decades, but its effectiveness remains a matter of dispute. Here, we examine how punishment's impact varies across cooperative settings through a large-scale integrative experiment. We vary 14 parameters that characterize public goods games, sampling 360 experimental conditions and collecting 147,618 decisions from 7,100 participants. Our results reveal striking heterogeneity in punishment effectiveness: while punishment consistently increases contributions, its impact on payoffs (i.e., efficiency) ranges from dramatically enhancing welfare (up to 43% improvement) to severely undermining it (up to 44% reduction) depending on the cooperative context. To characterize these patterns, we developed models that outperformed human forecasters (laypeople and domain experts) in predicting punishment outcomes in new experiments. Communication emerged as the most predictive feature, followed by contribution framing (opt-out vs. opt-in), contribution type (variable vs. all-or-nothing), game length (number of rounds), peer outcome visibility (whether participants can see others' earnings), and the availability of a reward mechanism. Interestingly, however, most of these features interact to influence punishment effectiveness rather than operating independently. For example, the extent to which longer games increase the effectiveness of punishment depends on whether groups can communicate. Together, our results refocus the debate over punishment from whether or not it "works" to the specific conditions under which it does and does not work. More broadly, our study demonstrates how integrative experiments can be combined with machine learning to uncover generalizable patterns, potentially involving interactions between multiple features, and help generate novel explanations in complex social phenomena.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q^{+} and an easy-but-brittle prompt q^{-}(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q^{+} into sharp positive guidance while turning rare failures on q^{-} into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

The development of state-of-the-art systems in different applied areas of machine learning (ML) is driven by benchmarks, which have shaped the paradigm of evaluating generalisation capabilities from multiple perspectives. Although the paradigm is shifting towards more fine-grained evaluation across diverse tasks, the delicate question of how to aggregate the performances has received particular interest in the community. In general, benchmarks follow the unspoken utilitarian principles, where the systems are ranked based on their mean average score over task-specific metrics. Such aggregation procedure has been viewed as a sub-optimal evaluation protocol, which may have created the illusion of progress. This paper proposes Vote'n'Rank, a framework for ranking systems in multi-task benchmarks under the principles of the social choice theory. We demonstrate that our approach can be efficiently utilised to draw new insights on benchmarking in several ML sub-fields and identify the best-performing systems in research and development case studies. The Vote'n'Rank's procedures are more robust than the mean average while being able to handle missing performance scores and determine conditions under which the system becomes the winner.

We employ an audit design to investigate biases in state-of-the-art large language models, including GPT-4. In our study, we prompt the models for advice involving a named individual across a variety of scenarios, such as during car purchase negotiations or election outcome predictions. We find that the advice systematically disadvantages names that are commonly associated with racial minorities and women. Names associated with Black women receive the least advantageous outcomes. The biases are consistent across 42 prompt templates and several models, indicating a systemic issue rather than isolated incidents. While providing numerical, decision-relevant anchors in the prompt can successfully counteract the biases, qualitative details have inconsistent effects and may even increase disparities. Our findings underscore the importance of conducting audits at the point of LLM deployment and implementation to mitigate their potential for harm against marginalized communities.

Large Language Models (LLMs) are increasingly being explored for clinical question answering and decision support, yet safe deployment critically requires reliable handling of patient measurements in heterogeneous clinical notes. Existing evaluations of LLMs for clinical numerical reasoning provide limited operation-level coverage, restricted primarily to arithmetic computation, and rarely assess the robustness of numerical understanding across clinical note formats. We introduce ClinicNumRobBench, a benchmark of 1,624 context-question instances with ground-truth answers that evaluates four main types of clinical numeracy: value retrieval, arithmetic computation, relational comparison, and aggregation. To stress-test robustness, ClinicNumRobBench presents longitudinal MIMIC-IV vital-sign records in three semantically equivalent representations, including a real-world note-style variant derived from the Open Patients dataset, and instantiates queries using 42 question templates. Experiments on 14 LLMs show that value retrieval is generally strong, with most models exceeding 85% accuracy, while relational comparison and aggregation remain challenging, with some models scoring below 15%. Fine-tuning on medical data can reduce numeracy relative to base models by over 30%, and performance drops under note-style variation indicate LLM sensitivity to format. ClinicNumRobBench offers a rigorous testbed for clinically reliable numerical reasoning. Code and data URL are available on https://github.com/MinhVuong2000/ClinicNumRobBench.

Large language models (LLMs) have demonstrated remarkable performance in reasoning tasks, where reinforcement learning (RL) serves as a key algorithm for enhancing their reasoning capabilities. Currently, there are two mainstream reward paradigms: model-based rewards and rule-based rewards. However, both approaches suffer from limitations: rule-based rewards lack robustness, while model-based rewards are vulnerable to reward hacking. To address these issues, we propose Cooper(Co-optimizing Policy Model and Reward Model), a RL framework that jointly optimizes both the policy model and the reward model. Cooper leverages the high precision of rule-based rewards when identifying correct responses, and dynamically constructs and selects positive-negative sample pairs for continued training the reward model. This design enhances robustness and mitigates the risk of reward hacking. To further support Cooper, we introduce a hybrid annotation strategy that efficiently and accurately generates training data for the reward model. We also propose a reference-based reward modeling paradigm, where the reward model takes a reference answer as input. Based on this design, we train a reward model named VerifyRM, which achieves higher accuracy on VerifyBench compared to other models of the same size. We conduct reinforcement learning using both VerifyRM and Cooper. Our experiments show that Cooper not only alleviates reward hacking but also improves end-to-end RL performance, for instance, achieving a 0.54% gain in average accuracy on Qwen2.5-1.5B-Instruct. Our findings demonstrate that dynamically updating reward model is an effective way to combat reward hacking, providing a reference for better integrating reward models into RL.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

In this work, we present a modular and interpretable framework that uses Large Language Models (LLMs) to automate candidate assessment in recruitment. The system integrates diverse sources, including job descriptions, CVs, interview transcripts, and HR feedback; to generate structured evaluation reports that mirror expert judgment. Unlike traditional ATS tools that rely on keyword matching or shallow scoring, our approach employs role-specific, LLM-generated rubrics and a multi-agent architecture to perform fine-grained, criteria-driven evaluations. The framework outputs detailed assessment reports, candidate comparisons, and ranked recommendations that are transparent, auditable, and suitable for real-world hiring workflows. Beyond rubric-based analysis, we introduce an LLM-Driven Active Listwise Tournament mechanism for candidate ranking. Instead of noisy pairwise comparisons or inconsistent independent scoring, the LLM ranks small candidate subsets (mini-tournaments), and these listwise permutations are aggregated using a Plackett-Luce model. An active-learning loop selects the most informative subsets, producing globally coherent and sample-efficient rankings. This adaptation of listwise LLM preference modeling (previously explored in financial asset ranking) provides a principled and highly interpretable methodology for large-scale candidate ranking in talent acquisition.

As language models shift from single-shot answer generation toward multi-step reasoning that retrieves and consumes evidence mid-inference, evaluating the role of individual retrieved items becomes more important. Existing RAG evaluation typically targets final-answer quality, citation faithfulness, or answer-level attribution, but none of these directly targets the intervention-based, per-evidence-item utility view we study here. We introduce CUE-R, a lightweight intervention-based framework for measuring per-evidence-item operational utility in single-shot RAG using shallow observable retrieval-use traces. CUE-R perturbs individual evidence items via REMOVE, REPLACE, and DUPLICATE operators, then measures changes along three utility axes (correctness, proxy-based grounding faithfulness, and confidence error) plus a trace-divergence signal. We also outline an operational evidence-role taxonomy for interpreting intervention outcomes. Experiments on HotpotQA and 2WikiMultihopQA with Qwen-3 8B and GPT-5.2 reveal a consistent pattern: REMOVE and REPLACE substantially harm correctness and grounding while producing large trace shifts, whereas DUPLICATE is often answer-redundant yet not fully behaviorally neutral. A zero-retrieval control confirms that these effects arise from degradation of meaningful retrieval. A two-support ablation further shows that multi-hop evidence items can interact non-additively: removing both supports harms performance far more than either single removal. Our results suggest that answer-only evaluation misses important evidence effects and that intervention-based utility analysis is a practical complement for RAG evaluation.

Abstractive summarization models are commonly trained using maximum likelihood estimation, which assumes a deterministic (one-point) target distribution in which an ideal model will assign all the probability mass to the reference summary. This assumption may lead to performance degradation during inference, where the model needs to compare several system-generated (candidate) summaries that have deviated from the reference summary. To address this problem, we propose a novel training paradigm which assumes a non-deterministic distribution so that different candidate summaries are assigned probability mass according to their quality. Our method achieves a new state-of-the-art result on the CNN/DailyMail (47.78 ROUGE-1) and XSum (49.07 ROUGE-1) datasets. Further analysis also shows that our model can estimate probabilities of candidate summaries that are more correlated with their level of quality.

A common approach for aligning language models to human preferences is to first learn a reward model from preference data, and then use this reward model to update the language model. We study two closely related problems that arise in this approach. First, any monotone transformation of the reward model preserves preference ranking; is there a choice that is ``better'' than others? Second, we often wish to align language models to multiple properties: how should we combine multiple reward models? Using a probabilistic interpretation of the alignment procedure, we identify a natural choice for transformation for (the common case of) rewards learned from Bradley-Terry preference models. This derived transformation has two important properties. First, it emphasizes improving poorly-performing outputs, rather than outputs that already score well. This mitigates both underfitting (where some prompts are not improved) and reward hacking (where the model learns to exploit misspecification of the reward model). Second, it enables principled aggregation of rewards by linking summation to logical conjunction: the sum of transformed rewards corresponds to the probability that the output is ``good'' in all measured properties, in a sense we make precise. Experiments aligning language models to be both helpful and harmless using RLHF show substantial improvements over the baseline (non-transformed) approach.

Object counting methods typically rely on manually annotated datasets. The cost of creating such datasets has restricted the versatility of these networks to count objects from specific classes (such as humans or penguins), and counting objects from diverse categories remains a challenge. The availability of robust text-to-image latent diffusion models (LDMs) raises the question of whether these models can be utilized to generate counting datasets. However, LDMs struggle to create images with an exact number of objects based solely on text prompts but they can be used to offer a dependable sorting signal by adding and removing objects within an image. Leveraging this data, we initially introduce an unsupervised sorting methodology to learn object-related features that are subsequently refined and anchored for counting purposes using counting data generated by LDMs. Further, we present a density classifier-guided method for dividing an image into patches containing objects that can be reliably counted. Consequently, we can generate counting data for any type of object and count them in an unsupervised manner. Our approach outperforms other unsupervised and few-shot alternatives and is not restricted to specific object classes for which counting data is available. Code to be released upon acceptance.

Learning from feedback is an instrumental process for advancing the capabilities and safety of frontier models, yet its effectiveness is often constrained by cost and scalability. We present a pilot study that explores scaling reward models through unsupervised approaches. We operationalize reward-based scaling (RBS), in its simplest form, as preference learning over document prefixes and suffixes drawn from large-scale web corpora. Its advantage is demonstrated in various aspects: despite using no human annotations, training on 11M tokens of math-focused web data yields steady gains on RewardBench v1 and v2, and these improvements consistently transfer across diverse initialization backbones spanning model families and scales. Across models, our method improves RewardBench v2 accuracy by up to +7.7 points on average, with gains of up to +16.1 on in-domain math subsets and consistent improvements on out-of-domain safety and general subsets. When applied to best-of-N selection and policy optimization, these reward models substantially improve downstream math performance and match or exceed strong supervised reward model baselines of similar size. Overall, we demonstrate the feasibility and promise of training reward models without costly and potentially unreliable human annotations.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

Search agents powered by large language models can autonomously decompose queries, retrieve information, and synthesize answers through multi-step reasoning. However, the rapid growth of training methods has outpaced controlled comparison: existing works differ in retrieval corpora, reward designs, and training protocols, making it unclear what actually drives improvements. We present a controlled empirical study that isolates three under-explored dimensions of search agent training. First, we identify a critical data-coverage issue in the widely used Wikipedia 2018 corpus and show that correcting it alone yields larger gains than the differences between training algorithms. Second, we systematically compare outcome-based and process-based reward methods across three base models, finding that the simplest outcome-based approach achieves competitive or superior performance in most settings, and that process-level credit assignment can over-correct agent behavior. Third, we analyze training data diversity, off-policy data utilization, and search budget scaling, distilling practical guidelines for training effective search agents. Our code is available at https://github.com/YiboZhao624/SearchAgentReview.

To enhance the efficiency and practicality of federated bandit learning, recent advances have introduced incentives to motivate communication among clients, where a client participates only when the incentive offered by the server outweighs its participation cost. However, existing incentive mechanisms naively assume the clients are truthful: they all report their true cost and thus the higher cost one participating client claims, the more the server has to pay. Therefore, such mechanisms are vulnerable to strategic clients aiming to optimize their own utility by misreporting. To address this issue, we propose an incentive compatible (i.e., truthful) communication protocol, named Truth-FedBan, where the incentive for each participant is independent of its self-reported cost, and reporting the true cost is the only way to achieve the best utility. More importantly, Truth-FedBan still guarantees the sub-linear regret and communication cost without any overheads. In other words, the core conceptual contribution of this paper is, for the first time, demonstrating the possibility of simultaneously achieving incentive compatibility and nearly optimal regret in federated bandit learning. Extensive numerical studies further validate the effectiveness of our proposed solution.

Object counting is pivotal for understanding the composition of scenes. Previously, this task was dominated by class-specific methods, which have gradually evolved into more adaptable class-agnostic strategies. However, these strategies come with their own set of limitations, such as the need for manual exemplar input and multiple passes for multiple categories, resulting in significant inefficiencies. This paper introduces a new, more practical approach enabling simultaneous counting of multiple object categories using an open vocabulary framework. Our solution, OmniCount, stands out by using semantic and geometric insights from pre-trained models to count multiple categories of objects as specified by users, all without additional training. OmniCount distinguishes itself by generating precise object masks and leveraging point prompts via the Segment Anything Model for efficient counting. To evaluate OmniCount, we created the OmniCount-191 benchmark, a first-of-its-kind dataset with multi-label object counts, including points, bounding boxes, and VQA annotations. Our comprehensive evaluation in OmniCount-191, alongside other leading benchmarks, demonstrates OmniCount's exceptional performance, significantly outpacing existing solutions and heralding a new era in object counting technology.

The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.

While reinforcement learning with verifiable rewards (RLVR) has advanced LLM reasoning in structured domains like mathematics and programming, its application to general-domain reasoning tasks remains challenging due to the absence of verifiable reward signals. To this end, methods like Reinforcement Learning with Reference Probability Reward (RLPR) have emerged, leveraging the probability of generating the final answer as a reward signal. However, these outcome-focused approaches neglect crucial step-by-step supervision of the reasoning process itself. To address this gap, we introduce Probabilistic Process Supervision (P2S), a novel self-supervision framework that provides fine-grained process rewards without requiring a separate reward model or human-annotated reasoning steps. During reinforcement learning, P2S synthesizes and filters a high-quality reference reasoning chain (gold-CoT). The core of our method is to calculate a Path Faithfulness Reward (PFR) for each reasoning step, which is derived from the conditional probability of generating the gold-CoT's suffix, given the model's current reasoning prefix. Crucially, this PFR can be flexibly integrated with any outcome-based reward, directly tackling the reward sparsity problem by providing dense guidance. Extensive experiments on reading comprehension and medical Question Answering benchmarks show that P2S significantly outperforms strong baselines.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

Summarization models often generate text that is poorly calibrated to quality metrics because they are trained to maximize the likelihood of a single reference (MLE). To address this, recent work has added a calibration step, which exposes a model to its own ranked outputs to improve relevance or, in a separate line of work, contrasts positive and negative sets to improve faithfulness. While effective, much of this work has focused on how to generate and optimize these sets. Less is known about why one setup is more effective than another. In this work, we uncover the underlying characteristics of effective sets. For each training instance, we form a large, diverse pool of candidates and systematically vary the subsets used for calibration fine-tuning. Each selection strategy targets distinct aspects of the sets, such as lexical diversity or the size of the gap between positive and negatives. On three diverse scientific long-form summarization datasets (spanning biomedical, clinical, and chemical domains), we find, among others, that faithfulness calibration is optimal when the negative sets are extractive and more likely to be generated, whereas for relevance calibration, the metric margin between candidates should be maximized and surprise--the disagreement between model and metric defined candidate rankings--minimized. Code to create, select, and optimize calibration sets is available at https://github.com/griff4692/calibrating-summaries

Recent approaches in personalized reward modeling have primarily focused on leveraging user interaction history to align model judgments with individual preferences. However, existing approaches largely treat user context as a static or implicit conditioning signal, failing to capture the dynamic and multi-faceted nature of human judgment. In this paper, we propose P-Check, a novel personalized reward modeling framework, designed to train a plug-and-play checklist generator that synthesizes dynamic evaluation criteria for guiding the reward prediction. To better align these checklists with personalized nuances, we introduce Preference-Contrastive Criterion Weighting, a training strategy that assigns saliency scores to criteria based on their discriminative power for personalized judgment. We conduct extensive experiments and demonstrate that P-Check not only improves reward accuracy but also enhances downstream personalized generation, and remains robust in OOD scenarios.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for enhancing the reasoning ability of Large Language Models (LLMs). Yet current RLVR methods often explore poorly, leading to premature convergence and entropy collapse. To address this challenge, we introduce Curiosity-Driven Exploration (CDE), a framework that leverages the model's own intrinsic sense of curiosity to guide exploration. We formalize curiosity with signals from both the actor and the critic: for the actor, we use perplexity over its generated response, and for the critic, we use the variance of value estimates from a multi-head architecture. Both signals serve as an exploration bonus within the RLVR framework to guide the model. Our theoretical analysis shows that the actor-wise bonus inherently penalizes overconfident errors and promotes diversity among correct responses; moreover, we connect the critic-wise bonus to the well-established count-based exploration bonus in RL. Empirically, our method achieves an approximate +3 point improvement over standard RLVR using GRPO/PPO on AIME benchmarks. Further analysis identifies a calibration collapse mechanism within RLVR, shedding light on common LLM failure modes.

Logical reasoning is a critical benchmark for evaluating the capabilities of large language models (LLMs), as it reflects their ability to derive valid conclusions from given premises. While the combination of test-time scaling with dedicated outcome or process reward models has opened up new avenues to enhance LLMs performance in complex reasoning tasks, this space is under-explored in deductive logical reasoning. We present a set of Outcome Reward Models (ORMs) for deductive reasoning. To train the ORMs we mainly generate data using Chain-of-Thought (CoT) with single and multiple samples. Additionally, we propose a novel tactic to further expand the type of errors covered in the training dataset of the ORM. In particular, we propose an echo generation technique that leverages LLMs' tendency to reflect incorrect assumptions made in prompts to extract additional training data, covering previously unexplored error types. While a standard CoT chain may contain errors likely to be made by the reasoner, the echo strategy deliberately steers the model toward incorrect reasoning. We show that ORMs trained on CoT and echo-augmented data demonstrate improved performance on the FOLIO, JustLogic, and ProverQA datasets across four different LLMs.

Process Reward Models (PRMs) provide step-level feedback for reasoning, but current PRMs usually output only a single reward score for each step. Downstream methods must therefore treat imperfect step-level reward predictions as reliable decision signals, with no indication of when these predictions should be trusted. We propose BetaPRM, a distributional PRM that predicts both a step-level success probability and the reliability of that prediction. Given step-success supervision from Monte Carlo continuations, BetaPRM learns a Beta belief that explains the observed number of successful continuations through a Beta-Binomial likelihood, rather than regressing to the finite-sample success ratio as a point target. This learned reliability signal indicates when a step reward should be trusted, enabling downstream applications to distinguish reliable rewards from uncertain ones. As one application, we introduce Adaptive Computation Allocation (ACA) for PRM-guided Best-of-N reasoning. ACA uses the learned reliability signal to stop when a high-reward solution is reliable and to spend additional computation on uncertain candidate prefixes. Experiments across four backbones and four reasoning benchmarks show that BetaPRM improves PRM-guided Best-of-N selection while preserving standard step-level error detection. Built on this signal, ACA improves the accuracy--token tradeoff over fixed-budget Best-of-16, reducing token usage by up to 33.57% while improving final-answer accuracy.

Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful solution should contain enough method-level information that, when applied to a neighborhood of related questions, it should yield better downstream performance than incorrect solutions. Building on this idea, we propose Consequence-Based Utility, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related yet verifiable questions. Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions. Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality. Specifically, for GPT-OSS-120B, it improves Acc@1 from 67.2 to 76.3 and AUC from 71.4 to 79.6, with similarly large AUC gains on GPT-OSS-20B (69.0 to 79.2). Furthermore, compared to LLM-Judges, it also exhibits a larger solver-evaluator gap, maintaining a stronger correct-wrong separation even on instances where the underlying solver often fails to solve.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula (1-β^{n})/(1-β), where n is the number of samples and βin [0,1) is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

We introduce CompareBench, a benchmark for evaluating visual comparison reasoning in vision-language models (VLMs), a fundamental yet understudied skill. CompareBench consists of 1000 QA pairs across four tasks: quantity (600), temporal (100), geometric (200), and spatial (100). It is derived from two auxiliary datasets that we constructed: TallyBench (2000 counting images with QA) and HistCaps (515 historical images with bilingual captions). We evaluate both closed-source APIs (OpenAI, Gemini, Claude) and open-source models (Qwen2.5-VL and Qwen3-VL series). Results show clear scaling trends but also reveal critical limitations: even the strongest models consistently fail at temporal ordering and spatial relations, and they often make mistakes in basic counting and geometric comparisons that are trivial for humans. These findings demonstrate that visual comparison remains a systematic blind spot for current VLMs. By providing controlled, diverse, and diagnostic evaluation, CompareBench establishes a foundation for advancing more reliable multimodal reasoning.

Large language models have demonstrated remarkable capabilities in complex mathematical reasoning tasks, but they inevitably generate errors throughout multi-step solutions. Process-level Reward Models (PRMs) have shown great promise by providing supervision and evaluation at each intermediate step, thereby effectively improving the models' reasoning abilities. However, training effective PRMs requires high-quality process reward data, yet existing methods for constructing such data are often labour-intensive or inefficient. In this paper, we propose an uncertainty-driven framework for automated process reward data construction, encompassing both data generation and annotation processes for PRMs. Additionally, we identify the limitations of both majority vote and PRMs, and introduce two generic uncertainty-aware output aggregation methods: Hybrid Majority Reward Vote and Weighted Reward Frequency Vote, which combine the strengths of majority vote with PRMs. Extensive experiments on ProcessBench, MATH, and GSMPlus show the effectiveness and efficiency of the proposed PRM data construction framework, and demonstrate that the two output aggregation methods further improve the mathematical reasoning abilities across diverse PRMs. The code and data will be publicly available at https://github.com/Jiuzhouh/UnPRM.

Reward models are crucial for aligning large language models (LLMs) with human values and intentions. Existing approaches follow either Generative (GRMs) or Discriminative (DRMs) paradigms, yet both suffer from limitations: GRMs typically demand costly point-wise supervision, while DRMs produce uncalibrated relative scores that lack probabilistic interpretation. To address these challenges, we introduce a novel reward modeling paradigm: Probabilistic Reward Model (PRM). Instead of modeling reward as a deterministic scalar, our approach treats it as a random variable, learning a full probability distribution for the quality of each response. To make this paradigm practical, we present its closed-form, discrete realization: the Ordinal Probabilistic Reward Model (OPRM), which discretizes the quality score into a finite set of ordinal ratings. Building on OPRM, we propose a data-efficient training strategy called Region Flooding Tuning (RgFT). It enables rewards to better reflect absolute text quality by incorporating quality-level annotations, which guide the model to concentrate the probability mass within corresponding rating sub-regions. Experiments on various reward model benchmarks show that our method improves accuracy by 2.9%sim7.4% compared to prior reward models, demonstrating strong performance and data efficiency. Analysis of the score distribution provides evidence that our method captures not only relative rankings but also absolute quality.

Reinforcement learning with verifiable rewards (RLVR) has become a central paradigm for improving reasoning and code generation in large language models, and GRPO-style training is widely adopted for its simplicity and effectiveness. However, an important design choice remains underexplored: how token-level policy gradient terms are aggregated within each sampled group. Standard GRPO uses sequence aggregation, while recent work has advocated token aggregation as a better alternative. We show that these two rules induce different optimization biases: token aggregation introduces sign-length coupling, while sequence aggregation implicitly downweights longer responses through sequence-level equal weighting. To address this tension, we propose Balanced Aggregation (BA), a simple drop-in replacement that computes token-level means separately within the positive and negative subsets and then combines them with sequence-count-based weights. Experiments with Qwen2.5-Math-7B and Qwen3-1.7B on DAPO-17k and Polaris, evaluated on six reasoning and coding benchmarks, show that BA consistently improves training stability and final performance over standard token and sequence aggregation. Our analysis further shows that the relative effectiveness of token and sequence aggregation is largely governed by response-length variation and the positive-negative length gap, highlighting aggregation as a critical design dimension in GRPO-style RLVR.

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose LamPO, a Lambda-Style Policy Optimization method that replaces scalar group advantages with a Pairwise Decomposed Advantage. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances reasoning of Large Language Models (LLMs) but usually exhibits limited generation diversity due to the over-incentivization of positive rewards. Although methods like Negative Sample Reinforcement (NSR) mitigate this issue by upweighting penalty from negative samples, they may suppress the semantic distributions shared between positive and negative responses. To boost reasoning ability without losing diversity, this paper proposes negative sample projection Residual Reinforcement Learning (ResRL) that decouples similar semantic distributions among positive and negative responses. We theoretically link Lazy Likelihood Displacement (LLD) to negative-positive head-gradient interference and derive a single-forward proxy that upper-bounds representation alignment to guide conservative advantage reweighting. ResRL then projects negative-token hidden representations onto an SVD-based low-rank positive subspace and uses projection residuals to modulate negative gradients, improving reasoning while preserving diversity and outperforming strong baselines on average across twelve benchmarks spanning Mathematics, Code, Agent Tasks, and Function Calling. Notably, ResRL surpasses NSR on mathematical reasoning by 9.4\% in Avg@16 and 7.0\% in Pass@128. Code is available at https://github.com/1229095296/ResRL.git.

Reinforcement learning with verifiable rewards has enabled strong post-training gains in domains such as math and coding, though many open-ended settings rely on rubric-based rewards. We study reward hacking in rubric-based RL, where a policy is optimized against a training verifier but evaluated against a cross-family panel of three frontier judges, reducing dependence on any single evaluator. Our framework separates two sources of divergence: verifier failure, where the training verifier credits rubric criteria that reference verifiers reject, and rubric-design limitations, where even strong rubric-based verifiers favor responses that rubric-free judges rate worse overall. Across medical and science domains, weak verifiers produce large proxy-reward gains that do not transfer to the reference verifiers; exploitation grows over training and concentrates in recurring failures such as partial satisfaction of compound criteria, treating implicit content as explicit, and imprecise topical matching. Stronger verifiers substantially reduce, but do not eliminate, verifier exploitation. We also introduce a self-internalization gap, a verifier-free diagnostic based on policy log-probabilities, which tracks reference-verifier quality, detecting when the policy trained using the weak verifier stops improving. Finally, in our setting, stronger verification does not prevent reward hacking when the rubric leaves important failure modes unspecified: rubric-based verifiers prefer the RL checkpoint, while rubric-free judges prefer the base model. These disagreements coincide with gains concentrated in completeness and presence-based criteria, alongside declines in factual correctness, conciseness, relevance, and overall quality. Together, these results suggest that stronger verification reduces reward hacking, but does not by itself ensure that rubric gains correspond to broader quality gains.

Effective reward design is a central challenge in Reinforcement Learning (RL) for code generation. Mainstream pass/fail outcome rewards enforce functional correctness via executing unit tests, but the resulting sparsity limits potential performance gains. While recent work has explored external Reward Models (RM) to generate richer, continuous rewards, the learned RMs suffer from reward misalignment and prohibitive computational cost. In this paper, we introduce VeRPO (Verifiable Dense Reward Policy Optimization), a novel RL framework for code generation that synthesizes robust and dense rewards fully grounded in verifiable execution feedback. The core idea of VeRPO is constructing dense rewards from weighted partial success: by dynamically estimating the difficulty weight of each unit test based on the execution statistics during training, a dense reward is derived from the sum of weights of the passed unit tests. To solidify the consistency between partial success and end-to-end functional correctness, VeRPO further integrates the dense signal with global execution outcomes, establishing a robust and dense reward paradigm relying solely on verifiable execution feedback. Extensive experiments across diverse benchmarks and settings demonstrate that VeRPO consistently outperforms outcome-driven and RM-based baselines, achieving up to +8.83\% gain in pass@1 with negligible time cost (< 0.02\%) and zero GPU memory overhead.

Large reasoning models (LRMs) are typically trained using reinforcement learning with verifiable reward (RLVR) to enhance their reasoning abilities. In this paradigm, policies are updated using both positive and negative self-generated rollouts, which correspond to distinct sample polarities. In this paper, we provide a systematic investigation into how these sample polarities affect RLVR training dynamics and behaviors. We find that positive samples sharpen existing correct reasoning patterns, while negative samples encourage exploration of new reasoning paths. We further explore how adjusting the advantage values of positive and negative samples at both the sample level and the token level affects RLVR training. Based on these insights, we propose an Adaptive and Asymmetric token-level Advantage shaping method for Policy Optimization, namely A3PO, that more precisely allocates advantage signals to key tokens across different polarities. Experiments across five reasoning benchmarks demonstrate the effectiveness of our approach.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key ingredient for unlocking complex reasoning capabilities in large language models. Recent work ProRL has shown promise in scaling RL by increasing the number of training steps. However, performance plateaus after thousands of steps, with clear diminishing returns from allocating more computation to additional training. In this work, we investigate a complementary paradigm for scaling RL, BroR-Lincreasing the number of rollouts per example to hundreds to exhaustively Broaden exploration, which yields continuous performance gains beyond the saturation point observed in ProRL when scaling the number of training steps. Our approach is motivated by a mass balance equation analysis allowing us to characterize the rate of change in probability mass for correct and incorrect tokens during the reinforcement process. We show that under a one-step RL assumption, sampled rollout tokens always contribute to correct-mass expansion, while unsampled tokens outside rollouts may lead to gains or losses depending on their distribution and the net reward balance. Importantly, as the number of rollouts per example N increases, the effect of unsampled terms diminishes, ensuring overall correct-mass expansion. To validate our theoretical analysis, we conduct simulations under more relaxed conditions and find that a sufficiently large rollout size N-corresponding to ample exploration-guarantees an increase in the probability mass of all correct tokens. Empirically, BroRL revives models saturated after 3K ProRL training steps and demonstrates robust, continuous improvement, achieving state-of-the-art results for the 1.5B model across diverse benchmarks.

The dynamic imbalance of the fore-background is a major challenge in video object counting, which is usually caused by the sparsity of target objects. This remains understudied in existing works and often leads to severe under-/over-prediction errors. To tackle this issue in video object counting, we propose a density-embedded Efficient Masked Autoencoder Counting (E-MAC) framework in this paper. To empower the model's representation ability on density regression, we develop a new Density-Embedded Masked mOdeling (DEMO) method, which first takes the density map as an auxiliary modality to perform multimodal self-representation learning for image and density map. Although DEMO contributes to effective cross-modal regression guidance, it also brings in redundant background information, making it difficult to focus on the foreground regions. To handle this dilemma, we propose an efficient spatial adaptive masking derived from density maps to boost efficiency. Meanwhile, we employ an optical flow-based temporal collaborative fusion strategy to effectively capture the dynamic variations across frames, aligning features to derive multi-frame density residuals. The counting accuracy of the current frame is boosted by harnessing the information from adjacent frames. In addition, considering that most existing datasets are limited to human-centric scenarios, we first propose a large video bird counting dataset, DroneBird, in natural scenarios for migratory bird protection. Extensive experiments on three crowd datasets and our DroneBird validate our superiority against the counterparts. The code and dataset are available.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

Reinforcement Learning from Human Feedback relies on reward models to align large language models with human preferences. However, RLHF often suffers from reward hacking, wherein policy learning exploits flaws in the trained reward model to maximize reward scores without genuinely aligning with human preferences. A significant example of such reward hacking is length bias, where reward models usually favor longer responses irrespective of actual response quality. Previous works on length bias have notable limitations, these approaches either mitigate bias without characterizing the bias form, or simply assume a linear length-reward relation. To accurately model the intricate nature of length bias and facilitate more effective bias mitigation, we propose FiMi-RM (Bias Fitting to Mitigate Length Bias of Reward Model in RLHF), a framework that autonomously learns and corrects underlying bias patterns. Our approach consists of three stages: First, we train a standard reward model which inherently contains length bias. Next, we deploy a lightweight fitting model to explicitly capture the non-linear relation between length and reward. Finally, we incorporate this learned relation into the reward model to debias. Experimental results demonstrate that FiMi-RM achieves a more balanced length-reward distribution. Furthermore, when applied to alignment algorithms, our debiased reward model improves length-controlled win rate and reduces verbosity without compromising its performance.