Daily Papers

Speculative decoding accelerates autoregressive speech generation by letting a fast draft model propose tokens that a larger target model verifies. However, for speech LLMs that generate acoustic tokens, exact token matching is overly restrictive: many discrete tokens are acoustically or semantically interchangeable, reducing acceptance rates and limiting speedups. We introduce Principled Coarse-Graining (PCG), which verifies proposals at the level of Acoustic Similarity Groups (ASGs) derived from the target model's embedding space. By splitting each token's probability mass across the overlapping groups that contain it, we define an overlap-aware coarse-grained distribution and perform rejection sampling on the resulting group variable. This yields an exactness guarantee at the group level while allowing the accepted draft token to stand in for any member of the group in practice. On LibriTTS, PCG increases acceptance and throughput relative to standard speculative decoding and prior speech-specific relaxations while maintaining intelligibility and speaker similarity. These results suggest acoustically aware, group-level acceptance as a simple and general way to accelerate speech token generation while maintaining speech quality.

Late-interaction retrieval (ColBERT, ColPali) scores a query against a document via the MaxSim operator. The standard PyTorch implementation materialises the full query-token x document-token similarity tensor only to reduce it away. At ColPali scale this is the single largest tensor in the pipeline (e.g. 21 GB in FP16 for 10K documents) and limits both candidate set size at inference and batch size during contrastive training. We present Flash-MaxSim (FM), an IO-aware fused GPU kernel that computes the same MaxSim scores without ever materialising the tensor, and extends the same principle to the training backward. At ColPali scale on A100 this cuts inference memory up to 9x and training memory by two orders of magnitude, unlocking candidate sets and contrastive batch sizes a single GPU could not previously reach. The kernel is a drop-in replacement, exact up to floating-point evaluation order under its stated FP32-accumulation protocol: rankings match the FP32 reference within 5e-4 of nDCG@10 on BEIR and REAL-MM-RAG. A separate INT8 path trades exactness for halved index storage at high fidelity. Released open-source.

Discrete diffusion models have emerged as powerful frameworks for generating structured categorical data. However, efficiently sampling from reward-tilted distributions remains a fundamental challenge. While Twisted Sequential Monte Carlo (SMC) offers asymptotic exactness for this task, estimating the optimal twist function in discrete state spaces necessitates costly Monte Carlo approximations, resulting a severe computational bottleneck at inference. To overcome this limitation, we introduce Contrastive Distribution Matching (CDM), a novel framework that amortizes the cost of SMC inference by learning a parameterized twist function via positive and negative samples. For efficient training, we reformulate the gradient estimator to leverage the closed-form forward kernels of discrete diffusion models. In practice, evaluating our learned twist function incurs less than 5% additional computational overhead compared to a single forward pass of the base model. Through extensive empirical evaluations, we demonstrate that CDM consistently outperforms existing baselines under matched wall-clock time. We validate the effectiveness and versatility of our approach across a diverse range of applications, including toxic text generation, regulatory DNA sequence design, protein designability, and diffusion large language model alignment.

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

This paper analyzes the limitations of existing unlearning evaluation metrics in terms of practicality, exactness, and robustness in real-world LLM unlearning scenarios. To overcome these limitations, we propose a new metric called Distribution Correction-based Unlearning Evaluation (DCUE). It identifies core tokens and corrects distributional biases in their confidence scores using a validation set. The evaluation results are quantified using the Kolmogorov-Smirnov test. Experimental results demonstrate that DCUE overcomes the limitations of existing metrics, which also guides the design of more practical and reliable unlearning algorithms in the future.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

We study a capability the dominant paradigm in synthetic tabular data does not provide: exact satisfaction of a declared analytical outcome with no source data. Imitation methods (copulas, GANs, diffusion) learn a real distribution and sample from it, and are judged on fidelity to real data. A large, practical class of needs is different: generating data with no source data ("cold start") that reproduces a declared outcome (a revenue curve, a churn rate, a group share) across a relational schema. Off-the-shelf imitation tools offer no interface for such targets, and no sampler can hit an exact aggregate, because sampling has variance. On a real public dataset, off-the-shelf learned synthesizers trained on that very data miss the declared monthly aggregate by 74 to 86 percent; a per-period steelman cuts the miss to about 19 percent and still cannot reach 0; a closed-form generator reaches exactly 0. We name this task outcome-conformant synthesis, argue its evaluation axis is conformance rather than fidelity, and show the two axes are orthogonal. We contribute: (1) a formal account showing a widely-used family of exact-aggregate generators is exactly conditional-sum sampling of a Gamma population (via Lukacs' characterization), with closed-form exactness, a closed-form marginal CV, and scale-invariance; a controlled experiment maps the boundary, enforcing the exact aggregate costs at most 0.006 in 1-Wasserstein distance to an arbitrary external marginal, the rest being shape-family mismatch; (2) SpecBench, to our knowledge the first benchmark to measure conformance to analytical outcomes for cold-start relational synthesis; and (3) a closed-form, deterministic reference system. Exact aggregation alone is trivial; the contribution is conformance jointly with closed-form marginals, integrity, determinism, and zero source data. We concede fidelity to imitation where real data exists.

Relevance judgments are crucial for evaluating information retrieval systems, but traditional human-annotated labels are time-consuming and expensive. As a result, many researchers turn to automatic alternatives to accelerate method development. Among these, Large Language Models (LLMs) provide a scalable solution by generating relevance labels directly through prompting. However, prompting an LLM for a relevance label without constraints often results in not only incorrect predictions but also outputs that are difficult for humans to interpret. We propose the Multi-Criteria framework for LLM-based relevance judgments, decomposing the notion of relevance into multiple criteria--such as exactness, coverage, topicality, and contextual fit--to improve the robustness and interpretability of retrieval evaluations compared to direct grading methods. We validate this approach on three datasets: the TREC Deep Learning tracks from 2019 and 2020, as well as LLMJudge (based on TREC DL 2023). Our results demonstrate that Multi-Criteria judgments enhance the system ranking/leaderboard performance. Moreover, we highlight the strengths and limitations of this approach relative to direct grading approaches, offering insights that can guide the development of future automatic evaluation frameworks in information retrieval.

In interactions between users and language model agents, user utterances frequently exhibit ellipsis (omission of words or phrases) or imprecision (lack of exactness) to prioritize efficiency. This can lead to varying interpretations of the same input based on different assumptions or background knowledge. It is thus crucial for agents to adeptly handle the inherent ambiguity in queries to ensure reliability. However, even state-of-the-art large language models (LLMs) still face challenges in such scenarios, primarily due to the following hurdles: (1) LLMs are not explicitly trained to deal with ambiguous utterances; (2) the degree of ambiguity perceived by the LLMs may vary depending on the possessed knowledge. To address these issues, we propose Alignment with Perceived Ambiguity (APA), a novel pipeline that aligns LLMs to manage ambiguous queries by leveraging their own assessment of ambiguity (i.e., perceived ambiguity). Experimental results on question-answering datasets demonstrate that APA empowers LLMs to explicitly detect and manage ambiguous queries while retaining the ability to answer clear questions. Furthermore, our finding proves that APA excels beyond training with gold-standard labels, especially in out-of-distribution scenarios.

Variable-order Markov models generate sequences over a finite alphabet by conditioning each symbol on the longest available suffix of the generated history. Regular constraints, by contrast, describe finite-horizon control requirements by an automaton: fixed positions, forced endings, metrical patterns, and forbidden copied fragments are all special cases. Existing exact methods already handle regular constraints with belief propagation for first-order Markov chains. The contribution here is the variable-order extension: identifying the state space on which the existing BP-regular machinery must be run when the generator is a variable-order/backoff model. A first-order constraint layer can enforce useful support conditions, but it computes future mass after merging histories that a variable-order generator deliberately keeps distinct. We formalize this mismatch and give the sparse construction obtained by replacing the first-order Markov state with the observed context state, then taking the standard product with the regular constraint automaton. For a fixed trained context graph and automaton, inference is linear in the sequence horizon; in general it is polynomial in the number of reachable product edges. This gives the correct variable-order distribution conditioned on regular constraints without expanding to all K-tuples. The same finite-source interface supports reversible data augmentation by inverse count lookup, matching materialized transposition augmentation without storing transformed corpora. We also separate exact BP inference from generation-time backoff policies, such as singleton avoidance, whose stochastic semantics must be made explicit if exactness is claimed.

Existing multimodal large language models have achieved high-fidelity visual perception and exploratory visual generation. However, a precision paradox persists in complex reasoning tasks: optical perception systems transcribe symbols without capturing logical topology, while pixel-based generative models produce visual artifacts lacking mathematical exactness. To bridge this gap, we propose that reasoning over visual inputs be reconceptualized as optical decompression-the process of reconstructing latent logical structures from compressed visual tokens. Guided by the axiom that Parsing is Reasoning, we introduce Thinking with Drafting (TwD), which utilizes a minimalist Domain-Specific Language (DSL) as a grounding intermediate representation. Unlike standard approaches that hallucinate answers directly, TwD forces the model to draft its mental model into executable code, rendering deterministic visual proofs for self-verification. To validate this, we present VisAlg, a visual algebra benchmark. Experiments demonstrate that TwD serve as a superior cognitive scaffold. Our work establishes a closed-loop system where visual generation acts not as a creative output but as a logical verifier, offering a generalizable path for visual reasoning.

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models through simulating a set of weighted particles. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and in conditional image generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.