Daily Papers

Activation functions are core components of all deep learning architectures. Currently, the most popular activation functions are smooth ReLU variants like GELU and SiLU. These are self-gated activation functions where the range of the gating function is between zero and one. In this paper, we explore the viability of using arctan as a gating mechanism. A self-gated activation function that uses arctan as its gating function has a monotonically increasing first derivative. To make this activation function competitive, it is necessary to introduce a trainable parameter for every MLP block to expand the range of the gating function beyond zero and one. We find that this technique also improves existing self-gated activation functions. We conduct an empirical evaluation of Expanded ArcTan Linear Unit (xATLU), Expanded GELU (xGELU), and Expanded SiLU (xSiLU) and show that they outperform existing activation functions within a transformer architecture. Additionally, expanded gating ranges show promising results in improving first-order Gated Linear Units (GLU).

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

Training large transformers is slow, but recent innovations on GPU architecture give us an advantage. NVIDIA Ampere GPUs can execute a fine-grained 2:4 sparse matrix multiplication twice as fast as its dense equivalent. In the light of this property, we comprehensively investigate the feasibility of accelerating feed-forward networks (FFNs) of transformers in pre-training. First, we define a ``flip rate'' to monitor the stability of a 2:4 training process. Utilizing this metric, we propose three techniques to preserve accuracy: to modify the sparse-refined straight-through estimator by applying the masked decay term on gradients, to determine a feasible decay factor in warm-up stage, and to enhance the model's quality by a dense fine-tuning procedure near the end of pre-training. Besides, we devise two techniques to practically accelerate training: to calculate transposable 2:4 masks by convolution, and to accelerate gated activation functions by reducing GPU L2 cache miss. Experiments show that our 2:4 sparse training algorithm achieves similar convergence to dense training algorithms on several transformer pre-training tasks, while actual acceleration can be observed on different shapes of transformer block apparently. Our toolkit is available at https://github.com/huyz2023/2by4-pretrain.

Transformers are central to recent successes in natural language processing and computer vision. Transformers have a mostly uniform backbone where layers alternate between feed-forward and self-attention in order to build a deep network. Here we investigate this design choice and find that more complex blocks that have different permutations of layer primitives can be more efficient. Using this insight, we develop a complex block, named Brainformer, that consists of a diverse sets of layers such as sparsely gated feed-forward layers, dense feed-forward layers, attention layers, and various forms of layer normalization and activation functions. Brainformer consistently outperforms the state-of-the-art dense and sparse Transformers, in terms of both quality and efficiency. A Brainformer model with 8 billion activated parameters per token demonstrates 2x faster training convergence and 5x faster step time compared to its GLaM counterpart. In downstream task evaluation, Brainformer also demonstrates a 3% higher SuperGLUE score with fine-tuning compared to GLaM with a similar number of activated parameters. Finally, Brainformer largely outperforms a Primer dense model derived with NAS with similar computation per token on fewshot evaluations.

Transformer architecture currently represents the main driver behind many successes in a variety of tasks addressed by deep learning, especially the recent advances in natural language processing (NLP) culminating with large language models (LLM). In addition, transformer architecture has found a wide spread of interest from computer vision (CV) researchers and practitioners, allowing for many advancements in vision-related tasks and opening the door for multi-task and multi-modal deep learning architectures that share the same principle of operation. One drawback to these architectures is their reliance on the scaled dot product attention mechanism with the softmax activation function, which is computationally expensive and requires large compute capabilities both for training and inference. This paper investigates substituting the attention mechanism usually adopted for transformer architecture with an architecture incorporating gated linear unit (GLU) activation within a multi-layer perceptron (MLP) structure in conjunction with the default MLP incorporated in the traditional transformer design. Another step forward taken by this paper is to eliminate the second non-gated MLP to further reduce the computational cost. Experimental assessments conducted by this research show that both proposed modifications and reductions offer competitive performance in relation to baseline architectures, in support of the aims of this work in establishing a more efficient yet capable alternative to the traditional attention mechanism as the core component in designing transformer architectures.

Activation functions are fundamental elements of deep learning architectures as they significantly influence training dynamics. ReLU, while widely used, is prone to the dying neuron problem, which has been mitigated by variants such as LeakyReLU, PReLU, and ELU that better handle negative neuron outputs. Recently, self-gated activations like GELU and Swish have emerged as state-of-the-art alternatives, leveraging their smoothness to ensure stable gradient flow and prevent neuron inactivity. In this work, we introduce the Gompertz Linear Unit (GoLU), a novel self-gated activation function defined as GoLU(x) = x , Gompertz(x), where Gompertz(x) = e^{-e^{-x}}. The GoLU activation leverages the asymmetry in the Gompertz function to reduce variance in the latent space more effectively compared to GELU and Swish, while preserving robust gradient flow. Extensive experiments across diverse tasks, including Image Classification, Language Modeling, Semantic Segmentation, Object Detection, Instance Segmentation, and Diffusion, highlight GoLU's superior performance relative to state-of-the-art activation functions, establishing GoLU as a robust alternative to existing activation functions.

SwiGLU has become a standard gated activation in modern Transformer MLPs, yet its gate sharpness -- the smoothness and selectivity of the gating function -- is typically fixed throughout training. In this work, we propose Confidence-Aware SwiGLU (κ-SwiGLU), a variant of SwiGLU for Mixture-of-Experts (MoE) models that adjusts expert gate sharpness according to token-level routing confidence. Specifically, κ-SwiGLU parameterizes the SiLU gate sharpness coefficient as a learnable function of the router logit, enabling each expert gate unit to interpolate between smooth, broadly active gating and sharp, selective gating. We evaluate κ-SwiGLU on the FineWeb-Edu dataset across MoE Transformer models ranging from 8 to 28 layers. Across these settings, κ-SwiGLU improves mean CORE performance while adding negligible parameters and incurring only a small computational overhead, demonstrating that confidence-aware gate sharpness is a promising mechanism for improving MoE MLPs. The code is available at https://github.com/askerlee/kappa-swiglu.

Interpretability researchers have attempted to understand MLP neurons of language models based on both the contexts in which they activate and their output weight vectors. They have paid little attention to a complementary aspect: the interactions between input and output. For example, when neurons detect a direction in the input, they might add much the same direction to the residual stream ("enrichment neurons") or reduce its presence ("depletion neurons"). We address this aspect by examining the cosine similarity between input and output weights of a neuron. We apply our method to 12 models and find that enrichment neurons dominate in early-middle layers whereas later layers tend more towards depletion. To explain this finding, we argue that enrichment neurons are largely responsible for enriching concept representations, one of the first steps of factual recall. Our input-output perspective is a complement to activation-dependent analyses and to approaches that treat input and output separately.

Large language models (LLMs) based on transformers have made significant strides in recent years, the success of which is driven by scaling up their model size. Despite their high algorithmic performance, the computational and memory requirements of LLMs present unprecedented challenges. To tackle the high compute requirements of LLMs, the Mixture-of-Experts (MoE) architecture was introduced which is able to scale its model size without proportionally scaling up its computational requirements. Unfortunately, MoE's high memory demands and dynamic activation of sparse experts restrict its applicability to real-world problems. Previous solutions that offload MoE's memory-hungry expert parameters to CPU memory fall short because the latency to migrate activated experts from CPU to GPU incurs high performance overhead. Our proposed Pre-gated MoE system effectively tackles the compute and memory challenges of conventional MoE architectures using our algorithm-system co-design. Pre-gated MoE employs our novel pre-gating function which alleviates the dynamic nature of sparse expert activation, allowing our proposed system to address the large memory footprint of MoEs while also achieving high performance. We demonstrate that Pre-gated MoE is able to improve performance, reduce GPU memory consumption, while also maintaining the same level of model quality. These features allow our Pre-gated MoE system to cost-effectively deploy large-scale LLMs using just a single GPU with high performance.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

Several variants of the Long Short-Term Memory (LSTM) architecture for recurrent neural networks have been proposed since its inception in 1995. In recent years, these networks have become the state-of-the-art models for a variety of machine learning problems. This has led to a renewed interest in understanding the role and utility of various computational components of typical LSTM variants. In this paper, we present the first large-scale analysis of eight LSTM variants on three representative tasks: speech recognition, handwriting recognition, and polyphonic music modeling. The hyperparameters of all LSTM variants for each task were optimized separately using random search, and their importance was assessed using the powerful fANOVA framework. In total, we summarize the results of 5400 experimental runs (approx 15 years of CPU time), which makes our study the largest of its kind on LSTM networks. Our results show that none of the variants can improve upon the standard LSTM architecture significantly, and demonstrate the forget gate and the output activation function to be its most critical components. We further observe that the studied hyperparameters are virtually independent and derive guidelines for their efficient adjustment.

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x cdot sigmoid(beta x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9\% for Mobile NASNet-A and 0.6\% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network.

The objective of continual learning (CL) is to learn tasks sequentially without retraining on earlier tasks. However, when subjected to CL, traditional neural networks exhibit catastrophic forgetting and limited generalization. To overcome these problems, we introduce a novel method called 'Gate and Obstruct Network' (GateON). GateON combines learnable gating of activity and online estimation of parameter relevance to safeguard crucial knowledge from being overwritten. Our method generates partially overlapping pathways between tasks which permits forward and backward transfer during sequential learning. GateON addresses the issue of network saturation after parameter fixation by a re-activation mechanism of fixed neurons, enabling large-scale continual learning. GateON is implemented on a wide range of networks (fully-connected, CNN, Transformers), has low computational complexity, effectively learns up to 100 MNIST learning tasks, and achieves top-tier results for pre-trained BERT in CL-based NLP tasks.

Gating mechanisms have been widely utilized, from early models like LSTMs and Highway Networks to recent state space models, linear attention, and also softmax attention. Yet, existing literature rarely examines the specific effects of gating. In this work, we conduct comprehensive experiments to systematically investigate gating-augmented softmax attention variants. Specifically, we perform a comprehensive comparison over 30 variants of 15B Mixture-of-Experts (MoE) models and 1.7B dense models trained on a 3.5 trillion token dataset. Our central finding is that a simple modification-applying a head-specific sigmoid gate after the Scaled Dot-Product Attention (SDPA)-consistently improves performance. This modification also enhances training stability, tolerates larger learning rates, and improves scaling properties. By comparing various gating positions and computational variants, we attribute this effectiveness to two key factors: (1) introducing non-linearity upon the low-rank mapping in the softmax attention, and (2) applying query-dependent sparse gating scores to modulate the SDPA output. Notably, we find this sparse gating mechanism mitigates 'attention sink' and enhances long-context extrapolation performance, and we also release related https://github.com/qiuzh20/gated_attention{codes} and https://huggingface.co/QwQZh/gated_attention{models} to facilitate future research.

Parameter-efficient fine-tuning (PEFT) methods such as adapt large pretrained models by adding small weight-space updates. While effective, weight deltas are hard to interpret mechanistically, and they do not directly expose which internal computations are reused versus bypassed for a new task. We explore an alternative view inspired by neuromodulation: adaptation as a change in mode -- selecting and rescaling existing computations -- rather than rewriting the underlying weights. We propose , a simple activation-space PEFT technique that freezes base weights and learns per-neuron thresholds and gains. During training, a smooth gate decides whether a neuron's activation participates; at inference the gate can be hardened to yield explicit conditional computation and neuron-level attributions. As a proof of concept, we study ``mode specialization'' on MNIST (0^circ) versus rotated MNIST (45^circ). We pretrain a small MLP on a 50/50 mixture (foundation), freeze its weights, and then specialize to the rotated mode using . Across seeds, improves rotated accuracy over the frozen baseline while using only a few hundred trainable parameters per layer, and exhibits partial activation sparsity (a minority of units strongly active). Compared to , trades some accuracy for substantially fewer trainable parameters and a more interpretable ``which-neurons-fire'' mechanism. We discuss limitations, including reduced expressivity when the frozen base lacks features needed for the target mode.

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as O(1/log(n)), where n denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates.

The success of artificial neural networks (ANNs) hinges greatly on the judicious selection of an activation function, introducing non-linearity into network and enabling them to model sophisticated relationships in data. However, the search of activation functions has largely relied on empirical knowledge in the past, lacking theoretical guidance, which has hindered the identification of more effective activation functions. In this work, we offer a proper solution to such issue. Firstly, we theoretically demonstrate the existence of the worst activation function with boundary conditions (WAFBC) from the perspective of information entropy. Furthermore, inspired by the Taylor expansion form of information entropy functional, we propose the Entropy-based Activation Function Optimization (EAFO) methodology. EAFO methodology presents a novel perspective for designing static activation functions in deep neural networks and the potential of dynamically optimizing activation during iterative training. Utilizing EAFO methodology, we derive a novel activation function from ReLU, known as Correction Regularized ReLU (CRReLU). Experiments conducted with vision transformer and its variants on CIFAR-10, CIFAR-100 and ImageNet-1K datasets demonstrate the superiority of CRReLU over existing corrections of ReLU. Extensive empirical studies on task of large language model (LLM) fine-tuning, CRReLU exhibits superior performance compared to GELU, suggesting its broader potential for practical applications.

In this paper, we introduce the gated perceptron, an enhancement of the conventional perceptron, which incorporates an additional input computed as the product of the existing inputs. This allows the perceptron to capture non-linear interactions between features, significantly improving its ability to classify and regress on complex datasets. We explore its application in both linear and non-linear regression tasks using the Iris dataset, as well as binary and multi-class classification problems, including the PIMA Indian dataset and Breast Cancer Wisconsin dataset. Our results demonstrate that the gated perceptron can generate more distinct decision regions compared to traditional perceptrons, enhancing its classification capabilities, particularly in handling non-linear data. Performance comparisons show that the gated perceptron competes with state-of-the-art classifiers while maintaining a simple architecture.

We introduce Gated-SwinRMT, a family of hybrid vision transformers that combine the shifted-window attention of the Swin Transformer with the Manhattan-distance spatial decay of Retentive Networks (RMT), augmented by input-dependent gating. Self-attention is decomposed into consecutive width-wise and height-wise retention passes within each shifted window, where per-head exponential decay masks provide a two-dimensional locality prior without learned positional biases. Two variants are proposed. Gated-SwinRMT-SWAT substitutes softmax with sigmoid activation, implements balanced ALiBi slopes with multiplicative post-activation spatial decay, and gates the value projection via SwiGLU; the Normalized output implicitly suppresses uninformative attention scores. Gated-SwinRMT-Retention retains softmax-normalized retention with an additive log-space decay bias and incorporates an explicit G1 sigmoid gate -- projected from the block input and applied after local context enhancement (LCE) but prior to the output projection~W_O -- to alleviate the low-rank W_V !cdot! W_O bottleneck and enable input-dependent suppression of attended outputs. We assess both variants on Mini-ImageNet (224{times}224, 100 classes) and CIFAR-10 (32{times}32, 10 classes) under identical training protocols, utilizing a single GPU due to resource limitations. At {approx}77--79\,M parameters, Gated-SwinRMT-SWAT achieves 80.22% and Gated-SwinRMT-Retention 78.20% top-1 test accuracy on Mini-ImageNet, compared with 73.74% for the RMT baseline. On CIFAR-10 -- where small feature maps cause the adaptive windowing mechanism to collapse attention to global scope -- the accuracy advantage compresses from +6.48\,pp to +0.56\,pp.

Conditional computation is a popular strategy to make Transformers more efficient. Existing methods often target individual modules (e.g., mixture-of-experts layers) or skip layers independently of one another. However, interpretability research has demonstrated that the middle layers of Transformers exhibit greater redundancy, and that early layers aggregate information into token positions. Guided by these insights, we propose a novel architecture that dynamically skips a variable number of layers from the middle outward. In particular, a learned gating mechanism determines whether to bypass a symmetric span of central blocks based on the input, and a gated attention mechanism prevents subsequent tokens from attending to skipped token positions. Residual norms are controlled with a 'sandwich' or 'perilayernorm' scheme and gate sparsity with an adaptive regularization loss. We had aimed to reduce compute requirements for 'simpler' tokens and potentially foster an emergent multi-level representational hierarchy but, at the scales investigated, our approach does not achieve improvements in the trade-off between validation cross-entropy and estimated FLOPs compared to dense baselines with fewer layers. We release our code at https://github.com/tim-lawson/skip-middle.

Retrieval-augmented generation (RAG) enhances LLMs by incorporating external knowledge to support response generation. However, conflicts between retrieved context and parametric knowledge have emerged as a critical challenge in RAG systems. To mitigate such conflicts, numerous studies have attempted to identify and edit knowledge-related internal neurons, aiming to improve the ability of LLMs to rely on contextual evidence during generation. However, these neuron-level approaches may introduce unintended cascading effects that compromise the general capabilities of LLMs, as the modified neurons are often entangled with broader model behaviors and functionalities. In this paper, we introduce SHIFT, a novel framework that reformulates neuron-level modification as learnable gate modulation, allowing LLMs to adaptively regulate internal activations for knowledge conflict resolution. Technically, our SHIFT equips LLMs with a lightweight gate module and optimizes fewer than 0.01% trainable parameters while keeping the backbone model frozen. During generation, the gate module adjusts the model's internal representations to adaptively leverage contextual and parametric knowledge. Extensive experiments on six datasets validate the effectiveness of our SHIFT in comparison with various competing baselines. All datasets and code are available at https://github.com/OpenBMB/SHIFT.

The simulation of human neurons and neurotransmission mechanisms has been realized in deep neural networks based on the theoretical implementations of activation functions. However, recent studies have reported that the threshold potential of neurons exhibits different values according to the locations and types of individual neurons, and that the activation functions have limitations in terms of representing this variability. Therefore, this study proposes a simple yet effective activation function that facilitates different thresholds and adaptive activations according to the positions of units and the contexts of inputs. Furthermore, the proposed activation function mathematically exhibits a more generalized form of Swish activation function, and thus we denoted it as Adaptive SwisH (ASH). ASH highlights informative features that exhibit large values in the top percentiles in an input, whereas it rectifies low values. Most importantly, ASH exhibits trainable, adaptive, and context-aware properties compared to other activation functions. Furthermore, ASH represents general formula of the previously studied activation function and provides a reasonable mathematical background for the superior performance. To validate the effectiveness and robustness of ASH, we implemented ASH into many deep learning models for various tasks, including classification, detection, segmentation, and image generation. Experimental analysis demonstrates that our activation function can provide the benefits of more accurate prediction and earlier convergence in many deep learning applications.

The widely used ReLU is favored for its hardware efficiency, {as the implementation at inference is a one bit sign case,} yet suffers from issues such as the ``dying ReLU'' problem, where during training, neurons fail to activate and constantly remain at zero, as highlighted by Lu et al. Traditional approaches to mitigate this issue often introduce more complex and less hardware-friendly activation functions. In this work, we propose a Hysteresis Rectified Linear Unit (HeLU), an efficient activation function designed to address the ``dying ReLU'' problem with minimal complexity. Unlike traditional activation functions with fixed thresholds for training and inference, HeLU employs a variable threshold that refines the backpropagation. This refined mechanism allows simpler activation functions to achieve competitive performance comparable to their more complex counterparts without introducing unnecessary complexity or requiring inductive biases. Empirical evaluations demonstrate that HeLU enhances model generalization across diverse datasets, offering a promising solution for efficient and effective inference suitable for a wide range of neural network architectures.

Activation functions are fundamental in deep neural networks and directly impact gradient flow, optimization stability, and generalization. Although ReLU remains standard because of its simplicity, it suffers from vanishing gradients and lacks adaptability. Alternatives like Swish and GELU introduce smooth transitions, but fail to dynamically adjust to input statistics. We propose VeLU, a Variance-enhanced Learning Unit as an activation function that dynamically scales based on input variance by integrating ArcTan-Sin transformations and Wasserstein-2 regularization, effectively mitigating covariate shifts and stabilizing optimization. Extensive experiments on ViT_B16, VGG19, ResNet50, DenseNet121, MobileNetV2, and EfficientNetB3 confirm VeLU's superiority over ReLU, ReLU6, Swish, and GELU on six vision benchmarks. The codes of VeLU are publicly available on GitHub.

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

We introduce GateSkip, a simple residual-stream gating mechanism that enables token-wise layer skipping in decoder-only LMs. Each Attention/MLP branch is equipped with a sigmoid-linear gate that condenses the branch's output before it re-enters the residual stream. During inference we rank tokens by the gate values and skip low-importance ones using a per-layer budget. While early-exit or router-based Mixture-of-Depths models are known to be unstable and need extensive retraining, our smooth, differentiable gates fine-tune stably on top of pretrained models. On long-form reasoning, we save up to 15\% compute while retaining over 90\% of baseline accuracy. On instruction-tuned models we see accuracy gains at full compute and match baseline quality near 50\% savings. The learned gates give insight into transformer information flow (e.g., BOS tokens act as anchors), and the method combines easily with quantization, pruning, and self-speculative decoding.

Recent work has found that sparse autoencoders (SAEs) are an effective technique for unsupervised discovery of interpretable features in language models' (LMs) activations, by finding sparse, linear reconstructions of LM activations. We introduce the Gated Sparse Autoencoder (Gated SAE), which achieves a Pareto improvement over training with prevailing methods. In SAEs, the L1 penalty used to encourage sparsity introduces many undesirable biases, such as shrinkage -- systematic underestimation of feature activations. The key insight of Gated SAEs is to separate the functionality of (a) determining which directions to use and (b) estimating the magnitudes of those directions: this enables us to apply the L1 penalty only to the former, limiting the scope of undesirable side effects. Through training SAEs on LMs of up to 7B parameters we find that, in typical hyper-parameter ranges, Gated SAEs solve shrinkage, are similarly interpretable, and require half as many firing features to achieve comparable reconstruction fidelity.

Linear attention Transformers and their gated variants, celebrated for enabling parallel training and efficient recurrent inference, still fall short in recall-intensive tasks compared to traditional Transformers and demand significant resources for training from scratch. This paper introduces Gated Slot Attention (GSA), which enhances Attention with Bounded-memory-Control (ABC) by incorporating a gating mechanism inspired by Gated Linear Attention (GLA). Essentially, GSA comprises a two-layer GLA linked via softmax, utilizing context-aware memory reading and adaptive forgetting to improve memory capacity while maintaining compact recurrent state size. This design greatly enhances both training and inference efficiency through GLA's hardware-efficient training algorithm and reduced state size. Additionally, retaining the softmax operation is particularly beneficial in "finetuning pretrained Transformers to RNNs" (T2R) settings, reducing the need for extensive training from scratch. Extensive experiments confirm GSA's superior performance in scenarios requiring in-context recall and in T2R settings.

Because learning sometimes involves sensitive data, machine learning algorithms have been extended to offer privacy for training data. In practice, this has been mostly an afterthought, with privacy-preserving models obtained by re-running training with a different optimizer, but using the model architectures that already performed well in a non-privacy-preserving setting. This approach leads to less than ideal privacy/utility tradeoffs, as we show here. Instead, we propose that model architectures are chosen ab initio explicitly for privacy-preserving training. To provide guarantees under the gold standard of differential privacy, one must bound as strictly as possible how individual training points can possibly affect model updates. In this paper, we are the first to observe that the choice of activation function is central to bounding the sensitivity of privacy-preserving deep learning. We demonstrate analytically and experimentally how a general family of bounded activation functions, the tempered sigmoids, consistently outperform unbounded activation functions like ReLU. Using this paradigm, we achieve new state-of-the-art accuracy on MNIST, FashionMNIST, and CIFAR10 without any modification of the learning procedure fundamentals or differential privacy analysis.

The activation function plays a crucial role in model optimisation, yet the optimal choice remains unclear. For example, the Sigmoid activation is the de-facto activation in balanced classification tasks, however, in imbalanced classification, it proves inappropriate due to bias towards frequent classes. In this work, we delve deeper in this phenomenon by performing a comprehensive statistical analysis in the classification and intermediate layers of both balanced and imbalanced networks and we empirically show that aligning the activation function with the data distribution, enhances the performance in both balanced and imbalanced tasks. To this end, we propose the Adaptive Parametric Activation (APA) function, a novel and versatile activation function that unifies most common activation functions under a single formula. APA can be applied in both intermediate layers and attention layers, significantly outperforming the state-of-the-art on several imbalanced benchmarks such as ImageNet-LT, iNaturalist2018, Places-LT, CIFAR100-LT and LVIS and balanced benchmarks such as ImageNet1K, COCO and V3DET. The code is available at https://github.com/kostas1515/AGLU.

Sparse Autoencoders (SAEs) extract interpretable features from Large Language Models, but standard variants enforce non-negativity, forcing separate latents for diametrically opposed concepts (e.g., "pressure too high" vs. "pressure too low") and wasting dictionary capacity when features are anticorrelated. We propose the Sign-Aware Gated SAE (SA-GSAE): two-sided gated sparsity with signed magnitude and auxiliary supervision. A polarity-sensitive gate selects support on either sign, a signed-magnitude path avoids L1 shrinkage, and an auxiliary reconstruction prevents gate collapse. Bipolar sharing - one latent encoding both signs along a shared direction - is realised via a new Bi-Jump-ReLU activation; parameter accounting shows sign-awareness stays parameter-efficient even when anticorrelated pairs are rare. On real LLM activations across three mid-depth hookpoints on Pythia-1B and SmolLM3-3B (6 cells, 3 seeds), a half-width SA-GSAE at width H strictly Pareto-dominates a full-width Gated SAE at 2H over the entire swept L0 overlap on 3 of 6 cells (both MLP-output hookpoints and resid-mid/Pythia-1B); on the remaining 3 it matches R^2 within 0.025 (max gap -0.008) while cutting dead fraction by 0.35-0.62 absolute. Sweep-geomean dead-fraction reductions are ~100x-500x on MLP-output cells and Pythia-1B resid, ~2x-4x on attention cells and SmolLM3-3B resid. Ablations show the two-sided gate and auxiliary loss are load-bearing (no auxiliary collapses LR to 0.27, 98% dead); tying r_i^+ = r_i^- is indistinguishable (|Delta R^2| = 0.0015), and we recommend this symmetric variant as default. MLP-output gains come from most latents carrying both polarities; on attention, bipolar structure concentrates in a small set of top latents. Full-width SA-GSAE exhibits a reproducible reconstruction collapse at SmolLM3-3B resid that the half-width entirely avoids.

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows networks to learn optimal per-neuron activation functions while preserving computational efficiency at inference. In the first phase, neurons adaptively select from a pool of candidate activation functions (ReLU, Sigmoid, Tanh, Leaky ReLU, ELU, SELU) using a differentiable hard-mixture mechanism. In the second phase, each neuron's activation function is fixed according to the learned selection, resulting in a computationally efficient network that supports continued training with optimized vectorized operations. We evaluate SmartMixed on the MNIST dataset using feedforward neural networks of varying depths. The analysis shows that neurons in different layers exhibit distinct preferences for activation functions, providing insights into the functional diversity within neural architectures.

Catastrophic forgetting remains a significant challenge to continual learning for decades. While recent works have proposed effective methods to mitigate this problem, they mainly focus on the algorithmic side. Meanwhile, we do not fully understand what architectural properties of neural networks lead to catastrophic forgetting. This study aims to fill this gap by studying the role of activation functions in the training dynamics of neural networks and their impact on catastrophic forgetting. Our study reveals that, besides sparse representations, the gradient sparsity of activation functions also plays an important role in reducing forgetting. Based on this insight, we propose a new class of activation functions, elephant activation functions, that can generate both sparse representations and sparse gradients. We show that by simply replacing classical activation functions with elephant activation functions, we can significantly improve the resilience of neural networks to catastrophic forgetting. Our method has broad applicability and benefits for continual learning in regression, class incremental learning, and reinforcement learning tasks. Specifically, we achieves excellent performance on Split MNIST dataset in just one single pass, without using replay buffer, task boundary information, or pre-training.

Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.

Gated Linear Units (arXiv:1612.08083) consist of the component-wise product of two linear projections, one of which is first passed through a sigmoid function. Variations on GLU are possible, using different nonlinear (or even linear) functions in place of sigmoid. We test these variants in the feed-forward sublayers of the Transformer (arXiv:1706.03762) sequence-to-sequence model, and find that some of them yield quality improvements over the typically-used ReLU or GELU activations.

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Pad\'e Activation Units (PAUs) can both approximate common activation functions and also learn new ones while providing compact representations. Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance. Moreover, PAUs pave the way to approximations with provable robustness. https://github.com/ml-research/pau

We propose Mish, a novel self-regularized non-monotonic activation function which can be mathematically defined as: f(x)=xtanh(softplus(x)). As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks against the best combinations of architectures and activation functions. We also observe that data augmentation techniques have a favorable effect on benchmarks like ImageNet-1k and MS-COCO across multiple architectures. For example, Mish outperformed Leaky ReLU on YOLOv4 with a CSP-DarkNet-53 backbone on average precision (AP_{50}^{val}) by 2.1% in MS-COCO object detection and ReLU on ResNet-50 on ImageNet-1k in Top-1 accuracy by approx1% while keeping all other network parameters and hyperparameters constant. Furthermore, we explore the mathematical formulation of Mish in relation with the Swish family of functions and propose an intuitive understanding on how the first derivative behavior may be acting as a regularizer helping the optimization of deep neural networks. Code is publicly available at https://github.com/digantamisra98/Mish.

While Attention Residuals has shown some effectiveness in addressing the widespread issue of unbounded activation growth across deep residual layers, it inevitably incurs significant communication overhead. To circumvent this bottleneck, we propose Multi-Gate Residuals (MGR), which stabilizes activation scales without additional communication burden. It utilizes a straightforward scoring and gating mechanism to maintain multi-stream context, coupled with Attention Pooling to extract hidden states from the stream states. Empirical experiments demonstrate that MGR is practical for large-scale training and deployment, offering tangible performance improvements over existing architectures.

Linear Transformers have gained attention as efficient alternatives to standard Transformers, but their performance in retrieval and long-context tasks has been limited. To address these limitations, recent work has explored two distinct mechanisms: gating for adaptive memory control and the delta update rule for precise memory modifications. We observe that these mechanisms are complementary: gating enables rapid memory erasure while the delta rule facilitates targeted updates. Building on this insight, we introduce the gated delta rule and develop a parallel training algorithm optimized for modern hardware. Our proposed architecture, Gated DeltaNet, consistently surpasses existing models like Mamba2 and DeltaNet across multiple benchmarks, including language modeling, common-sense reasoning, in-context retrieval, length extrapolation, and long-context understanding. We further enhance performance by developing hybrid architectures that combine Gated DeltaNet layers with sliding window attention or Mamba2 layers, achieving both improved training efficiency and superior task performance.

Accurate air quality forecasts are vital for public health alerts, exposure assessment, and emissions control. In practice, observational data are often missing in varying proportions and patterns due to collection and transmission issues. These incomplete spatiotemporal records impede reliable inference and risk assessment and can lead to overconfident extrapolation. To address these challenges, we propose an end to end framework, the channel gated learning unit based spatiotemporal bayesian neural field (CGLUBNF). It uses Fourier features with a graph attention encoder to capture multiscale spatial dependencies and seasonal temporal dynamics. A channel gated learning unit, equipped with learnable activations and gated residual connections, adaptively filters and amplifies informative features. Bayesian inference jointly optimizes predictive distributions and parameter uncertainty, producing point estimates and calibrated prediction intervals. We conduct a systematic evaluation on two real world datasets, covering four typical missing data patterns and comparing against five state of the art baselines. CGLUBNF achieves superior prediction accuracy and sharper confidence intervals. In addition, we further validate robustness across multiple prediction horizons and analysis the contribution of extraneous variables. This research lays a foundation for reliable deep learning based spatio-temporal forecasting with incomplete observations in emerging sensing paradigms, such as real world vehicle borne mobile monitoring.

Recent advancements in Large Language Models (LLMs) have set themselves apart with their exceptional performance in complex language modelling tasks. However, these models are also known for their significant computational and storage requirements, primarily due to the quadratic computation complexity of softmax attention. To mitigate this issue, linear attention has been designed to reduce the quadratic space-time complexity that is inherent in standard transformers. In this work, we embarked on a comprehensive exploration of three key components that substantially impact the performance of the Gated Linear Attention module: feature maps, normalization, and the gating mechanism. We developed a feature mapping function to address some crucial issues that previous suggestions overlooked. Then we offered further rationale for the integration of normalization layers to stabilize the training process. Moreover, we explored the saturation phenomenon of the gating mechanism and augmented it with a refining module. We conducted extensive experiments and showed our architecture outperforms previous Gated Linear Attention mechanisms in extensive tasks including training from scratch and post-linearization with continual pre-training.

The input tokens to Vision Transformers carry little semantic meaning as they are defined as regular equal-sized patches of the input image, regardless of its content. However, processing uniform background areas of an image should not necessitate as much compute as dense, cluttered areas. To address this issue, we propose a dynamic mixed-scale tokenization scheme for ViT, MSViT. Our method introduces a conditional gating mechanism that selects the optimal token scale for every image region, such that the number of tokens is dynamically determined per input. The proposed gating module is lightweight, agnostic to the choice of transformer backbone, and trained within a few epochs (e.g., 20 epochs on ImageNet) with little training overhead. In addition, to enhance the conditional behavior of the gate during training, we introduce a novel generalization of the batch-shaping loss. We show that our gating module is able to learn meaningful semantics despite operating locally at the coarse patch-level. We validate MSViT on the tasks of classification and segmentation where it leads to improved accuracy-complexity trade-off.

Modern autoregressive models rely on attention, yet the Softmax full attention in Transformers scales quadratically with sequence length. Sliding Window Attention (SWA) achieves linear-time encoding/decoding by constraining the attention pattern, but under an Associative Memory interpretation, its difference-style update renders the training objective effectively unbounded. In contrast, Softmax attention normalizes updates, leading to memory shrinkage and gradient vanishing. We propose GatedFWA: a Memory-Gated (Flash) Windowed Attention mechanism that preserves SWAs efficiency while stabilizing memory updates and making gradient flow controllable. In essence, GatedFWA accumulate a per-token/head gate into a decay bias added to the attention logits, acting as a learnable contraction in the memory recurrence. We implement a fused one-pass gate preprocessing and a FlashAttention-compatible kernel that injects the gate under a sliding mask, ensuring I/O efficiency and numerical stability. On language modelling benchmarks, GatedFWA delivers competitive throughput with negligible overhead and better use of global context, and it integrates cleanly with token compression/selection methods such as NSA and generalizes to various autoregressive domains.

Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right - similar to why we study the human brain - and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization (AM), which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network (DGN). The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).

This paper localizes the policy routing mechanism in alignment-trained language models. An intermediate-layer attention gate reads detected content and triggers deeper amplifier heads that boost the signal toward refusal. In smaller models the gate and amplifier are single heads; at larger scale they become bands of heads across adjacent layers. The gate contributes under 1% of output DLA, but interchange testing (p<0.001) and knockout cascade confirm it is causally necessary. Interchange screening at n>=120 detects the same motif in twelve models from six labs (2B to 72B), though specific heads differ by lab. Per-head ablation weakens up to 58x at 72B and misses gates that interchange identifies; interchange is the only reliable audit at scale. Modulating the detection-layer signal continuously controls policy from hard refusal through evasion to factual answering. On safety prompts the same intervention turns refusal into harmful guidance, showing the safety-trained capability is gated by routing rather than removed. Thresholds vary by topic and by input language, and the circuit relocates across generations within a family while behavioral benchmarks register no change. Routing is early-commitment: the gate commits at its own layer before deeper layers finish processing the input. Under an in-context substitution cipher, gate interchange necessity collapses 70 to 99% across three models and the model switches to puzzle-solving. Injecting the plaintext gate activation into the cipher forward pass restores 48% of refusals in Phi-4-mini, localizing the bypass to the routing interface. A second method, cipher contrast analysis, uses plain/cipher DLA differences to map the full cipher-sensitive routing circuit in O(3n) forward passes. Any encoding that defeats detection-layer pattern matching bypasses the policy regardless of whether deeper layers reconstruct the content.

Ranking model plays an essential role in e-commerce search and recommendation. An effective ranking model should give a personalized ranking list for each user according to the user preference. Existing algorithms usually extract a user representation vector from the user behavior sequence, then feed the vector into a feed-forward network (FFN) together with other features for feature interactions, and finally produce a personalized ranking score. Despite tremendous progress in the past, there is still room for improvement. Firstly, the personalized patterns of feature interactions for different users are not explicitly modeled. Secondly, most of existing algorithms have poor personalized ranking results for long-tail users with few historical behaviors due to the data sparsity. To overcome the two challenges, we propose Attention Weighted Mixture of Experts (AW-MoE) with contrastive learning for personalized ranking. Firstly, AW-MoE leverages the MoE framework to capture personalized feature interactions for different users. To model the user preference, the user behavior sequence is simultaneously fed into expert networks and the gate network. Within the gate network, one gate unit and one activation unit are designed to adaptively learn the fine-grained activation vector for experts using an attention mechanism. Secondly, a random masking strategy is applied to the user behavior sequence to simulate long-tail users, and an auxiliary contrastive loss is imposed to the output of the gate network to improve the model generalization for these users. This is validated by a higher performance gain on the long-tail user test set. Experiment results on a JD real production dataset and a public dataset demonstrate the effectiveness of AW-MoE, which significantly outperforms state-of-art methods. Notably, AW-MoE has been successfully deployed in the JD e-commerce search engine, ...

A causal-decoder block is hierarchical: lower layers build the residual basis that upper layers attend over. We identify a failure mode in GPT pretraining: upper layers commit to sharp attention patterns before lower-layer features stabilize. We call this premature upper-layer attention specialization. Temporarily slowing only upper-layer Q/K projections during early training improves final perplexity and downstream accuracy without altering other parameters; it prevents upper attention from collapsing onto an immature residual basis. In LLaMA-style blocks, the same intervention is nearly unnecessary. Through ablations, we isolate multiplicative gated FFNs (not RMSNorm or bias removal) as the component that suppresses the upstream residual writes driving the failure. A pathwise analysis unifies both findings: the learning-rate intervention reduces a step-size factor, while gated FFNs reduce a residual-energy factor on the same growth pathway. Our results identify upper-layer Q/K timing as a concrete interaction point between decoder architecture and optimization.

Architecture optimization, which is a technique for finding an efficient neural network that meets certain requirements, generally reduces to a set of multiple-choice selection problems among alternative sub-structures or parameters. The discrete nature of the selection problem, however, makes this optimization difficult. To tackle this problem we introduce a novel concept of a trainable gate function. The trainable gate function, which confers a differentiable property to discretevalued variables, allows us to directly optimize loss functions that include non-differentiable discrete values such as 0-1 selection. The proposed trainable gate can be applied to pruning. Pruning can be carried out simply by appending the proposed trainable gate functions to each intermediate output tensor followed by fine-tuning the overall model, using any gradient-based training methods. So the proposed method can jointly optimize the selection of the pruned channels while fine-tuning the weights of the pruned model at the same time. Our experimental results demonstrate that the proposed method efficiently optimizes arbitrary neural networks in various tasks such as image classification, style transfer, optical flow estimation, and neural machine translation.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Large pretrained models, coupled with fine-tuning, are slowly becoming established as the dominant architecture in machine learning. Even though these models offer impressive performance, their practical application is often limited by the prohibitive amount of resources required for every inference. Early-exiting dynamic neural networks (EDNN) circumvent this issue by allowing a model to make some of its predictions from intermediate layers (i.e., early-exit). Training an EDNN architecture is challenging as it consists of two intertwined components: the gating mechanism (GM) that controls early-exiting decisions and the intermediate inference modules (IMs) that perform inference from intermediate representations. As a result, most existing approaches rely on thresholding confidence metrics for the gating mechanism and strive to improve the underlying backbone network and the inference modules. Although successful, this approach has two fundamental shortcomings: 1) the GMs and the IMs are decoupled during training, leading to a train-test mismatch; and 2) the thresholding gating mechanism introduces a positive bias into the predictive probabilities, making it difficult to readily extract uncertainty information. We propose a novel architecture that connects these two modules. This leads to significant performance improvements on classification datasets and enables better uncertainty characterization capabilities.

The Transformer architecture, underpinned by the self-attention mechanism, has become the de facto standard for sequence modeling tasks. However, its core computational primitive scales quadratically with sequence length (O(N^2)), creating a significant bottleneck for processing long contexts. In this paper, we propose the Gated Associative Memory (GAM) network, a novel, fully parallel architecture for sequence modeling that exhibits linear complexity (O(N)) with respect to sequence length. The GAM block replaces the self-attention layer with two parallel pathways: a causal convolution to efficiently capture local, position-dependent context, and a parallel associative memory retrieval mechanism to model global, content-based patterns. These pathways are dynamically fused using a gating mechanism, allowing the model to flexibly combine local and global information for each token. We implement GAM from scratch and conduct a rigorous comparative analysis against a standard Transformer model and a modern linear-time baseline (Mamba) on the WikiText-2 benchmark, as well as against the Transformer on the TinyStories dataset. Our experiments demonstrate that GAM is consistently faster, outperforming both baselines on training speed, and achieves a superior or competitive final validation perplexity across all datasets, establishing it as a promising and efficient alternative for sequence modeling.

Active Speaker Detection (ASD) aims to identify who is currently speaking in each frame of a video. Most state-of-the-art approaches rely on late fusion to combine visual and audio features, but late fusion often fails to capture fine-grained cross-modal interactions, which can be critical for robust performance in unconstrained scenarios. In this paper, we introduce GateFusion, a novel architecture that combines strong pretrained unimodal encoders with a Hierarchical Gated Fusion Decoder (HiGate). HiGate enables progressive, multi-depth fusion by adaptively injecting contextual features from one modality into the other at multiple layers of the Transformer backbone, guided by learnable, bimodally-conditioned gates. To further strengthen multimodal learning, we propose two auxiliary objectives: Masked Alignment Loss (MAL) to align unimodal outputs with multimodal predictions, and Over-Positive Penalty (OPP) to suppress spurious video-only activations. GateFusion establishes new state-of-the-art results on several challenging ASD benchmarks, achieving 77.8% mAP (+9.4%), 86.1% mAP (+2.9%), and 96.1% mAP (+0.5%) on Ego4D-ASD, UniTalk, and WASD benchmarks, respectively, and delivering competitive performance on AVA-ActiveSpeaker. Out-of-domain experiments demonstrate the generalization of our model, while comprehensive ablations show the complementary benefits of each component.

Backdoor attacks pose significant security risks for Large Language Models (LLMs), yet the internal mechanisms by which triggers operate remain poorly understood. We present the first mechanistic analysis of language-switching backdoors, studying the GAPperon model family (1B, 8B, 24B parameters) which contains triggers injected during pretraining that cause output language switching. Using activation patching, we localize trigger formation to early layers (7.5-25% of model depth) and identify which attention heads process trigger information. Our central finding is that trigger-activated heads substantially overlap with heads naturally encoding output language across model scales, with Jaccard indices between 0.18 and 0.66 over the top heads identified. This suggests that backdoor triggers do not form isolated circuits but instead co-opt the model's existing language components. These findings have implications for backdoor defense: detection methods may benefit from monitoring known functional components rather than searching for hidden circuits, and mitigation strategies could potentially leverage this entanglement between injected and natural behaviors.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

Linear attention replaces the unbounded cache of softmax attention with a fixed-size recurrent state, reducing sequence mixing to linear time and decoding to constant memory. The hard part is not just what to forget, but how to edit this compressed memory without scrambling existing associations. Delta-rule models subtract the current read before writing a new value, and Kimi Delta Attention (KDA) sharpens forgetting with channel-wise decay. But the active edit still uses a single scalar gate to control two different things: how much old content to erase on the key side and how much new content to commit on the value side. We introduce Gated DeltaNet-2, which generalizes both Gated DeltaNet and KDA by inheriting adaptive forgetting and channel-wise decay while addressing their shared limitation, the scalar tie between erasing and writing. Gated Delta Rule-2 separates these roles with a channel-wise erase gate b_t and a channel-wise write gate w_t, reducing to KDA when both gates collapse to the same scalar and to Gated DeltaNet when the decay also collapses. We derive a fast-weight update view, a chunkwise WY algorithm with channel-wise decay absorbed into asymmetric erase factors, and a gate-aware backward pass that preserves efficient parallel training. At 1.3B parameters trained on 100B FineWeb-Edu tokens, Gated DeltaNet-2 achieves the strongest overall results among Mamba-2, Gated DeltaNet, KDA, and Mamba-3 variants across language modeling, commonsense reasoning, and retrieval. Its advantage is most pronounced on long-context RULER needle-in-a-haystack benchmarks, where it improves the evaluated multi-key retrieval setting and remains strong in both recurrent and hybrid settings. Code is available at https://github.com/NVlabs/GatedDeltaNet-2.

We propose a novel attention gate (AG) model for medical imaging that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting salient features useful for a specific task. This enables us to eliminate the necessity of using explicit external tissue/organ localisation modules of cascaded convolutional neural networks (CNNs). AGs can be easily integrated into standard CNN architectures such as the U-Net model with minimal computational overhead while increasing the model sensitivity and prediction accuracy. The proposed Attention U-Net architecture is evaluated on two large CT abdominal datasets for multi-class image segmentation. Experimental results show that AGs consistently improve the prediction performance of U-Net across different datasets and training sizes while preserving computational efficiency. The code for the proposed architecture is publicly available.

Autoregressive models with continuous tokens form a promising paradigm for visual generation, especially for text-to-image (T2I) synthesis, but they suffer from high computational cost. We study how to design compute-efficient linear attention within this framework. Specifically, we conduct a systematic empirical analysis of scaling behavior with respect to parameter counts under different design choices, focusing on (1) normalization paradigms in linear attention (division-based vs. subtraction-based) and (2) depthwise convolution for locality augmentation. Our results show that although subtraction-based normalization is effective for image classification, division-based normalization scales better for linear generative transformers. In addition, incorporating convolution for locality modeling plays a crucial role in autoregressive generation, consistent with findings in diffusion models. We further extend gating mechanisms, commonly used in causal linear attention, to the bidirectional setting and propose a KV gate. By introducing data-independent learnable parameters to the key and value states, the KV gate assigns token-wise memory weights, enabling flexible memory management similar to forget gates in language models. Based on these findings, we present LINA, a simple and compute-efficient T2I model built entirely on linear attention, capable of generating high-fidelity 1024x1024 images from user instructions. LINA achieves competitive performance on both class-conditional and T2I benchmarks, obtaining 2.18 FID on ImageNet (about 1.4B parameters) and 0.74 on GenEval (about 1.5B parameters). A single linear attention module reduces FLOPs by about 61 percent compared to softmax attention. Code and models are available at: https://github.com/techmonsterwang/LINA.

We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifically tailored for problems requiring high precision. This innovation has led to the creation of a new class of neural networks, which we call (Comple)XNet, or simply XNet. We will demonstrate that XNet is particularly effective for high-dimensional challenges such as image classification and solving Partial Differential Equations (PDEs). Our evaluations show that XNet significantly outperforms established benchmarks like MNIST and CIFAR-10 in computer vision, and offers substantial advantages over Physics-Informed Neural Networks (PINNs) in both low-dimensional and high-dimensional PDE scenarios.

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

We study the influence of different activation functions in the output layer of deep neural network models for soft and hard label prediction in the learning with disagreement task. In this task, the goal is to quantify the amount of disagreement via predicting soft labels. To predict the soft labels, we use BERT-based preprocessors and encoders and vary the activation function used in the output layer, while keeping other parameters constant. The soft labels are then used for the hard label prediction. The activation functions considered are sigmoid as well as a step-function that is added to the model post-training and a sinusoidal activation function, which is introduced for the first time in this paper.

Many self-attention sublayers in large language models (LLMs) can be removed with little to no loss. We attribute this to the Attention Suppression Hypothesis: during pre-training, some deep attention layers learn to mute their own contribution, leaving the residual stream and the MLP to carry the representation. We propose Gate-Norm, a one-shot, weight-only criterion that ranks attention sublayers by query--key coupling and removes the least coupled ones, requiring no calibration data, no forward passes, no fine-tuning, and no specialized kernels. On 40-layer, 13B-parameter LLaMA models, Gate-Norm prunes the model in under a second. Pruning 8--16 attention sublayers yields up to 1.30times higher inference throughput while keeping average zero-shot accuracy within 2% of the unpruned baseline across BoolQ, RTE, HellaSwag, WinoGrande, ARC-Easy/Challenge, and OpenBookQA. Across these settings, Gate-Norm matches data-driven pruning methods in accuracy while being sim 1000times faster to score layers, enabling practical, data-free compression of LLMs.

In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning algorithm DQN achieved human-level performance in many Atari 2600 games. The purpose of this study is twofold. First, we propose two activation functions for neural network function approximation in reinforcement learning: the sigmoid-weighted linear unit (SiLU) and its derivative function (dSiLU). The activation of the SiLU is computed by the sigmoid function multiplied by its input. Second, we suggest that the more traditional approach of using on-policy learning with eligibility traces, instead of experience replay, and softmax action selection with simple annealing can be competitive with DQN, without the need for a separate target network. We validate our proposed approach by, first, achieving new state-of-the-art results in both stochastic SZ-Tetris and Tetris with a small 10times10 board, using TD(λ) learning and shallow dSiLU network agents, and, then, by outperforming DQN in the Atari 2600 domain by using a deep Sarsa(λ) agent with SiLU and dSiLU hidden units.

Which functions can be used as activations in deep neural networks? This article explores families of functions based on orthonormal bases, including the Hermite polynomial basis and the Fourier trigonometric basis, as well as a basis resulting from the tropicalization of a polynomial basis. Our study shows that, through simple variance-preserving initialization and without additional clamping mechanisms, these activations can successfully be used to train deep models, such as GPT-2 for next-token prediction on OpenWebText and ConvNeXt for image classification on ImageNet. Our work addresses the issue of exploding and vanishing activations and gradients, particularly prevalent with polynomial activations, and opens the door for improving the efficiency of large-scale learning tasks. Furthermore, our approach provides insight into the structure of neural networks, revealing that networks with polynomial activations can be interpreted as multivariate polynomial mappings. Finally, using Hermite interpolation, we show that our activations can closely approximate classical ones in pre-trained models by matching both the function and its derivative, making them especially useful for fine-tuning tasks. These activations are available in the torchortho library, which can be accessed via: https://github.com/K-H-Ismail/torchortho.

We propose a new method for exemplar-free class incremental training of ViTs. The main challenge of exemplar-free continual learning is maintaining plasticity of the learner without causing catastrophic forgetting of previously learned tasks. This is often achieved via exemplar replay which can help recalibrate previous task classifiers to the feature drift which occurs when learning new tasks. Exemplar replay, however, comes at the cost of retaining samples from previous tasks which for many applications may not be possible. To address the problem of continual ViT training, we first propose gated class-attention to minimize the drift in the final ViT transformer block. This mask-based gating is applied to class-attention mechanism of the last transformer block and strongly regulates the weights crucial for previous tasks. Importantly, gated class-attention does not require the task-ID during inference, which distinguishes it from other parameter isolation methods. Secondly, we propose a new method of feature drift compensation that accommodates feature drift in the backbone when learning new tasks. The combination of gated class-attention and cascaded feature drift compensation allows for plasticity towards new tasks while limiting forgetting of previous ones. Extensive experiments performed on CIFAR-100, Tiny-ImageNet and ImageNet100 demonstrate that our exemplar-free method obtains competitive results when compared to rehearsal based ViT methods.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

We can better understand deep neural networks by identifying which features each of their neurons have learned to detect. To do so, researchers have created Deep Visualization techniques including activation maximization, which synthetically generates inputs (e.g. images) that maximally activate each neuron. A limitation of current techniques is that they assume each neuron detects only one type of feature, but we know that neurons can be multifaceted, in that they fire in response to many different types of features: for example, a grocery store class neuron must activate either for rows of produce or for a storefront. Previous activation maximization techniques constructed images without regard for the multiple different facets of a neuron, creating inappropriate mixes of colors, parts of objects, scales, orientations, etc. Here, we introduce an algorithm that explicitly uncovers the multiple facets of each neuron by producing a synthetic visualization of each of the types of images that activate a neuron. We also introduce regularization methods that produce state-of-the-art results in terms of the interpretability of images obtained by activation maximization. By separately synthesizing each type of image a neuron fires in response to, the visualizations have more appropriate colors and coherent global structure. Multifaceted feature visualization thus provides a clearer and more comprehensive description of the role of each neuron.

Attention-free language models that combine gating and convolutions are growing in popularity due to their efficiency and increasingly competitive performance. To better understand these architectures, we pretrain a suite of 17 attention and "gated-convolution" language models, finding that SoTA gated-convolution architectures still underperform attention by up to 2.1 perplexity points on the Pile. In fine-grained analysis, we find 82% of the gap is explained by each model's ability to recall information that is previously mentioned in-context, e.g. "Hakuna Matata means no worries Hakuna Matata it means no" rightarrow "??". On this task, termed "associative recall", we find that attention outperforms gated-convolutions by a large margin: a 70M parameter attention model outperforms a 1.4 billion parameter gated-convolution model on associative recall. This is surprising because prior work shows gated convolutions can perfectly solve synthetic tests for AR capability. To close the gap between synthetics and real language, we develop a new formalization of the task called multi-query associative recall (MQAR) that better reflects actual language. We perform an empirical and theoretical study of MQAR that elucidates differences in the parameter-efficiency of attention and gated-convolution recall. Informed by our analysis, we evaluate simple convolution-attention hybrids and show that hybrids with input-dependent sparse attention patterns can close 97.4% of the gap to attention, while maintaining sub-quadratic scaling. Our code is accessible at: https://github.com/HazyResearch/zoology.

Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis and polynomial functions, such as B-splines, ReLU-KAN utilizes a combination of ReLU functions to mimic the structure of B-splines and take advantage of ReLU's speed. However, ReLU-KAN is not built for multiple inputs, and its limitations stem from ReLU's handling of negative values, which can restrict feature extraction. To address these issues, we introduce Activation Function-Based Kolmogorov-Arnold Networks (AF-KAN), expanding ReLU-KAN with various activations and their function combinations. This novel KAN also incorporates parameter reduction methods, primarily attention mechanisms and data normalization, to enhance performance on image classification datasets. We explore different activation functions, function combinations, grid sizes, and spline orders to validate the effectiveness of AF-KAN and determine its optimal configuration. In the experiments, AF-KAN significantly outperforms MLP, ReLU-KAN, and other KANs with the same parameter count. It also remains competitive even when using fewer than 6 to 10 times the parameters while maintaining the same network structure. However, AF-KAN requires a longer training time and consumes more FLOPs. The repository for this work is available at https://github.com/hoangthangta/All-KAN.

Deep Neural Networks (DNNs) are extensively employed in safety-critical applications where ensuring hardware reliability is a primary concern. To enhance the reliability of DNNs against hardware faults, activation restriction techniques significantly mitigate the fault effects at the DNN structure level, irrespective of accelerator architectures. State-of-the-art methods offer either neuron-wise or layer-wise clipping activation functions. They attempt to determine optimal clipping thresholds using heuristic and learning-based approaches. Layer-wise clipped activation functions cannot preserve DNNs resilience at high bit error rates. On the other hand, neuron-wise clipping activation functions introduce considerable memory overhead due to the addition of parameters, which increases their vulnerability to faults. Moreover, the heuristic-based optimization approach demands numerous fault injections during the search process, resulting in time-consuming threshold identification. On the other hand, learning-based techniques that train thresholds for entire layers concurrently often yield sub-optimal results. In this work, first, we demonstrate that it is not essential to incorporate neuron-wise activation functions throughout all layers in DNNs. Then, we propose a hybrid clipped activation function that integrates neuron-wise and layer-wise methods that apply neuron-wise clipping only in the last layer of DNNs. Additionally, to attain optimal thresholds in the clipping activation function, we introduce ProAct, a progressive training methodology. This approach iteratively trains the thresholds on a layer-by-layer basis, aiming to obtain optimal threshold values in each layer separately.

Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not.

Large language models (LLMs) excel at generating fluent text, but their internal reasoning remains opaque and difficult to control. Sparse autoencoders (SAEs) make hidden activations more interpretable by exposing latent features that often align with human concepts. Yet, these features are fragile and passive, offering no mechanism for systematic reasoning or model control. To address this, we introduce ActivationReasoning (AR), a framework that embeds explicit logical reasoning into the latent space of LLMs. It proceeds in three stages: (1) Finding latent representations, first latent concept representations are identified (e.g., via SAEs) and organized into a dictionary; (2) Activating propositions, at inference time AR detects activating concepts and maps them to logical propositions; and (3)Logical reasoning, applying logical rules over these propositions to infer higher-order structures, compose new concepts, and steer model behavior. We evaluate AR on multi-hop reasoning (PrOntoQA), abstraction and robustness to indirect concept cues (Rail2Country), reasoning over natural and diverse language (ProverQA), and context-sensitive safety (BeaverTails). Across all tasks, AR scales robustly with reasoning complexity, generalizes to abstract and context-sensitive tasks, and transfers across model backbones. These results demonstrate that grounding logical structure in latent activations not only improves transparency but also enables structured reasoning, reliable control, and alignment with desired behaviors, providing a path toward more reliable and auditable AI.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: https://github.com/shivram1987/ActivationFunctions.

In recent years, text-to-image (T2I) diffusion models have garnered significant attention for their ability to generate high-quality images reflecting text prompts. However, their growing popularity has also led to the emergence of backdoor threats, posing substantial risks. Currently, effective defense strategies against such threats are lacking due to the diversity of backdoor targets in T2I synthesis. In this paper, we propose NaviDet, the first general input-level backdoor detection framework for identifying backdoor inputs across various backdoor targets. Our approach is based on the new observation that trigger tokens tend to induce significant neuron activation variation in the early stage of the diffusion generation process, a phenomenon we term Early-step Activation Variation. Leveraging this insight, NaviDet detects malicious samples by analyzing neuron activation variations caused by input tokens. Through extensive experiments, we demonstrate the effectiveness and efficiency of our method against various T2I backdoor attacks, surpassing existing baselines with significantly lower computational overhead. Furthermore, we rigorously demonstrate that our method remains effective against potential adaptive attacks.

Medical image segmentation relies on the ability of encoder-decoder architectures to translate rich feature representations into accurate pixel-level predictions under challenging conditions such as low contrast, structural ambiguity, and scale variability. While recent advances in large-scale pretraining and transformer-based encoders have substantially improved feature extraction, segmentation accuracy remains constrained by decoder design, particularly in terms of cross-scale alignment, contextual integration, and boundary preservation. In this work, we revisit medical image segmentation from a decoder-centric perspective and propose a context-aware gated decoder that systematically regulates feature fusion and contextual aggregation throughout the decoding process. The proposed decoder integrates lightweight multi-scale channel recalibration, gated skip fusion with spatial competition and a global context aggregation mechanism that injects encoder-wide information into intermediate decoding stages. This design enables effective translation of strong pretrained encoder representations into spatially consistent predictions. Extensive experiments across 11 medical image segmentation benchmarks validate the effectiveness and demonstrate that the proposed approach consistently outperforms strong baselines while remaining computationally practical. Code: https://github.com/saadwazir/MedCAGD

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

Toxic text classification for online moderation remains challenging under extreme class imbalance, where rare but high-risk labels such as threat and severe_toxic are consistently underdetected by conventional models. We propose CoGate-LSTM, a parameter-efficient recurrent architecture built around a novel cosine-similarity feature gating mechanism that adaptively rescales token embeddings by their directional similarity to a learned toxicity prototype. Unlike token-position attention, the gate emphasizes feature directions most informative for minority toxic classes. The model combines frozen multi-source embeddings (GloVe, FastText, and BERT-CLS), a character-level BiLSTM, embedding-space SMOTE, and weighted focal loss. On the Jigsaw Toxic Comment benchmark, CoGate-LSTM achieves 0.881 macro-F1 (95% CI: [0.873, 0.889]) and 96.0% accuracy, outperforming fine-tuned BERT by 6.9 macro-F1 points (p < 0.001) and XGBoost by 4.7, while using only 7.3M parameters (about 15times fewer than BERT) and 48 ms CPU inference latency. Gains are strongest on minority labels, with F1 improvements of +71% for severe_toxic, +33% for threat, and +28% for identity_hate relative to fine-tuned BERT. Ablations identify cosine gating as the primary driver of performance (-4.8 macro-F1 when removed), with additional benefits from character-level fusion (-2.4) and multi-head attention (-2.9). CoGate-LSTM also transfers reasonably across datasets, reaching a 0.71 macro-F1 zero-shot on the Contextual Abuse Dataset and 0.73 with lightweight threshold adaptation. These results show that direction-aware feature gating offers an effective and efficient alternative to large, fully fine-tuned transformers for classifying imbalanced toxic comments.

Imitation Learning (IL) enables robots to acquire manipulation skills from expert demonstrations. Diffusion Policy (DP) models multi-modal expert behaviors but suffers performance degradation as observation horizons increase, limiting long-horizon manipulation. We propose Self-Evolving Gated Attention (SEGA), a temporal module that maintains a time-evolving latent state via gated attention, enabling efficient recurrent updates that compress long-horizon observations into a fixed-size representation while filtering irrelevant temporal information. Integrating SEGA into DP yields Self-Evolving Diffusion Policy (SeedPolicy), which resolves the temporal modeling bottleneck and enables scalable horizon extension with moderate overhead. On the RoboTwin 2.0 benchmark with 50 manipulation tasks, SeedPolicy outperforms DP and other IL baselines. Averaged across both CNN and Transformer backbones, SeedPolicy achieves 36.8% relative improvement in clean settings and 169% relative improvement in randomized challenging settings over the DP. Compared to vision-language-action models such as RDT with 1.2B parameters, SeedPolicy achieves competitive performance with one to two orders of magnitude fewer parameters, demonstrating strong efficiency and scalability. These results establish SeedPolicy as a state-of-the-art imitation learning method for long-horizon robotic manipulation. Code is available at: https://github.com/Youqiang-Gui/SeedPolicy.

This paper considers the Pointer Value Retrieval (PVR) benchmark introduced in [ZRKB21], where a 'reasoning' function acts on a string of digits to produce the label. More generally, the paper considers the learning of logical functions with gradient descent (GD) on neural networks. It is first shown that in order to learn logical functions with gradient descent on symmetric neural networks, the generalization error can be lower-bounded in terms of the noise-stability of the target function, supporting a conjecture made in [ZRKB21]. It is then shown that in the distribution shift setting, when the data withholding corresponds to freezing a single feature (referred to as canonical holdout), the generalization error of gradient descent admits a tight characterization in terms of the Boolean influence for several relevant architectures. This is shown on linear models and supported experimentally on other models such as MLPs and Transformers. In particular, this puts forward the hypothesis that for such architectures and for learning logical functions such as PVR functions, GD tends to have an implicit bias towards low-degree representations, which in turn gives the Boolean influence for the generalization error under quadratic loss.

Cortical circuits exhibit intricate recurrent architectures that are remarkably similar across different brain areas. Such stereotyped structure suggests the existence of common computational principles. However, such principles have remained largely elusive. Inspired by gated-memory networks, namely long short-term memory networks (LSTMs), we introduce a recurrent neural network in which information is gated through inhibitory cells that are subtractive (subLSTM). We propose a natural mapping of subLSTMs onto known canonical excitatory-inhibitory cortical microcircuits. Our empirical evaluation across sequential image classification and language modelling tasks shows that subLSTM units can achieve similar performance to LSTM units. These results suggest that cortical circuits can be optimised to solve complex contextual problems and proposes a novel view on their computational function. Overall our work provides a step towards unifying recurrent networks as used in machine learning with their biological counterparts.

We propose the Swish-T family, an enhancement of the existing non-monotonic activation function Swish. Swish-T is defined by adding a Tanh bias to the original Swish function. This modification creates a family of Swish-T variants, each designed to excel in different tasks, showcasing specific advantages depending on the application context. The Tanh bias allows for broader acceptance of negative values during initial training stages, offering a smoother non-monotonic curve than the original Swish. We ultimately propose the Swish-T_{C} function, while Swish-T and Swish-T_{B}, byproducts of Swish-T_{C}, also demonstrate satisfactory performance. Furthermore, our ablation study shows that using Swish-T_{C} as a non-parametric function can still achieve high performance. The superiority of the Swish-T family has been empirically demonstrated across various models and benchmark datasets, including MNIST, Fashion MNIST, SVHN, CIFAR-10, and CIFAR-100. The code is publicly available at https://github.com/ictseoyoungmin/Swish-T-pytorch.

The structure of biological neural circuits-modular, hierarchical, and sparsely interconnected-reflects an efficient trade-off between wiring cost, functional specialization, and robustness. These principles offer valuable insights for artificial neural network (ANN) design, especially as networks grow in depth and scale. Sparsity, in particular, has been widely explored for reducing memory and computation, improving speed, and enhancing generalization. Motivated by systems neuroscience findings, we explore how patterns of functional connectivity in the mouse visual cortex-specifically, ensemble-to-ensemble communication, can inform ANN design. We introduce G2GNet, a novel architecture that imposes sparse, modular connectivity across feedforward layers. Despite having significantly fewer parameters than fully connected models, G2GNet achieves superior accuracy on standard vision benchmarks. To our knowledge, this is the first architecture to incorporate biologically observed functional connectivity patterns as a structural bias in ANN design. We complement this static bias with a dynamic sparse training (DST) mechanism that prunes and regrows edges during training. We also propose a Hebbian-inspired rewiring rule based on activation correlations, drawing on principles of biological plasticity. G2GNet achieves up to 75% sparsity while improving accuracy by up to 4.3% on benchmarks, including Fashion-MNIST, CIFAR-10, and CIFAR-100, outperforming dense baselines with far fewer computations.

As one of the energy-efficient alternatives of conventional neural networks (CNNs), spiking neural networks (SNNs) have gained more and more interest recently. To train the deep models, some effective batch normalization (BN) techniques are proposed in SNNs. All these BNs are suggested to be used after the convolution layer as usually doing in CNNs. However, the spiking neuron is much more complex with the spatio-temporal dynamics. The regulated data flow after the BN layer will be disturbed again by the membrane potential updating operation before the firing function, i.e., the nonlinear activation. Therefore, we advocate adding another BN layer before the firing function to normalize the membrane potential again, called MPBN. To eliminate the induced time cost of MPBN, we also propose a training-inference-decoupled re-parameterization technique to fold the trained MPBN into the firing threshold. With the re-parameterization technique, the MPBN will not introduce any extra time burden in the inference. Furthermore, the MPBN can also adopt the element-wised form, while these BNs after the convolution layer can only use the channel-wised form. Experimental results show that the proposed MPBN performs well on both popular non-spiking static and neuromorphic datasets. Our code is open-sourced at https://github.com/yfguo91/MPBN{MPBN}.

Modern neural networks rely on generic activation functions (ReLU, GELU, SiLU) that ignore the mathematical structure inherent in scientific data. We propose Neuro-Symbolic Activation Discovery, a framework that uses Genetic Programming to extract interpretable mathematical formulas from data and inject them as custom activation functions. Our key contribution is the discovery of a Geometric Transfer phenomenon: activation functions learned from particle physics data successfully generalize to ecological classification, outperforming standard activations (ReLU, GELU, SiLU) in both accuracy and parameter efficiency. On the Forest Cover dataset, our Hybrid Transfer model achieves 82.4% accuracy with only 5,825 parameters, compared to 83.4% accuracy requiring 31,801 parameters for a conventional heavy network -- a 5.5x parameter reduction with only 1% accuracy loss. We introduce a Parameter Efficiency Score (E_{param} = AUC / log_{10}(Params)) and demonstrate that lightweight hybrid architectures consistently achieve 18-21% higher efficiency than over-parameterized baselines. Crucially, we establish boundary conditions: while Physics to Ecology transfer succeeds (both involve continuous Euclidean measurements), Physics to Text transfer fails (discrete word frequencies require different mathematical structures). Our work opens pathways toward domain-specific activation libraries for efficient scientific machine learning.

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective, which reframes language modeling as a constrained optimization problem: minimizing representation entropy subject to optimal prediction performance. Empirically, we observe an emergent memorization-compression cycle during LLM pretraining, evidenced by oscillation positive/negative gradient alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of representation entropy. This pattern closely mirrors the predictive-compressive trade-off prescribed by IBLM and also parallels the biological alternation between awake learning and sleep consolidation. Motivated by this observation, we propose Gated Phase Transition (GAPT), a training algorithm that adaptively switches between memorization and compression phases. When applied to GPT-2 pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining task on arithmetic multiplication. In a setting designed to simulate catastrophic forgetting, GAPT reduces interference by compressing and separating representations, achieving a 97% improvement in separation - paralleling the functional role of sleep consolidation.

Retrieval-augmented generation stores all content indiscriminately, degrading accuracy as noise accumulates. Parametric approaches compress knowledge into weights, precluding selective updates. Neither mirrors biological memory, which gates encoding based on salience and archives rather than deletes superseded information. We introduce write-time gating that filters incoming knowledge objects using composite salience scores (source reputation, novelty, reliability) while maintaining version chains that preserve prior states. Using real LLM evaluation without oracle access to quality labels, write gating achieves 100 percent accuracy versus 13 percent for ungated stores. The critical finding emerges under distractor scaling: at 8:1 distractor ratios, read-time filtering (Self-RAG) collapses to 0 percent while write gating maintains 100 percent, revealing a structural advantage of write-time over read-time curation. Validation on Wikipedia (20 entities), procedurally generated pharmacology data, and 2026 arXiv papers confirms these findings. The gating advantage scales inversely with parametric memory support: +25pp for Wikipedia, +48pp for post-cutoff arXiv, +65pp for procedural data with zero training knowledge. Signal ablation confirms the method does not depend on oracle-correlated metadata. Write gating matches Self-RAG accuracy at one-ninth the query-time cost.

Wider adoption of neural networks in many critical domains such as finance and healthcare is being hindered by the need to explain their predictions and to impose additional constraints on them. Monotonicity constraint is one of the most requested properties in real-world scenarios and is the focus of this paper. One of the oldest ways to construct a monotonic fully connected neural network is to constrain signs on its weights. Unfortunately, this construction does not work with popular non-saturated activation functions as it can only approximate convex functions. We show this shortcoming can be fixed by constructing two additional activation functions from a typical unsaturated monotonic activation function and employing each of them on the part of neurons. Our experiments show this approach of building monotonic neural networks has better accuracy when compared to other state-of-the-art methods, while being the simplest one in the sense of having the least number of parameters, and not requiring any modifications to the learning procedure or post-learning steps. Finally, we prove it can approximate any continuous monotone function on a compact subset of R^n.

We present causal head gating (CHG), a scalable method for interpreting the functional roles of attention heads in transformer models. CHG learns soft gates over heads and assigns them a causal taxonomy - facilitating, interfering, or irrelevant - based on their impact on task performance. Unlike prior approaches in mechanistic interpretability, which are hypothesis-driven and require prompt templates or target labels, CHG applies directly to any dataset using standard next-token prediction. We evaluate CHG across multiple large language models (LLMs) in the Llama 3 model family and diverse tasks, including syntax, commonsense, and mathematical reasoning, and show that CHG scores yield causal, not merely correlational, insight validated via ablation and causal mediation analyses. We also introduce contrastive CHG, a variant that isolates sub-circuits for specific task components. Our findings reveal that LLMs contain multiple sparse task-sufficient sub-circuits, that individual head roles depend on interactions with others (low modularity), and that instruction following and in-context learning rely on separable mechanisms.

Recent advances in diffusion-based controllable visual generation have led to remarkable improvements in image quality. However, these powerful models are typically deployed on cloud servers due to their large computational demands, raising serious concerns about user data privacy. To enable secure and efficient on-device generation, we explore in this paper controllable diffusion models built upon linear attention architectures, which offer superior scalability and efficiency, even on edge devices. Yet, our experiments reveal that existing controllable generation frameworks, such as ControlNet and OminiControl, either lack the flexibility to support multiple heterogeneous condition types or suffer from slow convergence on such linear-attention models. To address these limitations, we propose a novel controllable diffusion framework tailored for linear attention backbones like SANA. The core of our method lies in a unified gated conditioning module working in a dual-path pipeline, which effectively integrates multi-type conditional inputs, such as spatially aligned and non-aligned cues. Extensive experiments on multiple tasks and benchmarks demonstrate that our approach achieves state-of-the-art controllable generation performance based on linear-attention models, surpassing existing methods in terms of fidelity and controllability.

Modern neural networks demonstrate state-of-the-art performance on numerous existing benchmarks; however, their high computational requirements and energy consumption prompt researchers to seek more efficient solutions for real-world deployment. Logic gate networks (LGNs) learns a large network of logic gates for efficient image classification. However, learning a network that can solve a simple problem like CIFAR-10 can take days to weeks to train. Even then, almost half of the network remains unused, causing a discretization gap. This discretization gap hinders real-world deployment of LGNs, as the performance drop between training and inference negatively impacts accuracy. We inject Gumbel noise with a straight-through estimator during training to significantly speed up training, improve neuron utilization, and decrease the discretization gap. We theoretically show that this results from implicit Hessian regularization, which improves the convergence properties of LGNs. We train networks 4.5 times faster in wall-clock time, reduce the discretization gap by 98%, and reduce the number of unused gates by 100%.

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear Unit (GELU) activation function has emerged as a dominant method, surpassing traditional functions such as the Rectified Linear Unit (ReLU) in various applications. This study presents a rigorous mathematical investigation of the GELU activation function, exploring its differentiability, boundedness, stationarity, and smoothness properties in detail. Additionally, we conduct an extensive experimental comparison of the GELU function against a broad range of alternative activation functions, utilizing a residual convolutional network trained on the CIFAR-10, CIFAR-100, and STL-10 datasets as the empirical testbed. Our results demonstrate the superior performance of GELU compared to other activation functions, establishing its suitability for a wide range of deep learning applications. This comprehensive study contributes to a more profound understanding of the underlying mathematical properties of GELU and provides valuable insights for practitioners aiming to select activation functions that optimally align with their specific objectives and constraints in deep learning.

Neural algorithmic reasoning is an emerging research direction that endows neural networks with the ability to mimic algorithmic executions step-by-step. A common paradigm in existing designs involves the use of historical embeddings in predicting the results of future execution steps. Our observation in this work is that such historical dependence intrinsically contradicts the Markov nature of algorithmic reasoning tasks. Based on this motivation, we present our ForgetNet, which does not use historical embeddings and thus is consistent with the Markov nature of the tasks. To address challenges in training ForgetNet at early stages, we further introduce G-ForgetNet, which uses a gating mechanism to allow for the selective integration of historical embeddings. Such an enhanced capability provides valuable computational pathways during the model's early training phase. Our extensive experiments, based on the CLRS-30 algorithmic reasoning benchmark, demonstrate that both ForgetNet and G-ForgetNet achieve better generalization capability than existing methods. Furthermore, we investigate the behavior of the gating mechanism, highlighting its degree of alignment with our intuitions and its effectiveness for robust performance.

The Spiking Neural Network (SNN) has attracted more and more attention recently. It adopts binary spike signals to transmit information. Benefitting from the information passing paradigm of SNNs, the multiplications of activations and weights can be replaced by additions, which are more energy-efficient. However, its ``Hard Reset" mechanism for the firing activity would ignore the difference among membrane potentials when the membrane potential is above the firing threshold, causing information loss. Meanwhile, quantifying the membrane potential to 0/1 spikes at the firing instants will inevitably introduce the quantization error thus bringing about information loss too. To address these problems, we propose to use the ``Soft Reset" mechanism for the supervised training-based SNNs, which will drive the membrane potential to a dynamic reset potential according to its magnitude, and Membrane Potential Rectifier (MPR) to reduce the quantization error via redistributing the membrane potential to a range close to the spikes. Results show that the SNNs with the ``Soft Reset" mechanism and MPR outperform their vanilla counterparts on both static and dynamic datasets.

Top-K sparse softmax gating mixture of experts has been widely used for scaling up massive deep-learning architectures without increasing the computational cost. Despite its popularity in real-world applications, the theoretical understanding of that gating function has remained an open problem. The main challenge comes from the structure of the top-K sparse softmax gating function, which partitions the input space into multiple regions with distinct behaviors. By focusing on a Gaussian mixture of experts, we establish theoretical results on the effects of the top-K sparse softmax gating function on both density and parameter estimations. Our results hinge upon defining novel loss functions among parameters to capture different behaviors of the input regions. When the true number of experts k_{ast} is known, we demonstrate that the convergence rates of density and parameter estimations are both parametric on the sample size. However, when k_{ast} becomes unknown and the true model is over-specified by a Gaussian mixture of k experts where k > k_{ast}, our findings suggest that the number of experts selected from the top-K sparse softmax gating function must exceed the total cardinality of a certain number of Voronoi cells associated with the true parameters to guarantee the convergence of the density estimation. Moreover, while the density estimation rate remains parametric under this setting, the parameter estimation rates become substantially slow due to an intrinsic interaction between the softmax gating and expert functions.

Activation sparsity denotes the existence of substantial weakly-contributed elements within activation outputs that can be eliminated, benefiting many important applications concerned with large language models (LLMs). Although promoting greater activation sparsity within LLMs deserves deep studies, existing works lack comprehensive and quantitative research on the correlation between activation sparsity and potentially influential factors. In this paper, we present a comprehensive study on the quantitative scaling properties and influential factors of the activation sparsity within decoder-only Transformer-based LLMs. Specifically, we propose PPL-p% sparsity, a precise and performance-aware activation sparsity metric that is applicable to any activation function. Through extensive experiments, we find several important phenomena. Firstly, different activation functions exhibit comparable performance but opposite training-time sparsity trends. The activation ratio (i.e., 1-sparsity ratio) evolves as a convergent increasing power-law and decreasing logspace power-law with the amount of training data for SiLU-activated and ReLU-activated LLMs, respectively. These demonstrate that ReLU is more efficient as the activation function than SiLU and can leverage more training data to improve activation sparsity. Secondly, the activation ratio linearly increases with the width-depth ratio below a certain bottleneck point, indicating the potential advantage of a deeper architecture at a fixed parameter scale. Finally, at similar width-depth ratios, we surprisingly find that the limit value of activation sparsity varies weakly with the parameter scale, i.e., the activation patterns within LLMs are insensitive to the parameter scale. These empirical laws towards LLMs with greater activation sparsity have important implications for making LLMs more efficient and interpretable.

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of a non-differentiable activation function by convolving it with approximate identities. In particular, we present smooth approximations of Leaky ReLU and show that they outperform several well-known activation functions in various datasets and models. We call this function Smooth Activation Unit (SAU). Replacing ReLU by SAU, we get 5.12% improvement with ShuffleNet V2 (2.0x) model on CIFAR100 dataset.

Traditional image editing typically relies on manual prompting, making it labor-intensive and inaccessible to individuals with limited motor control or language abilities. Leveraging recent advances in brain-computer interfaces (BCIs) and generative models, we propose LoongX, a hands-free image editing approach driven by multimodal neurophysiological signals. LoongX utilizes state-of-the-art diffusion models trained on a comprehensive dataset of 23,928 image editing pairs, each paired with synchronized electroencephalography (EEG), functional near-infrared spectroscopy (fNIRS), photoplethysmography (PPG), and head motion signals that capture user intent. To effectively address the heterogeneity of these signals, LoongX integrates two key modules. The cross-scale state space (CS3) module encodes informative modality-specific features. The dynamic gated fusion (DGF) module further aggregates these features into a unified latent space, which is then aligned with edit semantics via fine-tuning on a diffusion transformer (DiT). Additionally, we pre-train the encoders using contrastive learning to align cognitive states with semantic intentions from embedded natural language. Extensive experiments demonstrate that LoongX achieves performance comparable to text-driven methods (CLIP-I: 0.6605 vs. 0.6558; DINO: 0.4812 vs. 0.4636) and outperforms them when neural signals are combined with speech (CLIP-T: 0.2588 vs. 0.2549). These results highlight the promise of neural-driven generative models in enabling accessible, intuitive image editing and open new directions for cognitive-driven creative technologies. Datasets and code will be released to support future work and foster progress in this emerging area.

The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, a_i and a_j, diverge to pminfinity, and their input weight vectors, w_i and w_j, become equal to each other. At convergence, the two neurons implement a gated linear unit: a_iσ(w_i cdot x) + a_jσ(w_j cdot x) rightarrow σ(w cdot x) + (v cdot x) σ'(w cdot x). Geometrically, these channels to infinity are asymptotically parallel to symmetry-induced lines of critical points. Gradient flow solvers, and related optimization methods like SGD or ADAM, reach the channels with high probability in diverse regression settings, but without careful inspection they look like flat local minima with finite parameter values. Our characterization provides a comprehensive picture of these quasi-flat regions in terms of gradient dynamics, geometry, and functional interpretation. The emergence of gated linear units at the end of the channels highlights a surprising aspect of the computational capabilities of fully connected layers.

Recent work on domain-specific reasoning with large language models (LLMs) often relies on training-intensive approaches that require parameter updates. While activation steering has emerged as a parameter efficient alternative, existing methods apply static, manual interventions that fail to adapt to the dynamic nature of complex reasoning. To address this limitation, we propose RISER (Router-based Intervention for Steerable Enhancement of Reasoning), a plug-and-play intervention framework that adaptively steers LLM reasoning in activation space. RISER constructs a library of reusable reasoning vectors and employs a lightweight Router to dynamically compose them for each input. The Router is optimized via reinforcement learning under task-level rewards, activating latent cognitive primitives in an emergent and compositional manner. Across seven diverse benchmarks, RISER yields 3.4-6.5% average zero-shot accuracy improvements over the base model while surpassing CoT-style reasoning with 2-3x higher token efficiency and robust accuracy gains. Further analysis shows that RISER autonomously combines multiple vectors into interpretable, precise control strategies, pointing toward more controllable and efficient LLM reasoning.

A long standing goal in neuroscience has been to elucidate the functional organization of the brain. Within higher visual cortex, functional accounts have remained relatively coarse, focusing on regions of interest (ROIs) and taking the form of selectivity for broad categories such as faces, places, bodies, food, or words. Because the identification of such ROIs has typically relied on manually assembled stimulus sets consisting of isolated objects in non-ecological contexts, exploring functional organization without robust a priori hypotheses has been challenging. To overcome these limitations, we introduce a data-driven approach in which we synthesize images predicted to activate a given brain region using paired natural images and fMRI recordings, bypassing the need for category-specific stimuli. Our approach -- Brain Diffusion for Visual Exploration ("BrainDiVE") -- builds on recent generative methods by combining large-scale diffusion models with brain-guided image synthesis. Validating our method, we demonstrate the ability to synthesize preferred images with appropriate semantic specificity for well-characterized category-selective ROIs. We then show that BrainDiVE can characterize differences between ROIs selective for the same high-level category. Finally we identify novel functional subdivisions within these ROIs, validated with behavioral data. These results advance our understanding of the fine-grained functional organization of human visual cortex, and provide well-specified constraints for further examination of cortical organization using hypothesis-driven methods.

Large language models, such as OpenAI's ChatGPT, have demonstrated exceptional language understanding capabilities in various NLP tasks. Sparsely activated mixture-of-experts (MoE) has emerged as a promising solution for scaling models while maintaining a constant number of computational operations. Existing MoE model adopts a fixed gating network where each token is computed by the same number of experts. However, this approach contradicts our intuition that the tokens in each sequence vary in terms of their linguistic complexity and, consequently, require different computational costs. Little is discussed in prior research on the trade-off between computation per token and model performance. This paper introduces adaptive gating in MoE, a flexible training strategy that allows tokens to be processed by a variable number of experts based on expert probability distribution. The proposed framework preserves sparsity while improving training efficiency. Additionally, curriculum learning is leveraged to further reduce training time. Extensive experiments on diverse NLP tasks show that adaptive gating reduces at most 22.5% training time while maintaining inference quality. Moreover, we conduct a comprehensive analysis of the routing decisions and present our insights when adaptive gating is used.

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

This paper presents a novel model for multimodal learning based on gated neural networks. The Gated Multimodal Unit (GMU) model is intended to be used as an internal unit in a neural network architecture whose purpose is to find an intermediate representation based on a combination of data from different modalities. The GMU learns to decide how modalities influence the activation of the unit using multiplicative gates. It was evaluated on a multilabel scenario for genre classification of movies using the plot and the poster. The GMU improved the macro f-score performance of single-modality approaches and outperformed other fusion strategies, including mixture of experts models. Along with this work, the MM-IMDb dataset is released which, to the best of our knowledge, is the largest publicly available multimodal dataset for genre prediction on movies.

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

Activation Functions introduce non-linearity in the deep neural networks. This nonlinearity helps the neural networks learn faster and efficiently from the dataset. In deep learning, many activation functions are developed and used based on the type of problem statement. ReLU's variants, SWISH, and MISH are goto activation functions. MISH function is considered having similar or even better performance than SWISH, and much better than ReLU. In this paper, we propose an activation function named APTx which behaves similar to MISH, but requires lesser mathematical operations to compute. The lesser computational requirements of APTx does speed up the model training, and thus also reduces the hardware requirement for the deep learning model. Source code: https://github.com/mr-ravin/aptx_activation

Natively trained spiking language models struggle to combine Transformer-like language quality, stable multi-domain pre-training, and high activation sparsity. We present SymbolicLight V1, a spike-gated dual-path language model that combines binary Leaky Integrate-and-Fire spike dynamics with a continuous residual stream. Its Dual-Path SparseTCAM module replaces dense self-attention with an exponential-decay aggregation path for long-range memory and a spike-gated local attention path for short-range precision, complemented by a dynamic context-conditioned decoding head and a bilingual tokenizer. A 194M-parameter SymbolicLight V1 model trained from scratch on a 3B-token Chinese-English corpus reaches held-out validation PPL 8.88-8.93 across four independent runs at >89% per-element activation sparsity. It trails GPT-2 201M by 7.7% in PPL while surpassing GPT-2 124M under the reported comparison. Component ablations at matched 0.5B-token training budgets show that the spike-gated local attention path is the largest contributor, and that replacing LIF dynamics with a deterministic top-k mask at matched sparsity causes a larger degradation, indicating that temporal integration rather than sparsity alone drives performance. We also report a 0.8B-parameter scale-up run trained on 48.8B tokens as evidence of optimization and sparsity preservation, not as a primary quality comparison. Current dense-hardware inference is slower than GPT-2, so neuromorphic deployment is presented as a future sparsity-driven opportunity rather than an achieved hardware speedup.

The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice, however, there are significant algorithmic and performance challenges. In this work, we address these challenges and finally realize the promise of conditional computation, achieving greater than 1000x improvements in model capacity with only minor losses in computational efficiency on modern GPU clusters. We introduce a Sparsely-Gated Mixture-of-Experts layer (MoE), consisting of up to thousands of feed-forward sub-networks. A trainable gating network determines a sparse combination of these experts to use for each example. We apply the MoE to the tasks of language modeling and machine translation, where model capacity is critical for absorbing the vast quantities of knowledge available in the training corpora. We present model architectures in which a MoE with up to 137 billion parameters is applied convolutionally between stacked LSTM layers. On large language modeling and machine translation benchmarks, these models achieve significantly better results than state-of-the-art at lower computational cost.

We consider an existing conjecture addressing the asymptotic behavior of neural networks in the large width limit. The results that follow from this conjecture include tight bounds on the behavior of wide networks during stochastic gradient descent, and a derivation of their finite-width dynamics. We prove the conjecture for deep networks with polynomial activation functions, greatly extending the validity of these results. Finally, we point out a difference in the asymptotic behavior of networks with analytic (and non-linear) activation functions and those with piecewise-linear activations such as ReLU.

Spiking Neural Networks (SNNs) have garnered significant attention as a central paradigm in neuromorphic computing, owing to their energy efficiency and biological plausibility. However, training deep SNNs has critically depended on explicit normalization schemes, leading to a trade-off between performance and biological realism. To resolve this conflict, we propose a normalization-free learning framework that incorporates lateral inhibition inspired by cortical circuits. Our framework replaces the traditional feedforward SNN layer with distinct excitatory (E) and inhibitory (I) neuronal populations that capture the key features of the cortical E-I interaction. The E-I circuit dynamically regulates neuronal activity through subtractive and divisive inhibition, which respectively control the excitability and gain of neurons. To stabilize end-to-end training of the biologically constrained SNNs, we propose two key techniques: E-I Init and E-I Prop. E-I Init is a dynamic parameter initialization scheme that balances excitatory and inhibitory inputs while performing gain control. E-I Prop decouples the backpropagation of the circuit from the forward pass, regulating gradient flow. Experiments across multiple datasets and network architectures demonstrate that our framework enables stable training of deep normalization-free SNNs with biological realism, achieving competitive performance. Therefore, our work not only provides a solution to training deep SNNs but also serves as a computational platform for further exploring the functions of E-I interaction in large-scale cortical computation. Code is available at https://github.com/vwOvOwv/DeepEISNN.

Robotic manipulation tasks exhibit varying memory requirements, ranging from Markovian tasks that require no memory to non-Markovian tasks that depend on historical information spanning single or multiple interaction trials. Surprisingly, simply extending observation histories of a visuomotor policy often leads to a significant performance drop due to distribution shift and overfitting. To address these issues, we propose Gated Memory Policy (GMP), a visuomotor policy that learns both when to recall memory and what to recall. To learn when to recall memory, GMP employs a learned memory gate mechanism that selectively activates history context only when necessary, improving robustness and reactivity. To learn what to recall efficiently, GMP introduces a lightweight cross-attention module that constructs effective latent memory representations. To further enhance robustness, GMP injects diffusion noise into historical actions, mitigating sensitivity to noisy or inaccurate histories during both training and inference. On our proposed non-Markovian benchmark MemMimic, GMP achieves a 30.1% average success rate improvement over long-history baselines, while maintaining competitive performance on Markovian tasks in RoboMimic. All code, data and in-the-wild deployment instructions are available on our project website https://gated-memory-policy.github.io/.

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs with static inputs and outputs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs employing piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

Activity difference based learning algorithms-such as contrastive Hebbian learning and equilibrium propagation-have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.

We introduce stochastic activations. This novel strategy randomly selects between several non-linear functions in the feed-forward layer of a large language model. In particular, we choose between SILU or RELU depending on a Bernoulli draw. This strategy circumvents the optimization problem associated with RELU, namely, the constant shape for negative inputs that prevents the gradient flow. We leverage this strategy in two ways: (1) We use stochastic activations during pre-training and fine-tune the model with RELU, which is used at inference time to provide sparse latent vectors. This reduces the inference FLOPs and translates into a significant speedup in the CPU. Interestingly, this leads to much better results than training from scratch with the RELU activation function. (2) We evaluate stochastic activations for generation. This strategy performs reasonably well: it is only slightly inferior to the best deterministic non-linearity, namely SILU combined with temperature scaling. This offers an alternative to existing strategies by providing a controlled way to increase the diversity of the generated text.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

Purpose: This paper proposes a new network framework called EAR-U-Net, which leverages EfficientNetB4, attention gate, and residual learning techniques to achieve automatic and accurate liver segmentation. Methods: The proposed method is based on the U-Net framework. First, we use EfficientNetB4 as the encoder to extract more feature information during the encoding stage. Then, an attention gate is introduced in the skip connection to eliminate irrelevant regions and highlight features of a specific segmentation task. Finally, to alleviate the problem of gradient vanishment, we replace the traditional convolution of the decoder with a residual block to improve the segmentation accuracy. Results: We verified the proposed method on the LiTS17 and SLiver07 datasets and compared it with classical networks such as FCN, U-Net, Attention U-Net, and Attention Res-U-Net. In the Sliver07 evaluation, the proposed method achieved the best segmentation performance on all five standard metrics. Meanwhile, in the LiTS17 assessment, the best performance is obtained except for a slight inferior on RVD. Moreover, we also participated in the MICCIA-LiTS17 challenge, and the Dice per case score was 0.952. Conclusion: The proposed method's qualitative and quantitative results demonstrated its applicability in liver segmentation and proved its good prospect in computer-assisted liver segmentation.

Massive activations are scalar values in transformer hidden states that achieve values orders of magnitude larger than typical activations and have been shown to be critical for model functionality. While prior work has characterized these phenomena in fully trained models, the temporal dynamics of their emergence during training remain poorly understood. We present the first comprehensive analysis of massive activation development throughout transformer training, using the Pythia model family as our testbed. Through systematic analysis of various model sizes across multiple training checkpoints, we demonstrate that massive activation emergence follows predictable mathematical patterns that can be accurately modeled using an exponentially-modulated logarithmic function with five key parameters. We develop a machine learning framework to predict these mathematical parameters from architectural specifications alone, achieving high accuracy for steady-state behavior and moderate accuracy for emergence timing and magnitude. These findings enable architects to predict and potentially control key aspects of massive activation emergence through design choices, with significant implications for model stability, training cycle length, interpretability, and optimization. Our findings demonstrate that the emergence of massive activations is governed by model design and can be anticipated, and potentially controlled, before training begins.