Daily Papers

We study the capacity of the self-attention key-query channel: for a fixed budget, how many distinct token-token relations can a single layer reliably encode? We introduce Relational Graph Recognition, where the key-query channel encodes a directed graph and, given a context (a subset of the vertices), must recover the neighbors of each vertex in the context. We measure resources by the total key dimension D_K = h,d_k. In a tractable multi-head model, we prove matching information-theoretic lower bounds and upper bounds via explicit constructions showing that recovering a graph with m' relations in d_{model}-dimensional embeddings requires D_K to grow essentially as m'/d_{model} up to logarithmic factors, and we obtain corresponding guarantees for scaled-softmax attention. This analysis yields a new, capacity-based rationale for multi-head attention: even in permutation graphs, where all queries attend to a single target, splitting a fixed D_K budget into multiple heads increases capacity by reducing interference from embedding superposition. Controlled experiments mirror the theory, revealing sharp phase transitions at the predicted capacity, and the multi-head advantage persists when adding softmax normalization, value routing, and a full Transformer block trained with frozen GPT-2 embeddings.

Transformer attention is typically implemented using softmax normalization, which enforces attention weights with unit sum normalization. While effective in many settings, this constraint can limit flexibility in controlling attention magnitudes and may contribute to overly concentrated or unstable attention patterns during training. Prior work has explored modifications such as attention sinks or gating mechanisms, but these approaches provide only limited or indirect control over attention reweighting. We propose Affine-Scaled Attention, a simple extension to standard attention that introduces input-dependent scaling and a corresponding bias term applied to softmax-normalized attention weights. This design relaxes the strict normalization constraint while maintaining aggregation of value representations, allowing the model to adjust both the relative distribution and the scale of attention in a controlled manner. We empirically evaluate Affine-Scaled Attention in large-scale language model pretraining across multiple model sizes. Experimental results show consistent improvements in training stability, optimization behavior, and downstream task performance compared to standard softmax attention and attention sink baselines. These findings suggest that modest reweighting of attention outputs provides a practical and effective way to improve attention behavior in Transformer models.

We report the effects of replacing the scaled dot-product (within softmax) attention with the negative-log of Euclidean distance. This form of attention simplifies to inverse distance weighting interpolation. Used in simple one hidden layer networks and trained with vanilla cross-entropy loss on classification problems, it tends to produce a key matrix containing prototypes and a value matrix with corresponding logits. We also show that the resulting interpretable networks can be augmented with manually-constructed prototypes to perform low-impact handling of special cases.

Modern large language models based on softmax scaled-dot-product attention are constrained by their training sequence length: as the key-value sequence grows, softmax probability mass can dilute across a wider distribution, inducing activation shift and long-context performance collapse. Moreover, long-context language modeling faces a structural tension: a sliding-window attention core maintains a bounded local representation and low perplexity but is blind to long-range dependencies, while full-context attention preserves global recall but suffers from out-of-distribution perplexity explosion. To resolve these limitations, we introduce ATMA, a hybrid convolutional-attention architecture that integrates a novel three-channel attention mechanism. ATMA factorizes the attention mixing step into: (1) a count-blind, unit-vector direction channel, (2) a bounded magnitude channel driven by the participation ratio of effective matches over an extreme-value-corrected null sink, and (3) a long-term recurrent compression memory optimized via a gated-delta fast-weights rule. Neither the Polar Attention core nor the recurrent memory is sufficient alone; their combination enables monotonic perplexity reduction and high-fidelity long-range retrieval simultaneously. We evaluate ATMA using a 100-run factorial ablation sweep, demonstrating that the combined Polar + memory model maintains induction needle-in-a-haystack retrieval accuracy above 90% out to 64K tokens (32 times the training length of 2K) while its document perplexity improves monotonically, outperforming softmax-based memory baselines which collapse at extreme context lengths. Code: https://github.com/kreasof-ai/atma

Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. The self-attention mechanism underpinning the strength of ViTs has a quadratic complexity in both computation and memory usage. This motivates the development of approximating the self-attention at linear complexity. However, an in-depth analysis in this work reveals that existing methods are either theoretically flawed or empirically ineffective for visual recognition. We identify that their limitations are rooted in the inheritance of softmax-based self-attention during approximations, that is, normalizing the scaled dot-product between token feature vectors using the softmax function. As preserving the softmax operation challenges any subsequent linearization efforts. By this insight, a family of Softmax-Free Transformers (SOFT) are proposed. Specifically, a Gaussian kernel function is adopted to replace the dot-product similarity, enabling a full self-attention matrix to be approximated under low-rank matrix decomposition. For computational robustness, we estimate the Moore-Penrose inverse using an iterative Newton-Raphson method in the forward process only, while calculating its theoretical gradients only once in the backward process. To further expand applicability (e.g., dense prediction tasks), an efficient symmetric normalization technique is introduced. Extensive experiments on ImageNet, COCO, and ADE20K show that our SOFT significantly improves the computational efficiency of existing ViT variants. With linear complexity, much longer token sequences are permitted by SOFT, resulting in superior trade-off between accuracy and complexity. Code and models are available at https://github.com/fudan-zvg/SOFT.

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.

In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need for the first time to a data-driven operator learning problem related to partial differential equations. An effort is put together to explain the heuristics of, and to improve the efficacy of the attention mechanism. By employing the operator approximation theory in Hilbert spaces, it is demonstrated for the first time that the softmax normalization in the scaled dot-product attention is sufficient but not necessary. Without softmax, the approximation capacity of a linearized Transformer variant can be proved to be comparable to a Petrov-Galerkin projection layer-wise, and the estimate is independent with respect to the sequence length. A new layer normalization scheme mimicking the Petrov-Galerkin projection is proposed to allow a scaling to propagate through attention layers, which helps the model achieve remarkable accuracy in operator learning tasks with unnormalized data. Finally, we present three operator learning experiments, including the viscid Burgers' equation, an interface Darcy flow, and an inverse interface coefficient identification problem. The newly proposed simple attention-based operator learner, Galerkin Transformer, shows significant improvements in both training cost and evaluation accuracy over its softmax-normalized counterparts.

This paper investigates the limitations of the normalization in attention mechanisms. We begin with a theoretical framework that enables the identification of the model's selective ability and the geometric separation involved in token selection. Our analysis includes explicit bounds on distances and separation criteria for token vectors under softmax scaling. Through experiments with pre-trained GPT-2 model, we empirically validate our theoretical results and analyze key behaviors of the attention mechanism. Notably, we demonstrate that as the number of selected tokens increases, the model's ability to distinguish informative tokens declines, often converging toward a uniform selection pattern. We also show that gradient sensitivity under softmax normalization presents challenges during training, especially at low temperature settings. These findings advance current understanding of softmax-based attention mechanism and motivate the need for more robust normalization and selection strategies in future attention architectures.

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax attention under both finite and infinite prompts. For i.i.d. Gaussian inputs, we lean on the fact that the softmax operator converges in the infinite-prompt limit to a linear operator acting on the underlying input-token measure. Building on this insight, we establish non-asymptotic concentration bounds for the output and gradient of softmax attention, quantifying how rapidly the finite-prompt model approaches its infinite-prompt counterpart, and prove that this concentration remains stable along the entire training trajectory in general in-context learning settings with sub-Gaussian tokens. In the case of in-context linear regression, we use the tractable infinite-prompt dynamics to analyze training at finite prompt length. Our results allow optimization analyses developed for linear attention to transfer directly to softmax attention when prompts are sufficiently long, showing that large-prompt softmax attention inherits the analytical structure of its linear counterpart. This, in turn, provides a principled and broadly applicable toolkit for studying the training dynamics and statistical behavior of softmax attention layers in large prompt regimes.

Attention architectures are widely used; they recently gained renewed popularity with Transformers yielding a streak of state of the art results. Yet, the geometrical implications of softmax-attention remain largely unexplored. In this work we highlight the limitations of constraining attention weights to the probability simplex and the resulting convex hull of value vectors. We show that Transformers are sequence length dependent biased towards token isolation at initialization and contrast Transformers to simple max- and sum-pooling - two strong baselines rarely reported. We propose to replace the softmax in self-attention with normalization, yielding a hyperparameter and data-bias robust, generally applicable architecture. We support our insights with empirical results from more than 25,000 trained models. All results and implementations are made available.

Since its introduction, softmax attention has become the backbone of modern transformer architectures due to its expressiveness and scalability across a wide range of tasks. However, the main drawback of softmax attention is the quadratic memory requirement and computational complexity with respect to the sequence length. By replacing the softmax nonlinearity, linear attention and similar methods have been introduced to avoid the quadratic bottleneck of softmax attention. Despite these linear forms of attention being derived from the original softmax formulation, they typically lag in terms of downstream accuracy. While strong intuition of the softmax nonlinearity on the query and key inner product suggests that it has desirable properties compared to other nonlinearities, the question of why this discrepancy exists still remains unanswered. This work demonstrates that linear attention is an approximation of softmax attention by deriving the recurrent form of softmax attention. Using this form, each part of softmax attention can be described in the language of recurrent neural networks (RNNs). Describing softmax attention as an RNN allows for the ablation of the components of softmax attention to understand the importance of each part and how they interact. In this way, our work helps explain why softmax attention is more expressive than its counterparts.

The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to flatten as the context size grows. This reduces the model's ability to prioritize key information effectively and potentially limits its length generalization. To address this problem, we propose Scalable-Softmax (SSMax), which replaces Softmax in scenarios where the input vector size varies. SSMax can be seamlessly integrated into existing Transformer-based architectures. Experimental results in language modeling show that models using SSMax not only achieve faster loss reduction during pretraining but also significantly improve performance in long contexts and key information retrieval. Furthermore, an analysis of attention scores reveals that SSMax enables the model to focus attention on key information even in long contexts. Additionally, although models that use SSMax from the beginning of pretraining achieve better length generalization, those that have already started pretraining can still gain some of this ability by replacing Softmax in the attention layers with SSMax, either during or after pretraining.

As the core operator of Transformers, Softmax Attention exhibits excellent global modeling capabilities. However, its quadratic complexity limits its applicability to vision tasks. In contrast, Linear Attention shares a similar formulation with Softmax Attention while achieving linear complexity, enabling efficient global information modeling. Nevertheless, Linear Attention suffers from a significant performance degradation compared to standard Softmax Attention. In this paper, we analyze the underlying causes of this issue based on the formulation of Linear Attention. We find that, unlike Softmax Attention, Linear Attention entirely disregards the magnitude information of the Query. This prevents the attention score distribution from dynamically adapting as the Query scales. As a result, despite its structural similarity to Softmax Attention, Linear Attention exhibits a significantly different attention score distribution. Based on this observation, we propose Magnitude-Aware Linear Attention (MALA), which modifies the computation of Linear Attention to fully incorporate the Query's magnitude. This adjustment allows MALA to generate an attention score distribution that closely resembles Softmax Attention while exhibiting a more well-balanced structure. We evaluate the effectiveness of MALA on multiple tasks, including image classification, object detection, instance segmentation, semantic segmentation, natural language processing, speech recognition, and image generation. Our MALA achieves strong results on all of these tasks. Code will be available at https://github.com/qhfan/MALA

The quadratic computational complexity of softmax transformers has become a bottleneck in long-context scenarios. In contrast, linear attention model families provide a promising direction towards a more efficient sequential model. These linear attention models compress past KV values into a single hidden state, thereby efficiently reducing complexity during both training and inference. However, their expressivity remains limited by the size of their hidden state. Previous work proposed interleaving softmax and linear attention layers to reduce computational complexity while preserving expressivity. Nevertheless, the efficiency of these models remains bottlenecked by their softmax attention layers. In this paper, we propose Neural Attention Search Linear (NAtS-L), a framework that applies both linear attention and softmax attention operations within the same layer on different tokens. NAtS-L automatically determines whether a token can be handled by a linear attention model, i.e., tokens that have only short-term impact and can be encoded into fixed-size hidden states, or require softmax attention, i.e., tokens that contain information related to long-term retrieval and need to be preserved for future queries. By searching for optimal Gated DeltaNet and softmax attention combinations across tokens, we show that NAtS-L provides a strong yet efficient token-level hybrid architecture.

We propose a new class of linear-time attention mechanisms based on a relaxed and computationally efficient formulation of the recently introduced E-Product, often referred to as the Yat-kernel (Bouhsine, 2025). The resulting interactions are geometry-aware and inspired by inverse-square interactions in physics. Our method, Spherical Linearized Attention with Yat Kernels (SLAY), constrains queries and keys to the unit sphere so that attention depends only on angular alignment. Using Bernstein's theorem, we express the spherical Yat-kernel as a nonnegative mixture of polynomial-exponential product kernels and derive a strictly positive random-feature approximation enabling linear-time O(L) attention. We establish positive definiteness and boundedness on the sphere and show that the estimator yields well-defined, nonnegative attention scores. Empirically, SLAY achieves performance that is nearly indistinguishable from standard softmax attention while retaining linear time and memory scaling, and consistently outperforms prior linear-time attention mechanisms such as Performers and Cosformers. To the best of our knowledge, SLAY represents the closest linear-time approximation to softmax attention reported to date, enabling scalable Transformers without the typical performance trade-offs of attention linearization.

Soft attention is a critical mechanism powering LLMs to locate relevant parts within a given context. However, individual attention weights are determined by the similarity of only a single query and key token vector. This "single token attention" bottlenecks the amount of information used in distinguishing a relevant part from the rest of the context. To address this issue, we propose a new attention method, Multi-Token Attention (MTA), which allows LLMs to condition their attention weights on multiple query and key vectors simultaneously. This is achieved by applying convolution operations over queries, keys and heads, allowing nearby queries and keys to affect each other's attention weights for more precise attention. As a result, our method can locate relevant context using richer, more nuanced information that can exceed a single vector's capacity. Through extensive evaluations, we demonstrate that MTA achieves enhanced performance on a range of popular benchmarks. Notably, it outperforms Transformer baseline models on standard language modeling tasks, and on tasks that require searching for information within long contexts, where our method's ability to leverage richer information proves particularly beneficial.

The attention mechanism within the transformer architecture enables the model to weigh and combine tokens based on their relevance to the query. While self-attention has enjoyed major success, it notably treats all queries q in the same way by applying the mapping V^topsoftmax(Kq), where V,K are the value and key embeddings respectively. In this work, we argue that this uniform treatment hinders the ability to control contextual sparsity and relevance. As a solution, we introduce the Selective Self-Attention (SSA) layer that augments the softmax nonlinearity with a principled temperature scaling strategy. By controlling temperature, SSA adapts the contextual sparsity of the attention map to the query embedding and its position in the context window. Through theory and experiments, we demonstrate that this alleviates attention dilution, aids the optimization process, and enhances the model's ability to control softmax spikiness of individual queries. We also incorporate temperature scaling for value embeddings and show that it boosts the model's ability to suppress irrelevant/noisy tokens. Notably, SSA is a lightweight method which introduces less than 0.5% new parameters through a weight-sharing strategy and can be fine-tuned on existing LLMs. Extensive empirical evaluations demonstrate that SSA-equipped models achieve a noticeable and consistent accuracy improvement on language modeling benchmarks.

Attention is a key part of the transformer architecture. It is a sequence-to-sequence mapping that transforms each sequence element into a weighted sum of values. The weights are typically obtained as the softmax of dot products between keys and queries. Recent work has explored alternatives to softmax attention in transformers, such as ReLU and sigmoid activations. In this work, we revisit sigmoid attention and conduct an in-depth theoretical and empirical analysis. Theoretically, we prove that transformers with sigmoid attention are universal function approximators and benefit from improved regularity compared to softmax attention. Through detailed empirical analysis, we identify stabilization of large initial attention norms during the early stages of training as a crucial factor for the successful training of models with sigmoid attention, outperforming prior attempts. We also introduce FLASHSIGMOID, a hardware-aware and memory-efficient implementation of sigmoid attention yielding a 17% inference kernel speed-up over FLASHATTENTION2 on H100 GPUs. Experiments across language, vision, and speech show that properly normalized sigmoid attention matches the strong performance of softmax attention on a wide range of domains and scales, which previous attempts at sigmoid attention were unable to fully achieve. Our work unifies prior art and establishes best practices for sigmoid attention as a drop-in softmax replacement in transformers.

Attention Model has now become an important concept in neural networks that has been researched within diverse application domains. This survey provides a structured and comprehensive overview of the developments in modeling attention. In particular, we propose a taxonomy which groups existing techniques into coherent categories. We review salient neural architectures in which attention has been incorporated, and discuss applications in which modeling attention has shown a significant impact. We also describe how attention has been used to improve the interpretability of neural networks. Finally, we discuss some future research directions in attention. We hope this survey will provide a succinct introduction to attention models and guide practitioners while developing approaches for their applications.

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this challenge, alternative architectures such as linear attention, State Space Models (SSMs), and Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives. While connections between these approaches exist, such models are commonly developed in isolation and there is a lack of theoretical understanding of the shared principles underpinning these architectures and their subtle differences, greatly influencing performance and scalability. In this paper, we introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation. Our framework facilitates rigorous comparisons, providing new insights on the distinctive characteristics of each model class. For instance, we compare linear attention and selective SSMs, detailing their differences and conditions under which both are equivalent. We also provide principled comparisons between softmax attention and other model classes, discussing the theoretical conditions under which softmax attention can be approximated. Additionally, we substantiate these new insights with empirical validations and mathematical arguments. This shows the DSF's potential to guide the systematic development of future more efficient and scalable foundation models.

Previous research observed accuracy degradation when replacing the attention softmax with a point-wise activation such as ReLU. In the context of vision transformers, we find that this degradation is mitigated when dividing by sequence length. Our experiments training small to large vision transformers on ImageNet-21k indicate that ReLU-attention can approach or match the performance of softmax-attention in terms of scaling behavior as a function of compute.

While linear attention reduces the quadratic complexity of standard Transformers to linear time, it often lags behind in expressivity due to the removal of softmax normalization. This omission eliminates global competition, a critical mechanism that enables models to sharply focus on relevant information amidst long-context noise. In this work, we propose Softmax Linear Attention (SLA), a framework designed to restore this competitive selection without sacrificing efficiency. By lifting the softmax operation from the token level to the head level, SLA leverages attention heads as coarse semantic slots, applying a competitive gating mechanism to dynamically select the most relevant subspaces. This reintroduces the ``winner-take-all'' dynamics essential for precise retrieval and robust long-context understanding. Distinct from prior methods that focus on refining local kernel functions, SLA adopts a broader perspective by exploiting the higher-level multi-head aggregation structure. Extensive experiments demonstrate that SLA consistently enhances state-of-the-art linear baselines (RetNet, GLA, GDN) across language modeling and long-context benchmarks, particularly in challenging retrieval scenarios where it significantly boosts robustness against noise, validating its capability to restore precise focus while maintaining linear complexity.

We present Rapid Attention Distillation to Linear Attention Decoders at Scale (RADLADS), a protocol for rapidly converting softmax attention transformers into linear attention decoder models, along with two new RWKV-variant architectures, and models converted from popular Qwen2.5 open source models in 7B, 32B, and 72B sizes. Our conversion process requires only 350-700M tokens, less than 0.005% of the token count used to train the original teacher models. Converting to our 72B linear attention model costs less than \$2,000 USD at today's prices, yet quality at inference remains close to the original transformer. These models achieve state-of-the-art downstream performance across a set of standard benchmarks for linear attention models of their size. We release all our models on HuggingFace under the Apache 2.0 license, with the exception of our 72B models which are also governed by the Qwen License Agreement. Models at https://huggingface.co/collections/recursal/radlads-6818ee69e99e729ba8a87102 Training Code at https://github.com/recursal/RADLADS-paper

Transformer has shown great successes in natural language processing, computer vision, and audio processing. As one of its core components, the softmax attention helps to capture long-range dependencies yet prohibits its scale-up due to the quadratic space and time complexity to the sequence length. Kernel methods are often adopted to reduce the complexity by approximating the softmax operator. Nevertheless, due to the approximation errors, their performances vary in different tasks/corpus and suffer crucial performance drops when compared with the vanilla softmax attention. In this paper, we propose a linear transformer called cosFormer that can achieve comparable or better accuracy to the vanilla transformer in both casual and cross attentions. cosFormer is based on two key properties of softmax attention: i). non-negativeness of the attention matrix; ii). a non-linear re-weighting scheme that can concentrate the distribution of the attention matrix. As its linear substitute, cosFormer fulfills these properties with a linear operator and a cosine-based distance re-weighting mechanism. Extensive experiments on language modeling and text understanding tasks demonstrate the effectiveness of our method. We further examine our method on long sequences and achieve state-of-the-art performance on the Long-Range Arena benchmark. The source code is available at https://github.com/OpenNLPLab/cosFormer.

Transformers and their attention mechanism have been revolutionary in the field of Machine Learning. While originally proposed for the language data, they quickly found their way to the image, video, graph, etc. data modalities with various signal geometries. Despite this versatility, generalizing the attention mechanism to scenarios where data is presented at different scales from potentially different modalities is not straightforward. The attempts to incorporate hierarchy and multi-modality within transformers are largely based on ad hoc heuristics, which are not seamlessly generalizable to similar problems with potentially different structures. To address this problem, in this paper, we take a fundamentally different approach: we first propose a mathematical construct to represent multi-modal, multi-scale data. We then mathematically derive the neural attention mechanics for the proposed construct from the first principle of entropy minimization. We show that the derived formulation is optimal in the sense of being the closest to the standard Softmax attention while incorporating the inductive biases originating from the hierarchical/geometric information of the problem. We further propose an efficient algorithm based on dynamic programming to compute our derived attention mechanism. By incorporating it within transformers, we show that the proposed hierarchical attention mechanism not only can be employed to train transformer models in hierarchical/multi-modal settings from scratch, but it can also be used to inject hierarchical information into classical, pre-trained transformer models post training, resulting in more efficient models in zero-shot manner.

Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at greater computational cost-has been relatively underexplored. In this work, we bridge this gap by proposing Local Linear Attention (LLA), a novel attention mechanism derived from nonparametric statistics through the lens of test-time regression. First, we show that LLA offers theoretical advantages over Linear and Softmax Attention for associative memory via a bias-variance trade-off analysis. Next, we address its computational challenges and propose two memory-efficient primitives to tackle the Theta(n^2 d) and Theta(n d^2) complexity. We then introduce FlashLLA, a hardware-efficient, blockwise algorithm that enables scalable and parallel computation on modern accelerators. In addition, we implement and profile a customized inference kernel that significantly reduces memory overheads. Finally, we empirically validate the advantages and limitations of LLA on test-time regression, in-context regression, associative recall and state tracking tasks. Experiment results demonstrate that LLA effectively adapts to non-stationarity, outperforming strong baselines in test-time training and in-context learning, and exhibiting promising evidence for its scalability and applicability in large-scale models. Code is available at https://github.com/Yifei-Zuo/Flash-LLA.

Linear attention transformers have become a strong alternative to softmax attention due to their efficiency. However, linear attention tends to be less expressive and results in reduced accuracy compared to softmax attention. To bridge the accuracy gap between softmax attention and linear attention, we manipulate Mamba-2, a very strong linear attention variant. We first simplify Mamba-2 down to its most fundamental and important components, evaluating which specific choices make it most accurate. From this simplified Mamba variant (Mamba-2S), we improve the A-mask and increase the order of the hidden state, resulting in a method, which we call 2Mamba, that is nearly as accurate as softmax attention, yet much more memory efficient for long context lengths. We also investigate elements to Mamba-2 that help surpass softmax attention accuracy. Code is provided for all our experiments.

Widely adopted in modern Vision Transformer designs, Softmax attention can effectively capture long-range visual information; however, it incurs excessive computational cost when dealing with high-resolution inputs. In contrast, linear attention naturally enjoys linear complexity and has great potential to scale up to higher-resolution images. Nonetheless, the unsatisfactory performance of linear attention greatly limits its practical application in various scenarios. In this paper, we take a step forward to close the gap between the linear and Softmax attention with novel theoretical analyses, which demystify the core factors behind the performance deviations. Specifically, we present two key perspectives to understand and alleviate the limitations of linear attention: the injective property and the local modeling ability. Firstly, we prove that linear attention is not injective, which is prone to assign identical attention weights to different query vectors, thus adding to severe semantic confusion since different queries correspond to the same outputs. Secondly, we confirm that effective local modeling is essential for the success of Softmax attention, in which linear attention falls short. The aforementioned two fundamental differences significantly contribute to the disparities between these two attention paradigms, which is demonstrated by our substantial empirical validation in the paper. In addition, more experiment results indicate that linear attention, as long as endowed with these two properties, can outperform Softmax attention across various tasks while maintaining lower computation complexity. Code is available at https://github.com/LeapLabTHU/InLine.

Large transformer models have achieved state-of-the-art results in numerous natural language processing tasks. Among the pivotal components of the transformer architecture, the attention mechanism plays a crucial role in capturing token interactions within sequences through the utilization of softmax function. Conversely, linear attention presents a more computationally efficient alternative by approximating the softmax operation with linear complexity. However, it exhibits substantial performance degradation when compared to the traditional softmax attention mechanism. In this paper, we bridge the gap in our theoretical understanding of the reasons behind the practical performance gap between softmax and linear attention. By conducting a comprehensive comparative analysis of these two attention mechanisms, we shed light on the underlying reasons for why softmax attention outperforms linear attention in most scenarios.

Self-attention lets each token retrieve information from the full context, but its quadratic cost in sequence length limits training and inference at long context. This paper presents a comparative study of softmax attention and four recent recurrent linear-attention architectures: DeltaNet, Gated DeltaNet, Kimi Delta Attention, and Gated DeltaNet-2. We express these mechanisms in a common recurrent-memory notation, making explicit how they differ in expressivity, memory decay, erase and write control, training throughput, and implementation complexity. Our experiments center on 350M-parameter models trained for 15B tokens, and include optimizer and learning-rate comparisons, hybrid-versus-pure stack comparisons, sequence-length runtime measurements, larger DeltaNet runs at 1.3B and 3B parameters, and a small set of downstream evaluations. The reported speed results measure training throughput and iteration time; we do not provide an empirical inference-speed benchmark. Within the reported 350M-parameter, 15B-token sweep, Kimi Delta Attention with Muon reaches the lowest final validation loss, a pure Gated DeltaNet stack trained with AdamW has the highest normalized training throughput, hybrid stacks generally improve loss at a throughput cost, and Muon consistently lowers final validation loss relative to AdamW in the matched architecture settings we evaluate. We introduce and evaluate lightweight cross-layer routing mechanisms for DeltaNet-style memories. The most natural DeltaNet-inspired formulation, forwarding a lower layer's delta-rule write error into the next layer's value target, does not improve over matched baselines. Routing into the aligned hidden stream and forwarding the write value instead yields a modest improvement in the matched runs we report: Cross-Layer Value Routing (CLVR) lowers final validation loss for both DeltaNet and Gated DeltaNet.

We introduce SANA-WM, an efficient 2.6B-parameter open-source world model natively trained for one-minute generation, synthesizing high-fidelity, 720p, minute-scale videos with precise camera control. SANA-WM achieves visual quality comparable to large-scale industrial baselines such as LingBot-World and HY-WorldPlay, while significantly improving efficiency. Four core designs drive our architecture: (1) Hybrid Linear Attention combines frame-wise Gated DeltaNet (GDN) with softmax attention for memory-efficient long-context modeling. (2) Dual-Branch Camera Control ensures precise 6-DoF trajectory adherence. (3) Two-Stage Generation Pipeline applies a long-video refiner to stage-1 outputs, improving quality and consistency across sequences. (4) Robust Annotation Pipeline extracts accurate metric-scale 6-DoF camera poses from public videos to yield high-quality, spatiotemporally consistent action labels. Driven by these designs, SANA-WMdemonstrates remarkable efficiency across data, training compute, and inference hardware: it uses only sim213K public video clips with metric-scale pose supervision, completes training in 15 days on 64 H100s, and generates each 60s clip on a single GPU; its distilled variant can be deployed on a single RTX 5090 with NVFP4 quantization to denoise a 60s 720p clip in 34s. On our one-minute world-model benchmark, SANA-WM demonstrates stronger action-following accuracy than prior open-source baselines and achieves comparable visual quality at 36times higher throughput for scalable world modeling.

Hybrid Transformer architectures, which combine softmax attention blocks and recurrent neural networks (RNNs), have shown a desirable performance-throughput tradeoff for long-context modeling, but their adoption and studies are hindered by the prohibitive cost of large-scale pre-training from scratch. Some recent studies have shown that pre-trained softmax attention blocks can be converted into RNN blocks through parameter transfer and knowledge distillation. However, these transfer methods require substantial amounts of training data (more than 10B tokens), and the resulting hybrid models also exhibit poor long-context performance, which is the scenario where hybrid models enjoy significant inference speedups over Transformer-based models. In this paper, we present HALO (Hybrid Attention via Layer Optimization), a pipeline for distilling Transformer models into RNN-attention hybrid models. We then present HypeNet, a hybrid architecture with superior length generalization enabled by a novel position encoding scheme (named HyPE) and various architectural modifications. We convert the Qwen3 series into HypeNet using HALO, achieving performance comparable to the original Transformer models while enjoying superior long-context performance and efficiency. The conversion requires just 2.3B tokens, less than 0.01% of their pre-training data

Transformers have become the cornerstone of modern large-scale language models; however, their dependence on softmax attention poses a major computational bottleneck, particularly in long-context settings. In this work, rather than following prevalent approaches such as linear attention (or SSMs) and local attention, we introduce an intermediate design called \rat between recurrence and attention mechanisms. It partitions the input into chunks, applies a simple linear recurrence within each chunk to capture local dependencies, and then performs softmax attention across chunks to model long-range interactions. By adjusting the size of the chunk, \rat enables flexible trade-offs, combining the strengths of RNN and attention. Empirically, with a chunk size of 16, the \rat layer achieves a \(7\times\) improvement in training speed with 100K token sequences and \(9\times\) in generation at 4K sequence length, while maintaining similar or sometimes even better accuracy compared to standard attention. We demonstrate this by training 1.3B parameter models from scratch and performing large-scale evaluations, including short- and long-context benchmarks, as well as supervised fine-tuning~(SFT). We further propose a hybrid architecture that interleaves \rat with local attention. By combining efficient long-range modeling with strong local interactions, this hybrid design not only improves inference speed and reduces cache memory usage compared to attention, but also consistently enhances performance, for example, achieving an average 1 point gain in commonsense reasoning tasks, up to 4 points on code tasks, and a 1 point Rouge-L increase in a summarization SFT task. Code is available at https://github.com/CLAIRE-Labo/RAT

Ultra-long-context capability is becoming indispensable for frontier LLMs: agentic workflows, repository-scale code reasoning, and persistent memory all require the model to jointly attend over hundreds of thousands to millions of tokens, yet the quadratic cost of softmax attention makes this untenable at deployment scale. We introduce MiniMax Sparse Attention (MSA), a blockwise sparse attention built upon Grouped Query Attention (GQA). A lightweight Index Branch scores key-value blocks and independently selects a Top-k subset for each GQA group, enabling group-specific sparse retrieval while maintaining efficient block-level execution; the Main Branch then performs exact block-sparse attention over only the selected blocks. Designed around a principle of simplicity and scalability, MSA is deliberately streamlined, making it straightforward to deploy efficiently across a broad range of GPUs. To translate sparsity into practical speedups, we co-design MSA with a GPU execution path that uses exp-free Top-k selection and KV-outer sparse attention to improve tensor-core utilization under block-granular access. On a 109B-parameter model with native multimodal training, MSA performs on par with GQA while reducing per-token attention compute by 28.4x at 1M context. Paired with our co-designed kernel, MSA achieves 14.2x prefill and 7.6x decoding wall-clock speedups on H800. Our inference kernel is available at: https://github.com/MiniMax-AI/MSA. A production-grade natively multimodal model powered by MSA has been publicly released at: https://huggingface.co/MiniMaxAI/MiniMax-M3.

Large language models have achieved remarkable success in recent years, primarily due to the implementation of self-attention mechanisms. However, traditional Softmax attention suffers from numerical instability and reduced performance as the length of inference tokens increases. This paper addresses these issues by decomposing the Softmax operation into a non-linear transformation and the l_1-norm. We identify the latter as essential for maintaining model performance. By replacing the non-linear transformation with the Softplus activation function and introducing a dynamic scale factor for different token lengths based on invariance entropy, we create a novel attention mechanism with performance better than conventional Softmax attention across various inference lengths. To further improve the length extrapolation ability of the proposed attention mechanism, we introduce a fine-tuning-free re-weighting mechanism that amplifies significant attention weights while diminishing weaker ones, enabling the model to concentrate more effectively on relevant tokens without requiring retraining. When combined with our proposed attention mechanism, this approach demonstrates significant promise in managing longer sequences, maintaining nearly constant validation loss even at 16times the training token length while ensuring numerical stability. Our code is available at: https://github.com/iminfine/freeatten.

Modeling long sequences of user behaviors has emerged as a critical frontier in generative recommendation. However, existing solutions face a dilemma: linear attention mechanisms achieve efficiency at the cost of retrieval precision due to limited state capacity, while softmax attention suffers from prohibitive computational overhead. To address this challenge, we propose HyTRec, a model featuring a Hybrid Attention architecture that explicitly decouples long-term stable preferences from short-term intent spikes. By assigning massive historical sequences to a linear attention branch and reserving a specialized softmax attention branch for recent interactions, our approach restores precise retrieval capabilities within industrial-scale contexts involving ten thousand interactions. To mitigate the lag in capturing rapid interest drifts within the linear layers, we furthermore design Temporal-Aware Delta Network (TADN) to dynamically upweight fresh behavioral signals while effectively suppressing historical noise. Empirical results on industrial-scale datasets confirm the superiority that our model maintains linear inference speed and outperforms strong baselines, notably delivering over 8% improvement in Hit Rate for users with ultra-long sequences with great efficiency.

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.

We present a scalable 3D reconstruction model that addresses a critical limitation in offline feed-forward methods: their computational and memory requirements grow quadratically w.r.t. the number of input images. Our approach is built on the key insight that this bottleneck stems from the varying-length Key-Value (KV) space representation of scene geometry, which we distill into a fixed-size Multi-Layer Perceptron (MLP) via test-time training. VGG-T^3 (Visual Geometry Grounded Test Time Training) scales linearly w.r.t. the number of input views, similar to online models, and reconstructs a 1k image collection in just 54 seconds, achieving a 11.6times speed-up over baselines that rely on softmax attention. Since our method retains global scene aggregation capability, our point map reconstruction error outperforming other linear-time methods by large margins. Finally, we demonstrate visual localization capabilities of our model by querying the scene representation with unseen images.

The softmax function is crucial in Transformer attention, which normalizes each row of the attention scores with summation to one, achieving superior performances over other alternative functions. However, the softmax function can face a gradient vanishing issue when some elements of the attention scores approach extreme values, such as probabilities close to one or zero. In this paper, we propose Self-Adjust Softmax (SA-Softmax) to address this issue by modifying softmax(x) to x cdot softmax(x) and its normalized variant (x - min(x_{min,0))}{max(0,x_{max})-min(x_{min},0)} cdot softmax(x). We theoretically show that SA-Softmax provides enhanced gradient properties compared to the vanilla softmax function. Moreover, SA-Softmax Attention can be seamlessly integrated into existing Transformer models to their attention mechanisms with minor adjustments. We conducted experiments to evaluate the empirical performance of Transformer models using SA-Softmax compared to the vanilla softmax function. These experiments, involving models with up to 2.7 billion parameters, are conducted across diverse datasets, language tasks, and positional encoding methods.

Softmax attention is the cornerstone of modern large language models, but its memory scales linearly and compute quadratically with sequence length. Linear recurrent models, such as linear attention and state space models, have become widely studied as alternatives to attention due to their linear compute and constant memory. While these sub-quadratic token mixing methods, or mixers, achieve promising efficiency gains and competitive results on a wide range of benchmarks, current linear recurrent models still lag behind on tasks that require long-context retrieval or in-context learning. A growing body of work studies hybrid architectures that attempt to mitigate these trade-offs by statically interleaving or merging attention and recurrent blocks. In this work, we explore a new axis of developing hybrid models: across the token sequence. We propose Oryx, a hybrid model that can, throughout a sequence, flexibly switch between different mixers, for example quadratic attention for rich context utilization and linear recurrences for efficient generation. Oryx ties at least 90% of its parameters across mixers, enabling attention and recurrent modes to operate over shared internal representations. We validate our design with Mamba-2 and Gated DeltaNet variants, up to 1.4B models. Under fixed token budgets and a mixed-training strategy, Oryx achieves comparable or better performance than its single-mixer baselines. At the 1.4B scale, all instances of Oryx outperform their respective baselines by at least 0.7 percentage points on averaged language modeling tasks. On retrieval tasks, Oryx achieves performance comparable to the Transformer baseline even when processing only a tiny fraction (<10%) of the tokens in attention mode. These results suggest that attention and linear recurrent models can share internal representations, and motivate sequence-axis hybridization as a promising direction.

We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.

Motivated by the factorization inherent in the original fast multipole method and the improved fast Gauss transform we introduce a factorable form of attention that operates efficiently in high dimensions. This approach reduces the computational and memory complexity of the attention mechanism in transformers from O(N^2) to O(N). In comparison to previous attempts, our work presents a linearly scaled attention mechanism that maintains the full representation of the attention matrix without compromising on sparsification and incorporates the all-to-all relationship between tokens. We explore the properties of our new attention metric and conduct tests in various standard settings. Results indicate that our attention mechanism has a robust performance and holds significant promise for diverse applications where self-attention is used.

Softmax-based dot-product attention is a cornerstone of Transformer architectures, enabling remarkable capabilities such as in-context learning. However, as context lengths increase, a fundamental limitation of the softmax function emerges: it tends to diffuse probability mass to irrelevant tokens degrading performance in long-sequence scenarios. Furthermore, attempts to sharpen focus by lowering softmax temperature hinder learnability due to vanishing gradients. We introduce LUCID Attention, an architectural modification that applies a preconditioner to the attention probabilities. This preconditioner, derived from exponentiated key-key similarities, minimizes overlap between the keys in a Reproducing Kernel Hilbert Space, thus allowing the query to focus on important keys among large number of keys accurately with same computational complexity as standard attention. Additionally, LUCID's preconditioning-based approach to retrieval bypasses the need for low temperature and the learnability problems associated with it. We validate our approach by training ~1 billion parameter language models evaluated on up to 128K tokens. Our results demonstrate significant gains on long-context retrieval tasks, specifically retrieval tasks from BABILong, RULER, SCROLLS and LongBench. For instance, LUCID achieves up to 18% improvement in BABILong and 14% improvement in RULER multi-needle performance compared to standard attention.

Attention based Transformer architecture has enabled significant advances in the field of natural language processing. In addition to new pre-training techniques, recent improvements crucially rely on working with a relatively larger embedding dimension for tokens. Unfortunately, this leads to models that are prohibitively large to be employed in the downstream tasks. In this paper we identify one of the important factors contributing to the large embedding size requirement. In particular, our analysis highlights that the scaling between the number of heads and the size of each head in the current architecture gives rise to a low-rank bottleneck in attention heads, causing this limitation. We further validate this in our experiments. As a solution we propose to set the head size of an attention unit to input sequence length, and independent of the number of heads, resulting in multi-head attention layers with provably more expressive power. We empirically show that this allows us to train models with a relatively smaller embedding dimension and with better performance scaling.

Mamba has recently garnered attention as an effective backbone for vision tasks. However, its underlying mechanism in visual domains remains poorly understood. In this work, we systematically investigate Mamba's representational properties and make three primary contributions. First, we theoretically analyze Mamba's relationship to Softmax and Linear Attention, confirming that it can be viewed as a low-rank approximation of Softmax Attention and thereby bridging the representational gap between Softmax and Linear forms. Second, we introduce a novel binary segmentation metric for activation map evaluation, extending qualitative assessments to a quantitative measure that demonstrates Mamba's capacity to model long-range dependencies. Third, by leveraging DINO for self-supervised pretraining, we obtain clearer activation maps than those produced by standard supervised approaches, highlighting Mamba's potential for interpretability. Notably, our model also achieves a 78.5 percent linear probing accuracy on ImageNet, underscoring its strong performance. We hope this work can provide valuable insights for future investigations of Mamba-based vision architectures.

Transformer-based architectures traditionally employ softmax to compute attention weights, which produces dense distributions over all tokens in a sequence. While effective in many settings, this density has been shown to be detrimental for tasks that demand precise focus on fixed-size patterns: as sequence length increases, non-informative tokens accumulate attention probability mass, leading to dispersion and representational collapse. We show in this paper that dynamically sparse attention mechanisms using α-entmax can avoid these issues, due to their ability to assign exact zeros to irrelevant tokens. Furthermore, we introduce Adaptive-Scalable Entmax (ASEntmax), which endows α-entmax with a learnable temperature parameter, allowing the attention distribution to interpolate between sparse (pattern-focused) and dense (softmax-like) regimes. Our empirical evaluation on synthetic tasks and language modeling demonstrates that ASEntmax substantially outperforms softmax, scalable softmax, and fixed-temperature α-entmax baselines, achieving up to 1000times length extrapolation on synthetic benchmarks and superior long-context generalization on language modeling while preserving short-context performance, including better perplexity trends and higher retrieval accuracies at 8times training length.

We introduce MiniMax-01 series, including MiniMax-Text-01 and MiniMax-VL-01, which are comparable to top-tier models while offering superior capabilities in processing longer contexts. The core lies in lightning attention and its efficient scaling. To maximize computational capacity, we integrate it with Mixture of Experts (MoE), creating a model with 32 experts and 456 billion total parameters, of which 45.9 billion are activated for each token. We develop an optimized parallel strategy and highly efficient computation-communication overlap techniques for MoE and lightning attention. This approach enables us to conduct efficient training and inference on models with hundreds of billions of parameters across contexts spanning millions of tokens. The context window of MiniMax-Text-01 can reach up to 1 million tokens during training and extrapolate to 4 million tokens during inference at an affordable cost. Our vision-language model, MiniMax-VL-01 is built through continued training with 512 billion vision-language tokens. Experiments on both standard and in-house benchmarks show that our models match the performance of state-of-the-art models like GPT-4o and Claude-3.5-Sonnet while offering 20-32 times longer context window. We publicly release MiniMax-01 at https://github.com/MiniMax-AI.

Vision Transformers (ViTs) have recently taken computer vision by storm. However, the softmax attention underlying ViTs comes with a quadratic complexity in time and memory, hindering the application of ViTs to high-resolution images. We revisit the attention design and propose a linear attention method to address the limitation, which doesn't sacrifice ViT's core advantage of capturing global representation like existing methods (e.g. local window attention of Swin). We further investigate the key difference between linear attention and softmax attention. Our empirical results suggest that linear attention lacks a fundamental property of concentrating the distribution of the attention matrix. Inspired by this observation, we introduce a local concentration module to enhance linear attention. By incorporating enhanced linear global attention and local window attention, we propose a new ViT architecture, dubbed L^2ViT. Notably, L^2ViT can effectively capture both global interactions and local representations while enjoying linear computational complexity. Extensive experiments demonstrate the strong performance of L^2ViT. On image classification, L^2ViT achieves 84.4% Top-1 accuracy on ImageNet-1K without any extra training data or label. By further pre-training on ImageNet-22k, it attains 87.0% when fine-tuned with resolution 384^2. For downstream tasks, L^2ViT delivers favorable performance as a backbone on object detection as well as semantic segmentation.

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns: a diagonal and homogeneous pattern in the key-query (KQ) weights, and a last-entry-only and zero-sum pattern in the output-value (OV) weights. Remarkably, these patterns consistently appear from gradient-based training starting from random initialization. Our analysis reveals that such emergent structures enable multi-head attention to approximately implement a debiased gradient descent predictor -- one that outperforms single-head attention and nearly achieves Bayesian optimality up to proportional factor. Furthermore, compared to linear transformers, the softmax attention readily generalizes to sequences longer than those seen during training. We also extend our study to scenarios with non-isotropic covariates and multi-task linear regression. In the former, multi-head attention learns to implement a form of pre-conditioned gradient descent. In the latter, we uncover an intriguing regime where the interplay between head number and task number triggers a superposition phenomenon that efficiently resolves multi-task in-context learning. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution, paving the way for deeper understanding and broader applications of in-context learning.

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

Attention-based mechanisms are widely used in machine learning, most prominently in transformers. However, hyperparameters such as the rank of the attention matrices and the number of heads are scaled nearly the same way in all realizations of this architecture, without theoretical justification. In this work we show that there are dramatic trade-offs between the rank and number of heads of the attention mechanism. Specifically, we present a simple and natural target function that can be represented using a single full-rank attention head for any context length, but that cannot be approximated by low-rank attention unless the number of heads is exponential in the embedding dimension, even for short context lengths. Moreover, we prove that, for short context lengths, adding depth allows the target to be approximated by low-rank attention. For long contexts, we conjecture that full-rank attention is necessary. Finally, we present experiments with off-the-shelf transformers that validate our theoretical findings.

We introduce three new attention mechanisms that outperform standard multi-head attention in terms of efficiency and learning capabilities, thereby improving the performance and broader deployability of Transformer models. Our first contribution is Optimised Attention, which performs similarly to standard attention, but has 3/4 as many parameters and one matrix multiplication fewer per head. Next, we introduce Efficient Attention, which performs on par with standard attention with only 1/2 as many parameters as many parameters and two matrix multiplications fewer per head and is up to twice as fast as standard attention. Lastly, we introduce Super Attention, which surpasses standard attention by a significant margin in both vision and natural language processing tasks while having fewer parameters and matrix multiplications. In addition to providing rigorous mathematical comparisons, we evaluate the presented attention mechanisms on MNIST, CIFAR100, IMDB Movie Reviews, and Amazon Reviews datasets.

A core limitation of standard softmax attention is that it does not define a notion of absolute query--key relevance: attention weights are obtained by redistributing a fixed unit mass across all keys according to their relative scores. As a result, relevance is defined only relative to competing keys, and irrelevant keys cannot be explicitly rejected. We introduce Multiscreen, a language-model architecture built around a mechanism we call screening, which enables absolute query--key relevance. Instead of redistributing attention across all keys, screening evaluates each key against an explicit threshold, discarding irrelevant keys and aggregating the remaining keys, thereby removing global competition among keys. Across experiments, Multiscreen achieves comparable validation loss with approximately 40% fewer parameters than a Transformer baseline and enables stable optimization at substantially larger learning rates. It maintains strong performance in long-context perplexity and shows little to no degradation in retrieval performance well beyond the training context length. Notably, even at the training context length, a Multiscreen model with approximately 92% fewer parameters consistently outperforms a larger Transformer in retrieval accuracy. Finally, Multiscreen reduces inference latency by up to 3.2times at 100K context length.

Despite the recent success in many applications, the high computational requirements of vision transformers limit their use in resource-constrained settings. While many existing methods improve the quadratic complexity of attention, in most vision transformers, self-attention is not the major computation bottleneck, e.g., more than 80% of the computation is spent on fully-connected layers. To improve the computational complexity of all layers, we propose a novel token downsampling method, called Token Pooling, efficiently exploiting redundancies in the images and intermediate token representations. We show that, under mild assumptions, softmax-attention acts as a high-dimensional low-pass (smoothing) filter. Thus, its output contains redundancy that can be pruned to achieve a better trade-off between the computational cost and accuracy. Our new technique accurately approximates a set of tokens by minimizing the reconstruction error caused by downsampling. We solve this optimization problem via cost-efficient clustering. We rigorously analyze and compare to prior downsampling methods. Our experiments show that Token Pooling significantly improves the cost-accuracy trade-off over the state-of-the-art downsampling. Token Pooling is a simple and effective operator that can benefit many architectures. Applied to DeiT, it achieves the same ImageNet top-1 accuracy using 42% fewer computations.

We propose a novel attention mechanism, named Cog Attention, that enables attention weights to be negative for enhanced expressiveness, which stems from two key factors: (1) Cog Attention can shift the token deletion and copying function from a static OV matrix to dynamic QK inner products, with the OV matrix now focusing more on refinement or modification. The attention head can simultaneously delete, copy, or retain tokens by assigning them negative, positive, or minimal attention weights, respectively. As a result, a single attention head becomes more flexible and expressive. (2) Cog Attention improves the model's robustness against representational collapse, which can occur when earlier tokens are over-squashed into later positions, leading to homogeneous representations. Negative weights reduce effective information paths from earlier to later tokens, helping to mitigate this issue. We develop Transformer-like models which use Cog Attention as attention modules, including decoder-only models for language modeling and U-ViT diffusion models for image generation. Experiments show that models using Cog Attention exhibit superior performance compared to those employing traditional softmax attention modules. Our approach suggests a promising research direction for rethinking and breaking the entrenched constraints of traditional softmax attention, such as the requirement for non-negative weights.

Modern language models increasingly adopt hybrid architectures that combine full attention with efficient attention modules, such as sliding-window attention (SWA) and recurrent sequence mixers. However, how these efficient modules shape model capabilities remains poorly understood. To address this gap, we conduct a systematic analysis across hybrid architectures from three perspectives: scaling behavior, mechanism analysis, and architecture design. First, from a scaling perspective, we find that efficient-attention design primarily affects how fast long-context capability emerges, while different hybrids eventually converge to comparable long-context performance under sufficient training. Second, mechanistically, we show that long-range retrieval is mainly carried by full attention, whereas efficient attention shapes its optimization trajectory. This explains a counter-intuitive phenomenon we call Large-Window Laziness: larger SWA windows can delay the formation of retrieval heads in full-attention layers. Third, guided by this mechanism, we show that applying NoPE to only the full-attention layers of a small-window SWA hybrid substantially improves long-context performance with negligible impact on short-context performance.

Sequence models lie at the heart of modern deep learning. However, rapid advancements have produced a diversity of seemingly unrelated architectures, such as Transformers and recurrent alternatives. In this paper, we introduce a unifying framework to understand and derive these sequence models, inspired by the empirical importance of associative recall, the capability to retrieve contextually relevant tokens. We formalize associative recall as a two-step process, memorization and retrieval, casting memorization as a regression problem. Layers that combine these two steps perform associative recall via ``test-time regression'' over its input tokens. Prominent layers, including linear attention, state-space models, fast-weight programmers, online learners, and softmax attention, arise as special cases defined by three design choices: the regression weights, the regressor function class, and the test-time optimization algorithm. Our approach clarifies how linear attention fails to capture inter-token correlations and offers a mathematical justification for the empirical effectiveness of query-key normalization in softmax attention. Further, it illuminates unexplored regions within the design space, which we use to derive novel higher-order generalizations of softmax attention. Beyond unification, our work bridges sequence modeling with classic regression methods, a field with extensive literature, paving the way for developing more powerful and theoretically principled architectures.

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.

Standard attention scales quadratically with sequence length. Efficient attention methods reduce this O(n^2) cost, but when retrofitted into pretrained models, they often degrade perplexity, downstream accuracy, or both. We introduce Focus, a method that learns which token pairs matter. Focus adds a small set of learnable centroids--as few as 148K parameters per layer--that act as gates: only token pairs belonging to the same centroid group attend to each other over long ranges. Focus is composable: it can be added to any pretrained model by training only the centroids while keeping all original weights frozen. Experiments show that composing Focus onto pretrained models yields zero degradation on downstream benchmarks across model sizes from 124M to 70B parameters and five attention architectures. Surprisingly, sparse Focus attention outperforms full attention at 124M scale (30.3 vs. 31.4 perplexity) and matches full attention when trained from scratch at 7B scale (13.82 vs. 13.89). Focus is also fast: top-k group membership gives a 2x speedup with better quality than the original pretrained model. Using our FlashAttention decomposition, Focus achieves an 8.6x speedup at 1M tokens without custom kernels.

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear complexity by approximating the Softmax operation through carefully designed mapping functions. However, current linear attention approaches either suffer from significant performance degradation or introduce additional computation overhead from the mapping functions. In this paper, we propose a novel Focused Linear Attention module to achieve both high efficiency and expressiveness. Specifically, we first analyze the factors contributing to the performance degradation of linear attention from two perspectives: the focus ability and feature diversity. To overcome these limitations, we introduce a simple yet effective mapping function and an efficient rank restoration module to enhance the expressiveness of self-attention while maintaining low computation complexity. Extensive experiments show that our linear attention module is applicable to a variety of advanced vision Transformers, and achieves consistently improved performances on multiple benchmarks. Code is available at https://github.com/LeapLabTHU/FLatten-Transformer.

Transformers are mostly relying on softmax attention, which introduces quadratic complexity with respect to sequence length and remains a major bottleneck for efficient inference. Prior work on linear or hybrid attention typically replaces softmax attention uniformly across all layers, often leading to significant performance degradation or requiring extensive retraining to recover model quality. This work proposes LayerBoost, a layer-aware attention reduction method that selectively modifies the attention mechanism based on the sensitivity of individual transformer layers. It first performs a systematic sensitivity analysis on a pretrained model to identify layers that are critical for maintaining performance. Guided by this analysis, three distinct strategies can be applied: retaining standard softmax attention in highly sensitive layers, replacing it with linear sliding window attention in moderately sensitive layers, and removing attention entirely in layers that exhibit low sensitivity. To recover performance after these architectural modifications, we introduce a lightweight distillation-based healing phase requiring only 10M additional training tokens. LayerBoost reduces inference latency and improves throughput by up to 68% at high concurrency, while maintaining competitive model quality. It matches base model performance on several benchmarks, exhibits only minor degradations on others, and significantly outperforms state-of-the-art attention linearization methods. These efficiency gains make our method particularly well-suited for high-concurrency serving and hardware-constrained deployment scenarios, where inference cost and memory footprint are critical bottlenecks.

Non-local (NL) block is a popular module that demonstrates the capability to model global contexts. However, NL block generally has heavy computation and memory costs, so it is impractical to apply the block to high-resolution feature maps. In this paper, to investigate the efficacy of NL block, we empirically analyze if the magnitude and direction of input feature vectors properly affect the attention between vectors. The results show the inefficacy of softmax operation which is generally used to normalize the attention map of the NL block. Attention maps normalized with softmax operation highly rely upon magnitude of key vectors, and performance is degenerated if the magnitude information is removed. By replacing softmax operation with the scaling factor, we demonstrate improved performance on CIFAR-10, CIFAR-100, and Tiny-ImageNet. In Addition, our method shows robustness to embedding channel reduction and embedding weight initialization. Notably, our method makes multi-head attention employable without additional computational cost.

Recently, numerous efficient Transformers have been proposed to reduce the quadratic computational complexity of standard Transformers caused by the Softmax attention. However, most of them simply swap Softmax with an efficient attention mechanism without considering the customized architectures specially for the efficient attention. In this paper, we argue that the handcrafted vanilla Transformer architectures for Softmax attention may not be suitable for efficient Transformers. To address this issue, we propose a new framework to find optimal architectures for efficient Transformers with the neural architecture search (NAS) technique. The proposed method is validated on popular machine translation and image classification tasks. We observe that the optimal architecture of the efficient Transformer has the reduced computation compared with that of the standard Transformer, but the general accuracy is less comparable. It indicates that the Softmax attention and efficient attention have their own distinctions but neither of them can simultaneously balance the accuracy and efficiency well. This motivates us to mix the two types of attention to reduce the performance imbalance. Besides the search spaces that commonly used in existing NAS Transformer approaches, we propose a new search space that allows the NAS algorithm to automatically search the attention variants along with architectures. Extensive experiments on WMT' 14 En-De and CIFAR-10 demonstrate that our searched architecture maintains comparable accuracy to the standard Transformer with notably improved computational efficiency.

Transformers often display an attention sink: probability mass concentrates on a fixed, content-agnostic position. We prove that computing a simple trigger-conditional behavior necessarily induces a sink in softmax self-attention models. Our results formalize a familiar intuition: normalization over a probability simplex must force attention to collapse onto a stable anchor to realize a default state (e.g., when the model needs to ignore the input). We instantiate this with a concrete task: when a designated trigger token appears, the model must return the average of all preceding token representations, and otherwise output zero, a task which mirrors the functionality of attention heads in the wild (Barbero et al., 2025; Guo et al., 2024). We also prove that non-normalized ReLU attention can solve the same task without any sink, confirming that the normalization constraint is the fundamental driver of sink behavior. Experiments validate our predictions and demonstrate they extend beyond the theoretically analyzed setting: softmax models develop strong sinks while ReLU attention eliminates them in both single-head and multi-head variants.

Linear attention reduces the quadratic cost of softmax attention to O(T), but its memory state grows as O(T) in Frobenius norm, causing progressive interference between stored associations. We introduce Variational Linear Attention (VLA), which reframes the memory update as an online regularised least-squares problem with an adaptive penalty matrix maintained via the Sherman-Morrison rank-1 formula. We prove that normalising the write direction to unit length gives the recurrence Jacobian spectral norm exactly 1 for all sequence lengths and head dimensions (Proposition 2), and that the state norm is self-limiting under bounded inputs (Proposition 1). Empirically, VLA reduces |S_t|_F by 109times relative to standard linear attention at T{=}1{,}000, achieves near-perfect exact-match accuracy on multi-query associative recall within the effective per-head memory regime (n_pairs < d_h), maintaining substantially higher retrieval performance than DeltaNet and standard linear attention under increasing memory load, and maintains 62\% accuracy at the per-head capacity boundary. A Triton-fused kernel achieves 14times speedup over sequential Python and O(T) scaling, crossing below softmax attention latency at approximately 43\,000 tokens.

Quantization has emerged as a standard technique for accelerating inference for generative models by enabling faster low-precision computations and reduced memory transfers. Recently, GPU accelerators have added first-class support for microscaling Block Floating Point (BFP) formats. Standard BFP algorithms use a fixed scale based on the maximum magnitude of the block. We observe that this scale choice can be suboptimal with respect to quantization errors. In this work, we propose ScaleSearch, an alternative strategy for selecting these scale factors: using a fine-grained search leveraging the mantissa bits in microscaling formats to minimize the quantization error for the given distribution. ScaleSearch can be integrated with existing quantization methods such as Post Training Quantization and low-precision attention, and is shown to improve their performance. Additionally, we introduce ScaleSearchAttention, an accelerated NVFP4-based attention algorithm, which uses ScaleSearch and adapted prior techniques to ensure near-0 performance loss for causal language modeling. Experiments show that ScaleSearch reduces quantization error by 27% for NVFP4 and improves language model PTQ by up to 15 points for MATH500 (Qwen3-8B), while ScaleSearchAttention improves Wikitext-2 PPL by upto 0.77 points for Llama 3.1 70B. The proposed methods closely match baseline performance while providing quantization accuracy improvements.

Linear attention reduces the quadratic cost of softmax attention by maintaining a recurrent fast-weight state, but it consistently lags on in-context retrieval and long-context tasks. Existing remedies act on the write side of memory through gating, delta updates, or kernel feature maps, but the read step is left unchanged: every past key contributes additively to the output, so useful targets are diluted by the bulk of stored vectors. We borrow one specific piece of softmax's geometry to construct a cheap read-time contraction of the query. A second-order Taylor expansion of the softmax log-partition at the isotropic-attention point gives a local quadratic model whose curvature coincides with the running key covariance, a quantity that can be maintained with the same recurrent/chunkwise mechanism as the linear-attention state. The associated linear operator contracts the query along the high-density directions of memory before it reads the state. We call this mechanism Curvature-Conditioned Query (CCQ). CCQ modifies only the read step and is composable with any linear-attention backbone. Attached to GLA and Gated DeltaNet, it improves perplexity, zero-shot downstream accuracy, S-NIAH retrieval at and beyond the training context, length-extrapolation perplexity from 4K to 20K, and LongBench accuracy, at small extra cost.

An efficient attention implementation is essential for large models due to its quadratic time complexity. Fortunately, attention commonly exhibits sparsity, i.e., many values in the attention map are near zero, allowing for the omission of corresponding computations. Many studies have utilized the sparse pattern to accelerate attention. However, most existing works focus on optimizing attention within specific models by exploiting certain sparse patterns of the attention map. A universal sparse attention that guarantees both the speedup and end-to-end performance of diverse models remains elusive. In this paper, we propose SpargeAttn, a universal sparse and quantized attention for any model. Our method uses a two-stage online filter: in the first stage, we rapidly and accurately predict the attention map, enabling the skip of some matrix multiplications in attention. In the second stage, we design an online softmax-aware filter that incurs no extra overhead and further skips some matrix multiplications. Experiments show that our method significantly accelerates diverse models, including language, image, and video generation, without sacrificing end-to-end metrics. The codes are available at https://github.com/thu-ml/SpargeAttn.

Vision Transformers (ViTs) based vision foundation models (VFMs) have achieved remarkable performance across diverse vision tasks, but suffer from quadratic complexity that limits scalability to long sequences. Existing linear attention approaches for ViTs are typically trained from scratch, requiring substantial computational resources, while linearization-based methods developed for large language model decoders do not transfer well to ViTs. To address these challenges, we propose ViT-AdaLA, a novel framework for effectively adapting and transferring prior knowledge from VFMs to linear attention ViTs. ViT-AdaLA consists of three stages: attention alignment, feature alignment, and supervised fine-tuning. In the attention alignment stage, we align vanilla linear attention with the original softmax-based attention in each block to approximate the behavior of softmax attention. However, residual approximation errors inevitably accumulate across layers. We mitigate this by fine-tuning the linearized ViT to align its final-layer features with a frozen softmax VFM teacher. Finally, the adapted prior knowledge is transferred to downstream tasks through supervised fine-tuning. Extensive experiments on classification and segmentation tasks demonstrate the effectiveness and generality of ViT-AdaLA over various state-of-the-art linear attention counterpart.

Transformer-based LLMs have achieved exceptional performance across a wide range of NLP tasks. However, the standard self-attention mechanism suffers from quadratic time complexity and linearly increased cache size. Sliding window attention (SWA) solves this problem by restricting the attention range to a fixed-size local context window. Nevertheless, SWA employs a uniform window size for each head in each layer, making it inefficient in capturing context of varying scales. To mitigate this limitation, we propose Multi-Scale Window Attention (MSWA) which applies diverse window sizes across heads and layers in the Transformer. It not only allows for different window sizes among heads within the same layer but also progressively increases window size allocation from shallow to deep layers, thus enabling the model to capture contextual information with different lengths and distances. Experimental results on language modeling and common-sense reasoning tasks substantiate that MSWA outperforms traditional local attention in both effectiveness and efficiency.

The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods leverage specialized low-rank factorizations across embedding dimensions or attention heads. From the point of view of classical low-rank approximation, these methods are unconventional and raise questions of which objects they really approximate and how to interpret the low-rank behavior of the resulting representations. To answer these questions, this work proposes a generalized view on the weight objects in the self-attention layer and a factorization strategy, which allows us to construct a parameter efficient scheme, called Tucker Attention. Tucker Attention requires an order of magnitude fewer parameters for comparable validation metrics, compared to GQA and MLA, as evaluated in LLM and ViT test cases. Additionally, Tucker Attention~encompasses GQA, MLA, MHA as special cases and is fully compatible with flash-attention and rotary position embeddings (RoPE). This generalization strategy yields insights of the actual ranks achieved by MHA, GQA, and MLA, and further enables simplifications for MLA.

The attention mechanism forms the foundational blocks for transformer language models. Recent approaches show that scaling the model achieves human-level performance. However, with increasing demands for scaling and constraints on hardware memory, the inference costs of these models remain high. To reduce the inference time, Multi-Query Attention (MQA) and Grouped-Query Attention (GQA) were proposed in (Shazeer, 2019) and (Ainslieet al., 2023) respectively. In this paper, we propose a variation of Grouped-Query Attention, termed Weighted Grouped-Query Attention (WGQA). We introduced new learnable parameters for each key and value head in the T5 decoder attention blocks, enabling the model to take a weighted average during finetuning. Our model achieves an average of 0.53% improvement over GQA, and the performance converges to traditional Multi-head attention (MHA) with no additional overhead during inference. We evaluated the introduction of these parameters and subsequent finetuning informs the model about the grouping mechanism during training, thereby enhancing performance. Additionally, we demonstrate the scaling laws in our analysis by comparing the results between T5-small and T5-base architecture.

The Softmax attention mechanism in Transformer models is notoriously computationally expensive, particularly due to its quadratic complexity, posing significant challenges in vision applications. In contrast, linear attention provides a far more efficient solution by reducing the complexity to linear levels. However, compared to Softmax attention, linear attention often experiences significant performance degradation. Our experiments indicate that this performance drop is due to the low-rank nature of linear attention's feature map, which hinders its ability to adequately model complex spatial information. In this paper, to break the low-rank dilemma of linear attention, we conduct rank analysis from two perspectives: the KV buffer and the output features. Consequently, we introduce Rank-Augmented Linear Attention (RALA), which rivals the performance of Softmax attention while maintaining linear complexity and high efficiency. Based on RALA, we construct the Rank-Augmented Vision Linear Transformer (RAVLT). Extensive experiments demonstrate that RAVLT achieves excellent performance across various vision tasks. Specifically, without using any additional labels, data, or supervision during training, RAVLT achieves an 84.4% Top-1 accuracy on ImageNet-1k with only 26M parameters and 4.6G FLOPs. This result significantly surpasses previous linear attention mechanisms, fully illustrating the potential of RALA. Code will be available at https://github.com/qhfan/RALA.

Transformers have achieved significant success across various domains, relying on self-attention to capture dependencies. However, the standard first-order attention mechanism is often limited by a low-rank bottleneck, struggling to capture intricate, multi-hop relationships within a single layer. In this paper, we propose the Nexus, a novel architecture designed to enhance representational power through a recursive framework. Unlike standard approaches that use static linear projections for Queries and Keys, Nexus dynamically refines these representations via nested self-attention mechanisms. Specifically, the Query and Key vectors are themselves outputs of inner attention loops, allowing tokens to aggregate global context and model high-order correlations prior to the final attention computation. We enforce a parameter-efficient weight-sharing strategy across recursive steps, ensuring that this enhanced expressivity incurs O(1) additional parameters. We provide theoretical analysis demonstrating that our method breaks the linear bottleneck of standard attention. Empirically, Nexus outperforms standard Transformers on multiple benchmarks.

The evolution of Large Vision-Language Models (LVLMs) has progressed from single to multi-image reasoning. Despite this advancement, our findings indicate that LVLMs struggle to robustly utilize information across multiple images, with predictions significantly affected by the alteration of image positions. To further explore this issue, we introduce Position-wise Question Answering (PQA), a meticulously designed task to quantify reasoning capabilities at each position. Our analysis reveals a pronounced position bias in LVLMs: open-source models excel in reasoning with images positioned later but underperform with those in the middle or at the beginning, while proprietary models show improved comprehension for images at the beginning and end but struggle with those in the middle. Motivated by this, we propose SoFt Attention (SoFA), a simple, training-free approach that mitigates this bias by employing linear interpolation between inter-image causal attention and bidirectional counterparts. Experimental results demonstrate that SoFA reduces position bias and enhances the reasoning performance of existing LVLMs.

While linear-complexity attention mechanisms offer a promising alternative to Softmax attention for overcoming the quadratic bottleneck, training such models from scratch remains prohibitively expensive. Inheriting weights from pretrained Transformers provides an appealing shortcut, yet the fundamental representational gap between Softmax and linear attention prevents effective weight transfer. In this work, we address this conversion challenge from two perspectives: architectural alignment and representational alignment. We identify Test-Time Training (TTT) as a linear-complexity architecture whose two-layer dynamic formulation is structurally aligned with Softmax attention, enabling direct inheritance of pretrained attention weights. To further align representational properties, including key shift-invariance and locality, we introduce key instance normalization and a lightweight locality enhancement module. We validate our approach by linearizing Stable Diffusion 3.5 and introduce SD3.5-T^5 (Transformer To Test Time Training). With only 1 hour of fine-tuning on 4timesH20 GPUs, SD3.5-T^5 achieves comparable text-to-image quality to the fine-tuned Softmax model, while accelerating inference by 1.32times and 1.47times at 1K and 2K resolutions. Code is available at https://github.com/LeapLabTHU/Transformer-to-TTT.

The quadratic complexity of the attention mechanism represents one of the biggest hurdles for processing long sequences using Transformers. Current methods, relying on sparse representations or stateful recurrence, sacrifice token-to-token interactions, which ultimately leads to compromises in performance. This paper introduces TaylorShift, a novel reformulation of the Taylor softmax that enables computing full token-to-token interactions in linear time and space. We analytically determine the crossover points where employing TaylorShift becomes more efficient than traditional attention, aligning closely with empirical measurements. Specifically, our findings demonstrate that TaylorShift enhances memory efficiency for sequences as short as 800 tokens and accelerates inference for inputs of approximately 1700 tokens and beyond. For shorter sequences, TaylorShift scales comparably with the vanilla attention. Furthermore, a classification benchmark across five tasks involving long sequences reveals no degradation in accuracy when employing Transformers equipped with TaylorShift. For reproducibility, we provide access to our code under https://github.com/tobna/TaylorShift.

Sparse attention offers a promising strategy to extend long-context capabilities in Transformer LLMs, yet its viability, its efficiency-accuracy trade-offs, and systematic scaling studies remain unexplored. To address this gap, we perform a careful comparison of training-free sparse attention methods at varying model scales, sequence lengths, and sparsity levels on a diverse collection of long-sequence tasks-including novel ones that rely on natural language while remaining controllable and easy to evaluate. Based on our experiments, we report a series of key findings: 1) an isoFLOPS analysis reveals that for very long sequences, larger and highly sparse models are preferable to smaller and dense ones. 2) The level of sparsity attainable while statistically guaranteeing accuracy preservation is higher during decoding than prefilling, and correlates with model size in the former. 3) There is no clear strategy that performs best across tasks and phases, with different units of sparsification or budget adaptivity needed for different scenarios. Even moderate sparsity levels often result in significant performance degradation on at least one task, highlighting that sparse attention is not a universal solution. 4) We introduce and validate novel scaling laws specifically tailored for sparse attention, providing evidence that our findings are likely to hold true beyond our range of experiments. Through these insights, we demonstrate that sparse attention is a key tool to enhance the capabilities of Transformer LLMs for processing longer sequences, but requires careful evaluation of trade-offs for performance-sensitive applications.

Attention mechanisms, particularly softmax attention, have been instrumental in the success of transformer-based models such as GPT. However, the quadratic memory complexity of softmax attention with respect to sequence length poses significant challenges for processing longer sequences. We introduce Cottention, a novel attention mechanism that replaces the softmax operation with cosine similarity. By leveraging the properties of cosine similarity and rearranging the attention equation, Cottention achieves native linear memory complexity with respect to sequence length, making it inherently more memory-efficient than softmax attention. We demonstrate that Cottention can be reformulated as a recurrent neural network (RNN) with a finite hidden state, allowing for constant memory usage during inference. We evaluate Cottention on both the bidirectional BERT and causal GPT tasks, demonstrating comparable performance to softmax attention while significantly reducing memory requirements. To ensure efficient computation, we develop a custom CUDA kernel for Cottention. Our results show that Cottention is a promising alternative to softmax attention, enabling the processing of longer sequences without sacrificing performance, due to its native linear memory complexity and ability to maintain a constant memory footprint during inference.

In this paper, we propose Superlinear attention, a fully trainable multi-step attention architecture that achieves subquadratic complexity for long sequences while preserving random context access (a.k.a.\ structural non-exclusion): no eligible token position is structurally excluded from being selected for attention. Superlinear attention reformulates standard causal self-attention as a multi-step search problem with N steps, yielding an overall complexity of O(L^{1+1{N}}). To illustrate the architecture, we present a baseline N=2 implementation, which is algorithmically analogous to standard jump search. In this O(L^{3/2}) instantiation, the first step performs O(L^{3/2}) span-search to select relevant spans of the sequence, and the second step applies O(L^{3/2}) span-attention (standard attention restricted to the selected spans). In an upscaled O(L^{1.54}) configuration for robustness, we achieve an average decoding throughput of 114 tokens/sec at 1M context length and 80 tokens/sec at 10M context in our implementation on a modified 30B hybrid MoE model on a single B200 GPU. With limited training, we also obtain strong performance on the NIAH (Needle In A Haystack) task up to 256K context length, demonstrating that the routed span selection is learnable end-to-end. This paper emphasizes architectural formulation, scaling analysis, and systems feasibility, and presents initial validation; comprehensive quality evaluations across diverse long-context tasks are left to future work.

Attention sinks, representation collapse, and norm stratification are treated as transformer-specific pathologies. We show they are not specific to attention: they are what content-based routing does under a fixed similarity metric. We give a reframing identity: softmax attention is Boltzmann-weighted aggregation over Euclidean distances with constant key norms, so its score omits a -|k|^2 term and is blind to key magnitude. This predicts that any router whose metric is ill-matched to its representations should compensate, by concentrating its routing and collapsing the routed representations. We test it on routers that score and aggregate over different axes: softmax attention over tokens (nine pretrained transformers), graph attention over nodes, a selective state-space model and a recurrent mixer over time, and learned residuals over depth. All develop the same signature, and two within-model ablations show it is caused by the routing mechanism rather than by incidental dynamics. The form is contingent, set by the strength of the positional brake each router carries alongside its content score; we sweep that brake and move the onset across its whole range. The mechanism is not contingent, and it does not require norm stratification: a router with norm-normalized keys concentrates just the same. We do not claim these models implement Riemannian geometry; the geometric view is a diagnostic that names the inadequacy of the flat, norm-blind metric.

Existing Large Vision-Language Models (LVLMs) exhibit insufficient visual attention, leading to hallucinations. To alleviate this problem, some previous studies adjust and amplify visual attention. These methods present a limitation that boosting attention for all visual tokens inevitably increases attention to task irrelevant tokens. To tackle this challenge, we propose a training free attentional intervention algorithm to enhance the attention of task-relevant tokens based on the argument that task-relevant tokens generally demonstrate high visual-textual similarities. Specifically, the vision-text cross-attention submatrices, which represent visual-textual correlations, are extracted to construct the reweighting matrices to reallocate attention. Besides, to enhance the contribution of visual tokens, we inject visual attention values into the beam search decoding to identify solutions with higher visual attention. Extensive experiments demonstrate that this method significantly reduces hallucinations across mainstream LVLMs, while preserving the accuracy and coherence of generated content.

Attention is the dominant source of latency during long-context LLM inference, an increasingly popular workload with reasoning models and RAG. We propose Kascade, a training-free sparse attention method that leverages known observations such as 1) post-softmax attention is intrinsically sparse, and 2) the identity of high-weight keys is stable across nearby layers. Kascade computes exact Top-k indices in a small set of anchor layers, then reuses those indices in intermediate reuse layers. The anchor layers are selected algorithmically, via a dynamic-programming objective that maximizes cross-layer similarity over a development set, allowing easy deployment across models. The method incorporates efficient implementation constraints (e.g. tile-level operations), across both prefill and decode attention. The Top-k selection and reuse in Kascade is head-aware and we show in our experiments that this is critical for high accuracy. Kascade achieves up to 4.1x speedup in decode attention and 2.2x speedup in prefill attention over FlashAttention-3 baseline on H100 GPUs while closely matching dense attention accuracy on long-context benchmarks such as LongBench and AIME-24.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various applications, but their performance on long-context tasks is often limited by the computational complexity of attention mechanisms. We introduce a novel approach to accelerate attention computation in LLMs, particularly for long-context scenarios. We leverage the inherent sparsity within attention mechanisms, both in conventional Softmax attention and ReLU attention (with ReLU^α activation, αin N_+), to significantly reduce the running time complexity. Our method employs a Half-Space Reporting (HSR) data structure to identify non-zero or ``massively activated'' entries in the attention matrix. We present theoretical analyses for two key scenarios: generation decoding and prompt prefilling. Our approach achieves a running time of O(mn^{4/5}) significantly faster than the naive approach O(mn) for generation decoding, where n is the context length, m is the query length, and d is the hidden dimension. We can also reduce the running time for prompt prefilling from O(mn) to O(mn^{1 - 1 / lfloor d/2rfloor} + mn^{4/5}). Our method introduces only provably negligible error for Softmax attention. This work represents a significant step towards enabling efficient long-context processing in LLMs.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

Following the success of dot-product attention in Transformers, numerous approximations have been recently proposed to address its quadratic complexity with respect to the input length. However, all approximations thus far have ignored the contribution of the value vectors to the quality of approximation. In this work, we argue that research efforts should be directed towards approximating the true output of the attention sub-layer, which includes the value vectors. We propose a value-aware objective, and show theoretically and empirically that an optimal approximation of a value-aware objective substantially outperforms an optimal approximation that ignores values, in the context of language modeling. Moreover, we show that the choice of kernel function for computing attention similarity can substantially affect the quality of sparse approximations, where kernel functions that are less skewed are more affected by the value vectors.

Linear attentions have shown potential for improving Transformer efficiency, reducing attention's quadratic complexity to linear in sequence length. This holds exciting promise for (1) training linear Transformers from scratch, (2) "finetuned-conversion" of task-specific Transformers into linear versions that recover task performance, and (3) "pretrained-conversion" of Transformers such as large language models into linear versions finetunable on downstream tasks. However, linear attentions often underperform standard softmax attention in quality. To close this performance gap, we find prior linear attentions lack key properties of softmax attention tied to good performance: low-entropy (or "spiky") weights and dot-product monotonicity. We further observe surprisingly simple feature maps that retain these properties and match softmax performance, but are inefficient to compute in linear attention. We thus propose Hedgehog, a learnable linear attention that retains the spiky and monotonic properties of softmax attention while maintaining linear complexity. Hedgehog uses simple trainable MLPs to produce attention weights mimicking softmax attention. Experiments show Hedgehog recovers over 99% of standard Transformer quality in train-from-scratch and finetuned-conversion settings, outperforming prior linear attentions up to 6 perplexity points on WikiText-103 with causal GPTs, and up to 8.7 GLUE score points on finetuned bidirectional BERTs. Hedgehog also enables pretrained-conversion. Converting a pretrained GPT-2 into a linear attention variant achieves state-of-the-art 16.7 perplexity on WikiText-103 for 125M subquadratic decoder models. We finally turn a pretrained Llama-2 7B into a viable linear attention Llama. With low-rank adaptation, Hedgehog-Llama2 7B achieves 28.1 higher ROUGE-1 points over the base standard attention model, where prior linear attentions lead to 16.5 point drops.

Transformer models have achieved remarkable results in a wide range of applications. However, their scalability is hampered by the quadratic time and memory complexity of the self-attention mechanism concerning the sequence length. This limitation poses a substantial obstacle when dealing with long documents or high-resolution images. In this work, we study the self-attention mechanism by analyzing the distribution of the attention matrix and its concentration ability. Furthermore, we propose instruments to measure these quantities and introduce a novel self-attention mechanism, Linear Log-Normal Attention, designed to emulate the distribution and concentration behavior of the original self-attention. Our experimental results on popular natural language benchmarks reveal that our proposed Linear Log-Normal Attention outperforms other linearized attention alternatives, offering a promising avenue for enhancing the scalability of transformer models. Our code is available in supplementary materials.

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

Large Language Models (LLMs) face efficiency bottlenecks due to the quadratic complexity of the attention mechanism when processing long contexts. Sparse attention methods offer a promising solution, but existing approaches often suffer from incomplete effective context and/or require complex implementation of pipeline. We present a comprehensive analysis of sparse attention for autoregressive LLMs from the respective of receptive field, recognize the suboptimal nature of existing methods for expanding the receptive field, and introduce PowerAttention, a novel sparse attention design that facilitates effective and complete context extension through the theoretical analysis. PowerAttention achieves exponential receptive field growth in d-layer LLMs, allowing each output token to attend to 2^d tokens, ensuring completeness and continuity of the receptive field. Experiments demonstrate that PowerAttention outperforms existing static sparse attention methods by 5sim 40%, especially on tasks demanding long-range dependencies like Passkey Retrieval and RULER, while maintaining a comparable time complexity to sliding window attention. Efficiency evaluations further highlight PowerAttention's superior speedup in both prefilling and decoding phases compared with dynamic sparse attentions and full attention (3.0times faster on 128K context), making it a highly effective and user-friendly solution for processing long sequences in LLMs.

We introduce Transformer-VQ, a decoder-only transformer computing softmax-based dense self-attention in linear time. Transformer-VQ's efficient attention is enabled by vector-quantized keys and a novel caching mechanism. In large-scale experiments, Transformer-VQ is shown highly competitive in quality, with strong results on Enwik8 (0.99 bpb), PG-19 (26.6 ppl), and ImageNet64 (3.16 bpb). Code: https://github.com/transformer-vq/transformer_vq

Self-attention has the promise of improving computer vision systems due to parameter-independent scaling of receptive fields and content-dependent interactions, in contrast to parameter-dependent scaling and content-independent interactions of convolutions. Self-attention models have recently been shown to have encouraging improvements on accuracy-parameter trade-offs compared to baseline convolutional models such as ResNet-50. In this work, we aim to develop self-attention models that can outperform not just the canonical baseline models, but even the high-performing convolutional models. We propose two extensions to self-attention that, in conjunction with a more efficient implementation of self-attention, improve the speed, memory usage, and accuracy of these models. We leverage these improvements to develop a new self-attention model family, HaloNets, which reach state-of-the-art accuracies on the parameter-limited setting of the ImageNet classification benchmark. In preliminary transfer learning experiments, we find that HaloNet models outperform much larger models and have better inference performance. On harder tasks such as object detection and instance segmentation, our simple local self-attention and convolutional hybrids show improvements over very strong baselines. These results mark another step in demonstrating the efficacy of self-attention models on settings traditionally dominated by convolutional models.

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with H heads, dimension d, and context size n < d, featuring Theta(Hd^2) parameters, can memorize Omega(Hn) examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator's saturation property. We validate our findings through experiments on synthetic data.

Linear attention has emerged as a viable alternative to softmax attention by reducing complexity from quadratic to linear in sequence length. To preserve two fundamental properties of softmax, non-negativity and entropy reduction, current works employ various linearly separatable kernel functions with L1 normalization instead of softmax operator. However, query norms are neglected by the normalization operation in linear attention, such degradation heavily leads to an entropy gap. Meanwhile, existing works inhibit negative values of query and key vectors resulting in a missing inner-product interactions after being mapped. To address these dual challenges, we propose a novel Norm-Aware Linear Attention mechanism serving to restore norm-guided dynamic spikiness and recover kernel-perturbed norm distributions. Specifically, we first decouple query and key matrices into two components: norm and direction, to achieve norm-aware spikiness control and norm consistency, respectively. We mathematically reveal that the extent of entropy reduction varies with the query norm in softmax normalization, motivating a query-norm aware kernel function for dynamic control over entropy reduction. Furthermore, to ensure norm consistency and enforce non-negativity constraints, we employ a norm-preserving mapping to project all elements of the angular matrix into positive values, leveraging cosine similarity to inhibit dimensions with opposite directions. We conduct extensive experiments demonstrating that the NaLaFormer improves performance on vision and language tasks, enhancing both expressiveness and efficiency by up to 4.2\%.

Recently, there has been growing interest in collecting reasoning-intensive pretraining data to improve LLMs' complex reasoning ability. Prior approaches typically rely on supervised classifiers to identify such data, which requires labeling by humans or LLMs, often introducing domain-specific biases. Due to the attention heads being crucial to in-context reasoning, we propose AttentionInfluence, a simple yet effective, training-free method without supervision signal. Our approach enables a small pretrained language model to act as a strong data selector through a simple attention head masking operation. Specifically, we identify retrieval heads and compute the loss difference when masking these heads. We apply AttentionInfluence to a 1.3B-parameter dense model to conduct data selection on the SmolLM corpus of 241B tokens, and mix the SmolLM corpus with the selected subset comprising 73B tokens to pretrain a 7B-parameter dense model using 1T training tokens and WSD learning rate scheduling. Our experimental results demonstrate substantial improvements, ranging from 1.4pp to 3.5pp, across several knowledge-intensive and reasoning-heavy benchmarks (i.e., MMLU, MMLU-Pro, AGIEval-en, GSM8K, and HumanEval). This demonstrates an effective weak-to-strong scaling property, with small models improving the final performance of larger models-offering a promising and scalable path for reasoning-centric data selection.

We revisit the I/O complexity of attention in large language models. Given query-key-value matrices Q,K,VinR^{ntimes d}, and a machine with fast memory size M, the goal is to compute the "attention matrix" A=softmax(Q K ^{top}/d) V with the minimal number of data transfers between fast and slow memory. Existing methods in the literature, most notably FlashAttention and its variants, incur an I/O cost that depends quadratically on n, while a trivial lower bound only requires Ω(nd) I/O's to read the inputs and write the output. In this work, we present a technique for computing attention where the I/O cost only depends almost-linearly on n in most parameter regimes. This is achieved by developing I/O-efficient algorithms inspired by the recent approximate attention framework of Alman and Song. We also prove corresponding lower bounds in each parameter regime to show that our algorithms are indeed close to I/O-optimal.

Transformer-based models have emerged as one of the most widely used architectures for natural language processing, natural language generation, and image generation. The size of the state-of-the-art models has increased steadily reaching billions of parameters. These huge models are memory hungry and incur significant inference latency even on cutting edge AI-accelerators, such as GPUs. Specifically, the time and memory complexity of the attention operation is quadratic in terms of the total context length, i.e., prompt and output tokens. Thus, several optimizations such as key-value tensor caching and FlashAttention computation have been proposed to deliver the low latency demands of applications relying on such large models. However, these techniques do not cater to the computationally distinct nature of different phases during inference. To that end, we propose LeanAttention, a scalable technique of computing self-attention for the token-generation phase (decode-phase) of decoder-only transformer models. LeanAttention enables scaling the attention mechanism implementation for the challenging case of long context lengths by re-designing the execution flow for the decode-phase. We identify that the associative property of online softmax can be treated as a reduction operation thus allowing us to parallelize the attention computation over these large context lengths. We extend the "stream-K" style reduction of tiled calculation to self-attention to enable parallel computation resulting in an average of 2.6x attention execution speedup over FlashAttention-2 and up to 8.33x speedup for 512k context lengths.

The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures -- Mamba-2 and Gated DeltaNet -- and find they perform well compared to their linear-time variants.

Large Vision-Language Models (LVLMs) have recently demonstrated strong multimodal understanding, yet their fine-grained visual perception is often constrained by low input resolutions. A common remedy is to partition high-resolution images into multiple sub-images for separate encoding, but this approach drastically inflates the number of visual tokens and introduces prohibitive inference overhead. To overcome this challenge, we propose Pyramid Token Pruning (PTP), a training-free strategy that hierarchically integrates bottom-up visual saliency at both region and token levels with top-down instruction-guided relevance. Inspired by human visual cognition, PTP selectively preserves more tokens from salient regions while further emphasizing those most relevant to task instructions. Extensive experiments on 13 diverse benchmarks show that PTP substantially reduces computational cost, memory usage, and inference latency, with negligible performance degradation.

In deep learning theory, the covariance matrix of the representations serves as a proxy to examine the network's trainability. Motivated by the success of Transformers, we study the covariance matrix of a modified Softmax-based attention model with skip connections in the proportional limit of infinite-depth-and-width. We show that at initialization the limiting distribution can be described by a stochastic differential equation (SDE) indexed by the depth-to-width ratio. To achieve a well-defined stochastic limit, the Transformer's attention mechanism is modified by centering the Softmax output at identity, and scaling the Softmax logits by a width-dependent temperature parameter. We examine the stability of the network through the corresponding SDE, showing how the scale of both the drift and diffusion can be elegantly controlled with the aid of residual connections. The existence of a stable SDE implies that the covariance structure is well-behaved, even for very large depth and width, thus preventing the notorious issues of rank degeneracy in deep attention models. Finally, we show, through simulations, that the SDE provides a surprisingly good description of the corresponding finite-size model. We coin the name shaped Transformer for these architectural modifications.

The quadratic computational complexity of the attention mechanism in current Large Language Models (LLMs) renders inference with long contexts prohibitively expensive. To address this challenge, various approaches aim to retain critical portions of the context to optimally approximate Full Attention (FA) through Key-Value (KV) compression or Sparse Attention (SA), enabling the processing of virtually unlimited text lengths in a streaming manner. However, these methods struggle to achieve performance levels comparable to FA, particularly in retrieval tasks. In this paper, our analysis of attention head patterns reveals that LLMs' attention distributions show strong local correlations, naturally reflecting a chunking mechanism for input context. We propose Ltri-LLM framework, which divides KVs into spans, stores them in an offline index, and retrieves the relevant KVs into memory for various queries. Experimental results on popular long text benchmarks show that Ltri-LLM can achieve performance close to FA while maintaining efficient, streaming-based inference.

The attention module, which is a crucial component in Transformer, cannot scale efficiently to long sequences due to its quadratic complexity. Many works focus on approximating the dot-then-exponentiate softmax function in the original attention, leading to sub-quadratic or even linear-complexity Transformer architectures. However, we show that these methods cannot be applied to more powerful attention modules that go beyond the dot-then-exponentiate style, e.g., Transformers with relative positional encoding (RPE). Since in many state-of-the-art models, relative positional encoding is used as default, designing efficient Transformers that can incorporate RPE is appealing. In this paper, we propose a novel way to accelerate attention calculation for Transformers with RPE on top of the kernelized attention. Based upon the observation that relative positional encoding forms a Toeplitz matrix, we mathematically show that kernelized attention with RPE can be calculated efficiently using Fast Fourier Transform (FFT). With FFT, our method achieves O(nlog n) time complexity. Interestingly, we further demonstrate that properly using relative positional encoding can mitigate the training instability problem of vanilla kernelized attention. On a wide range of tasks, we empirically show that our models can be trained from scratch without any optimization issues. The learned model performs better than many efficient Transformer variants and is faster than standard Transformer in the long-sequence regime.

Transformers have recently gained significant attention in the computer vision community. However, the lack of scalability of self-attention mechanisms with respect to image size has limited their wide adoption in state-of-the-art vision backbones. In this paper we introduce an efficient and scalable attention model we call multi-axis attention, which consists of two aspects: blocked local and dilated global attention. These design choices allow global-local spatial interactions on arbitrary input resolutions with only linear complexity. We also present a new architectural element by effectively blending our proposed attention model with convolutions, and accordingly propose a simple hierarchical vision backbone, dubbed MaxViT, by simply repeating the basic building block over multiple stages. Notably, MaxViT is able to ''see'' globally throughout the entire network, even in earlier, high-resolution stages. We demonstrate the effectiveness of our model on a broad spectrum of vision tasks. On image classification, MaxViT achieves state-of-the-art performance under various settings: without extra data, MaxViT attains 86.5% ImageNet-1K top-1 accuracy; with ImageNet-21K pre-training, our model achieves 88.7% top-1 accuracy. For downstream tasks, MaxViT as a backbone delivers favorable performance on object detection as well as visual aesthetic assessment. We also show that our proposed model expresses strong generative modeling capability on ImageNet, demonstrating the superior potential of MaxViT blocks as a universal vision module. The source code and trained models will be available at https://github.com/google-research/maxvit.

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer architecture is a critical component of LLMs, as it allows the model to selectively focus on specific input parts. The softmax unit, which is a key part of the attention mechanism, normalizes the attention scores. Hence, the performance of LLMs in various NLP tasks depends significantly on the crucial role played by the attention mechanism with the softmax unit. In-context learning, as one of the celebrated abilities of recent LLMs, is an important concept in querying LLMs such as ChatGPT. Without further parameter updates, Transformers can learn to predict based on few in-context examples. However, the reason why Transformers becomes in-context learners is not well understood. Recently, several works [ASA+22,GTLV22,ONR+22] have studied the in-context learning from a mathematical perspective based on a linear regression formulation min_x| Ax - b |_2, which show Transformers' capability of learning linear functions in context. In this work, we study the in-context learning based on a softmax regression formulation min_{x} | langle exp(Ax), {bf 1}_n rangle^{-1} exp(Ax) - b |_2 of Transformer's attention mechanism. We show the upper bounds of the data transformations induced by a single self-attention layer and by gradient-descent on a ell_2 regression loss for softmax prediction function, which imply that when training self-attention-only Transformers for fundamental regression tasks, the models learned by gradient-descent and Transformers show great similarity.

The attention module is the key component in Transformers. While the global attention mechanism offers high expressiveness, its excessive computational cost restricts its applicability in various scenarios. In this paper, we propose a novel attention paradigm, Agent Attention, to strike a favorable balance between computational efficiency and representation power. Specifically, the Agent Attention, denoted as a quadruple (Q, A, K, V), introduces an additional set of agent tokens A into the conventional attention module. The agent tokens first act as the agent for the query tokens Q to aggregate information from K and V, and then broadcast the information back to Q. Given the number of agent tokens can be designed to be much smaller than the number of query tokens, the agent attention is significantly more efficient than the widely adopted Softmax attention, while preserving global context modelling capability. Interestingly, we show that the proposed agent attention is equivalent to a generalized form of linear attention. Therefore, agent attention seamlessly integrates the powerful Softmax attention and the highly efficient linear attention. Extensive experiments demonstrate the effectiveness of agent attention with various vision Transformers and across diverse vision tasks, including image classification, object detection, semantic segmentation and image generation. Notably, agent attention has shown remarkable performance in high-resolution scenarios, owning to its linear attention nature. For instance, when applied to Stable Diffusion, our agent attention accelerates generation and substantially enhances image generation quality without any additional training. Code is available at https://github.com/LeapLabTHU/Agent-Attention.

The quadratic cost of softmax attention limits Transformer scalability in high-resolution vision. We introduce Infinite Self-Attention (InfSA), a spectral reformulation that treats each attention layer as a diffusion step on a content-adaptive token graph, accumulating multi-hop interactions through a discounted Neumann series over attention matrices. This links self-attention to classical graph centrality (Katz, PageRank, eigenvector centrality) for interpretable token weighting. We also show the Neumann kernel equals the fundamental matrix of an absorbing Markov chain, so a token's centrality is its expected number of random-walk visits before absorption. We then propose Linear-InfSA, a linear-time variant that approximates the principal eigenvector of the implicit attention operator without forming the full attention matrix. It keeps an auxiliary state of fixed size proportional to per-head dimension dh (independent of sequence length N), is drop-in compatible with Vision Transformers, and supports stable training at 4096 by 4096 and inference at 9216 by 9216 (about 332k tokens). In a 4-layer ViT (53.5M parameters, 59 GFLOPs at 224 by 224), Linear-InfSA reaches 84.7% top-1 on ImageNet-1K, a +3.2 point architectural gain over an equal-depth softmax ViT trained with the same recipe. On ImageNet-V2, InfViT variants outperform all compared baselines (up to 79.8% vs 76.8%), indicating robustness under distribution shift. On an A100 40GB GPU, Linear-InfViT runs at 231 images/s and 0.87 J/image (13x better throughput and energy than equal-depth ViT) and is the only tested model to complete 9216 by 9216 inference without out-of-memory. The linear approximation closely matches the dominant eigenvector of the quadratic operator (cosine 0.985).

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.

Attention mechanisms have become ubiquitous in NLP. Recent architectures, notably the Transformer, learn powerful context-aware word representations through layered, multi-headed attention. The multiple heads learn diverse types of word relationships. However, with standard softmax attention, all attention heads are dense, assigning a non-zero weight to all context words. In this work, we introduce the adaptively sparse Transformer, wherein attention heads have flexible, context-dependent sparsity patterns. This sparsity is accomplished by replacing softmax with alpha-entmax: a differentiable generalization of softmax that allows low-scoring words to receive precisely zero weight. Moreover, we derive a method to automatically learn the alpha parameter -- which controls the shape and sparsity of alpha-entmax -- allowing attention heads to choose between focused or spread-out behavior. Our adaptively sparse Transformer improves interpretability and head diversity when compared to softmax Transformers on machine translation datasets. Findings of the quantitative and qualitative analysis of our approach include that heads in different layers learn different sparsity preferences and tend to be more diverse in their attention distributions than softmax Transformers. Furthermore, at no cost in accuracy, sparsity in attention heads helps to uncover different head specializations.

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

Training causal transformers at extreme sequence lengths is bottlenecked by the quadratic time and memory of scaled dot-product attention (SDPA). In this work, we propose Lighthouse Attention, a training-only symmetrical selection-based hierarchical attention algorithm that wraps around ordinary SDPA and can be easily removed towards the end of the training. Our hierarchical selection is also gradient-free, which exempts us from dealing with a complicated and potentially inefficient backward pass kernel. Our contribution is three-fold: (i) A subquadratic hierarchical pre- and post-processing step that does adaptive compression and decompression of the sequence. (ii) A symmetrical compression strategy that pools queries, keys and values at the same time, while preserving left-to-right causality, which greatly improves parallelism. (iii) A two stage training approach which we pre-train for the majority of the time with Lighthouse Attention and recover a full attention model at the end with a short training. We run preliminary small scale LLM pre-training experiments that show the effectiveness of our method compared to full attention training with all other settings matched, where we achieve a faster total training time and lower final loss after the recovery phase. Full code is available at: https://github.com/ighoshsubho/lighthouse-attention

Recent advances in transformer-based Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their quadratic computational complexity concerning sequence length remains a significant bottleneck for processing long documents. As a result, many efforts like sparse attention and state space models have been proposed to improve the efficiency of LLMs over long sequences. Though effective, these approaches compromise the performance or introduce structural complexity. This calls for a simple yet efficient model that preserves the fundamental Transformer architecture. To this end, we introduce SWAT, which enables efficient long-context handling via Sliding Window Attention Training. This paper first attributes the inefficiency of Transformers to the attention sink phenomenon resulting from the high variance of softmax operation. Then, we replace softmax with the sigmoid function and utilize a balanced ALiBi and Rotary Position Embedding for efficient information compression and retention. Experiments demonstrate that SWAT achieves SOTA performance compared with state-of-the-art linear recurrent architectures on eight benchmarks. Code is available at https://anonymous.4open.science/r/SWAT-attention.

The Large Vision-Language Model (LVLM) integrates computer vision and natural language processing techniques, offering substantial application potential. However, these models demand extensive resources during inference. Adaptive attention techniques can dynamically reduce computational redundancy and thus improve efficiency. Although current adaptive attention methods significantly reduce the memory requirements of Transformer-based language models, they are not tailored for LVLMs. We observe that LVLMs generate responses from both remote image tokens and local text tokens, and different modalities have different attention patterns. This observation inspires us to manage the attention for each modality separately. Specifically, for visual input, we store the cache of potentially useful information but only compute the most critical parts. For language input, we care more about local information. Based on our observation and analysis of vision-language attention patterns, we develop A-VL, a plug-and-play adaptive attention tailored for LVLM inference. Extensive evaluations on three vision-language tasks and five datasets show the effectiveness of our designs. Our approach A-VL outperforms existing adaptive attention methods in reducing memory usage and computational load without compromising performance.

Convolutional neural networks have allowed remarkable advances in single image super-resolution (SISR) over the last decade. Among recent advances in SISR, attention mechanisms are crucial for high-performance SR models. However, the attention mechanism remains unclear on why and how it works in SISR. In this work, we attempt to quantify and visualize attention mechanisms in SISR and show that not all attention modules are equally beneficial. We then propose attention in attention network (A^2N) for more efficient and accurate SISR. Specifically, A^2N consists of a non-attention branch and a coupling attention branch. A dynamic attention module is proposed to generate weights for these two branches to suppress unwanted attention adjustments dynamically, where the weights change adaptively according to the input features. This allows attention modules to specialize to beneficial examples without otherwise penalties and thus greatly improve the capacity of the attention network with few parameters overhead. Experimental results demonstrate that our final model A^2N could achieve superior trade-off performances comparing with state-of-the-art networks of similar sizes. Codes are available at https://github.com/haoyuc/A2N.

Distilling pretrained softmax attention Transformers into more efficient hybrid architectures that interleave softmax and linear attention layers is a promising approach for improving the inference efficiency of LLMs without requiring expensive pretraining from scratch. A critical factor in the conversion process is layer selection, i.e., deciding on which layers to convert to linear attention variants. This paper describes a simple and efficient recipe for layer selection that uses layer importance scores derived from a small amount of training on generic text data. Once the layers have been selected we use a recent pipeline for the distillation process itself \citep[RADLADS;][]{goldstein2025radlads}, which consists of attention weight transfer, hidden state alignment, KL-based distribution matching, followed by a small amount of finetuning. We find that this approach is more effective than existing approaches for layer selection, including heuristics that uniformly interleave linear attentions based on a fixed ratio, as well as more involved approaches that rely on specialized diagnostic datasets.

To address the high resolution of image pixels, the Swin Transformer introduces window attention. This mechanism divides an image into non-overlapping windows and restricts attention computation to within each window, significantly enhancing computational efficiency. To further optimize this process, one might consider replacing standard attention with flash attention, which has proven to be more efficient in language models. However, a direct substitution is ineffective. Flash attention is designed for long sequences, whereas window attention deals with shorter sequences but must handle numerous of them in parallel. In this report, we present an optimized solution called Flash Window Attention, tailored specifically for window attention. Flash Window Attention improves attention computation efficiency by up to 300% and enhances end-to-end runtime efficiency by up to 30%. Our code is available online.

Transformer-based large language models (LLMs) have achieved remarkable success, yet their standard attention mechanism incurs quadratic computation and memory costs with respect to sequence length, posing a major bottleneck for long-context training. Prior work tackles this challenge along two directions: (1) kernel-level optimizations, which accelerate dense and sparse attention operators; and (2) module-level strategies, often referred to as distributed attention or context parallel training, which scale attention across multiple devices. However, systematic evaluation still remains limited: operator-level comparisons are often incomplete, while context parallel strategies are typically framework-specific, with unclear performance analysis across contexts. To address these gaps, we propose a unified benchmark that integrates representative attention kernels and context parallel mechanisms with a modular and extensible interface for evaluation. The benchmark evaluates methods along two critical dimensions: (1) attention mask patterns, which strongly affect efficiency, scalability, and usability, and (2) sequence length and distributed scale, which determine performance under extreme long-context training. Through comprehensive experiments on the cluster of up to 96 GPUs, our benchmark enables reproducible comparisons, highlights method-specific trade-offs, and provides practical guidance for designing and deploying attention mechanisms in long-context LLM training.

Transformer-based architectures have become the prevailing backbone of large language models. However, the quadratic time and memory complexity of self-attention remains a fundamental obstacle to efficient long-context modeling. To address this limitation, recent research has introduced two principal categories of efficient attention mechanisms. Linear attention methods achieve linear complexity through kernel approximations, recurrent formulations, or fastweight dynamics, thereby enabling scalable inference with reduced computational overhead. Sparse attention techniques, in contrast, limit attention computation to selected subsets of tokens based on fixed patterns, block-wise routing, or clustering strategies, enhancing efficiency while preserving contextual coverage. This survey provides a systematic and comprehensive overview of these developments, integrating both algorithmic innovations and hardware-level considerations. In addition, we analyze the incorporation of efficient attention into largescale pre-trained language models, including both architectures built entirely on efficient attention and hybrid designs that combine local and global components. By aligning theoretical foundations with practical deployment strategies, this work aims to serve as a foundational reference for advancing the design of scalable and efficient language models.

Inspired by recent work in machine translation and object detection, we introduce an attention based model that automatically learns to describe the content of images. We describe how we can train this model in a deterministic manner using standard backpropagation techniques and stochastically by maximizing a variational lower bound. We also show through visualization how the model is able to automatically learn to fix its gaze on salient objects while generating the corresponding words in the output sequence. We validate the use of attention with state-of-the-art performance on three benchmark datasets: Flickr8k, Flickr30k and MS COCO.

Human attention modelling has proven, in recent years, to be particularly useful not only for understanding the cognitive processes underlying visual exploration, but also for providing support to artificial intelligence models that aim to solve problems in various domains, including image and video processing, vision-and-language applications, and language modelling. This survey offers a reasoned overview of recent efforts to integrate human attention mechanisms into contemporary deep learning models and discusses future research directions and challenges. For a comprehensive overview on the ongoing research refer to our dedicated repository available at https://github.com/aimagelab/awesome-human-visual-attention.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.