Daily Papers

We present IMU-1, a 430M-parameter language model trained on 72B tokens that approaches the benchmark performance of models trained on 56x more data. We describe a validated training recipe combining recent architectural interventions (QK-norm attention, per-head gating, value residuals, LayerNorm scaling) with optimization advances (NorMuon with cautious weight decay, muP parametrization) and a three-stage training schedule with post-hoc checkpoint EMA. We provide ablations for each component and release code, weights and data to enable reproduction: https://huggingface.co/thepowerfuldeez/imu1_base

Stability of neural network weights is critical when training transformer models. The query and key weights are particularly problematic, as they tend to grow large without any intervention. Applying normalization to queries and keys, known as `QK norm', fixes stability issues in practice, but is not always applicable. For example, QK norm is not compatible with Multi Latent Attention (MLA) because QK norm requires full materialization of queries and keys during inference, which is not done in MLA. In this paper we suggest that controlling the changes to logits is important for stability. We show that these changes are controllable by assigning parameter-dependent learning rates to the query and key weights. We find that our cheap intervention allows us to increase the base learning rate of the network, outperform other methods in the MLA setting, and achieve performance competitive with QK norm when using Multi-head Attention.

Low-bit attention, such as SageAttention, has emerged as an effective approach for accelerating model inference, but its applicability to training remains poorly understood. In prior work, we introduced SageBwd, a trainable INT8 attention that quantizes six of seven attention matrix multiplications while preserving fine-tuning performance. However, SageBwd exhibited a persistent performance gap to full-precision attention (FPA) during pre-training. In this work, we investigate why this gap occurs and demonstrate that SageBwd matches full-precision attention during pretraining. Through experiments and theoretical analysis, we reach a few important insights and conclusions: (i) QK-norm is necessary for stable training at large tokens per step, (ii) quantization errors primarily arise from the backward-pass score gradient dS, (iii) reducing tokens per step enables SageBwd to match FPA performance in pre-training, and (iv) K-smoothing remains essential for training stability, while Q-smoothing provides limited benefit during pre-training.

Long-context large language models (LLMs) have achieved remarkable advancements, driven by techniques like Rotary Position Embedding (RoPE) (Su et al., 2023) and its extensions (Chen et al., 2023; Liu et al., 2024c; Peng et al., 2023). By adjusting RoPE parameters and incorporating training data with extended contexts, we can train performant models with considerably longer input sequences. However, existing RoPE-based methods exhibit performance limitations when applied to extended context lengths. This paper presents a comprehensive analysis of various attention mechanisms, including RoPE, No Positional Embedding (NoPE), and Query-Key Normalization (QK-Norm), identifying their strengths and shortcomings in long-context modeling. Our investigation identifies distinctive attention patterns in these methods and highlights their impact on long-context performance, providing valuable insights for architectural design. Building on these findings, we propose a novel architectural based on a hybrid attention mechanism that not only surpasses conventional RoPE-based transformer models in long context tasks but also achieves competitive performance on benchmarks requiring shorter context lengths.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

Low-resource language translation is a challenging but socially valuable NLP task. Building on recent work adapting the Transformer's normalization to this setting, we propose QKNorm, a normalization technique that modifies the attention mechanism to make the softmax function less prone to arbitrary saturation without sacrificing expressivity. Specifically, we apply ell_2 normalization along the head dimension of each query and key matrix prior to multiplying them and then scale up by a learnable parameter instead of dividing by the square root of the embedding dimension. We show improvements averaging 0.928 BLEU over state-of-the-art bilingual benchmarks for 5 low-resource translation pairs from the TED Talks corpus and IWSLT'15.

Feed-forward networks hold two thirds of a transformer's non-embedding parameters, yet the architecture has not received a necessity test that controls parameters, compute, and depth at once. We pretrain attention-only decoder transformers (Simple Attention Networks, SANs) against standard transformers matched separately for parameter count, training FLOPs, and depth (2 to 48 layers), for up to 105B tokens at 6M to 87M parameters. Deleting feed-forward layers in place is costly: the standard transformer leads by 0.47 nats at matched depth and 0.26 nats at matched FLOPs. Reallocating the freed budget into attention depth closes the gap: at matched parameters the difference is 0.006 nats (0.27 percent of loss), reproducible to one part in ten thousand across seed pairs, shrinking across 5B, 30B, and 105B budgets, and holding near 0.02 nats across a 29x size range. Three measurements localize the remaining gap to parametric recall: attention-only models are better on context-grounded answers and worse where knowledge must come from weights. Weight spectra show why: routing matrices (Q/K) crystallize early, content matrices accumulate rank slowly, and removing feed-forward layers relocates this accumulation to the attention output projection. QK-normalization, not feed-forward layers or residual gating, keeps 48-layer attention-only stacks trainable. The deficit concentrates on low-context query prediction and localizes there entirely by the largest budget. A pre-registered test confirms the account: it predicts a 0.02 to 0.05 nat gap on knowledge-dense web text; a matched pair trained on fineweb-edu measures 0.040. Within the tested regime, attention does the rest.

Despite the central role of attention heads in Transformers, we lack tools to understand why a model attends to a particular token. To address this, we study the query-key (QK) space -- the bilinear joint embedding space between queries and keys. We present a contrastive covariance method to decompose the QK space into low-rank, human-interpretable components. It is when features in keys and queries align in these low-rank subspaces that high attention scores are produced. We first study our method both analytically and empirically in a simplified setting. We then apply our method to large language models to identify human-interpretable QK subspaces for categorical semantic features and binding features. Finally, we demonstrate how attention scores can be attributed to our identified features.

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\%.

As the length of input text increases, the key-value (KV) cache in LLMs imposes prohibitive GPU memory costs and limits long-context inference on resource constrained devices. Existing approaches, such as KV quantization and pruning, reduce memory usage but suffer from numerical precision loss or suboptimal retention of key-value pairs. In this work, Low Rank Query and Key attention (LRQK) is introduced, a two-stage framework that jointly decomposes full-precision query and key matrices into compact rank-\(r\) factors during the prefill stage, and then employs these low-dimensional projections to compute proxy attention scores in \(O(lr)\) time at each decode step. By selecting only the top-\(k\) tokens and a small fixed set of recent tokens, LRQK employs a mixed GPU-CPU cache with a hit-and-miss mechanism where only missing full-precision KV pairs are transferred, thereby preserving exact attention outputs while reducing CPU-GPU data movement. Extensive experiments on the RULER and LongBench benchmarks with LLaMA-3-8B and Qwen2.5-7B demonstrate that LRQK matches or surpasses leading sparse-attention methods in long context settings, while delivering significant memory savings with minimal accuracy loss. Our code is available at https://github.com/tenghuilee/LRQK.

Vision-language models (VLMs) often generate fluent but visually unsupported descriptions, especially by mentioning objects absent from the image. We propose QK Product Steering, a data-free, training-free, and zero-inference-cost weight edit for reducing object hallucination. The method directly edits the per-head query-key product, the operator that produces pre-softmax attention logits, by suppressing a small number of dominant singular modes in selected middle layers. The edited product is then mapped back to the query weights through a closed-form query-only update while keeping shared key weights fixed, making the edit compatible with grouped-query attention. We further decompose the QK product into symmetric and antisymmetric components to distinguish mutual content-similarity patterns from directional attention patterns. Across three GQA-based VLMs, QK Product Steering achieves an average relative CHAIR_s reduction of 4.0%, while matched random-mode controls show negligible change. Interpretability ablations show that the hallucination signal is specific to dominant QK modes and is primarily localized to the symmetric mutual-attention channel. Overall, QK Product Steering offers a simple alternative to decoding-time mitigation, requiring no additional data, fine-tuning, or inference-time overhead while largely preserving general multimodal capability.

Accommodating long sequences efficiently in autoregressive Transformers, especially within an extended context window, poses significant challenges due to the quadratic computational complexity and substantial KV memory requirements inherent in self-attention mechanisms. In this work, we introduce SPARSEK Attention, a novel sparse attention mechanism designed to overcome these computational and memory obstacles while maintaining performance. Our approach integrates a scoring network and a differentiable top-k mask operator, SPARSEK, to select a constant number of KV pairs for each query, thereby enabling gradient-based optimization. As a result, SPARSEK Attention offers linear time complexity and constant memory footprint during generation. Experimental results reveal that SPARSEK Attention outperforms previous sparse attention methods and provides significant speed improvements during both training and inference, particularly in language modeling and downstream tasks. Furthermore, our method can be seamlessly integrated into pre-trained Large Language Models (LLMs) with minimal fine-tuning, offering a practical solution for effectively managing long-range dependencies in diverse applications.

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

Transformers have become the standard solution for various AI tasks, with the query, key, and value (QKV) attention formulation playing a central role. However, the individual contribution of these three projections and the impact of omitting some remain poorly understood. We systematically evaluate three projection sharing constraints: a) Q-K=V (shared key-value), b) Q=K-V (shared query-key), and c) Q=K=V (single projection). The last two variants produce symmetric attention maps; to address this, we also explore asymmetric attention via 2D positional encodings. Through experiments spanning synthetic tasks, vision (MNIST, CIFAR, TinyImageNet, anomaly), and language modeling (300M and 1.2B parameter models on 10B tokens), we discovered that our transformers perform on par or occasionally better than the QKV transformer. In language modeling, Q-K=V projection sharing achieves 50% KV cache reduction with only 3.1% perplexity degradation. Crucially, projection sharing is complementary to head sharing (GQA/MQA): combining Q-K=V with GQA-4 yields 87.5% cache reduction, while Q-K=V + MQA achieves 96.9%, enabling practical on-device inference. We show that Q-K=V preserves quality because keys and values can occupy similar representational spaces and attention operates in a low-rank regime, whereas Q=K-V breaks attention directionality. Our results systematically characterize projection sharing as an underexplored instance of weight tying in attention, with direct, quantifiable inference memory benefits, particularly valuable for edge deployment. The code is publicly available at https://github.com/Brainchip-Inc/Do-Transformers-Need-3-Projections

We propose Keyless Attention, an attention mechanism that eliminates the key projection entirely, operating over queries and values only. This yields a Value-Only Cache that reduces KV cache memory and access overhead by exactly 50% over standard attention, while matching or exceeding standard attention's decode throughput. Beyond efficiency, we introduce Depth-m Attention Factorization: standard attention computes a depth-2 factorization of the attention bilinear form, while Keyless Attention realizes a depth-m instance of this family. At m=3, Keyless Attention matches the projection matrix count of standard attention via a value-space routing matrix that replaces the key projection and introduces a coupling between routing and retrieval. Experiments across five models and four architectures (GPT-2 280M, GPT-2 557M, Pythia 410M, Qwen2 1.5B, and Llama 3.2 1B) show that Keyless Attention matches or outperforms standard QKV attention on perplexity in 4 out of 5 models. On downstream zero-shot evaluation (GPT-2 557M), Keyless Attention outperforms on 4 out of 5 commonsense reasoning benchmarks, while achieving 50% KV cache reduction throughout.

We introduce Sigma, an efficient large language model specialized for the system domain, empowered by a novel architecture including DiffQKV attention, and pre-trained on our meticulously collected system domain data. DiffQKV attention significantly enhances the inference efficiency of Sigma by optimizing the Query (Q), Key (K), and Value (V) components in the attention mechanism differentially, based on their varying impacts on the model performance and efficiency indicators. Specifically, we (1) conduct extensive experiments that demonstrate the model's varying sensitivity to the compression of K and V components, leading to the development of differentially compressed KV, and (2) propose augmented Q to expand the Q head dimension, which enhances the model's representation capacity with minimal impacts on the inference speed. Rigorous theoretical and empirical analyses reveal that DiffQKV attention significantly enhances efficiency, achieving up to a 33.36% improvement in inference speed over the conventional grouped-query attention (GQA) in long-context scenarios. We pre-train Sigma on 6T tokens from various sources, including 19.5B system domain data that we carefully collect and 1T tokens of synthesized and rewritten data. In general domains, Sigma achieves comparable performance to other state-of-arts models. In the system domain, we introduce the first comprehensive benchmark AIMicius, where Sigma demonstrates remarkable performance across all tasks, significantly outperforming GPT-4 with an absolute improvement up to 52.5%.

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.

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.

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.

A standard way to evaluate the abilities of LLM involves presenting a multiple-choice question and selecting the option with the highest logit as the model's predicted answer. However, such a format for evaluating LLMs has limitations, since even if the model knows the correct answer, it may struggle to select the corresponding letter simply due to difficulties in following this rigid format. To address this, we introduce new scores that better capture and reveal model's underlying knowledge: the Query-Key Score (QK-score), derived from the interaction between query and key representations in attention heads, and the Attention Score, based on attention weights. These scores are extracted from specific select-and-copy heads, which show consistent performance across popular Multi-Choice Question Answering (MCQA) datasets. Based on these scores, our method improves knowledge extraction, yielding up to 16\% gain for LLaMA2-7B and up to 10\% for larger models on popular MCQA benchmarks. At the same time, the accuracy on a simple synthetic dataset, where the model explicitly knows the right answer, increases by almost 60\%, achieving nearly perfect accuracy, therefore demonstrating the method's efficiency in mitigating MCQA format limitations. To support our claims, we conduct experiments on models ranging from 7 billion to 70 billion parameters in both zero- and few-shot setups.

Layer-wise quantization is a key technique for efficiently compressing large models without expensive retraining. Previous methods typically quantize the weights of each layer by "uniformly" optimizing the layer reconstruction loss across all output tokens. However, in this paper, we demonstrate that better-quantized models can be obtained by prioritizing learning from important tokens (e.g. which have large attention scores). Building on this finding, we propose RSQ (Rotate, Scale, then Quantize), which (1) applies rotations (orthogonal transformation) to the model to mitigate outliers (those with exceptionally large magnitude), (2) scales the token feature based on its importance, and (3) quantizes the model using the GPTQ framework with the second-order statistics computed by scaled tokens. To compute token importance, we explore both heuristic and dynamic strategies. Based on a thorough analysis of all approaches, we adopt attention concentration, which uses attention scores of each token as its importance, as the best approach. We demonstrate that RSQ consistently outperforms baseline methods across multiple downstream tasks and three model families: LLaMA3, Mistral, and Qwen2.5. Additionally, models quantized with RSQ achieve superior performance on long-context tasks, further highlighting its effectiveness. Lastly, RSQ demonstrates generalizability across various setups, including different model sizes, calibration datasets, bit precisions, and quantization methods.

As the demand for long-context large language models (LLMs) increases, models with context windows of up to 128K or 1M tokens are becoming increasingly prevalent. However, long-context LLM inference is challenging since the inference speed decreases significantly as the sequence length grows. This slowdown is primarily caused by loading a large KV cache during self-attention. Previous works have shown that a small portion of critical tokens will dominate the attention outcomes. However, we observe the criticality of a token highly depends on the query. To this end, we propose Quest, a query-aware KV cache selection algorithm. Quest keeps track of the minimal and maximal Key values in KV cache pages and estimates the criticality of a given page using Query vectors. By only loading the Top-K critical KV cache pages for attention, Quest significantly speeds up self-attention without sacrificing accuracy. We show that Quest can achieve up to 2.23x self-attention speedup, which reduces inference latency by 7.03x while performing well on tasks with long dependencies with negligible accuracy loss. Code is available at http://github.com/mit-han-lab/Quest .

We introduce Adaptive Filter Attention (AFA), a novel attention mechanism that incorporates a learnable dynamics model directly into the computation of attention weights. Rather than comparing queries and keys directly, we model the input sequence as discrete observations of a linear stochastic differential equation (SDE). By imposing a linear dynamics model with simultaneously diagonalizable state matrices and noise covariances, we can make use of a closed-form solution to the differential Lyapunov equation to efficiently propagate pairwise uncertainties through the dynamics. Attention naturally arises as the maximum likelihood solution for this linear SDE, with attention weights corresponding to robust residual-based reweightings of the propagated pairwise precisions. Imposing an additional constraint on the state matrix's eigenvalues leads to a simplified variant with the same computational and memory complexity as standard attention. In the limit of vanishing dynamics and process noise, and using a small-angle approximation, we recover ordinary dot-product attention.

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.

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.

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.

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.

The emergence of LLMs has ignited a fresh surge of breakthroughs in NLP applications, particularly in domains such as question-answering systems and text generation. As the need for longer context grows, a significant bottleneck in model deployment emerges due to the linear expansion of the Key-Value (KV) cache with the context length. Existing methods primarily rely on various hypotheses, such as sorting the KV cache based on attention scores for replacement or eviction, to compress the KV cache and improve model throughput. However, heuristics used by these strategies may wrongly evict essential KV cache, which can significantly degrade model performance. In this paper, we propose QAQ, a Quality Adaptive Quantization scheme for the KV cache. We theoretically demonstrate that key cache and value cache exhibit distinct sensitivities to quantization, leading to the formulation of separate quantization strategies for their non-uniform quantization. Through the integration of dedicated outlier handling, as well as an improved attention-aware approach, QAQ achieves up to 10x the compression ratio of the KV cache size with a neglectable impact on model performance. QAQ significantly reduces the practical hurdles of deploying LLMs, opening up new possibilities for longer-context applications. The code is available at github.com/ClubieDong/KVCacheQuantization.

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.

We generalize the attention mechanism by viewing it through the lens of Entropic Optimal Transport, revealing that standard attention corresponds to a transport problem regularized by an implicit uniform prior. We introduce Generalized Optimal transport Attention with Trainable priors (GOAT), a new attention mechanism that replaces this naive assumption with a learnable, continuous prior. This prior maintains full compatibility with optimized kernels such as FlashAttention. GOAT also provides an EOT-based explanation of attention sinks and materializes a solution for them, avoiding the representational trade-offs of standard attention. Finally, by absorbing spatial information into the core attention computation, GOAT learns an extrapolatable prior that combines the flexibility of learned positional embeddings with the length generalization of fixed encodings.

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.

In the classical transformer attention scheme, we are given three n times d size matrices Q, K, V (the query, key, and value tokens), and the goal is to compute a new n times d size matrix D^{-1} exp(QK^top) V where D = diag( exp(QK^top) {bf 1}_n ). In this work, we study a generalization of attention which captures triple-wise correlations. This generalization is able to solve problems about detecting triple-wise connections that were shown to be impossible for transformers. The potential downside of this generalization is that it appears as though computations are even more difficult, since the straightforward algorithm requires cubic time in n. However, we show that in the bounded-entry setting (which arises in practice, and which is well-studied in both theory and practice), there is actually a near-linear time algorithm. More precisely, we show that bounded entries are both necessary and sufficient for quickly performing generalized computations: bullet On the positive side, if all entries of the input matrices are bounded above by o(sqrt[3]{log n}) then we show how to approximate the ``tensor-type'' attention matrix in n^{1+o(1)} time. bullet On the negative side, we show that if the entries of the input matrices may be as large as Omega(sqrt[3]{log n}), then there is no algorithm that runs faster than n^{3-o(1)} (assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory). We also show that our construction, algorithms, and lower bounds naturally generalize to higher-order tensors and correlations. Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm. Our results thus yield a natural tradeoff between the boundedness of the entries, and order of the tensor one may use for more expressive, efficient attention computation.

Self-Attention Mechanism (SAM) excels at distilling important information from the interior of data to improve the computational efficiency of models. Nevertheless, many Quantum Machine Learning (QML) models lack the ability to distinguish the intrinsic connections of information like SAM, which limits their effectiveness on massive high-dimensional quantum data. To tackle the above issue, a Quantum Kernel Self-Attention Mechanism (QKSAM) is introduced to combine the data representation merit of Quantum Kernel Methods (QKM) with the efficient information extraction capability of SAM. Further, a Quantum Kernel Self-Attention Network (QKSAN) framework is proposed based on QKSAM, which ingeniously incorporates the Deferred Measurement Principle (DMP) and conditional measurement techniques to release half of quantum resources by mid-circuit measurement, thereby bolstering both feasibility and adaptability. Simultaneously, the Quantum Kernel Self-Attention Score (QKSAS) with an exponentially large characterization space is spawned to accommodate more information and determine the measurement conditions. Eventually, four QKSAN sub-models are deployed on PennyLane and IBM Qiskit platforms to perform binary classification on MNIST and Fashion MNIST, where the QKSAS tests and correlation assessments between noise immunity and learning ability are executed on the best-performing sub-model. The paramount experimental finding is that a potential learning advantage is revealed in partial QKSAN subclasses that acquire an impressive more than 98.05% high accuracy with very few parameters that are much less in aggregate than classical machine learning models. Predictably, QKSAN lays the foundation for future quantum computers to perform machine learning on massive amounts of data while driving advances in areas such as quantum computer vision.

Standard sequence mixing layers used in language models struggle to balance efficiency and performance. Self-attention performs well on long context tasks but has expensive quadratic compute and linear memory costs, while linear attention and SSMs use only linear compute and constant memory but struggle with long context processing. In this paper, we develop a sequence mixing layer that aims to find a better compromise between memory-compute costs and long-context processing, which we call online vector-quantized (OVQ) attention. OVQ-attention requires linear compute costs and constant memory, but, unlike linear attention and SSMs, it uses a sparse memory update that allows it to greatly increase the size of its memory state and, consequently, memory capacity. We develop a theoretical basis for OVQ-attention based on Gaussian mixture regression, and we test it on a variety of synthetic long context tasks and on long context language modeling. OVQ-attention shows significant improvements over linear attention baselines and the original VQ-attention, on which OVQ-attention was inspired. It demonstrates competitive, and sometimes identical, performance to strong self-attention baselines up 64k sequence length, despite using a small fraction of the memory of full self-attention.

We present an approximate attention mechanism named HyperAttention to address the computational challenges posed by the growing complexity of long contexts used in Large Language Models (LLMs). Recent work suggests that in the worst-case scenario, quadratic time is necessary unless the entries of the attention matrix are bounded or the matrix has low stable rank. We introduce two parameters which measure: (1) the max column norm in the normalized attention matrix, and (2) the ratio of row norms in the unnormalized attention matrix after detecting and removing large entries. We use these fine-grained parameters to capture the hardness of the problem. Despite previous lower bounds, we are able to achieve a linear time sampling algorithm even when the matrix has unbounded entries or a large stable rank, provided the above parameters are small. HyperAttention features a modular design that easily accommodates integration of other fast low-level implementations, particularly FlashAttention. Empirically, employing Locality Sensitive Hashing (LSH) to identify large entries, HyperAttention outperforms existing methods, giving significant speed improvements compared to state-of-the-art solutions like FlashAttention. We validate the empirical performance of HyperAttention on a variety of different long-context length datasets. For example, HyperAttention makes the inference time of ChatGLM2 50\% faster on 32k context length while perplexity increases from 5.6 to 6.3. On larger context length, e.g., 131k, with causal masking, HyperAttention offers 5-fold speedup on a single attention layer.

INT2 KV-cache quantization is attractive for long-context LLM serving, but it remains difficult to make both accurate and deployable. Simple rotations such as Hadamard transforms reduce outliers, but still degrade at INT2 because they are not aligned with downstream attention. We propose OSCAR, an Ultra-low-bit KV Cache quantization method that estimates attention-aware covariance structures offline and uses them to derive fixed rotations and clipping thresholds for quantization. In this way, it aligns KV quantization with the covariance structures that attention actually consumes. More importantly, we not only provide theoretical justification but also develop a fully deployable OSCAR system with a custom INT2 attention kernel that remains compatible with paged KV-cache serving and fused kernel pipelines, enabling seamless integration into modern LLM serving frameworks such as SGLang and vLLM. We evaluate our methods on recent reasoning models with reasoning traces of up to 32k tokens across 5 tasks. On Qwen3-4B-Thinking-2507 and Qwen3-8B, OSCAR reduces the BF16 accuracy gap to 3.78 and 1.42 points, respectively, while naive rotation INT2 collapses to nearly zero. We further scale OSCAR to Qwen3-32B and GLM-4.7 (358B params), where it remains effectively on par with BF16. On long context - RULER-NIAH up to 128K, OSCAR remains robust on both Qwen3 models, while naive rotation INT2 collapses. System-wise, OSCAR reduces KV-cache memory by approximately 8x, improves throughput by up to 7x at large batch sizes under the same memory budget, and accelerates batch-size-1 decoding by up to 3x over BF16 due to reduced memory bandwidth overhead.

Autoregressive language models rely on a Key-Value (KV) Cache, which avoids re-computing past hidden states during generation, making it faster. As model sizes and context lengths grow, the KV Cache becomes a significant memory bottleneck, which calls for compression methods that limit its size during generation. In this paper, we discover surprising properties of Query (Q) and Key (K) vectors that allow us to efficiently approximate attention scores without computing the attention maps. We propose Q-Filters, a training-free KV Cache compression method that filters out less crucial Key-Value pairs based on a single context-agnostic projection. Contrarily to many alternatives, Q-Filters is compatible with FlashAttention, as it does not require direct access to attention weights. Experimental results in long-context settings demonstrate that Q-Filters is competitive with attention-based compression methods such as SnapKV in retrieval tasks while consistently outperforming efficient compression schemes such as Streaming-LLM in generation setups. Notably, Q-Filters achieves a 99% accuracy in the needle-in-a-haystack task with a x32 compression level while reducing the generation perplexity drop by up to 65% in text generation compared to Streaming-LLM.

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 have emerged as the prevailing standard solution for various AI tasks, including computer vision and natural language processing. The widely adopted Query, Key, and Value formulation (QKV) has played a significant role in this. Nevertheless, no research has examined the essentiality of these three components for transformer performance. Therefore, we conducted an evaluation of the key-value formulation (KV), which generates symmetric attention maps, along with an asymmetric version that incorporates a 2D positional encoding into the attention matrix. Remarkably, this transformer requires fewer parameters and computation than the original one. Through experiments encompassing three task types -- synthetics (such as reversing or sorting a list), vision (mnist or cifar classification), and NLP (character generation and translation) -- we discovered that the KV transformer occasionally outperforms the QKV transformer. However, it also exhibits instances of underperformance compared to QKV, making it challenging to draw a definitive conclusion. Nonetheless, we consider the reported results to be encouraging and anticipate that they may pave the way for more efficient transformers in the future.

The Transformer architecture, underpinned by the Multi-Head Attention (MHA) mechanism, has become the de facto standard for state-of-the-art models in artificial intelligence. However, the quadratic computational complexity of MHA with respect to sequence length presents a significant barrier to scaling, particularly for applications involving long contexts. Prevailing solutions, such as Multi-Query Attention (MQA) and Grouped-Query Attention (GQA), have effectively addressed the memory bandwidth bottleneck that dominates autoregressive inference latency by sharing Key and Value projections. While highly successful, these methods do not reduce the fundamental number of floating-point operations (FLOPs) required for the attention score computation, which remains a critical bottleneck for training and full-sequence processing. This paper introduces Sparse Query Attention (SQA), a novel attention architecture that pursues an alternative and complementary optimization path. Instead of reducing Key/Value heads, SQA reduces the number of Query heads. This architectural modification directly decreases the computational complexity of the attention mechanism by a factor proportional to the reduction in query heads, thereby lowering the overall FLOPs. This work presents the theoretical foundation of SQA, its mathematical formulation, and a family of architectural variants. Empirical benchmarks on long sequences (32k-200k tokens) demonstrate that SQA can achieve significant throughput improvements of up to 3x in computation-bound scenarios such as model pre-training, fine-tuning, and encoder-based tasks, with only a minimal impact on model quality in preliminary smallscale experiments. SQA was discovered serendipitously during the development of the upcoming Reactive Transformer architecture, suggesting its potential as a powerful tool for building more efficient and scalable models

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.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices Kin R^{ntimes n}. K's columns are indexed by a set of n keys k_1,k_2ldots, k_nin R^d, rows by a set of n queries q_1,q_2,ldots,q_nin R^d , and its i,j entry is K_{ij} = e^{-|q_i-k_j|_2^2/2sigma^2} for some bandwidth parameter sigma>0. Given a vector xin R^n and error parameter epsilon>0, our task is to output a yin R^n such that |Kx-y|_2leq epsilon |x|_2 in time subquadratic in n and linear in d. Our algorithms rely on the following modelling assumption about the matrices K: the sum of the entries of K scales linearly in n, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Large Vision-Language Models (LVLMs) have shown significant capability in vision-language understanding. However, one critical issue that persists in these models is sycophancy, which means models are unduly influenced by leading or deceptive prompts, resulting in biased outputs and hallucinations. Despite the progress in LVLMs, evaluating and mitigating sycophancy is yet much under-explored. In this work, we fill this gap by systematically analyzing sycophancy on various VL benchmarks with curated leading queries and further proposing a text contrastive decoding method for mitigation. While the specific sycophantic behavior varies significantly among models, our analysis reveals the severe deficiency of all LVLMs in resilience of sycophancy across various tasks. For improvement, we propose Leading Query Contrastive Decoding (LQCD), a model-agnostic method focusing on calibrating the LVLMs' over-reliance on leading cues by identifying and suppressing the probabilities of sycophancy tokens at the decoding stage. Extensive experiments show that LQCD effectively mitigate sycophancy, outperforming both prompt engineering methods and common methods for hallucination mitigation. We further demonstrate that LQCD does not hurt but even slightly improves LVLMs' responses to neutral queries, suggesting it being a more effective strategy for general-purpose decoding but not limited to sycophancy.

Efficient attention algorithms are critical to mitigate the quadratic cost of attention in long-context workloads. Prior work utilises block-scaled quantisation techniques on Blackwell GPUs to move attention computation to 4-bit precision to accelerate inference. However, these techniques result in significant quality degradation in long-context settings. We show that the output impact of quantisation error is highly non-uniform and increases with the importance of each query-key interaction, concentrating functionally relevant error in a small number of attention blocks that contain the most important tokens. We propose ThriftAttention, a low-bit attention variant that delivers near-FP16 long-context quality at FP4 inference efficiency. This approach proceeds in two stages. First, a heuristic rapidly selects a small number of important query-key block pairs for FP16 precision. Second, the selected blocks are computed in FP16 and the remaining blocks in FP4, with both paths merged via online softmax into a single output. We demonstrate across long-context benchmarks and model families that by computing only 5% of query-key blocks in FP16, ThriftAttention recovers on average 89.1% of the FP4-to-FP16 performance gap. We show ThriftAttention's advantage grows with sequence length, mitigating the systematic FP4 quality degradation observed at longer contexts. The code is available at https://github.com/joesharratt1229/ThriftAttention.

The quest for algorithms that enable cognitive abilities is an important part of machine learning. A common trait in many recently investigated cognitive-like tasks is that they take into account different data modalities, such as visual and textual input. In this paper we propose a novel and generally applicable form of attention mechanism that learns high-order correlations between various data modalities. We show that high-order correlations effectively direct the appropriate attention to the relevant elements in the different data modalities that are required to solve the joint task. We demonstrate the effectiveness of our high-order attention mechanism on the task of visual question answering (VQA), where we achieve state-of-the-art performance on the standard VQA dataset.

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from computation for efficient inference. Sparse attention inference methods aim to reduce this computational burden; however, they also come with a troublesome performance degradation. We discover that one reason for this degradation is that the sparse calculation induces a distributional shift in the attention outputs. The distributional shift causes decoding-time queries to fail to align well with the appropriate keys from the prefill stage, leading to a drop in performance. We propose a simple, novel, and effective procedure for correcting this distributional shift, bringing the distribution of sparse attention outputs closer to that of quadratic attention. Our method can be applied on top of any sparse attention method, and results in an average 36%pt performance increase, recovering 88% of quadratic attention accuracy on the 131K RULER benchmark when applied on top of sliding window attention with sink tokens while only adding a small overhead. Our method can maintain approximately 98.5% sparsity over full quadratic attention, making our model 32 times faster than Flash Attention 2 when processing 1M token prefills.

Kolmogorov-Arnold networks (KANs) are a remarkable innovation consisting of learnable activation functions with the potential to capture more complex relationships from data. Although KANs are useful in finding symbolic representations and continual learning of one-dimensional functions, their effectiveness in diverse machine learning (ML) tasks, such as vision, remains questionable. Presently, KANs are deployed by replacing multilayer perceptrons (MLPs) in deep network architectures, including advanced architectures such as vision Transformers (ViTs). In this paper, we are the first to design a general learnable Kolmogorov-Arnold Attention (KArAt) for vanilla ViTs that can operate on any choice of basis. However, the computing and memory costs of training them motivated us to propose a more modular version, and we designed particular learnable attention, called Fourier-KArAt. Fourier-KArAt and its variants either outperform their ViT counterparts or show comparable performance on CIFAR-10, CIFAR-100, and ImageNet-1K datasets. We dissect these architectures' performance and generalization capacity by analyzing their loss landscapes, weight distributions, optimizer path, attention visualization, and spectral behavior, and contrast them with vanilla ViTs. The goal of this paper is not to produce parameter- and compute-efficient attention, but to encourage the community to explore KANs in conjunction with more advanced architectures that require a careful understanding of learnable activations. Our open-source code and implementation details are available on: https://subhajitmaity.me/KArAt

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.

Linear attention has recently gained significant attention for long-context inference due to its constant decoding cost with respect to context length. However, existing serving systems typically serve linear attention by recurrently computing and updating a large linear attention state in every decoding step. Since the state is much larger than the per-token key and value, recurrent decoding incurs substantial memory access and becomes inefficient for serving linear attention. In this paper, we propose KVBuffer, an IO-aware serving mechanism for linear attention. By buffering recent keys and values, KVBuffer enables serving systems to compute linear attention outputs in more flexible and memory-efficient ways. For decoding, KVBuffer enables chunkwise computation, which reduces average memory access and decoding latency by deferring state updates and applying them in batch. For speculative decoding, KVBuffer verifies draft tokens in parallel and avoids storing temporary states. For short contexts, KVBuffer computes attention outputs directly from buffered keys and values, without creating or updating the linear attention state. We implement KVBuffer in SGLang for Qwen3-Next. Our evaluations show that KVBuffer can reduce linear attention decoding latency by up to 45.17% and increase the maximum number of serving requests by 5x for speculative decoding when verifying four draft tokens.

Vision-language models (VLMs) show remarkable performance in multimodal tasks. However, excessively long multimodal inputs lead to oversized Key-Value (KV) caches, resulting in significant memory consumption and I/O bottlenecks. Previous KV quantization methods for Large Language Models (LLMs) may alleviate these issues but overlook the attention saliency differences of multimodal tokens, resulting in suboptimal performance. In this paper, we investigate the attention-aware token saliency patterns in VLM and propose AKVQ-VL. AKVQ-VL leverages the proposed Text-Salient Attention (TSA) and Pivot-Token-Salient Attention (PSA) patterns to adaptively allocate bit budgets. Moreover, achieving extremely low-bit quantization requires effectively addressing outliers in KV tensors. AKVQ-VL utilizes the Walsh-Hadamard transform (WHT) to construct outlier-free KV caches, thereby reducing quantization difficulty. Evaluations of 2-bit quantization on 12 long-context and multimodal tasks demonstrate that AKVQ-VL maintains or even improves accuracy, outperforming LLM-oriented methods. AKVQ-VL can reduce peak memory usage by 2.13x, support up to 3.25x larger batch sizes and 2.46x throughput.

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

Over the past few years, deep neural models have made considerable advances in image quality assessment (IQA). However, the underlying reasons for their success remain unclear, owing to the complex nature of deep neural networks. IQA aims to describe how the human visual system (HVS) works and to create its efficient approximations. On the other hand, Saliency Prediction task aims to emulate HVS via determining areas of visual interest. Thus, we believe that saliency plays a crucial role in human perception. In this work, we conduct an empirical study that reveals the relation between IQA and Saliency Prediction tasks, demonstrating that the former incorporates knowledge of the latter. Moreover, we introduce a novel SACID dataset of saliency-aware compressed images and conduct a large-scale comparison of classic and neural-based IQA methods. All supplementary code and data will be available at the time of publication.

Transformer attention computes a single softmax-weighted average over values -- a one-pass estimate that cannot correct its own errors. We introduce gradient-boosted attention, which applies the principle of gradient boosting within a single attention layer: a second attention pass, with its own learned projections, attends to the prediction error of the first and applies a gated correction. Under a squared reconstruction objective, the construction maps onto Friedman's gradient boosting machine, with each attention pass as a base learner and the per-dimension gate as the shrinkage parameter. We show that a single Hopfield-style update erases all query information orthogonal to the stored-pattern subspace, and that further iteration under local contraction can collapse distinct queries in the same region to the same fixed point. We also show that separate projections for the correction pass can recover residual information inaccessible to the shared-projection approach of Tukey's twicing. On a 10M-token subset of WikiText-103, gradient-boosted attention achieves a test perplexity of 67.9 compared to 72.2 for standard attention, 69.6 for Twicing Attention, and 69.0 for a parameter-matched wider baseline, with two rounds capturing most of the benefit.

Attention-based Multiple Instance Learning aggregators in medical imaging are prone to attention concentration, producing overconfident and unstable predictions. We introduce QG-MIL, a gated transformer aggregator that addresses this through four synergistic architectural components: RMSNorm-based pre-normalization, per-head QK normalization, fine-grained attention output gating, and SwiGLU-style feed-forward modules. Together, these design choices stabilize training and distribute attention more uniformly across instances without auxiliary losses, masking, or multi-stage regularization. We evaluate QG-MIL across six benchmarks spanning whole-slide pathology and cell-level hematology, covering two fundamentally different MIL scales. The best-performing QG-MIL variants outperform leading baselines on all six benchmarks, with an average improvement of +6.1 mean macro F1 points. Attention overlays and attention mass analysis confirm more distributed instance weighting. Ablation studies show that while individual components can match the full model on specific datasets, the QG-MIL design provides the most consistent cross-domain performance and tightest variance when compared to selected baselines. We release a configurable implementation to support reproducibility at: https://github.com/unica-visual-intelligence-lab/QG-MIL

KV cache stores key and value states from previous tokens to avoid re-computation, yet it demands substantial storage space, especially for long sequences. Adaptive KV cache compression seeks to discern the saliency of tokens, preserving vital information while aggressively compressing those of less importance. However, previous methods of this approach exhibit significant performance degradation at high compression ratios due to inaccuracies in identifying salient tokens. In this paper, we present ZipCache, an accurate and efficient KV cache quantization method for LLMs. First, we construct a strong baseline for quantizing KV cache. Through the proposed channel-separable tokenwise quantization scheme, the memory overhead of quantization parameters are substantially reduced compared to fine-grained groupwise quantization. To enhance the compression ratio, we propose normalized attention score as an effective metric for identifying salient tokens by considering the lower triangle characteristics of the attention matrix. Moreover, we develop an efficient approximation method that decouples the saliency metric from full attention scores, enabling compatibility with fast attention implementations like FlashAttention. Extensive experiments demonstrate that ZipCache achieves superior compression ratios, fast generation speed and minimal performance losses compared with previous KV cache compression methods. For instance, when evaluating Mistral-7B model on GSM8k dataset, ZipCache is capable of compressing the KV cache by 4.98times, with only a 0.38% drop in accuracy. In terms of efficiency, ZipCache also showcases a 37.3% reduction in prefill-phase latency, a 56.9% reduction in decoding-phase latency, and a 19.8% reduction in GPU memory usage when evaluating LLaMA3-8B model with a input length of 4096.

Extended reasoning in large language models (LLMs) creates severe KV cache memory bottlenecks. Leading KV cache compression methods estimate KV importance using attention scores from recent post-RoPE queries. However, queries rotate with position during RoPE, making representative queries very few, leading to poor top-key selection and unstable reasoning. To avoid this issue, we turn to the pre-RoPE space, where we observe that Q and K vectors are highly concentrated around fixed non-zero centers and remain stable across positions -- Q/K concentration. We show that this concentration causes queries to preferentially attend to keys at specific distances (e.g., nearest keys), with the centers determining which distances are preferred via a trigonometric series. Based on this, we propose TriAttention to estimate key importance by leveraging these centers. Via the trigonometric series, we use the distance preference characterized by these centers to score keys according to their positions, and also leverage Q/K norms as an additional signal for importance estimation. On AIME25 with 32K-token generation, TriAttention matches Full Attention reasoning accuracy while achieving 2.5x higher throughput or 10.7x KV memory reduction, whereas leading baselines achieve only about half the accuracy at the same efficiency. TriAttention enables OpenClaw deployment on a single consumer GPU, where long context would otherwise cause out-of-memory with Full Attention.

The dot product attention mechanism, originally designed for natural language processing tasks, is a cornerstone of modern Transformers. It adeptly captures semantic relationships between word pairs in sentences by computing a similarity overlap between queries and keys. In this work, we explore the suitability of Transformers, focusing on their attention mechanisms, in the specific domain of the parametrization of variational wave functions to approximate ground states of quantum many-body spin Hamiltonians. Specifically, we perform numerical simulations on the two-dimensional J_1-J_2 Heisenberg model, a common benchmark in the field of quantum many-body systems on lattice. By comparing the performance of standard attention mechanisms with a simplified version that excludes queries and keys, relying solely on positions, we achieve competitive results while reducing computational cost and parameter usage. Furthermore, through the analysis of the attention maps generated by standard attention mechanisms, we show that the attention weights become effectively input-independent at the end of the optimization. We support the numerical results with analytical calculations, providing physical insights of why queries and keys should be, in principle, omitted from the attention mechanism when studying large systems.

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.

In standard causal attention, each token's query, key, and value (QKV) are static and encode only preceding context. We introduce CAuSal aTtention with Lookahead kEys (CASTLE), an attention mechanism that continually updates each token's keys as the context unfolds. We term these updated keys lookahead keys because they belong to earlier positions yet integrate information from tokens that appear later relative to those positions, while strictly preserving the autoregressive property. Although the mechanism appears sequential, we derive a mathematical equivalence that avoids explicitly materializing lookahead keys at each position and enables efficient parallel training. On language modeling benchmarks, CASTLE consistently outperforms standard causal attention across model scales, reducing validation perplexity and improving performance on a range of downstream tasks.

Long-context prefill remains expensive because full/GQA layers still score the historical sequence, even in hybrid models with local, sparse, linear, or recurrent components. We study how much dense attention is needed to preserve task-level behavior under explicit support granularity and top-k budgets. We introduce an attention-mass top-k oracle for existing GQA checkpoints: for each layer and query position, it computes dense attention, selects head-averaged token support, and recomputes attention only on that support. The oracle is a diagnostic reference, not a deployable accelerator, and separates sparse-budget feasibility from indexer error and runtime realization effects. On Qwen-family retrieval-heavy evaluations, the longest per-query oracle rows stay within 1 point of dense, and a Qwen3.5-9B RULER-style sweep from 4K to 100K stays within 0.48 points. Guided by the oracle, we derive a head-collapsed auxiliary indexer trained by KL distillation from dense attention-mass distributions while keeping the backbone frozen. With separately distilled Qwen3.5-0.8B and Qwen3.5-9B indexers, the reported 16K/32K validation macro gaps are +2.04 and +1.13 points, treated as quality preservation rather than improvement; fused selection-block-shared support can introduce a larger realization gap. Preliminary single-card TTFT measurements show distilled-indexer sparse serving speedups of 1.71x for Qwen3.5-0.8B on NPU and 1.93x for Qwen3.5-9B on GPU against its dense FlashAttention-2 baseline. Additional random-init stress rows reach 3.44x, indicating sparse-runtime headroom but not validated output quality. This first release separates oracle feasibility, distilled-indexer quality, and runtime headroom, leaving a fully matched quality-latency frontier to future work.

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.

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.

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

Window-based attention has become a popular choice in vision transformers due to its superior performance, lower computational complexity, and less memory footprint. However, the design of hand-crafted windows, which is data-agnostic, constrains the flexibility of transformers to adapt to objects of varying sizes, shapes, and orientations. To address this issue, we propose a novel quadrangle attention (QA) method that extends the window-based attention to a general quadrangle formulation. Our method employs an end-to-end learnable quadrangle regression module that predicts a transformation matrix to transform default windows into target quadrangles for token sampling and attention calculation, enabling the network to model various targets with different shapes and orientations and capture rich context information. We integrate QA into plain and hierarchical vision transformers to create a new architecture named QFormer, which offers minor code modifications and negligible extra computational cost. Extensive experiments on public benchmarks demonstrate that QFormer outperforms existing representative vision transformers on various vision tasks, including classification, object detection, semantic segmentation, and pose estimation. The code will be made publicly available at https://github.com/ViTAE-Transformer/QFormer{QFormer}.

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.

Although quantization for linear layers has been widely used, its application to accelerate the attention process remains limited. SageAttention utilizes 8-bit matrix multiplication, 16-bit matrix multiplication with 16-bit accumulator, and precision-enhancing methods, implementing an accurate and 2x speedup kernel compared to FlashAttention2. To further enhance the efficiency of attention computation while maintaining precision, we propose SageAttention2, which utilizes significantly faster 4-bit matrix multiplication (Matmul) alongside additional precision-enhancing techniques. First, we propose to quantize matrixes (Q, K) to INT4 in a warp-level granularity and quantize matrixes (widetilde P, V) to FP8. Second, we propose a method to smooth Q and V, enhancing the accuracy of attention with INT4 QK and FP8 PV. Third, we analyze the quantization accuracy across timesteps and layers, then propose an adaptive quantization method to ensure the end-to-end metrics over various models. The operations per second (OPS) of SageAttention2 surpass FlashAttention2 and xformers by about 3x and 5x on RTX4090, respectively. Comprehensive experiments confirm that our approach incurs negligible end-to-end metrics loss across diverse models, including those for large language processing, image generation, and video generation. The codes are available at https://github.com/thu-ml/SageAttention.

We introduce Shakti VLM, a family of vision-language models in the capacity of 1B and 4B parameters designed to address data efficiency challenges in multimodal learning. While recent VLMs achieve strong performance through extensive training data, Shakti models leverage architectural innovations to attain competitive results with fewer tokens. Key advancements include QK-Normalization for attention stability, hybrid normalization techniques, and enhanced positional encoding. A three-stage training strategy further optimizes learning efficiency. Evaluations show that Shakti-Shakti-VLM-1B and Shakti-VLM-4B excel in document understanding, Visual Reasoning, OCR extraction, and general multimodal reasoning. Our results highlight that high performance can be achieved through model design and training strategy rather than sheer data volume, making Shakti an efficient solution for enterprise-scale multimodal tasks.

We revisit the relationship between attention mechanisms and large kernel ConvNets in visual transformers and propose a new spatial attention named Large Kernel Convolutional Attention (LKCA). It simplifies the attention operation by replacing it with a single large kernel convolution. LKCA combines the advantages of convolutional neural networks and visual transformers, possessing a large receptive field, locality, and parameter sharing. We explained the superiority of LKCA from both convolution and attention perspectives, providing equivalent code implementations for each view. Experiments confirm that LKCA implemented from both the convolutional and attention perspectives exhibit equivalent performance. We extensively experimented with the LKCA variant of ViT in both classification and segmentation tasks. The experiments demonstrated that LKCA exhibits competitive performance in visual tasks. Our code will be made publicly available at https://github.com/CatworldLee/LKCA.

Memory consumption of the Key-Value (KV) cache represents a major bottleneck for efficient large language model inference. While attention-score-based KV cache pruning shows promise, it faces critical practical limitations: attention scores from future tokens are unavailable during compression, and modern implementations like Flash Attention do not materialize the full attention matrix, making past scores inaccessible. To overcome these challenges, we introduce Expected Attention, a training-free compression method that estimates KV pairs importance by predicting how future queries will attend to them. Our approach leverages the distributional properties of LLM activations to compute expected attention scores in closed form for each KV pair. These scores enable principled ranking and pruning of KV pairs with minimal impact on the residual stream, achieving effective compression without performance degradation. Importantly, our method operates seamlessly across both prefilling and decoding phases, consistently outperforming state-of-the-art baselines in both scenarios. Finally, we release KVPress, a comprehensive library to enable researchers to implement and benchmark KV cache compression methods, already including more than 20 techniques.

Recent advances in large language models (LLMs) have showcased exceptional performance in long-context tasks, while facing significant inference efficiency challenges with limited GPU memory. Existing solutions first proposed the sliding-window approach to accumulate a set of historical key-value (KV) pairs for reuse, then further improvements selectively retain its subsets at each step. However, due to the sparse attention distribution across a long context, it is hard to identify and recall relevant KV pairs, as the attention is distracted by massive candidate pairs. Additionally, we found it promising to select representative tokens as probe-Query in each sliding window to effectively represent the entire context, which is an approach overlooked by existing methods. Thus, we propose ActQKV, a training-free, Activation-aware approach that dynamically determines probe-Query and leverages it to retrieve the relevant KV pairs for inference. Specifically, ActQKV monitors a token-level indicator, Activation Bias, within each context window, enabling the proper construction of probe-Query for retrieval at pre-filling stage. To accurately recall the relevant KV pairs and minimize the irrelevant ones, we design a dynamic KV cut-off mechanism guided by information density across layers at the decoding stage. Experiments on the Long-Bench and infty Benchmarks demonstrate its state-of-the-art performance with competitive inference quality and resource efficiency.

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.

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining even more accurate compressed models by directly training over such representations, i.e., Quantization-Aware Training (QAT), is still open: for example, a recent study (arXiv:2411.04330v2) put the "optimal" bit-width at which models can be trained using QAT, while staying accuracy-competitive with standard FP16/BF16 precision, at 8-bits weights and activations. We advance this state-of-the-art via a new method called QuEST, which is Pareto-competitive with FP16, i.e., it provides better accuracy at lower model size, while training models with weights and activations in 4-bits or less. Moreover, QuEST allows stable training with 1-bit weights and activations. QuEST achieves this by improving two key aspects of QAT methods: (1) accurate and fast quantization of the (continuous) distributions of weights and activations via Hadamard normalization and MSE-optimal fitting; (2) a new trust gradient estimator based on the idea of explicitly minimizing the error between the noisy gradient computed over quantized states and the "true" (but unknown) full-precision gradient. Experiments on Llama-type architectures show that QuEST induces stable scaling laws across the entire range of hardware-supported precisions, and can be extended to sparse representations. We provide GPU kernel support showing that models produced by QuEST can be executed efficiently. Our code is available at https://github.com/IST-DASLab/QuEST.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

At the core of the Transformer, the Softmax normalizes the attention matrix to be right stochastic. Previous research has shown that this often destabilizes training and that enforcing the attention matrix to be doubly stochastic (through Sinkhorn's algorithm) consistently improves performance across different tasks, domains and Transformer flavors. However, Sinkhorn's algorithm is iterative, approximative, non-parametric and thus inflexible w.r.t. the obtained doubly stochastic matrix (DSM). Recently, it has been proven that DSMs can be obtained with a parametric quantum circuit, yielding a novel quantum inductive bias for DSMs with no known classical analogue. Motivated by this, we demonstrate the feasibility of a hybrid classical-quantum doubly stochastic Transformer (QDSFormer) that replaces the Softmax in the self-attention layer with a variational quantum circuit. We study the expressive power of the circuit and find that it yields more diverse DSMs that better preserve information than classical operators. Across multiple small-scale object recognition tasks, we find that our QDSFormer consistently surpasses both a standard Vision Transformer and other doubly stochastic Transformers. Beyond the established Sinkformer, this comparison includes a novel quantum-inspired doubly stochastic Transformer (based on QR decomposition) that can be of independent interest. The QDSFormer also shows improved training stability and lower performance variation suggesting that it may mitigate the notoriously unstable training of ViTs on small-scale data.

Chunk-wise autoregressive video diffusion models rely on a KV cache of previously generated chunks to avoid redundant computation, but this cache quickly becomes a memory bottleneck as videos grow longer. Methods that quantize the KV cache to low bitwidths reduce memory pressure but degrade video quality. We show that a key driver of this degradation is a systematic bias in attention weights: due to the convexity of the exponential in softmax attention, quantization noise inflates the contribution of cached keys, a phenomenon we call the Jensen bias. This effect causes quantized keys to steal attention mass from the unquantized current chunk. We derive a per-attention-score correction that removes this bias in expectation, computed on the fly from the quantization step sizes of the cached keys and the query norm. Using a second-order Taylor approximation, the additional computational overhead is negligible, and no additional memory is needed alongside the cache. Evaluated on MAGI-1, SkyReels-V2, and HY-WorldPlay at INT2 quantization, our correction recovers most of the quality lost to aggressive quantization, reaching near-BF16 video quality, and can outperform INT4 quantization while using 50% less memory.

The deployment of large language models (LLMs) is often hindered by the extensive memory requirements of the Key-Value (KV) cache, especially as context lengths increase. Existing approaches to reduce the KV cache size involve either fine-tuning the model to learn a compression strategy or leveraging attention scores to reduce the sequence length. We analyse the attention distributions in decoder-only Transformers-based models and observe that attention allocation patterns stay consistent across most layers. Surprisingly, we find a clear correlation between the L_2 and the attention scores over cached KV pairs, where a low L_2 of a key embedding usually leads to a high attention score during decoding. This finding indicates that the influence of a KV pair is potentially determined by the key embedding itself before being queried. Based on this observation, we compress the KV cache based on the L_2 of key embeddings. Our experimental results show that this simple strategy can reduce the KV cache size by 50% on language modelling and needle-in-a-haystack tasks and 90% on passkey retrieval tasks without losing accuracy.

Scaling the effective context length is essential for advancing large language models (LLMs) toward artificial general intelligence (AGI). However, the quadratic increase in computational complexity inherent in traditional attention mechanisms presents a prohibitive overhead. Existing approaches either impose strongly biased structures, such as sink or window attention which are task-specific, or radically modify the attention mechanism into linear approximations, whose performance in complex reasoning tasks remains inadequately explored. In this work, we propose a solution that adheres to the ``less structure'' principle, allowing the model to determine where to attend autonomously, rather than introducing predefined biases. We introduce Mixture of Block Attention (MoBA), an innovative approach that applies the principles of Mixture of Experts (MoE) to the attention mechanism. This novel architecture demonstrates superior performance on long-context tasks while offering a key advantage: the ability to seamlessly transition between full and sparse attention, enhancing efficiency without the risk of compromising performance. MoBA has already been deployed to support Kimi's long-context requests and demonstrates significant advancements in efficient attention computation for LLMs. Our code is available at https://github.com/MoonshotAI/MoBA.

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.

Saliency methods seek to explain the predictions of a model by producing an importance map across each input sample. A popular class of such methods is based on backpropagating a signal and analyzing the resulting gradient. Despite much research on such methods, relatively little work has been done to clarify the differences between such methods as well as the desiderata of these techniques. Thus, there is a need for rigorously understanding the relationships between different methods as well as their failure modes. In this work, we conduct a thorough analysis of backpropagation-based saliency methods and propose a single framework under which several such methods can be unified. As a result of our study, we make three additional contributions. First, we use our framework to propose NormGrad, a novel saliency method based on the spatial contribution of gradients of convolutional weights. Second, we combine saliency maps at different layers to test the ability of saliency methods to extract complementary information at different network levels (e.g.~trading off spatial resolution and distinctiveness) and we explain why some methods fail at specific layers (e.g., Grad-CAM anywhere besides the last convolutional layer). Third, we introduce a class-sensitivity metric and a meta-learning inspired paradigm applicable to any saliency method for improving sensitivity to the output class being explained.

Neighborhood attention reduces the cost of self attention by restricting each token's attention span to its nearest neighbors. This restriction, parameterized by a window size and dilation factor, draws a spectrum of possible attention patterns between linear projection and self attention. Neighborhood attention, and more generally sliding window attention patterns, have long been bounded by infrastructure, particularly in higher-rank spaces (2-D and 3-D), calling for the development of custom kernels, which have been limited in either functionality, or performance, if not both. In this work, we first show that neighborhood attention can be represented as a batched GEMM problem, similar to standard attention, and implement it for 1-D and 2-D neighborhood attention. These kernels on average provide 895% and 272% improvement in full precision latency compared to existing naive kernels for 1-D and 2-D neighborhood attention respectively. We find certain inherent inefficiencies in all unfused neighborhood attention kernels that bound their performance and lower-precision scalability. We also developed fused neighborhood attention; an adaptation of fused dot-product attention kernels that allow fine-grained control over attention across different spatial axes. Known for reducing the quadratic time complexity of self attention to a linear complexity, neighborhood attention can now enjoy a reduced and constant memory footprint, and record-breaking half precision latency. We observe that our fused kernels successfully circumvent some of the unavoidable inefficiencies in unfused implementations. While our unfused GEMM-based kernels only improve half precision performance compared to naive kernels by an average of 496% and 113% in 1-D and 2-D problems respectively, our fused kernels improve naive kernels by an average of 1607% and 581% in 1-D and 2-D problems respectively.

This work focuses on object goal visual navigation, aiming at finding the location of an object from a given class, where in each step the agent is provided with an egocentric RGB image of the scene. We propose to learn the agent's policy using a reinforcement learning algorithm. Our key contribution is a novel attention probability model for visual navigation tasks. This attention encodes semantic information about observed objects, as well as spatial information about their place. This combination of the "what" and the "where" allows the agent to navigate toward the sought-after object effectively. The attention model is shown to improve the agent's policy and to achieve state-of-the-art results on commonly-used datasets.

Achieving reliable 4-bit attention is a prerequisite for end-to-end FP4 computation on emerging FP4-capable GPUs, yet attention remains the main obstacle due to FP4's tiny dynamic range and attention's heavy-tailed activations. This paper presents the first systematic study of 4-bit quantization-aware training (QAT) for attention. We find that "drop-in" QAT, which naively combines an FP4 forward pass with a high-precision Flash Attention (FA)-style backward pass, leads to training instability. We identify two key principles for stable FP4 attention: (1) matching low-precision recomputation of attention scores in the backward pass, and (2) resolving implicit precision assumptions in FA's gradient calculation. Based on these insights, we propose Attn-QAT and implement fused Triton kernels for training as well as FP4 inference kernels. Across diffusion and language models, Attn-QAT recovers the quality drop from FP4 attention without explicit outlier-mitigation heuristics used in prior FP4 attention, and delivers up to a 1.5x speedup on an RTX 5090. Video demos can be found at https://drive.google.com/drive/folders/190F6xbBDUF2kGQYIcXBt3ehSYij5jlim?usp=sharing.

We propose novel attention architectures, Multi-matrix Factorization Attention (MFA) and MFA-Key-Reuse (MFA-KR). Existing variants for standard Multi-Head Attention (MHA), including SOTA methods like MLA, fail to maintain as strong performance under stringent Key-Value cache (KV cache) constraints. MFA enhances model capacity by efficiently scaling up both the number and dimension of attention heads through low-rank matrix factorization in the Query-Key (QK) circuit. Extending MFA, MFA-KR further reduces memory requirements by repurposing the key cache as value through value projection re-parameterization. MFA's design enables strong model capacity when working under tight KV cache budget, while MFA-KR is suitable for even harsher KV cache limits with minor performance trade-off. Notably, in our extensive and large-scale experiments, the proposed architecture outperforms MLA and performs comparably to MHA, while reducing KV cache usage by up to 56% and 93.7%, respectively.

Transformers have achieved widespread and remarkable success, while the computational complexity of their attention modules remains a major bottleneck for vision tasks. Existing methods mainly employ 8-bit or 4-bit quantization to balance efficiency and accuracy. In this paper, with theoretical justification, we indicate that binarization of attention preserves the essential similarity relationships, and propose BinaryAttention, an effective method for fast and accurate 1-bit qk-attention. Specifically, we retain only the sign of queries and keys in computing the attention, and replace the floating dot products with bit-wise operations, significantly reducing the computational cost. We mitigate the inherent information loss under 1-bit quantization by incorporating a learnable bias, and enable end-to-end acceleration. To maintain the accuracy of attention, we adopt quantization-aware training and self-distillation techniques, mitigating quantization errors while ensuring sign-aligned similarity. BinaryAttention is more than 2x faster than FlashAttention2 on A100 GPUs. Extensive experiments on vision transformer and diffusion transformer benchmarks demonstrate that BinaryAttention matches or even exceeds full-precision attention, validating its effectiveness. Our work provides a highly efficient and effective alternative to full-precision attention, pushing the frontier of low-bit vision and diffusion transformers. The codes and models can be found at https://github.com/EdwardChasel/BinaryAttention.

While originally designed for natural language processing tasks, the self-attention mechanism has recently taken various computer vision areas by storm. However, the 2D nature of images brings three challenges for applying self-attention in computer vision. (1) Treating images as 1D sequences neglects their 2D structures. (2) The quadratic complexity is too expensive for high-resolution images. (3) It only captures spatial adaptability but ignores channel adaptability. In this paper, we propose a novel linear attention named large kernel attention (LKA) to enable self-adaptive and long-range correlations in self-attention while avoiding its shortcomings. Furthermore, we present a neural network based on LKA, namely Visual Attention Network (VAN). While extremely simple, VAN surpasses similar size vision transformers(ViTs) and convolutional neural networks(CNNs) in various tasks, including image classification, object detection, semantic segmentation, panoptic segmentation, pose estimation, etc. For example, VAN-B6 achieves 87.8% accuracy on ImageNet benchmark and set new state-of-the-art performance (58.2 PQ) for panoptic segmentation. Besides, VAN-B2 surpasses Swin-T 4% mIoU (50.1 vs. 46.1) for semantic segmentation on ADE20K benchmark, 2.6% AP (48.8 vs. 46.2) for object detection on COCO dataset. It provides a novel method and a simple yet strong baseline for the community. Code is available at https://github.com/Visual-Attention-Network.

Multi-head attention layers, as used in the Transformer neural sequence model, are a powerful alternative to RNNs for moving information across and between sequences. While training these layers is generally fast and simple, due to parallelizability across the length of the sequence, incremental inference (where such paralleization is impossible) is often slow, due to the memory-bandwidth cost of repeatedly loading the large "keys" and "values" tensors. We propose a variant called multi-query attention, where the keys and values are shared across all of the different attention "heads", greatly reducing the size of these tensors and hence the memory bandwidth requirements of incremental decoding. We verify experimentally that the resulting models can indeed be much faster to decode, and incur only minor quality degradation from the baseline.

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.

Efficient inference is critical for long-context language models, where attention computation and KV-cache access dominate the cost. Recent work RAT+, introduces a recurrence-augmented attention backbone that enables flexible dilated attention at inference time. In this paper, we investigate whether this exponentially decaying memory can also improve existing query-aware sparse inference methods. Using representative methods including Quest, MoBA, and SnapKV, we show that RAT+ consistently improves accuracy over standard attention across sparse budgets on eight needle-in-a-haystack tasks. We validate these gains both on the released checkpoints from the RAT+ paper and on OLMo2-7B, which we continue pretraining with the added memory module for 10B tokens. Finally, we propose two hypotheses explaining why this memory module benefits query-aware sparse inference and design targeted experiments to support them.

We provide a probabilistic interpretation of attention and show that the standard dot-product attention in transformers is a special case of Maximum A Posteriori (MAP) inference. The proposed approach suggests the use of Expectation Maximization algorithms for online adaptation of key and value model parameters. This approach is useful for cases in which external agents, e.g., annotators, provide inference-time information about the correct values of some tokens, e.g, the semantic category of some pixels, and we need for this new information to propagate to other tokens in a principled manner. We illustrate the approach on an interactive semantic segmentation task in which annotators and models collaborate online to improve annotation efficiency. Using standard benchmarks, we observe that key adaptation boosts model performance (sim10% mIoU) in the low feedback regime and value propagation improves model responsiveness in the high feedback regime. A PyTorch layer implementation of our probabilistic attention model will be made publicly available here: https://github.com/apple/ml-probabilistic-attention.

Long-context Large Language Model inference is severely bottlenecked by the massive Key-Value (KV) cache, yet existing sparse attention methods often suffer from static fixed-budget (Top-k) retrieval or rely on proxy scores that are computationally expensive and biased. To address these limitations, we propose RaBitQCache, a novel sparse attention framework that utilizes randomized rotated binary quantization and high-throughput binary-INT4 arithmetic to efficiently estimate attention weights. Our proxy score serves as an unbiased estimator with a proven error bound, enabling adaptive Top-p retrieval that dynamically adjusts the token budget based on actual attention sparsity. We further implement a hardware-aware system with asynchronous pipelining and lazy updates to mask overhead. Evaluations demonstrate that RaBitQCache significantly accelerates inference and reduces memory I/O while preserving generation quality compared to state-of-the-art baselines. Code is available at https://github.com/Sakuraaa0/RaBitQCache.git.

The Transformer architecture has revolutionized deep learning through its Self-Attention mechanism, which effectively captures contextual information. However, the memory footprint of Self-Attention presents significant challenges for long-sequence tasks. Grouped Query Attention (GQA) addresses this issue by grouping queries and mean-pooling the corresponding key-value heads - reducing the number of overall parameters and memory requirements in a flexible manner without adversely compromising model accuracy. In this work, we introduce enhancements to GQA, focusing on two novel approaches that deviate from the static nature of grouping: Key-Distributed GQA (KDGQA) and Dynamic Key-Distributed GQA (DGQA), which leverage information from the norms of the key heads to inform query allocation. Specifically, KDGQA looks at the ratios of the norms of the key heads during each forward pass, while DGQA examines the ratios of the norms as they evolve through training. Additionally, we present Perturbed GQA (PGQA) as a case-study, which introduces variability in (static) group formation via subtracting noise from the attention maps. Our experiments with up-trained Vision Transformers, for Image Classification on datasets such as CIFAR-10, CIFAR-100, Food101, and Tiny ImageNet, demonstrate the promise of these variants in improving upon the original GQA through more informed and adaptive grouping mechanisms: specifically ViT-L experiences accuracy gains of up to 8% when utilizing DGQA in comparison to GQA and other variants. We further analyze the impact of the number of Key-Value Heads on performance, underscoring the importance of utilizing query-key affinities. Code is available on GitHub.

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.

Post-Training Quantization (PTQ) has emerged as an effective technique for alleviating the substantial computational and memory overheads of Vision-Language Models (VLMs) by compressing both weights and activations without retraining the full model. Existing PTQ methods primarily rely on static identification and global compensation of sensitive or outlier channels, yet they often overlook the distributional differences of these important channels across inputs, leading to unsatisfactory quantization. In this work, we observe that the distributions and occurrence frequencies of important channels vary significantly both across modalities and among tokens, even within the same modality. Accordingly, we propose Quant Experts (QE), a token-aware adaptive error compensation with mixture-of-experts for VLMs quantization. QE divides the important channels into token-independent and token-dependent groups. For the former, a shared expert is designed for most tokens to compensate for global quantization error using a low-rank adapter. For the latter, routed experts including multiple routed low-rank adapters are elaborated to compensate for local quantization error related to specific tokens. Extensive experiments demonstrate that QE consistently enhances task accuracy across various quantization settings and model scales, ranging from 2B to 70B parameters, while maintaining performance comparable to full-precision models.

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.

We present a very simple algorithm for attention that requires O(1) memory with respect to sequence length and an extension to self-attention that requires O(log n) memory. This is in contrast with the frequently stated belief that self-attention requires O(n^2) memory. While the time complexity is still O(n^2), device memory rather than compute capability is often the limiting factor on modern accelerators. Thus, reducing the memory requirements of attention allows processing of longer sequences than might otherwise be feasible. We provide a practical implementation for accelerators that requires O(n) memory, is numerically stable, and is within a few percent of the runtime of the standard implementation of attention. We also demonstrate how to differentiate the function while remaining memory-efficient. For sequence length 16384, the memory overhead of self-attention is reduced by 59X for inference and by 32X for differentiation.

Large language models (LLMs) represent a groundbreaking advancement in the domain of natural language processing due to their impressive reasoning abilities. Recently, there has been considerable interest in increasing the context lengths for these models to enhance their applicability to complex tasks. However, at long context lengths and large batch sizes, the key-value (KV) cache, which stores the attention keys and values, emerges as the new bottleneck in memory usage during inference. To address this, we propose Eigen Attention, which performs the attention operation in a low-rank space, thereby reducing the KV cache memory overhead. Our proposed approach is orthogonal to existing KV cache compression techniques and can be used synergistically with them. Through extensive experiments over OPT, MPT, and Llama model families, we demonstrate that Eigen Attention results in up to 40% reduction in KV cache sizes and up to 60% reduction in attention operation latency with minimal drop in performance.

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.

Effectively representing medical images, especially retinal images, presents a considerable challenge due to variations in appearance, size, and contextual information of pathological signs called lesions. Precise discrimination of these lesions is crucial for diagnosing vision-threatening issues such as diabetic retinopathy. While visual attention-based neural networks have been introduced to learn spatial context and channel correlations from retinal images, they often fall short in capturing localized lesion context. Addressing this limitation, we propose a novel attention mechanism called Guided Context Gating, an unique approach that integrates Context Formulation, Channel Correlation, and Guided Gating to learn global context, spatial correlations, and localized lesion context. Our qualitative evaluation against existing attention mechanisms emphasize the superiority of Guided Context Gating in terms of explainability. Notably, experiments on the Zenodo-DR-7 dataset reveal a substantial 2.63% accuracy boost over advanced attention mechanisms & an impressive 6.53% improvement over the state-of-the-art Vision Transformer for assessing the severity grade of retinopathy, even with imbalanced and limited training samples for each class.

Block sparse attention is a hardware friendly way to alleviate the key-value (KV) cache read bottleneck in large language models (LLMs). However, it is not prevalent among leading open-weight LLMs, which rely instead on dense attention or fine-grained selection, thereby motivating our analysis. We study DeepSeek's Native Sparse Attention (NSA) as a representative method, whose three-branch design lets us isolate block selection, the most challenging and consequential stage. We formalize selection and reduce it to ranking blocks by a single quantity, the attention mass: the sum of a block's attention scores. We show that if selection retrieves the blocks with the largest attention mass, block sparse attention can match the quality of dense attention. However, computing the exact attention mass requires reading every key, so the problem of block selection ultimately reduces to approximating this mass from a compact summary instead of the full keys. Via a cumulant expansion, we show why existing methods falter: their selection strategies attempt to estimate the attention mass, but are confined to a first-order approximation. Therefore, we propose COBS (Cumulant Order Block Sparse Attention), an attention method that builds on NSA, incorporating a novel selector that stores a compressed second-order statistic per block. On the 32k RULER long-context retrieval benchmark, COBS raises the NSA baseline's mean score from 0.2999 to 0.8195, approaching dense attention at 0.9040 and closing about 86% of the gap, while using only 1.21x the KV cache read traffic of the NSA baseline and 15.15x less read traffic than dense. The same model preserves short-context behavior and attains lower position-wise negative log-likelihood (NLL) than dense attention in our comparison.

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.

The transformer architecture has driven breakthroughs in recent years on tasks which require modeling pairwise relationships between sequential elements, as is the case in natural language understanding. However, long seqeuences pose a problem due to the quadratic complexity of the attention operation. Previous research has aimed to lower the complexity by sparsifying or linearly approximating the attention matrix. Yet, these approaches cannot straightforwardly distill knowledge from a teacher's attention matrix and often require complete retraining from scratch. Furthermore, previous sparse and linear approaches lose interpretability if they cannot produce full attention matrices. To address these challenges, we propose SEA: Sparse linear attention with an Estimated Attention mask. SEA estimates the attention matrix with linear complexity via kernel-based linear attention, then subsequently creates a sparse attention matrix with a top-k selection to perform a sparse attention operation. For language modeling tasks (Wikitext2), previous linear and sparse attention methods show roughly two-fold worse perplexity scores over the quadratic OPT-1.3B baseline, while SEA achieves better perplexity than OPT-1.3B, using roughly half the memory of OPT-1.3B, providing interpretable attention matrix. We believe that our work will have a large practical impact, as it opens the possibility of running large transformers on resource-limited devices with less memory.

Layer Normalization (LayerNorm) is an inherent component in all Transformer-based models. In this paper, we show that LayerNorm is crucial to the expressivity of the multi-head attention layer that follows it. This is in contrast to the common belief that LayerNorm's only role is to normalize the activations during the forward pass, and their gradients during the backward pass. We consider a geometric interpretation of LayerNorm and show that it consists of two components: (a) projection of the input vectors to a d-1 space that is orthogonal to the left[1,1,...,1right] vector, and (b) scaling of all vectors to the same norm of d. We show that each of these components is important for the attention layer that follows it in Transformers: (a) projection allows the attention mechanism to create an attention query that attends to all keys equally, offloading the need to learn this operation by the attention; and (b) scaling allows each key to potentially receive the highest attention, and prevents keys from being "un-select-able". We show empirically that Transformers do indeed benefit from these properties of LayeNorm in general language modeling and even in computing simple functions such as "majority". Our code is available at https://github.com/tech-srl/layer_norm_expressivity_role .

Recent advancements in Multi-modality Large Language Models (MLLMs) have demonstrated remarkable capabilities in complex high-level vision tasks. However, the exploration of MLLM potential in visual quality assessment, a vital aspect of low-level vision, remains limited. To address this gap, we introduce Q-Boost, a novel strategy designed to enhance low-level MLLMs in image quality assessment (IQA) and video quality assessment (VQA) tasks, which is structured around two pivotal components: 1) Triadic-Tone Integration: Ordinary prompt design simply oscillates between the binary extremes of positive and negative. Q-Boost innovates by incorporating a `middle ground' approach through neutral prompts, allowing for a more balanced and detailed assessment. 2) Multi-Prompt Ensemble: Multiple quality-centric prompts are used to mitigate bias and acquire more accurate evaluation. The experimental results show that the low-level MLLMs exhibit outstanding zeros-shot performance on the IQA/VQA tasks equipped with the Q-Boost strategy.

We investigate the mechanism underlying a previously identified phenomenon in Vision Transformers -- the emergence of high-norm tokens that lead to noisy attention maps. We observe that in multiple models (e.g., CLIP, DINOv2), a sparse set of neurons is responsible for concentrating high-norm activations on outlier tokens, leading to irregular attention patterns and degrading downstream visual processing. While the existing solution for removing these outliers involves retraining models from scratch with additional learned register tokens, we use our findings to create a training-free approach to mitigate these artifacts. By shifting the high-norm activations from our discovered register neurons into an additional untrained token, we can mimic the effect of register tokens on a model already trained without registers. We demonstrate that our method produces cleaner attention and feature maps, enhances performance over base models across multiple downstream visual tasks, and achieves results comparable to models explicitly trained with register tokens. We then extend test-time registers to off-the-shelf vision-language models to improve their interpretability. Our results suggest that test-time registers effectively take on the role of register tokens at test-time, offering a training-free solution for any pre-trained model released without them.

Dot-product attention mechanism plays a crucial role in modern deep architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact computation of this model incurs quadratic time and memory complexities in sequence length, hindering the training of long-sequence models. Critical bottlenecks are due to the computation of partition functions in the denominator of softmax function as well as the multiplication of the softmax matrix with the matrix of values. Our key observation is that the former can be reduced to a variant of the kernel density estimation (KDE) problem, and an efficient KDE solver can be further utilized to accelerate the latter via subsampling-based fast matrix products. Our proposed KDEformer can approximate the attention in sub-quadratic time with provable spectral norm bounds, while all prior results merely provide entry-wise error bounds. Empirically, we verify that KDEformer outperforms other attention approximations in terms of accuracy, memory, and runtime on various pre-trained models. On BigGAN image generation, we achieve better generative scores than the exact computation with over 4times speedup. For ImageNet classification with T2T-ViT, KDEformer shows over 18times speedup while the accuracy drop is less than 0.5%.

Linear attention has emerged as a cornerstone for efficient long-context architectures, as evidenced by its integration into state-of-the-art open-source models including Qwen3.5/3.6, Kimi Linear, and RWKV-7. Models that incorporate linear attention layers with the so-called Delta-Rule involve the inversion of triangular matrices as a core sub-routine. This operation often forms a performance bottleneck, and, due to its high-sensitivity to numerical errors, it can significantly deteriorate end-to-end model accuracy if it is not carefully implemented. This work provides a systematic analysis of both direct and iterative triangular inversion algorithms, targeting methods that are rich in matrix products, and, therefore, have the potential to efficiently utilize modern hardware. To that end, our analysis covers a broad spectrum of mathematical and practical aspects, with a heavy focus on numerical stability, computational complexity, and, ultimately, hardware efficiency and practical considerations. We provide a rigorous experimental evaluation to verify these properties in practical scenarios, and in low-precision floating-point representations, highlighting the strengths and limitations of each method. Performance benchmarks on NPUs reveal up to 4.3times speed-up against the state-of-the-art implementations of SGLang for triangular matrix inversion, leading to significant performance improvements on the entire layer level, while maintaining full end-to-end model accuracy.

Multi-headed Attention's (MHA) quadratic compute and linearly growing KV-cache make long-context transformers expensive to train and serve. Prior works such as Grouped Query Attention (GQA) and Multi-Latent Attention (MLA) shrink the cache, speeding decode, but leave compute, which determines prefill and training speed, largely unchanged. We introduce Compressed Convolutional Attention (CCA), a novel attention method which down-projects queries, keys, and values and performs the entire attention operation inside the shared latent space. This simple design dramatically cuts parameters, KV-cache, and FLOPs all at once by the desired compression factor. Because CCA is orthogonal to head-sharing, we combine the two to form Compressed Convolutional Grouped Query Attention (CCGQA), which further tightens the compute-bandwidth Pareto frontier so that users can tune compression toward either FLOP or memory limits without sacrificing quality. Experiments show that CCGQA consistently outperforms both GQA and MLA at equal KV-cache compression on dense and MoE models. Additionally, we show that CCGQA outperforms all other attention methods on MoE models with half the KV-cache of GQA and MLA, achieving an 8x KV-cache compression with no drop in performance compared to standard MHA. CCA and CCGQA also dramatically reduce the FLOP cost of attention which leads to substantially faster training and prefill than existing methods. On H100 GPUs, our fused CCA/CCGQA kernel reduces prefill latency by about 1.7x at a sequence length of 16k relative to MHA, and accelerates backward by about 1.3x.

With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. Recent works found promise in recasting the problem of quantum state reconstruction to learning the probability distribution of quantum state measurement vectors using generative neural network models. Here we propose the "Attention-based Quantum Tomography" (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. The AQT is based on the model proposed in "Attention is all you need" by Vishwani et al (2017) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for natural language processing captures the correlations among words in a sentence.

Key-value (KV) cache compression has emerged as a critical technique for reducing the memory and latency overhead of autoregressive language models during inference. Prior approaches predominantly rely on query-key attention scores to rank and evict cached tokens, assuming that attention intensity correlates with semantic importance. However, this heuristic overlooks the contribution of value vectors, which directly influence the attention output. In this paper, we propose CurDKV, a novel, value-centric KV compression method that selects keys and values based on leverage scores computed from CUR matrix decomposition. Our approach approximates the dominant subspace of the attention output softmax(QK^T)V, ensuring that the retained tokens best preserve the model's predictive behavior. Theoretically, we show that attention score approximation does not guarantee output preservation, and demonstrate that CUR-based selection minimizes end-to-end attention reconstruction loss. Empirically, CurDKV achieves up to 9.6% higher accuracy than state-of-the-art methods like SnapKV and ChunkKV under aggressive compression budgets on LLaMA and Mistral, while maintaining compatibility with FlashAttention and Grouped Query Attention. In addition to improved accuracy, CurDKV reduces generation latency by up to 40% at high compression, offering a practical speed-accuracy tradeoff.

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.

The key-value (KV) cache is a primary memory bottleneck in Transformers. We propose Low-Rank Key-Value (LRKV) attention, which reduces KV cache memory by exploiting redundancy across attention heads, while being compute efficient. Each layer uses a shared full-rank KV projection augmented with low-rank, head-specific residuals, providing a continuous trade-off between complete sharing and full independence. After pretraining models of size 128M to 6.3B parameters, LRKV consistently achieves the lowest test loss among standard MHA, MQA/GQA, and MLA while using only 45-53\% of MHA's KV cache. LRKV reaches equivalent baseline quality 18-25\% faster (measured in training steps). After supervised midtraining, LRKV achieves the highest downstream task performance across ARC-Easy, ARC-Challenge, MMLU, GSM8K, and HumanEval benchmarks.

Transformers serve as the foundation of most modern large language models. To mitigate the quadratic complexity of standard full attention, various efficient attention mechanisms, such as linear and hybrid attention, have been developed. A fundamental gap remains: their expressive power relative to full attention lacks a rigorous theoretical characterization. In this work, we theoretically characterize the performance differences among these attention mechanisms. Our theory applies to all linear attention variants that can be formulated as a recurrence, including Mamba, DeltaNet, etc. Specifically, we establish an expressiveness hierarchy: for the sequential function composition-a multi-step reasoning task that must occur within a model's forward pass, an (L+1)-layer full attention network is sufficient, whereas any hybrid network interleaving L-1 layers of full attention with a substantially larger number (2^{3L^2}) of linear attention layers cannot solve it. This result demonstrates a clear separation in expressive power between the two types of attention. Our work provides the first provable separation between hybrid attention and standard full attention, offering a theoretical perspective for understanding the fundamental capabilities and limitations of different attention mechanisms.

Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing tasks. These capabilities stem primarily from the self-attention mechanism, which enables modeling of long-range dependencies. However, the quadratic complexity of self-attention with respect to sequence length poses significant computational and memory challenges, especially as sequence length extends to extremes. While various sparse attention and KV cache compression methods have been proposed to improve efficiency, they often suffer from limitations such as reliance on fixed patterns, inability to handle both prefilling and decoding stages, or the requirement for additional training. In this paper, we propose Training-free Context-adaptive Attention (TCA-Attention), a training-free sparse attention mechanism that selectively attends to only the informative tokens for efficient long-context inference. Our method consists of two lightweight phases: i) an offline calibration phase that determines head-specific sparsity budgets via a single forward pass, and ii) an online token selection phase that adaptively retains core context tokens using a lightweight redundancy metric. TCA-Attention provides a unified solution that accelerates both prefilling and decoding while reducing KV cache memory footprint, without requiring parameter updates or architectural changes. Theoretical analysis shows that our approach maintains bounded approximation error. Extensive experiments demonstrate that TCA-Attention achieves a 2.8times speedup and reduces KV cache by 61% at 128K context length while maintaining performance comparable to full attention across various benchmarks, offering a practical plug-and-play solution for efficient long-context inference.

Inference on large language models can be expensive in terms of the compute and memory costs involved, especially when long sequence lengths are used. In particular, the self-attention mechanism used in such models contributes significantly to these costs, which has resulted in several recent works that propose sparse attention approximations for inference. In this work, we propose to approximate the self-attention computation by focusing on the dimensionality of key vectors computed in the attention block. Our analysis reveals that the key vectors lie in a significantly lower-dimensional space, consistently across several datasets and models. Exploiting this observation, we propose Loki, a novel sparse attention method that ranks and selects tokens in the KV-cache based on attention scores computed in low-dimensional space. Our evaluations show that Loki is able to maintain the efficacy of the models better than other popular approximation methods, while speeding up the attention computation due to reduced data movement (load/store) and compute costs.

Graphical user interface (GUI) agents built on vision-language models have emerged as a promising approach to automate human-computer workflows. However, they also face the inefficiency challenge as they process long sequences of high-resolution screenshots and solving long-horizon tasks, making inference slow, costly and memory-bound. While key-value (KV) caching can mitigate this, storing the full cache is prohibitive for image-heavy contexts. Existing cache-compression methods are sub-optimal as they do not account for the spatial and temporal redundancy of GUIs. In this work, we first analyze attention patterns in GUI agent workloads and find that, unlike in natural images, attention sparsity is uniformly high across all transformer layers. This insight motivates a simple uniform budget allocation strategy, which we show empirically outperforms more complex layer-varying schemes. Building on this, we introduce GUI-KV, a plug-and-play KV cache compression method for GUI agents that requires no retraining. GUI-KV combines two novel techniques: (i) spatial saliency guidance, which augments attention scores with the L2 norm of hidden states to better preserve semantically important visual tokens, and (ii) temporal redundancy scoring, which projects previous frames' keys onto the current frame's key subspace to preferentially prune redundant history. Across standard GUI agent benchmarks and models, GUI-KV outperforms competitive KV compression baselines, closely matching full-cache accuracy at modest budgets. Notably, in a 5-screenshot setting on the AgentNetBench benchmark, GUI-KV reduces decoding FLOPs by 38.9% while increasing step accuracy by 4.1% over the full-cache baseline. These results demonstrate that exploiting GUI-specific redundancies enables efficient and reliable agent performance.

Converting pretrained attention modules such as grouped-query attention (GQA) into multi-head latent attention (MLA) can improve expressivity without increasing KV-cache cost, making it attractive for efficient inference. However, many practical conversion baselines rely on weight-only low-rank approximations (e.g., SVD-style initializations) and uniform rank allocation. They focus on minimizing the difference between weight matrices rather than on how those weights affect input activations, ignore the covariance structure of activations, and enforce uniform rank across layers, causing activation drift and degraded attention fidelity. To address these issues, we propose CARE, a Covariance-Aware, Rank-Enhanced MLA conversion pipeline under a fixed KV width. CARE introduces three key steps: (i) activation-preserving factorization, which aligns the approximation with the actual input activations rather than just the weights; (ii) adjusted-rank allocation, which spreads a fixed KV budget across layers by giving more capacity to layers that need it most; and (iii) KV-parity mapping, which reparameterizes the converted K and V to fit the MLA format while keeping the KV-cache size unchanged. Our method outperforms a uniform-rank SVD baseline on Qwen3-4B/30B-A3B-Instruct-2507 and Llama-3.1-8B/70B-Instruct, reducing one-shot perplexity by up to 215x and improving mean accuracy by up to 1.70x at matched KV budgets. With a brief post-SVD healing fine-tune, we fully recover the original model's accuracy.

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.

Transformers-based models, such as BERT, have been one of the most successful deep learning models for NLP. Unfortunately, one of their core limitations is the quadratic dependency (mainly in terms of memory) on the sequence length due to their full attention mechanism. To remedy this, we propose, BigBird, a sparse attention mechanism that reduces this quadratic dependency to linear. We show that BigBird is a universal approximator of sequence functions and is Turing complete, thereby preserving these properties of the quadratic, full attention model. Along the way, our theoretical analysis reveals some of the benefits of having O(1) global tokens (such as CLS), that attend to the entire sequence as part of the sparse attention mechanism. The proposed sparse attention can handle sequences of length up to 8x of what was previously possible using similar hardware. As a consequence of the capability to handle longer context, BigBird drastically improves performance on various NLP tasks such as question answering and summarization. We also propose novel applications to genomics data.

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.

Chain-of-thought (CoT) supervised fine-tuning (SFT) is widely adopted to improve reasoning ability, yet we find that it systematically degrades long-context recall in hybrid linear-attention models. Across architectures including HypeNet and Jet-Nemotron, retrieval performance on Needle-In-A-Haystack (NIAH) deteriorates substantially after CoT-SFT, and the degradation becomes more severe under harder retrieval settings and longer context windows. For example, HypeNet-9B on NIAH-S2@256K decreases from 67.2% to 9.4%. We attribute this to CoT-SFT biasing attention gradients toward short-range patterns, disrupting query-key projections (W_Q, W_K) that are responsible for long-range routing. Motivated by this observation, we propose QK-Restore, a training-free method that restores only W_Q and W_K from the pre-SFT checkpoint while preserving all other post-SFT parameters. We further introduce a Procrustes variant to balance routing preservation and reasoning adaptation. Across architectures, QK-Restore consistently restores long-context capability at zero training cost while preserving reasoning performance; for instance, on HypeNet-5B it improves S3@256K from 65.4% to 76.4% while maintaining strong reasoning performance.