Attention Mechanisms

Large language models (LLMs) exhibit a wide range of capabilities, including mathematical reasoning, code generation, and linguistic behaviors. We show that Transformer architectures contain small subsets of attention heads that are necessary for certain capabilities. Zeroing out as few as five task-specific heads can degrade performance by up to $60\%$ on standard benchmarks measuring the capability of interest, while largely preserving performance on unrelated tasks. We introduce a compressed sensing-based method that exploits the sparsity of these heads to identify them via strategic knockouts and a small number of model evaluations. We validate these findings across Llama and Qwen models ranging from 1B to 14B parameters and a diverse set of capabilities including mathematical abilities and code generation, revealing a modular organization in which specialized capabilities are dependent on sparse, functionally distinct components. Overall, our results suggest that capability localization is a general organizational principle of Transformer language models, with implications for interpretability, model editing, and AI safety. Code is released at https://github.com/locuslab/llm-components.

Learned gates can approximate sparse attention patterns on frozen transformers, yet provide limited benefit over random gates when trained jointly with the model. We investigate this difference in a controlled 31M-parameter transformer and attribute it to routing absorption: model representations co-adapt to the imposed mask, reducing the incremental benefit of learned routing. Four experiments characterize the phenomenon. Differentiable soft gating yields perplexities of 48.73 plus or minus 0.60 with learned gates and 49.83 plus or minus 0.04 with frozen random gates over three seeds. Hard top-k masking provides no gradient path to the gate scores in the tested implementation. Gates distilled onto co-adapted and dense-trained Q/K/V both achieve high F1 against oracle masks, but hard-mask deployment yields perplexities of 601.6 and 48.6, respectively. Stochastic mask training also leaves a substantial deployment penalty: dense evaluation yields 78.2 perplexity, compared with 37.3 for the dense baseline. Experiments on Qwen3-1.7B show that increasing the number of trainable attention layers reduces the gap between learned and random gates. We relate these results to co-adaptation in Mixture-of-Experts and propose parameter asymmetry between the gate and the model as a contributing mechanism. For the tested per-query, token-level gates, freezing the model provides stable routing targets and enables effective post-hoc sparsification. The results motivate random-routing controls and separate evaluation of routing quality and model adaptation in sparse attention methods.

With the increasing availability of high-resolution remote sensing and aerial imagery, oriented object detection has become a key capability for geographic information updating, maritime surveillance, and disaster response. However, it remains challenging due to cluttered backgrounds, severe scale variation, and large orientation changes. Existing approaches largely improve performance through multi-scale feature fusion with feature pyramid networks or contextual modeling with attention, but they often lack explicit foreground modeling and do not leverage geometric orientation priors, which limits feature discriminability. To overcome these limitations, we propose FGAA-FPN, a Foreground-Guided Angle-Aware Feature Pyramid Network for oriented object detection. FGAA-FPN is built on a hierarchical functional decomposition that accounts for the distinct spatial resolution and semantic abstraction across pyramid levels, thereby strengthening multi-scale representations. Concretely, a Foreground-Guided Feature Modulation module learns foreground saliency under weak supervision to enhance object regions and suppress background interference in low-level features. In parallel, an Angle-Aware Multi-Head Attention module encodes relative orientation relationships to guide global interactions among high-level semantic features. Extensive experiments on DOTA v1.0 and DOTA v1.5 demonstrate that FGAA-FPN achieves state-of-the-art results, reaching 75.5% and 68.3% mAP, respectively.

A core bottleneck in large language model (LLM) inference is the cost of attending over the ever-growing key-value (KV) cache. Although near-oracle top-k KV selection can preserve the quality of dense attention while sharply reducing computation and bandwidth, existing sparse methods generally rely on posterior heuristics, i.e., selectors conditioned on observed attention or proxy scores. Such conditioning introduces posterior bias: it tends to distort true token importance and miss salient tokens, thereby impairing long-range reasoning. To tackle this problem, we propose Pre-hoc Sparsity (PrHS), which selects KV entries before attention scoring and provides explicit accuracy control. Let the attention mass of discarded entries be delta (the dropped mass). Through a marginal-to-mutual-information analysis, we derive an upper bound on the mutual-information loss that depends only on the dropped mass. This relation explains failure modes of posterior heuristics and enables verifiable guarantees by controlling the dropped mass in advance. Within PrHS, we instantiate three orthogonal pre-hoc selectors along the axes of time, depth, and layer. Extensive experiments on LLaMA and Mistral families validate PrHS. Across GSM8K and CoQA, PrHS reduces retrieval overhead by over 90%, achieving 3x higher retrieval sparsity than HShare at matched or better accuracy. It incurs under 1% average degradation on LongBench, lowers attention FLOPs by about 15% versus prior sparse baselines, and yields a 9.9x speedup in attention-operator latency and 2.8x higher throughput on NVIDIA A100-80GB GPUs than the dense baseline.

Efficient long-context inference faces two coupled bottlenecks: KV-cache memory grows linearly with context length, while attention computation grows quadratically. Existing approaches typically address one at the expense of irreversible token eviction, full-cache retention, or full-history reconstruction, limiting their effectiveness for multi-turn interaction and long-form reasoning. Motivated by two empirical properties, Long-Range Inter-Token Similarity and Smooth Residual Distribution, we propose ResidualKV, which factorizes the KV cache into a sparse set of globally retrieved references and compact, quantized residual codes for the remaining tokens. This representation preserves token-specific information without permanent eviction and, when combined with sparse attention, reconstructs only the selected states on demand. Dynamic-stride scheduling further reduces reference growth from linear to approximately logarithmic at ultra-long contexts. Across Llama, Qwen, LLaVA-OV, and Qwen3-VL backbones, ResidualKV maintains near-full-cache performance using only 13%-16% KV storage and 30% attention computation on LongBench, and 8%-10% storage and 10% computation in matched-budget multimodal evaluation. It also accelerates decoding by up to $1.5\times$ with KV-cache quantization and $3.4\times$ without it. These results show that global cross-token redundancy supports accurate, memory-efficient, and computation-efficient long-context inference. The source code is available at https://github.com/CURRENTF/ResidualKV.

We propose a variational quantum implementation of self-attention (QSA)-the core operation in transformers and large language models-which predicts future elements of a sequence by forming overlap-weighted combinations of past data. At variance with previous approaches, our QSA realizes the required nonlinearity through interference of state overlaps and a degree-$k$ polynomial kernel, and estimates a loss based on Rényi-$1/2$ entropic functionals via two observables' expectation values, avoiding the decoding of amplitude-encoded predictions into classical probabilities. QSA also accommodates a constrained, trainable data-embedding tying state overlaps to data-level similarities. Its dominant end-to-end training complexity scales as $O\left(μ^{-1}k^2Td\right)$, versus $O\left(T d^{k+1}\right)$ of the fairest classical comparison, with $μ$ a training signal; we show numerically that this allows a complexity advantage in the regime where sequence length $T$ dominates the embedding size $d$. In simulations, our QSA-based quantum transformer learns sequence prediction on classical data and on many-body transverse-field Ising trajectories-establishing trainable attention as a practical primitive for quantum dynamical modeling.

Generating long-form content, such as minute-long videos and extended texts, is increasingly important for modern generative models. Block diffusion improves inference efficiency via KV caching and block-wise causal inference and has been widely adopted in diffusion language models and video generation. However, in long-context settings, block diffusion still incurs substantial overhead from repeatedly computing attention over a growing KV cache. We identify an underexplored property of block diffusion: cross-step redundancy of attention within a block. Our analysis shows that attention outputs from tokens outside the current block remain largely stable across diffusion steps, while block-internal attention varies significantly. Based on this observation, we propose FlashBlock, a cached block-external attention mechanism that reuses stable attention output, reducing attention computation and KV cache access without modifying the diffusion process. Moreover, FlashBlock is orthogonal to sparse attention and can be combined as a complementary residual reuse strategy, substantially improving model accuracy under aggressive sparsification. Experiments on diffusion language models and video generation demonstrate up to 1.44$\times$ higher token throughput and up to 1.6$\times$ reduction in attention time, with negligible impact on generation quality. Project page: https://caesarhhh.github.io/FlashBlock/.

The self-attention mechanism, at the heart of the Transformer model, is able to effectively model pairwise interactions between tokens. However, numerous recent works have shown that it is unable to perform basic tasks involving detecting triples of correlated tokens, or compositional tasks where multiple input tokens need to be referenced to generate a result. Some higher-dimensional alternatives to self-attention have been proposed to address this, including higher-order attention and Strassen attention, which can perform some of these polyadic tasks in exchange for slower, superquadratic running times. In this work, we define a vast class of generalizations of self-attention, which we call poly-attention mechanisms. Our mechanisms can incorporate arbitrary higher-order (tensor) computations as well as arbitrary relationship structures between the input tokens, and they include the aforementioned alternatives as special cases. We then systematically study their computational complexity and representational strength, including giving new algorithms and matching complexity-theoretic lower bounds on the time complexity of computing the attention matrix exactly as well as approximately, and tightly determining which polyadic tasks they can each perform. Our results give interesting trade-offs between different desiderata for these mechanisms, including a tight relationship between how expressive a mechanism is, and how large the coefficients in the model may be so that the mechanism can be approximated in almost-linear time. Notably, we give a new attention mechanism which can be computed exactly in quadratic time, and which can perform function composition for any fixed number of functions. Prior mechanisms, even for just composing two functions, could only be computed in superquadratic time, and our new lower bounds show that faster algorithms for them are not possible.

Linearizing pretrained large language models (LLMs) primarily relies on intra-layer hybrid attention mechanisms to alleviate the quadratic complexity of standard softmax attention. Existing methods perform token routing based on sliding-window partitions, resulting in position-based selection and fails to capture token-specific global importance. Meanwhile, linear attention further suffers from distribution shift caused by learnable feature maps that distort pretrained feature magnitudes. Motivated by these limitations, we propose STILL, an intra-layer hybrid linearization framework for efficiently linearizing LLMs. STILL introduces a Self-Saliency Score with strong local-global consistency, enabling accurate token selection using sliding-window computation, and retains salient tokens for sparse softmax attention while summarizing the remaining context via linear attention. To preserve pretrained representations, we design a Norm-Preserved Feature Map (NP-Map) that decouples feature direction from magnitude and reinjects pretrained norms. We further adopt a unified training-inference architecture with chunk-wise parallelization and delayed selection to improve hardware efficiency. Experiments show that STILL matches or surpasses the original pretrained model on commonsense and general reasoning tasks, and achieves up to a 86.2% relative improvement over prior linearized attention methods on long-context benchmarks. Code is available at this URL.

Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce high-frequency variations that force adaptive solvers to take excessively small steps, driving up the Number of Function Evaluations (NFE). We propose a novel approach to Neural CDE path construction that replaces exact interpolation with Kernel and Gaussian Process (GP) smoothing, enabling explicit control over trajectory regularity. To recover details lost during smoothing, we propose an attention-based Multi-View CDE (MV-CDE) and its convolutional extension (MVC-CDE), which employ learnable queries to inform path reconstruction. This framework allows the model to distribute representational capacity across multiple trajectories, each capturing distinct temporal patterns. Empirical results demonstrate that our method, MVC-CDE with GP, achieves state-of-the-art accuracy while significantly reducing NFEs and total inference time compared to spline-based baselines.

Diffusion language models (DLMs) generate text through iterative denoising, but inference requires full-sequence attention at every iteration, resulting in substantial redundant computation on masked tokens. Block-wise diffusion can reduce this cost, yet it typically relies on retraining and constrained update orders, limiting its direct applicability to pretrained DLMs. Our token-level analysis reveals pronounced structural locality in DLM inference. Decoding is driven by a small set of prefix-localized active tokens; the influence of distant undecoded context diminishes rapidly, and decoded tokens exhibit stage-wise temporal stability, enabling reuse of intermediate representations except for a brief post-decode transient. Motivated by these observations, we propose \textbf{\placeholder}\footnote{The source code is available at https://github.com/vhicrgit/Window-Diffusion.}, a window-based token pruning and caching method for inference. We maintain a local computation window that slides rightward as denoising progresses, and partition undecoded tokens into: (i) \textit{active tokens} that are computed online, (ii) \textit{buffer tokens} whose KV states are cached and periodically refreshed, and (iii) \textit{far-field tokens} that are pruned outside the window. Computation is restricted to active and buffer tokens within the window, while far-field tokens are omitted at each stage. Experiments on LLaDA and Dream show that, under matched compute budgets, our method achieves up to $99\times$ inference speedup while largely preserving generation performance.

We study positional encodings for multi-view transformers that process tokens from a set of posed input images, and seek a mechanism that encodes patches uniquely, allows SE(3)-invariant attention with multi-frequency similarity, and can adapt to the geometry of the underlying 3D scene. We find that prior (absolute or relative) encoding schemes for multi-view attention do not meet these desiderata, and present RayRoPE to address this gap. RayRoPE represents patch positions based on associated rays and computes query-frame projective coordinates to ensure SE(3) invariance. To adapt to scene geometry, RayRoPE predicts (without direct supervision) a per-token depth to obtain its position along the corresponding ray, while also modeling uncertainty and analytically computing the expected positional encoding. We validate our method on the tasks of novel-view synthesis, stereo depth estimation, and feed-forward 3DGS reconstruction. While remaining efficient, RayRoPE consistently improves over alternate position encoding schemes (e.g., 24% relative improvement on LPIPS in RE10K).

Softmax attention struggles with long contexts due to structural limitations: the strict sum-to-one constraint forces attention sinks on irrelevant tokens, and probability mass disperses as sequence lengths increase. We tackle these problems with Threshold Differential Attention (TDA), a sink-free attention mechanism that achieves ultra-sparsity and improved robustness at longer sequence lengths without the computational overhead of projection methods or the performance degradation caused by noise accumulation of standard rectified attention. TDA applies row-wise extreme-value thresholding with a length-dependent gate, retaining only exceedances. Inspired by the differential transformer, TDA also subtracts an inhibitory view to enhance expressivity. Theoretically, we prove that TDA controls the expected number of spurious survivors per row to $O(1)$ and that consensus spurious matches across independent views vanish as context grows. Empirically, TDA produces $>99\%$ exact zeros and eliminates attention sinks while maintaining competitive performance on standard and long-context benchmarks.

Large Language Models (LLMs) are known to contain significant redundancy, yet a systematic explanation for why certain components, particularly in higher layers, are more redundant has remained elusive. In this work, we identify the BOS sink phenomenon as a key mechanism driving this layer-wise sensitivity. We show that attention heads with high BOS sink scores are strongly associated with functional redundancy: such heads, especially in deeper layers, contribute little to predictive performance and effectively serve as dumping grounds for superfluous attention weights. Leveraging this insight, we introduce a simple pruning strategy that removes high-BOS sink heads. Experiments on Gemma-3, Llama-3.1, and Qwen3 demonstrate that this approach identifies redundant transformer components more reliably than weight- and activation-based criteria in terms of downstream task retention, remaining close to dense baselines at low-to-moderate pruning ratios. We further find that high-scoring sink heads sustain their focus on BOS as context length grows. Overall, our results suggest that structural properties of attention offer a more direct basis for model compression than magnitude-based methods.

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

In this paper, we introduce Exact Flow Linear Attention~(EFLA), an exact-flow formulation of delta-rule linear attention. We show that the delta-rule update can be interpreted as an explicit Euler discretization of an underlying continuous-time system. EFLA replaces this first-order update with the exact closed-form flow. By exploiting the rank-1 structure of the dynamics matrix, both the matrix exponential and the input integral collapse to a simple update that preserves delta-rule linear attention's algebraic structure, parameter count, linear-time complexity, and chunkwise parallelism. This attention mechanism removes the Euler discretization error of the delta-rule dynamics without introducing additional parameters. Experiments on robustness tests, language modeling benchmarks, and the MAD synthetic benchmark show that EFLA improves stability under corrupted and high-energy inputs, reduces perplexity, and achieves stronger downstream performance compared to SSM and Euler-style baselines. These results establish exact-flow integration as a principled and scalable update mechanism for delta-rule linear attention.

Modern large language models increasingly require long contexts for reasoning and multi-document tasks, but attention's quadratic complexity creates a severe computational bottleneck. We present Block Sparse Flash Attention (BSFA), a drop-in replacement that accelerates long-context inference while preserving model quality. Unlike methods that predict importance before computing scores, BSFA computes exact query-key similarities to select the top-k most important value blocks for each query. By comparing per-block maximum scores against calibrated thresholds, we skip approximately 50% of the computation and memory transfers for pruned blocks. Our training-free approach requires only a one-time threshold calibration on a small dataset to learn the per-layer and per-head attention score distributions. We provide a CUDA kernel implementation that can be used as a drop-in replacement for FlashAttention. On Llama-3.1-8B, BSFA achieves up to 1.13x end-to-end speedup on LongBench with only a 1.1% accuracy drop, and up to 1.24x on Needle-in-a-Haystack retrieval at a 1% accuracy drop. The attention kernel itself accelerates by up to 1.38x. We compare BSFA against five recent sparse attention baselines (SpargeAttention, MInference, FlexPrefill, XAttention, and BLASST), and verify the method on Qwen2.5-7B and on A6000 and H100 GPUs. The implementation is available at https://github.com/Danielohayon/Block-Sparse-Flash-Attention.

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 $1.30\times$ higher inference throughput while keeping average zero-shot accuracy within 1.5 percentage points 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 $\sim 1000\times$ faster to score layers, enabling practical, data-free compression of LLMs.

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (\textit{RoPE}) encode positions through \textit{fixed-angle} rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce \textit{Selective RoPE}, an \textit{input-dependent} rotary embedding mechanism, that generalizes \textit{RoPE}, and enables rotation in \textit{arbitrary angles} for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with \textit{Selective RoPE}, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.

Specialized attention heads dubbed induction heads (IHs) have been argued to underlie the remarkable in-context learning capabilities of modern language models; yet, a precise characterization of their emergence, especially in the context of language modeling, remains wanting. In this study, we investigate the relationship between statistical properties of the training data and IH formation in both natural and synthetic training data settings. We show that: (1) a simple equation combining batch size and context size predicts the point at which IHs form and that this emergence point is agnostic to model size; (2) surface bigram repetition frequency and reliability strongly affect the formation of IHs, and we find an effective decision boundary in terms of these two values; (3) local dependency with high bigram repetition frequency and reliability is sufficient for IH formation, but categoriality and the shape of the marginal distribution appear to modulate IH formation near the decision boundary.

Convolutional Neural Networks and Vision Transformers are the two dominant architectural families in computer vision, defined by spatially local convolution and global self-attention respectively. Despite their apparent differences, we show that both operations are special cases of a single $k$-nearest neighbor aggregation framework: convolution selects neighbors by spatial proximity while attention selects by feature similarity, placing them at two ends of a shared operational spectrum. We introduce Convolutional Nearest Neighbors (ConvNN), a unified framework that exactly recovers standard and depthwise convolution, self-attention, and sparse attention variants including KVT-attention as special cases, and exposes the design space of neighbor-selection strategies between them through configurable similarity functions, positional encodings, and aggregation kernels. We validate ConvNN on ImageNet-1K classification across two complementary architectures: a hybrid branching layer in ResNet-50 that combines local and global feature learning, improving top-1 accuracy by 3.0% over the ResNet-50 baseline, and ConvNN-attention in ViT-Base that achieves 81.64% top-1 accuracy, surpassing standard multi-head self-attention by 0.7%. Together, these results demonstrate that ConvNN provides a principled foundation for designing operations that bridge convolutional and attention-based computation.

The substantial inference costs of attention in transformers motivated the development of efficient sequence mixers: namely sparse and sliding window attention, convolutions and linear attention. Although these approaches result in impressive reductions in inference costs, they often trade-off with quality, specifically in-context recall. Apriori fixing this quality-cost tradeoff at training time means being suboptimal from the get-go: some downstream applications might fundamentally require more memory for in-context recall, while other tasks may require lower latency and memory. We propose a conceptually simple meta-sequence mixer with inference-cost controllability: the Compress & Attend Transformer (CAT). CAT decodes chunks of tokens by attending to compressed chunks of the sequence so far. Both compression and decoding can use any existing sequence mixer. Decoding from the compressed sequence yields compute and memory savings, with chunk size setting the operating point on the quality-cost trade-off. Importantly, training CAT across multiple chunk sizes at once unlocks test-time control of this trade-off without any retraining, all in a single model. Instantiated with the most basic choice, dense attention as the mixer, CAT surprisingly suffices to match 10 popular and diverse efficient models (linear, hybrids, sparse) on real-world long-context recall at comparable inference costs, all from a single trained model. CAT further performs competitively on long-context understanding benchmarks while providing 1.4-3.7x higher generation throughput than a dense transformer. Code is at: https://github.com/rajesh-lab/cat-transformer

Mechanistic interpretability aims to reverse-engineer large language models (LLMs) into human-understandable computational circuits. However, the complexity of pretrained models often obscures the minimal mechanisms required for specific reasoning tasks. In this work, we train small, attention-only transformers from scratch on a symbolic version of the Indirect Object Identification (IOI) task, a benchmark for studying coreference-like reasoning in transformers. Surprisingly, a single-layer model with only two attention heads achieves perfect IOI accuracy, despite lacking MLPs and normalization layers. Through residual stream decomposition, spectral analysis, and embedding interventions, we find that the two heads specialize into additive and contrastive subcircuits that jointly implement IOI resolution. Furthermore, we show that a two-layer, one-head model composes information from the previous layer primarily through query-key interactions. These results demonstrate that task-specific training induces highly interpretable, minimal circuits, offering a controlled testbed for probing the computational foundations of transformer reasoning.

Decoding throughput improvements from larger inference batches are limited by GPU memory, which is largely consumed by the key-value (KV) cache. Prior training-free KV cache offloading alleviates this by keeping redundant context on the CPU and fetching only a sparse subset for attention, but it often degrades long-generation quality due to training-inference mismatch on sparse patterns. Meanwhile, trainable sparse attention is incompatible with efficient offloading, as unconstrained KV accesses may force large CPU-to-GPU transfers and erase throughput gains. To this end, we propose NOSA, a trainable sparse attention mechanism natively designed for KV cache offloading. NOSA explicitly constrains the volume of CPU-GPU KV transfers, thereby achieving low communication overhead and high decoding throughput. We further build NOSI, a KV cache offloading inference system that fully unlocks NOSA's efficiency. Empirical results on 1,3,8B LLMs demonstrate that NOSA outperforms KV cache offloading baselines on general, long-input, and long-generation tasks, while boosting decoding throughput by up to 5.04x, 1.92x, and 1.83x over FullAttn, InfLLMv2, and ShadowKV, respectively. We release our code at https://github.com/thunlp/NOSA.

Transformers have achieved remarkable successes across a wide range of applications, yet the theoretical foundation of their model efficiency remains underexplored. In this work, we investigate how the model parameters -- mainly attention heads and head dimensions -- should be allocated across layers to balance expressivity and efficiency. We first provide mathematical analysis on the role of early layers in information extraction from an approximation perspective, with a theoretical characterization on the trade-off between the number of heads and head dimension under a fixed parameter budget. In addition, we uncover and prove the \emph{saturation} behavior of softmax activations: Continuously increasing head dimensions can lead to diminishing returns in learning errors, particularly for long sequences. Supported by both theory and experiments, this saturation pattern suggests that later layers can operate more efficiently with reduced parameters. Combining these insights, we propose principled strategies for allocating attention heads and dimensions across Transformers' layers, shedding light on theoretically-grounded model efficiency of Transformer-based architectures.

Attention is a core operation in large language models (LLMs). We present BD Attention (BDA), a lossless algorithmic reformulation of attention. BDA is enabled by a simple matrix identity from Basis Decomposition (BD), which restructures multi-head projections into a compact form while preserving exact outputs. Unlike I/O-aware system optimizations such as FlashAttention, BDA provides a mathematically guaranteed acceleration that is architecture-agnostic. On DeepSeek-V2-Lite (16B, FP16), BDA requires only 4s of offline preparation with no retraining required and, on modern GPUs, achieves 34% faster key/value projections and 25% smaller weights, while increasing perplexity (PPL) by just 0.02% (FP16) or 0.0004% (FP32), a negligible effect on model performance. These results position BDA as a theoretically exact method for lossless attention acceleration that is complementary to existing engineering-level optimizations. Our code is available at https://github.com/abcbdf/basis-decomposition-official.

Existing data poisoning attacks on retrieval-augmented generation (RAG) systems scale poorly because they require costly optimization of poisoned documents for each target phrase. We introduce Eyes-on-Me, a modular attack that decomposes an adversarial document into reusable Attention Attractors and Focus Regions. Attractors are optimized to direct attention to the Focus Region. Attackers can then insert semantic baits for the retriever or malicious instructions for the generator, adapting to new targets at near zero cost. This is achieved by steering a small subset of attention heads that we empirically identify as strongly correlated with attack success. Across 18 end-to-end RAG settings (3 datasets $\times$ 2 retrievers $\times$ 3 generators), Eyes-on-Me raises average attack success rates from 21.9 to 57.8 (+35.9 points, 2.6$\times$ over prior work). A single optimized attractor transfers to unseen black box retrievers and generators without retraining. Our findings establish a scalable paradigm for RAG data poisoning and show that modular, reusable components pose a practical threat to modern AI systems. They also contribute to interpretability research by revealing a strong link between attention concentration and model outputs.

Most existing approaches to referring segmentation achieve strong performance only through fine-tuning or by composing multiple pre-trained models, often at the cost of additional training and architectural modifications. Meanwhile, large-scale generative diffusion models encode rich semantic information, making them attractive as general-purpose feature extractors. In this work, we introduce a new method that directly exploits features (attention scores) from diffusion transformers for downstream tasks, requiring neither architectural modifications nor additional training. To systematically evaluate these features, we extend benchmarks with vision-language grounding tasks spanning both images and videos. Our key insight is that stop words act as attention magnets: they accumulate surplus attention and can be filtered to reduce noise. Moreover, we identify global attention sinks (GAS) emerging in deeper layers and show that they can be safely suppressed or redirected onto auxiliary tokens, leading to sharper and more accurate grounding maps. We further propose an attention redistribution strategy, where appended stop words partition background activations into smaller clusters, yielding sharper and more localized heatmaps. Building on these findings, we develop RefAM, a simple training-free grounding framework that combines cross-attention maps, GAS handling, and redistribution. Across zero-shot referring image and video segmentation benchmarks, our approach achieves strong performance and surpasses prior methods on most datasets, establishing a new state of the art among training-free methods, without task-specific training or architectural modification. For video, we localize the referent from the spatio-temporal features of a video diffusion transformer via a first-frame query that is then propagated; we therefore do not explicitly resolve temporal (which-frame) expressions.

We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined Wave-Induced Rotary Encodings (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.

Cross-attention is a core mechanism in encoder-decoder architectures, widespread in many fields, including speech-to-text (S2T) processing. Its scores have been repurposed for various downstream applications--such as timestamp estimation and audio-text alignment--under the assumption that they reflect the dependencies between input speech representation and the generated text. While the explanatory nature of attention mechanisms has been widely debated in the broader NLP literature, this assumption remains largely unexplored within the speech domain. To address this gap, we assess the explanatory power of cross-attention in S2T models by comparing its scores to input saliency maps derived from feature attribution. Our analysis spans monolingual and multilingual, single-task and multi-task models at multiple scales, and shows that attention scores moderately to strongly align with saliency-based explanations, particularly when aggregated across heads and layers. However, it also shows that cross-attention captures only about 50% of the input relevance and, in the best case, only partially reflects how the decoder attends to the encoder's representations--accounting for just 52-75% of the saliency. These findings uncover fundamental limitations in interpreting cross-attention as an explanatory proxy, suggesting that it offers an informative yet incomplete view of the factors driving predictions in S2T models.