Transformer Attention

Long-context large language models are limited not only by attention cost but also by out-of-memory (OOM) failures. A selected attention call may not fit in available device memory even when the kernel is optimized. Exact and approximate attention methods reduce memory use, but every fixed implementation still has a device-specific capacity boundary. We introduce Stream-CQSA, an attention-level OOM recovery framework based on CQS decomposition, derived from the theory of cyclic quorum sets (CQS). Stream-CQSA recursively partitions an infeasible attention call into independent subsequence tasks, executes each with a compatible inner kernel, and recomposes the local statistics to recover the full attention output. This recovery is exact relative to the wrapped attention kernel, whether that kernel is exact or approximate. Compared with FlashAttention-2, the major baseline, our native Stream-CQSA kernel improves 16-bit forward-output error relative to a dense float64 reference and matches 16-bit backward-gradient error where FlashAttention-2 fits in the GPU memory. At the longest feasible baseline length, it costs $1.5$--$1.9\times$ the forward runtime and $2.1$--$2.4\times$ the forward--backward runtime. Beyond that sequence length boundary, our method continues to return an output while FlashAttention-2 OOMs. Stream-CQSA is therefore not a faster attention method. Instead, it converts memory-capacity failure into a recoverable execution path by trading extra compute, host-device transfer, and recomposition for completion.

We investigate the integration of human-like working memory constraints into the Transformer architecture and implement several cognitively inspired attention variants, including fixed-width windows based and temporal decay based attention mechanisms. Our modified GPT-2 models are trained from scratch on developmentally plausible datasets (10M and 100M words). Performance is evaluated on grammatical judgment tasks (BLiMP) and alignment with human reading time data. Our results indicate that these cognitively-inspired constraints, particularly fixed-width attention, can significantly improve grammatical accuracy especially when training data is scarce. These constrained models also tend to show a stronger alignment with human processing metrics. The findings suggest that such constraints may serve as a beneficial inductive bias, guiding models towards more robust linguistic representations, especially in data-limited settings.

Retrieval-augmented generation (RAG) systems inject external knowledge to improve LLM outputs, yet the format of injected content -- distinct from its semantic relevance -- can independently distort the model's attention distribution. We identify and formalise a phenomenon we term the structural attention tax: knowledge graph (KG) triples, due to their relational delimiters and repeated slot patterns, capture 2-3x more attention per token than semantically equivalent natural-language text ($\hat{o}$(KG) $\approx$ 0.70 vs. $\hat{o}$(neutral) $\approx$ 0.25), compressing demonstration attention by up to 42% -- regardless of whether the triples are relevant or noise. We develop a formal framework decomposing attention scores into semantic and structural components (Eq. 2), derive a compression bound (Proposition 1) connecting token-level format bias to demonstration attention loss, and show that the structural term governs how much attention is diverted while the semantic term governs whether this helps or hurts. This decoupling reveals two orthogonal axes for improving retrieval-augmented ICL: optimising retrieval quality (semantic axis) and reducing format-driven attention capture (structural axis). Empirically, across two model families (Mistral-7B, LLaMA-3-8B) and three QA benchmarks, we observe that source-task alignment dominates: task-matched BM25 retrieval achieves 58-62% on HotpotQA vs. ConceptNet's 25-27%, a >30 pp gap that dwarfs all gating strategies ($\leq$2 pp). We derive five structure-aware mitigation strategies from the framework, ranging from zero-cost prompt modifications to training-time regularisation; format flattening (S3) is validated by both accuracy and attention-level evidence from a verbalized-triple control, while structural dispersal (S1) yields mixed results that illuminate the challenges of format-level intervention.

Scaling Transformers typically necessitates training larger models from scratch, as standard architectures struggle to expand without discarding learned representations. We identify the primary bottleneck in the attention mechanism's linear projections, which strictly confine feature extraction to fixed-dimensional subspaces, limiting both expressivity and incremental capacity. To address this, we introduce Nexusformer, which replaces linear $Q/K/V$ projections with a Nexus-Rank layer, a three-stage nonlinear mapping driven by dual activations in progressively higher dimensional spaces. This design overcomes the linearity constraint and enables lossless structured growth: new capacity can be injected along two axes via zero-initialized blocks that preserve pretrained knowledge. Experiments on language modeling and reasoning benchmarks demonstrate that Nexusformer matches Tokenformer's perplexity using up to 41.5% less training compute during progressive scaling (240M to 440M). Furthermore, our analysis of growth dynamics reveals that zero initialization induces a stable convergence trajectory, allowing us to derive a geometric scaling law that accurately predicts performance across expansion scales.

In recent years, the Vision Transformer (ViT) has garnered significant attention within the computer vision community. However, the core component of ViT, Self-Attention, lacks explicit spatial priors and suffers from quadratic computational complexity, limiting its applicability. To address these issues, we have proposed RMT, a robust vision backbone with explicit spatial priors for general purposes. RMT utilizes Manhattan distance decay to introduce spatial information and employs a horizontal and vertical decomposition attention method to model global information. Building on the strengths of RMT, Euclidean enhanced Vision Transformer (EVT) is an expanded version that incorporates several key improvements. Firstly, EVT uses a more reasonable Euclidean distance decay to enhance the modeling of spatial information, allowing for a more accurate representation of spatial relationships compared to the Manhattan distance used in RMT. Secondly, EVT abandons the decomposed attention mechanism featured in RMT and instead adopts a simpler spatially-independent grouping approach, providing the model with greater flexibility in controlling the number of tokens within each group. By addressing these modifications, EVT offers a more sophisticated and adaptable approach to incorporating spatial priors into the Self-Attention mechanism, thus overcoming some of the limitations associated with RMT and further enhancing its applicability in various computer vision tasks. Extensive experiments on Image Classification, Object Detection, Instance Segmentation, and Semantic Segmentation demonstrate that EVT exhibits exceptional performance. Without additional training data, EVT achieves 86.6% top1-acc on ImageNet-1k.

Text-attributed graphs integrate semantic information of node texts with topological structure, offering significant value in various applications such as document classification and information extraction. Existing approaches typically encode textual content using language models (LMs), followed by graph neural networks (GNNs) to process structural information. However, during the LM-based text encoding phase, most methods not only perform semantic interaction solely at the word-token granularity, but also neglect the structural dependencies among texts from different nodes. In this work, we propose DuConTE, a dual-granularity text encoder with topology-constrained attention. The model employs a cascaded architecture of two pretrained LMs, encoding semantics first at the word-token granularity and then at the node granularity. During the self-attention computation in each LM, we dynamically adjust the attention mask matrix based on node connectivity, guiding the model to learn semantic correlations informed by the graph structure. Furthermore, when composing node representations from word-token embeddings, we separately evaluate the importance of tokens under the center-node context and the neighborhood context, enabling the capture of more contextually relevant semantic information. Extensive experiments on multiple benchmark datasets demonstrate that DuConTE achieves state-of-the-art performance on the majority of them.

Global self-attention drives modern graph transformers, yet the softmax at its core imposes a structural constraint rarely examined directly: every attention row is non-negative and sums to one, so each per-head output is a mass-conserving convex combination of value vectors. A node can never "attend to nothing." We argue this conservation constraint is a single root cause behind three pathologies usually studied in isolation: the collapse of node representations with depth (over-smoothing), a low-rank bottleneck on per-head outputs, and brittle optimization in deep stacks. Drawing on how sigmoid gating removes analogous attention sinks in language models, we introduce SigGate-GT, a graph transformer that applies a learned, per-head, input-conditioned sigmoid gate to the attention output inside the GraphGPS framework. The gate is a smooth, per-dimension "volume control" that can drive head outputs toward zero, relaxing the constraint without abandoning attention's probabilistic interpretation. Analytically and through synthetic experiments, we show the gate strictly increases the stable rank of per-head outputs, and connect this rank gain to all three manifestations. On five molecular and long-range benchmarks, SigGate-GT matches the prior best on ZINC (0.059 MAE), records the strongest result among the graph-transformer baselines we evaluate on ogbg-molhiv (82.47% ROC-AUC), and is competitive on ogbg-molpcba and the Long-Range Graph Benchmark, with statistically significant gains over GraphGPS on all five datasets (p < 0.05). Mechanism analyses confirm the diagnosis: gating slows over-smoothing (a 30% mean relative gain in representation diversity across 4-16 layers), keeps attention entropy from collapsing, and stabilizes training across a 10x learning-rate range, at about 1% parameter overhead on OGB and under 3% wall-clock cost.

Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57\times$ energy efficiency on neuromorphic hardware, yet no theoretical framework guides their design. This paper establishes the first comprehensive expressivity theory for spiking self-attention. We prove that spiking attention with Leaky Integrate-and-Fire neurons is a universal approximator of continuous permutation-equivariant functions, providing explicit spike circuit constructions including a novel lateral inhibition network for softmax normalization with proven $O(1/\sqrt{T})$ convergence. We derive tight spike-count lower bounds via rate-distortion theory: $\varepsilon$-approximation requires $Ω(L_f^2 nd/\varepsilon^2)$ spikes, with rigorous information-theoretic derivation. Our key insight is input-dependent bounds using measured effective dimensions ($d_{\text{eff}}=47$--$89$ for CIFAR/ImageNet), explaining why $T=4$ timesteps suffice despite worst-case $T \geq 10{,}000$ predictions. We provide concrete design rules with calibrated constants ($C=2.3$, 95% CI: $[1.9, 2.7]$). Experiments on Spikformer, QKFormer, and SpikingResformer across vision and language benchmarks validate predictions with $R^2=0.97$ ($p<0.001$). Our framework provides the first principled foundation for neuromorphic transformer design.

Token pruning methods for Vision Transformers (ViTs) promise quadratic reductions in attention FLOPs by dropping uninformative patches. Yet standard variable-length attention APIs -- including FlashAttention-2's varlen and PyTorch's NestedTensor SDPA -- fail to translate these savings into proportional wall-clock gains at the short post-pruning sequence lengths typical of ViTs ($\leq$197 tokens). We identify a dispatch-overhead bottleneck: at these lengths, host-side kernel dispatch consumes ${\sim}$50,$μ$s regardless of workload, exceeding the actual GPU compute time at moderate-to-high pruning rates. We present a lightweight bidirectional Triton attention kernel whose dispatch floor is ${\sim}$24,$μ$s -- roughly 2.17$\times$ lower than FlashAttention-2 varlen -- allowing pruning savings to become visible in wall-clock time. Integrated into a complete pack-attend-unpack pipeline and evaluated on an NVIDIA RTX 4000 Ada Generation GPU, our system achieves 1.88$\times$ end-to-end throughput over padded PyTorch SDPA at standard 224$\times$224 inputs, scaling to 2.51$\times$ at 384$\times$384. Against FlashAttention-2 varlen -- the strongest baseline -- our kernel delivers 9-12% higher throughput at serving batch sizes (BS=1-4), and 2.17$\times$ lower kernel latency at 80% token pruning. Numerical correctness is verified with max absolute logit difference $<$0.004 and bit-exact top-1 predictions.

Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical implications of gated attention mechanisms remain poorly understood. We study attention through the geometry of its representations by modeling outputs as mean parameters of Gaussian distributions and analyzing the induced Fisher--Rao geometry. We show that ungated attention operator is restricted to intrinsically flat statistical manifolds due to its affine structure, while multiplicative gating enables non-flat geometries, including positively curved manifolds that are unattainable in the ungated setting. These results establish a geometric expressivity gap between ungated and gated attention. Empirically, we show that gated models exhibit higher representation curvature and improved performance on tasks requiring nonlinear decision boundaries whereas they provide no consistent advantage on tasks with linear decision boundaries. Furthermore, we identify a structured regime in which curvature accumulates under composition, yielding a systematic depth amplification effect.

The statistical essence of the Transformer architecture has long remained elusive: Is it a universal approximator, or a neural network version of known computational algorithms? Through rigorous algebraic proof, we show that the latter better describes Transformer's basic nature: Ordinary Least Squares (OLS) is a special case of the single-layer Linear Transformer. Using the spectral decomposition of the empirical covariance matrix, we construct a specific parameter setting where the attention mechanism's forward pass becomes mathematically equivalent to the OLS closed-form projection. This means attention can solve the problem in one forward pass, not by iterating. Building upon this prototypical case, we further uncover a decoupled slow and fast memory mechanism within Transformers. Finally, the evolution from our established linear prototype to standard Transformers is discussed. This progression facilitates the transition of the Hopfield energy function from linear to exponential memory capacity, thereby establishing a clear continuity between modern deep architectures and classical statistical inference.

We study signal propagation at initialization in transformers through the averaged partial Jacobian norm (APJN), a measure of gradient amplification across layers. We extend APJN analysis to transformers with bidirectional attention and permutation-symmetric input token configurations by deriving recurrence relations for activation statistics and APJNs across layers. Our theory predicts how attention modifies the asymptotic behavior of the APJN at large depth and matches APJNs measured in deep vision transformers. The criticality picture known from residual networks carries over to transformers: the pre-LayerNorm architecture exhibits power-law APJN growth, whereas transformers with LayerNorm replaced by elementwise $\tanh$-like nonlinearities have stretched-exponential APJN growth, indicating that the latter are subcritical. Applied to Dynamic Tanh (DyT) and Dynamic erf (Derf) transformers, the theory explains why these architectures can be more sensitive to initialization and optimization choices and require careful tuning for stable training.

Transformers can perform in-context classification from a few labeled examples, yet the inference-time algorithm remains opaque. We study multi-class linear classification in the hard no-margin regime and make the computation identifiable by enforcing feature- and label-permutation equivariance at every layer. This enables interpretability while maintaining functional equivalence and yields highly structured weights. From these models we extract an explicit depth-indexed recursion: an end-to-end identified, emergent update rule inside a softmax transformer, to our knowledge the first of its kind. Attention matrices formed from mixed feature-label Gram structure drive coupled updates of training points, labels, and the test probe. The resulting dynamics implement a geometry-driven algorithmic motif, which can provably amplify class separation and yields robust expected class alignment.

Spiking Transformers, which combine the scalability of Transformers with the sparse, energy-efficient property of Spiking Neural Networks (SNNs), have achieved impressive results in neuromorphic and vision tasks and attracted increasing attention. However, existing directly trained spiking transformers primarily focus on vision tasks. For language modeling with spiking transformer, convergence relies heavily on softmax-based spiking self-attention, which incurs high energy costs and poses challenges for neuromorphic deployment. To address this issue, we introduce Winner-Take-All (WTA) mechanisms into spiking transformers and propose two novel softmax-free, spike-driven self-attention modules: WTA Spiking Self-Attention (WSSA) and Causal WTA Spiking Self-Attention (CWSSA). Based on them, we design WTA-based Encoder-only Spiking Transformer (WE-Spikingformer) for masked language modeling and WTA-based Decoder-only Spiking Transformer (WD-Spikingformer) for causal language modeling, systematically exploring softmax-free, spiking-driven Transformer architectures trained end-to-end for natural language processing tasks. Extensive experiments on 16 datasets spanning natural language understanding, question-answering tasks, and commonsense reasoning tasks validate the effectiveness of our approach and highlight the promise of spiking transformers for general language modeling and energy-efficient artificial intelligence.

Sequence modelling requires determining which past tokens are causally relevant from the context and their importance: a process inherent to the attention layers in transformers, yet whose underlying learned mechanisms remain poorly understood. In this work, we formalize the task of estimating token importance as an in-context learning problem by introducing a framework based on Mixture of Transition Distributions, where a latent variable determines the influence of past tokens on the next. The distribution over this latent variable is parameterized by unobserved mixture weights that transformers must learn in-context. We demonstrate that transformers can implement Mirror Descent to learn these weights from the context. Specifically, we give an explicit construction of a three-layer transformer that exactly implements one step of Mirror Descent and prove that the resulting estimator is a first-order approximation of the Bayes-optimal predictor. Corroborating our construction and its learnability via gradient descent, we empirically show that transformers trained from scratch learn solutions consistent with our theory: their predictive distributions, attention patterns, and learned transition matrix closely match the construction, while deeper models achieve performance comparable to multi-step Mirror Descent.

We propose two complementary modifications to transformer attention blocks. First, a non-linear pre-projection MLP is inserted between layer norm and Q/K/V projections, constructing richer features in a position-agnostic manner before any positional encoding is applied. Second, a content skip connection routes the pre-projection's features around the attention mechanism, allowing content information to bypass position-aware attention where beneficial. In frozen-probe experiments on Pythia-160M and 410M, the combined approach achieves the strongest results across methods: +40.6% LAMBADA accuracy and -39% perplexity at 160M scale. Learned skip connection weights reveal a consistent pattern across model sizes: later transformer layers activate the content bypass more strongly than earlier layers, suggesting that deeper layers benefit from content information that does not pass through positional attention. All modifications add no K/V cache overhead.

While modern transformer neural networks achieve grandmaster-level performance in chess and other reasoning tasks, their internal computation process remains largely opaque. Focusing on Leela Chess Zero (LC0), we introduce a sparse decomposition framework to interpret its internal computation by decomposing its MLP and attention modules with sparse replacement layers, which capture the primary computation process of LC0. We conduct a detailed case study showing that these pathways expose rich, interpretable tactical considerations that are empirically verifiable. We further introduce three quantitative metrics and show that LC0 exhibits parallel reasoning behavior consistent with the inductive bias of its policy head architecture. To the best of our knowledge, this is the first work to decompose the internal computation of a transformer on both MLP and attention modules for interpretability. Combining sparse replacement layers and causal interventions in LC0 provides a comprehensive understanding of advanced tactical reasoning, offering critical insights into the underlying mechanisms of superhuman systems. Our code is available at https://github.com/JacklE0niden/Leela-SAEs.

As the foundational architecture of modern machine learning, Transformers have driven remarkable progress across diverse AI domains. Despite their transformative impact, a persistent challenge across various Transformers is Attention Sink (AS), in which a disproportionate amount of attention is focused on a small subset of specific yet uninformative tokens. AS complicates interpretability, significantly affecting the training and inference dynamics, and exacerbates issues such as hallucinations. In recent years, substantial research has been dedicated to understanding and harnessing AS. However, a comprehensive survey that systematically consolidates AS-related research and offers guidance for future advancements remains lacking. To address this gap, we present the first survey on AS, structured around three key dimensions that define the current research landscape: Fundamental Utilization, Mechanistic Interpretation, and Strategic Mitigation. Our work makes a pivotal contribution by highlighting the key concepts and main trends in the field, guiding researchers through the evolution of AS-related studies. We envision this survey as a valuable resource, empowering researchers to effectively manage AS within the current Transformer paradigm, while simultaneously inspiring innovative advancements for the next generation of Transformers. The paper list of this work is available at https://github.com/ZunhaiSu/Awesome-Attention-Sink.

The Hierarchical Kernel Transformer (HKT) is a multi-scale attention mechanism that processes sequences at L resolution levels via trainable causal downsampling, combining level-specific score matrices through learned convex weights. The total computational cost is bounded by 4/3 times that of standard attention, reaching 1.3125x for L = 3. Four theoretical results are established. (i) The hierarchical score matrix defines a positive semidefinite kernel under a sufficient condition on the symmetrised bilinear form (Proposition 3.1). (ii) The asymmetric score matrix decomposes uniquely into a symmetric part controlling reciprocal attention and an antisymmetric part controlling directional attention; HKT provides L independent such pairs across scales, one per resolution level (Propositions 3.5-3.6). (iii) The approximation error decomposes into three interpretable components with an explicit non-Gaussian correction and a geometric decay bound in L (Theorem 4.3, Proposition 4.4). (iv) HKT strictly subsumes single-head standard attention and causal convolution (Proposition 3.4). Experiments over 3 random seeds show consistent gains over retrained standard attention baselines: +4.77pp on synthetic ListOps (55.10+-0.29% vs 50.33+-0.12%, T = 512), +1.44pp on sequential CIFAR-10 (35.45+-0.09% vs 34.01+-0.19%, T = 1,024), and +7.47pp on IMDB character-level sentiment (70.19+-0.57% vs 62.72+-0.40%, T = 1,024), all at 1.31x overhead.

Transformer-based approaches have revolutionized image super-resolution by modeling long-range dependencies. However, the quadratic computational complexity of vanilla self-attention mechanisms poses significant challenges, often leading to compromises between efficiency and global context exploitation. Recent window-based attention methods mitigate this by localizing computations, but they often yield restricted receptive fields. To mitigate these limitations, we propose Selective Aggregation Transformer (SAT). This novel transformer efficiently captures long-range dependencies, leading to an enlarged model receptive field by selectively aggregating key-value matrices (reducing the number of tokens by 97%) via our Density-driven Token Aggregation algorithm while maintaining the full resolution of the query matrix. This design significantly reduces computational costs, resulting in lower complexity and enabling scalable global interactions without compromising reconstruction fidelity. SAT identifies and represents each cluster with a single aggregation token, utilizing density and isolation metrics to ensure that critical high-frequency details are preserved. Experimental results demonstrate that SAT outperforms the state-of-the-art method PFT by up to 0.22dB, while the total number of FLOPs can be reduced by up to 27%.

The self-attention mechanism is central to the success of Transformer architectures. However, standard row-stochastic attention has been shown to suffer from significant signal degradation across layers. In particular, it can induce rank collapse, resulting in increasingly uniform token representations, as well as entropy collapse, characterized by highly concentrated attention distributions. Recent work has highlighted the benefits of doubly stochastic attention as a form of entropy regularization, promoting a more balanced attention distribution and leading to improved empirical performance. In this paper, we study rank collapse across network depth and show that doubly stochastic attention matrices normalized with Sinkhorn algorithm preserve rank more effectively than standard softmax row-stochastic ones. As previously shown for softmax, skip connections are crucial to mitigate rank collapse. We empirically validate this phenomenon on both sentiment analysis and image classification tasks. Moreover, we derive a theoretical bound for the pure self-attention rank decay when using Sinkhorn normalization and find that rank decays to one doubly exponentially with depth, a phenomenon that has already been shown for softmax.

Self-attention in Transformers generates dynamic operands that force conventional Compute-in-Memory (CIM) accelerators into costly non-volatile memory (NVM) reprogramming cycles, degrading throughput and stressing device endurance. Existing solutions either reduce but retain NVM writes through matrix decomposition or sparsity, or move attention computation to digital CMOS at the expense of NVM density. We present TrilinearCIM, a Double-Gate FeFET (DG-FeFET)-based architecture that uses back-gate modulation to realize a three-operand multiply-accumulate primitive for in-memory attention computation without dynamic ferroelectric reprogramming. Evaluated on BERT-base (GLUE) and ViT-base (ImageNet and CIFAR), TrilinearCIM outperforms conventional CIM on seven of nine GLUE tasks while achieving up to 46.6% energy reduction and 20.4% latency improvement over conventional FeFET CIM at 37.3% area overhead. To our knowledge, this is the first architecture to perform complete Transformer attention computation exclusively in NVM cores without runtime reprogramming.

Graph transformers have shown promise in overcoming limitations of traditional graph neural networks, such as oversquashing and difficulties in modeling long-range dependencies. However, their application to large-scale graphs is hindered by the quadratic memory and computational complexity of the all-to-all attention mechanism. Although alternatives such as linearized attention and restricted attention patterns have been proposed, these often degrade performance or limit expressive power. To better balance efficiency and effectiveness, we introduce k-Maximum Inner Product (k-MIP) attention for graph transformers. k-MIP attention selects the most relevant key nodes per query via a top-k operation, yielding a sparse yet flexible attention pattern. Combined with an attention score computation based on symbolic matrices, this results in linear memory complexity and practical speedups of up to an order of magnitude compared to all-to-all attention, enabling the processing of graphs with over 500k nodes on a single A100 GPU. We provide a theoretical analysis of expressive power, showing that k-MIP attention does not compromise the expressiveness of graph transformers: specifically, we prove that k-MIP transformers can approximate any full-attention transformer to arbitrary precision. In addition, we analyze the expressive power of the GraphGPS framework, in which we integrate our attention mechanism, and establish an upper bound on its graph distinguishing capability in terms of the S-SEG-WL test. Finally, we validate our approach on the Long Range Graph Benchmark, the City-Networks benchmark, and two custom large-scale inductive point cloud datasets, consistently ranking among the top-performing scalable graph transformers.

Transformer-based methods have improved hyperspectral image classification (HSIC) by modeling long-range spatial-spectral dependencies; however, their attention mechanisms typically rely on dot-product similarity, which mixes feature magnitude and orientation and may be suboptimal for hyperspectral data. This work revisits attention scoring from a geometric perspective and introduces a cosine-normalized attention formulation that aligns similarity computation with the angular structure of hyperspectral signatures. By projecting query and key embeddings onto a unit hypersphere and applying a squared cosine similarity, the proposed method emphasizes angular relationships while reducing sensitivity to magnitude variations. The formulation is integrated into a spatial-spectral Transformer and evaluated under extremely limited supervision. Experiments on three benchmark datasets demonstrate that the proposed approach consistently achieves higher performance, outperforming several recent Transformer- and Mamba-based models despite using a lightweight backbone. In addition, a controlled analysis of multiple attention score functions shows that cosine-based scoring provides a reliable inductive bias for hyperspectral representation learning.

Scaled dot-product attention forms its queries and keys as independent linear projections, so the two never interact before the dot product that scores them. We study coupled query-key dynamics, a pre-scoring transformation that evolves each token's query and key jointly through a shared invertible coupling before standard scoring. We realize it as an alternating affine map in the style of real non-volume-preserving flows: the coupling is the identity at initialization, adds a small fraction of parameters per head, and leaves the softmax and surrounding architecture unchanged. We place coupling on top of existing attention methods rather than replacing them, and ask whether that composition helps. On WikiText-103, adding coupling to Differential Attention improves on it at both 150M and 455M parameters. At 455M the gain is significant at sequence length 512 (p=0.003, six seeds), survives a Bonferroni correction and replicates on a held-out test split; it also holds across rotary-embedding training lengths 512, 1024, and 2048. The same additive direction appears when coupling is added to query-key normalization (significant at 150M) and Multi-Token Attention (directional). Matched controls attribute the gain to the joint pre-scoring coupling rather than to added capacity, and show that removing the invertibility guarantee preserves the 455M gain yet is far worse than the base method at 150M, so invertibility is what makes the coupling reliable across scales. On its own, coupling lowers perplexity at 60M and 150M (one-sided Welch tests, p<0.05) but the gain narrows with scale and is not significant at 455M. We relate the construction to the expressivity of coupling flows, use an associative-recall study to map where coupling helps and where it degrades sharp retrieval, and conclude that coupling is most useful in composition with a scoring-stage method rather than as a standalone change.

We call query--key relevance absolute when its values lie on a fixed bounded scale, depend on neither competing keys nor sequence length, require no sequence-length-dependent calibration, and can all be zero. To realize this notion, we introduce screening, whose explicit threshold transforms bounded query--key similarities into relevance values, enabling exact rejection, empty selection, and direct inspection on a common scale. In a controlled comparison of 12 attention mechanisms on a matched Transformer backbone, only screening maintains both low long-context perplexity and robust retrieval beyond the training context; notably, it does so without inference-time scaling. Building on screening, we introduce Multiscreen, a language-model architecture composed of parallel gated screening tiles. Multiscreen retains these long-context gains while achieving greater parameter efficiency, stronger general zero-shot downstream performance, lower training cost at larger scales, and lower model-side time to first token than Transformer baselines. We further develop a normalization design that keeps Multiscreen training stable even at a learning rate of $1$ and show that an adapted version likewise stabilizes Transformer at the same learning rate.

The Transformer model architecture has become one of the most widely used in deep learning and the attention mechanism is at its core. The standard attention formulation uses a softmax operation applied to a scaled dot product between query and key vectors. We explore the role played by norms of the queries and keys, which can cause training instabilities when they arbitrarily increase. We demonstrate how this can happen even in simple Transformer models, in the presence of easy-to-learn spurious patterns in the data. We propose a new attention formulation, QUEry-modulated Spherical aTtention (QUEST), that constrains the keys to a hyperspherical latent space, while still allowing individual tokens to flexibly control the sharpness of the attention distribution. QUEST can be easily used as a drop-in replacement for standard attention. We focus on vision applications while also exploring other domains to highlight the method's generality. We show that (1) QUEST trains without instabilities and (2) produces models with improved performance (3) that are robust to data corruptions and adversarial attacks.

Using a statistical mechanics framework, we investigate the parameter space of transformer models trained on protein sequence data. We sample the loss landscape at varying temperatures using Langevin dynamics to characterize the low-loss manifold, and to understand the mechanisms underlying transformers' superior performance in protein structure prediction. We find that, at variance with networks not based on the attention mechanism, the lack of a first--order--like transition in the loss of the transformer produces a range of intermediate temperatures with good learning properties; this is true both for synthetic and natural protein sequences. We also show that the parameters of most layers are highly conserved at these temperatures if the dimension of the embedding is optimal, and we provide an operative way to find this dimension. Additionally, we show that the attention matrix is more predictive of the contact maps of the protein at higher temperatures and for higher dimensions of the embedding than those optimal for learning. Finally, we showed that the models sampled at intermediate temperatures can predict the free-energy variation upon mutation, better than models obtained through standard optimization techniques.

Long-context video understanding and generation pose a significant computational challenge for Transformer-based video models due to the quadratic complexity of self-attention. While existing sparse attention methods employ coarse-grained patterns to improve efficiency, they typically incur redundant computation and suboptimal performance. To address this issue, in this paper, we propose VecAttention, a novel framework of vector-wise sparse attention that achieves superior accuracy-efficiency trade-offs for video models. We observe that video attention maps exhibit a strong vertical-vector sparse pattern, and further demonstrate that this vertical-vector pattern offers consistently better accuracy-sparsity trade-offs compared with existing coarse-grained sparse patterns. Based on this observation, VecAttention dynamically selects and processes only informative vertical vectors through a lightweight important-vector selection that minimizes memory access overhead and an optimized kernel of vector sparse attention. Comprehensive evaluations on video understanding (VideoMME, LongVideoBench, and VCRBench) and generation (VBench) tasks show that VecAttention delivers a 2.65$\times$ speedup over full attention and a 1.83$\times$ speedup over state-of-the-art sparse attention methods, with comparable accuracy to full attention. Our code is available at https://github.com/anminliu/VecAttention.

Reconstructing continuous physical fields from sparse, irregular observations is a central challenge in scientific machine learning, particularly for systems governed by partial differential equations (PDEs). Existing physics-informed methods typically enforce governing equations as soft penalty terms during optimization, often leading to gradient imbalance, instability, and degraded physical consistency under limited data. We introduce the Physics-Guided Transformer (PGT), a neural architecture that embeds physical structure directly into the self-attention mechanism. Specifically, PGT incorporates a heat-kernel-derived additive bias into attention logits, encoding diffusion dynamics and temporal causality within the representation. Query coordinates attend to these physics-conditioned context tokens, and the resulting features are decoded using a FiLM-modulated sinusoidal implicit network that adaptively controls spectral response. We evaluate PGT on the one-dimensional heat equation and two-dimensional incompressible Navier-Stokes systems. In sparse 1D reconstruction with 100 observations, PGT achieves a relative L2 error of 5.9e-3, significantly outperforming both PINNs and sinusoidal representations. In the 2D cylinder wake problem, PGT uniquely achieves both low PDE residual (8.3e-4) and competitive relative error (0.034), outperforming methods that optimize only one objective. These results demonstrate that embedding physics within attention improves stability, generalization, and physical fidelity under data-scarce conditions.