Transformer Attention

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Overview

Transformer attention uses queries, keys, and values to decide which tokens should contribute information to one another, with positional encodings and masks shaping those interactions. Work seeks both to improve this basic mechanism and to reduce its costs, using approaches such as sparse, linear, kernel, and local attention, as well as efficient GPU kernels and compressed key-value caches. Researchers also add structural or domain-specific biases and study attention’s role in learning, retrieval, stability, and interpretability across language, vision, graphs, and time series. A central tension remains: methods that reduce computation or constrain interactions can improve speed and memory use, but may lose accuracy or long-range retrieval quality, and no single design is best across settings.

Latest papers 308

41 papers in the last four weeks, up 86% on the four weeks before. 0.2% of all new papers.

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Jul 20, 2026

An Adjoint-Sensitivity Framework for Lost-in-the-Middle Phenomena in Causal Residual Transformers

We develop an adjoint-sensitivity framework for positional influence in causal residual Transformers and separate unconditional analytic results from conditional boundary-shape conclusions. The principal unconditional theorem is the residual-to-depth-flow estimate for layer controls converging in L1L^1, complemented by a finite-token-to-Volterra attention estimate that explicitly controls the first cells near the causal endpoint. We define a normalized adjoint-energy influence density and derive its exact evolution along full-batch gradient flow. The adjoint admits an exact generator-term decomposition into residual transmission, nonlocal Volterra, and local channels, including all covariance cross terms. Causal masking can amplify early-position sensitivity and residual identity paths can transmit a right-localized terminal bias, but neither mechanism alone forces a U-shaped profile. We therefore state boundary advantages under independently checkable energy, correlation, and local-channel bounds; these conditions are sufficient rather than necessary. Finite-token influence balancing, positional reweighting, and task-aligned observability are presented as diagnostics or regularizers with explicit differentiation requirements, computational costs, and limitations. Controlled simulations illustrate that each intervention controls its designated surrogate, while observability balance or outer-loop reweighting need not monotonically reduce the influence-based Lost-in-the-Middle diagnostic.

Cheng Huan, Hongwei Yuan

Department of Statistics and Data Science, The Chinese University of Hong Kong. · Department of Mathematics, University of Macau.

Transformer AttentionPositional EncodingSensitivity Analysis
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Jul 19, 2026

The Geometry of Semantic Space: A Continuous Geometric Framework for the Transformer Architecture

We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle \calE=\calM×Rd\calE = \calM \times \R^d. Beginning from a single geometric axiom -- that the token sequence forms a discrete 11-manifold equipped with a canonical measure lattice -- we translate every core component of the modern Transformer (RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, SGD, Weight Decay) into a cohesive vocabulary of differential geometry, measure theory, and stochastic calculus. The resulting framework yields quantitative predictions spanning entropic optimal transport (Attention as a Schrödinger bridge) and non-equilibrium thermodynamics (SGD as Itô diffusion violating detailed balance). We conduct a six-part experimental campaign across five architectures (Qwen3, LLaMA\nobreakdash-3.1, Gemma\nobreakdash-3, GPT-2, Mistral) spanning 124124M to 88B parameters. The empirical observables are quantitatively consistent with the geometric predictions: the ε−1/2ε^{-1/2} Lipschitz scaling calibration at machine precision (R2=1.000R^2 = 1.000), the Lie--Trotter operator-splitting torsion, the symmetric ablation instability confirming the Dual-Law of Topological Stability, the \calO(1/k)\calO(1/\sqrt{k}) thermodynamic suppression of Poincaré recurrence on the RoPE torus, the thermodynamic context-limit phase transition, and the Non-Equilibrium Steady State parameter vortex -- verified across two optimizers (AdamW and Pure SGD) to exclude momentum artifacts. The results demonstrate that analyzing Transformers through the lens of continuous stochastic differential geometry provides a predictive descriptive vocabulary for the stability limits, context bounds, and optimization dynamics of Large Language Models.

Zhihua Liang

INFN, Sezione di Cagliari, I-09042 Monserrato (CA), Italy

TransformerTransformer AttentionRepresentation Geometry in Language Models
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Jul 15, 2026

Data-Efficient Adaptation of LLMs via Attention Head Reweighting

Learning effectively from limited data is critical in domains like security where labeled examples are scarce. Large language models (LLMs) have demonstrated some capabilities for data-efficient learning, especially through parameter-efficient adaptation methods, but continue to struggle when faced with few samples for difficult tasks. To meet this challenge, we propose Attention Head Reweighting (AHR), a data-efficient method that adapts LLMs to new text-classification tasks by learning only a single scalar per attention head. This drastically reduces the number of parameters that need to be learned by making use of the functional specialization of individual attention heads. Experiments on diverse open-source text classification datasets show that AHR can outperform standard baselines like LoRA when learning from limited samples, despite having 200-1000x fewer trainable parameters, as our AHR only modifies ~0.0001% of the model's parameters. In addition, our learned weights are easy to interpret and can be analyzed to better understand the mechanisms and attention heads responsible for in-context learning abilities in LLMs.

Tuomas Oikarinen, Zixiao Chen, Charlotte Siska +3

UC San Diego, Microsoft Research · Microsoft Security AI · UC San Diego +1

LLM Fine-TuningText ClassificationTransformer AttentionParameter-Efficient Fine-TuningData-Efficient Learning
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Jul 14, 2026

AVQ-Attention: Adaptive Vector-Quantized Attention

The O(N2)\mathcal{O}(N^2) complexity of attention over NN tokens remains a computational bottleneck in transformer models. Vector-Quantized (VQ) attention reduces this to O(MN)\mathcal{O}(MN) by representing keys with MM codewords, but applies uniform codebook capacity regardless of where attention mass concentrates: high-attention regions of key space may be coarsely approximated while low-attention regions waste representational capacity. We propose Adaptive Vector-Quantized (AVQ) Attention, which adaptively allocates codebook capacity based on attention importance. Starting from a small set of codewords, our method identifies the most important codes during the forward pass and refines them with pre-learned child codewords, achieving fine-grained quantization where it matters most while maintaining coarse quantization elsewhere. We develop an implementation using custom Triton kernels that enables the full adaptive refinement process, including importance scoring, child codeword insertion, and parent contribution replacement, to be carried out within the tiled computation paradigm of Flash Attention with minimal overhead. Our approach maintains O(MN)\mathcal{O}(MN) complexity while achieving improved accuracy-efficiency trade-offs compared to fixed-codebook VQ-attention.

Winfried van den dool, Patrick Forré, Amir Habibian +2

QUVA Lab, University of Amsterdam, The Netherlands · AMLab, Informatics Institute, University of Amsterdam, The Netherlands · AI4Science Lab, University of Amsterdam, The Netherlands +3

Transformer AttentionVector QuantizationEfficient AttentionAttention Quantization
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Jul 12, 2026

From Self-Attention to Connection Laplacian: A Unified Operator View of Transformers

Self-attention is a ubiquitous primitive in modern sequence models, yet its operator-level geometry is only partially understood. We view a token sequence as a vector field over the token-position graph and identify attention as a connection walk: messages are aggregated by a nonnegative walk matrix while being transported along each edge by a learned linear map. Within this framework, we prove that single-head attention (SHA) is exactly a connection propagation step with constant transport, and that multi-head attention (MHA) is exactly a single edge-dependent connection walk whose effective transport is an attention-gated mixture of headwise transports. We further clarify the conditions under which the corresponding generator reduces to a random-walk connection Laplacian, highlighting the roles of stochasticity, reversibility, and metric-compatible transports. Empirically, we find that trained Transformers across scales (from 124M to 8B) and structures (encoder/decoder) exhibit geometric structure consistent with our theory: effective attention graphs converge to stable geometric operators in deeper layers, learned transports self-organize into approximate scaled isometries, and both phenomena strengthen consistently with scale. Overall, the paper provides a precise connection-walk formalism that links self-attention to classical geometric operators, along with a set of operator-level tools for analyzing transformer models from a geometric perspective.

Binbin Lin, Wei Chen, Yalun Li +3

School of Software Technology, Zhejiang University, China · College of Computer Science and Technology, Zhejiang University, China · Alibaba Cloud, China

Self-AttentionTransformer AttentionRepresentation Geometry in Language ModelsMulti-Head Attention
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Jul 9, 2026

Hidden Decoding at Scale: Latent Computation Scaling for Large Language Models

Scaling Large Language Models (LLMs) has been driven mainly by enlarging the Transformer backbone, but for an already-strong model this requires another round of costly pretraining. We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed. Depth-recurrent (looped) Transformers pursue this goal but are hard to scale, because looped computation does not fit naturally with the pipeline parallelism used to train the largest models. We add computation along the sequence-length dimension, where the extra computation is simply a longer input and stays compatible with standard large-model training. We propose Hidden Decoding, a sequence-length scaling method applied during continued pretraining (CPT). It expands each token into n streams with independent embedding tables and keeps the intermediate streams' key-value cache as context, so each token performs more internal computation without adding or widening Transformer layers. To keep this affordable at scale, we introduce Stream-Factorized Attention, in which most layers attend only within each stream and only a few layers mix across streams, reducing the attention cost from quadratic to roughly linear in n. Experiments support two scaling results. At frontier scale, we train WeLM-HD4-80B and WeLM-HD4-617B at n=4 and improve their matched non-HD baselines, making Hidden Decoding the first demonstrated sequence-length scaling method at the 100B+ MoE scale. Across expansion factors, the gains grow as n increases, showing that sequence-length expansion is a practical fixed-backbone scaling path for frontier-scale LLMs.

Aiwei Liu, Cheng Shi, Chuhan Wu +45

Language Model Scaling LawsTransformer AttentionLanguage Model ScalingLLM Training
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Jul 8, 2026

FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attention

FFT-based spectral preprocessing of learned query-key (Q/K) projections substantially improves transformer attention on character-level language modelling. On TinyShakespeare: a fixed random spectral filter achieves val=1.031 (Delta=+0.443); a single learned frequency at paragraph scale achieves val=0.608 (Delta=+0.867); and four learned frequencies spanning paragraph to word scale achieve val=0.309 (Delta=+1.166), a 79% reduction over standard dot-product attention. The single-frequency result is confirmed across three random seeds (mean val=0.236, std=0.019). The four frequencies converge to a near-geometric multi-scale ordering (49, 27, 10, 6 tokens/cycle) corresponding to paragraph, sub-paragraph, phrase, and word scales. The gain is specific to spectral preprocessing: random orthogonal and non-orthogonal projections of Q/K produce no measurable improvement, suggesting the benefit comes from global frequency-domain mixing rather than metric distortion. All results are verified by a shuffled-validation diagnostic against positional leakage. Causal filters (Gaussian, Mexican Hat, Morlet) do not improve over standard attention at character-level tokenisation: the bilateral FFT kernel is structurally non-causal, coupling every position to future tokens. This defines an architectural boundary between bilateral spectral attention (this paper) and genuinely causal spectral attention at word-scale tokenisation (companion paper MorletQK). This work is architecturally distinct from FNet (Lee-Thorp et al., 2021), which replaces attention with Fourier mixing of token embeddings. Here, spectral preprocessing applies only to Q/K projections while the full attention score structure is preserved.

Athanasios Zeris

Independent Researcher, Athens, Greece.

Frequency-Domain Feature LearningTransformer AttentionLanguage Modeling
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Jul 8, 2026

Multiplication Beyond Groups: Stratified Fourier Mechanisms in Transformer Circuits

Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition. In this work, we investigate how small transformers learn modular integer multiplication over composite moduli, a fundamentally non-invertible operation due to the presence of zero-divisors. We propose the monoid extension: a localized generalization of Group Composition via Representation (GCR) that suggests the learned computation does not rely on a single global representation space. Instead, the model partitions the input space into local hierarchical algebraic regions, where group-like structure survives and Fourier mechanisms can be applied. In transformers trained on square-free modular multiplication, we find that embeddings organize around these regions, attention exhibits class-sensitive routing and low-rank write directions, and local character features explain a large fraction of the model's output logits. Our results suggest that representation-theoretic mechanisms previously identified for group operations can extend beyond groups to more general structures.

Zitong Andrew Chen, Junaid Hasan, Akhil Srinivasan +2

1UW Math AI Lab, University of Washington.

Transformer InterpretabilityTransformer AttentionModular ArithmeticLLM Mathematical Reasoning
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Jul 5, 2026

Legible-by-Construction: Attention and End-to-End Transformers

A companion paper showed that a transformer's feed-forward layer can be rebuilt from explicit fuzzy set operations - intersection, set-difference, and a self-forgetting sequence quantifier - so its hidden units read as named logical operators at no cost to language-model quality. That left the other half of the transformer opaque. Here we carry the same idea into attention and join the two into one model. The mechanism is minimal: a head's value is passed through a sigmoid, so each value channel becomes a readable detector of whether a feature holds at a token. This adds no parameters and leaves the standard head otherwise untouched. A Boolean variant goes further, restructuring the value into an explicit within-token intersection and negation-capable set-difference. In both designs the output projection is left free, not tied to the vocabulary, which is the load-bearing decision: bounding what a head detects while leaving what it writes unconstrained yields selective detectors, whereas constraining the write does not. A bounded value is shaped into a readable detector by two selectivity pressures - one for sparse firing, one for decisive firing at the rails - and which a design wants is not universal. Across five specialized-attention designs at 125M parameters, 44 to 62 percent of value channels become crisp, contextually selective detectors, and their legibility rises with depth rather than crystallizing only on punctuation. Language-model quality is at parity with a conventional baseline. Finally, we couple the Boolean attention to the legible feed-forward layer and train an end-to-end legible-by-construction language model at benchmark parity: its feed-forward units are named set and quantifier operations throughout, and we can take a token it generates and read the named units that compose to produce it.

Mark Oskin

School of Computer Science and Engineering University of Washington

Transformer InterpretabilityTransformer Attention
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Jul 4, 2026

LLT: Local Linear Transformer for PDE Operator Learning

Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations. Transformer-based neural operators are of particular interest, since attention can learn long-range dependencies in the computational domain. However, standard attention has two major limitations when applied to PDEs: it scales quadratically with the number of computational nodes, and it lacks an explicit bias toward local interactions. To address these issues, we introduce Local Linear Transformer (LLT) for PDE operator learning. The architecture combines linear global attention with local spatial mixing, and incorporates coordinate and geometry information. We evaluate LLT on several PDE problems, including elasticity, plasticity, airfoil flow, pipe flow, and Darcy flow. The reference data for these problems span finite-element, finite-volume, and finite-difference discretizations on structured and unstructured meshes. Compared with other neural-operator and transformer baselines from prior studies, LLT achieves competitive or lower relative L2L_2 error across these problems. On matched structured discretizations, wall-clock time per training iteration is reduced by factors of 1.8 to 2.5 relative to Transolver. We also scale the approach and apply it to a three-dimensional car aerodynamics dataset with 32,186 unstructured mesh points per sample. Together, these results indicate that LLT provides an accurate and computationally efficient operator for PDE problems across discretizations, mesh types, and problem settings.

Oded Ovadia, Eli Turkel

School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

PDE Surrogate ModelingTransformer AttentionLinear AttentionPDE Operator LearningNeural Operators
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Jul 2, 2026

X-LogSMask: Expand Transformer for Graph-Structured Data

Transformers have become general-purpose architectures, but their all-to-all self-attention is poorly matched to graph data, whose interactions are sparse, structured and multi-scale. Existing Graph Transformers address this mismatch through structural encodings, hybrid message-passing modules or learned attention constraints, often introducing additional complexity and limited interpretability. Here we introduce X-LogSMask, an explainable multi-head logarithmic structural mask that injects symmetrically normalized graph topology directly into attention logits. The logarithmic transform converts structural connectivity into a topology-aware gating signal, suppressing unsupported node interactions while preserving feature-dependent attention. By assigning different powers of the normalized adjacency matrix to different attention heads, X-LogSMask gives each head a defined structural radius and supports multi-hop information propagation within a single layer. We further show that a standard Transformer encoder can be interpreted as one-step message passing on a complete graph, motivating X-LogSMask as a topology-constrained alternative to unrestricted self-attention. Across 20 node-, edge- and graph-level benchmarks, Transformers equipped with X-LogSMask achieve state-of-the-art performance on 13 datasets and remain competitive in a lightweight one-layer configuration. These results show that simple, interpretable structural masks can make self-attention an effective graph-learning operator without changing the Transformer architecture. The code is available at https://github.com/LiLeyan-0120/X-LogSMask.

Leyan Li, Rennong Yang, Zhenxing Zhang +1

Graph Attention NetworksGraph Representation LearningTransformer AttentionGraph Transformer
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Jul 1, 2026

The Wiola Architecture for Efficient Small Language Models

We present Wiola, a fully original Small Language Model (SLM) architecture built from first principles, sharing no structural lineage with any existing model family including GPT, LLaMA, Mistral, or Falcon. Wiola introduces five independently novel components: (i) Spiral Rotary Positional Encoding (SRPE), which embeds token positions on a three-dimensional helical manifold combining absolute, relative, and hierarchical positional signals; (ii) Gated Cross-Layer Attention (GCLA), providing each decoder layer with soft cross-attention access to compressed summaries of two preceding layers for inter-layer coherence; (iii) Adaptive Token Merging (ATM), which dynamically merges se mantically redundant adjacent tokens in middle network layers to reduce attention complexity without information loss; (iv) Dual Stream Feed-Forward (DSFF), replacing the conventional MLP with two parallel streams fused by a learned per-dimension gate; and (v) WiolaRMSNorm, a modified normalisation introducing a per-dimension learned offset vector that prevents representation collapse. We provide complete mathematical derivations, architectural block diagrams, complexity analyses, and systematic comparisons against GPT-2, LLaMA-2, and Mistral. Wiola is released in four sizes (120M, 360M, 700M, and 1.5B parameters) and is fully compatible with the HuggingFace Transformers ecosystem, with all 22 architectural unit tests passing.

Aryuemaan Kumar Chowdhury, Afreen Shaik, Yaparla Bhargavi +1

Research and Development, Oscowl Ai IIT Hyderabad Hyderabad, India · Research and Development, Oscowl Ai Hyderabad, India

Rotary Positional EmbeddingsToken MergingTransformerDecoder-Only Language ModelsSmall Language ModelsTransformer Attention
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Jul 1, 2026

Holographic Quantum Transformer: A Generalist Neuro-Symbolic Architecture for Solving Frustrated Systems via Generative Attention

Simulating two-dimensional frustrated quantum matter is a grand challenge due to the sign problem and exponential Hilbert space complexity. In this work, we introduce the Holographic Quantum Transformer (HQT), a physics-inspired generative architecture that leverages global self-attention to resolve non-local entanglement patterns. We validate HQT on the square lattice J1−J2J_1-J_2 Heisenberg model. On the heavily frustrated 8×88 \times 8 lattice at the quantum critical point (J2=0.5J_2=0.5), HQT reaches a ground-state energy per site (E/NE/N) of −0.5001(1)\mathbf{-0.5001(1)}, consistent with the expected finite-size scaling trend. Beyond numerical accuracy, HQT exhibits intrinsic physical awareness, autonomously recovering the underlying J2J_2 interaction geometry through interpretable attention maps. Our central contribution is ``Holographic Transfer", a zero-shot size-extrapolation protocol with rapid alignment: a model trained on 8×88 \times 8 systems is directly projected onto larger 10×1010 \times 10 lattices via continuous positional-embedding interpolation and head re-initialization, achieving high-fidelity initialization and rapid convergence. This zero-shot protocol yields an energy of E/N=−0.49782(3)E/N = \mathbf{-0.49782(3)}, statistically consistent with the variational state of the art while requiring no from-scratch training on the target lattice. Our results establish generative attention as a scalable paradigm for transferable quantum simulation.

Xingran Guo, Tiaojie Xiao, Jie Liu +1

National University of Defense Technology Changsha, China · State University of New York at New Paltz New Paltz, NY, USA

Neural Quantum StatesZero-Shot LearningTransformer AttentionQuantum Many-Body Physics
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Jun 28, 2026

Generalization Analysis of Transformers in Distribution Regression

In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning. Numerous successful techniques, such as parameter-efficient fine-tuning and efficient scaling, have been proposed surrounding their applications to further enhance performance. However, the success of these strategies has always lacked the support of rigorous mathematical theory. To study the underlying mechanisms behind Transformers and related techniques, we first propose a Transformer learning framework motivated by distribution regression, with distributions being inputs, connect a two-stage sampling process with natural language processing, and present a mathematical formulation of the attention mechanism called attention operator. We demonstrate that by the attention operator, Transformers can compress distributions into function representations without loss of information. Moreover, with the advantages of our novel attention operator, Transformers exhibit a stronger capability to learn functionals with more complex structures than convolutional neural networks and fully connected networks. Finally, we obtain a generalization bound within the distribution regression framework. Through the aforementioned theoretical results, we further discuss some successful techniques emerging with large language models (LLMs), such as prompt tuning, parameter-efficient fine-tuning, and efficient scaling. We also provide theoretical insights behind these techniques within our novel analysis framework.

Peilin Liu, Ding-Xuan Zhou

School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia

Neural Network GeneralizationTransformer AttentionStatistical Learning Theory
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Jun 25, 2026

Prism Transformer: Progressive Head Schedules for Hierarchical Attention Processing

Multi-head attention conventionally partitions the hidden dimension equally across all heads at every layer, enforcing an identical representational subspace dimension (dh = dmodel/h) throughout the models depth. In this work, we identify this uniform allocation as a fundamental structural bottleneck: due to their restricted dimensional space, early-layer heads are unable to faithfully capture complex, high-dimensional contextual patterns. To resolve this, we introduce the Prism Transformer, a novel architectural paradigm that replaces the static, uniform head configuration with a progressive head schedule. By monotonically increasing the head count across layers, the Prism Transformer naturally establishes a local-to-global representational hierarchy: early layers leverage fewer, exceptionally wide heads to capture complex, local compositional patterns, while deep layers deploy many, narrow heads to decompose these patterns into specialized linguistic features. Crucially, this structural shift is parameter-neutral, compute-neutral, and introduces zero training or inference overhead, preserving identical weight matrices and FLOP budgets as the standard Transformer. Across three model scales (124M, 354M, and 757M), the Prism Transformer consistently outperforms uniform baselines, achieving consistent reductions in validation loss alongside consistent gains on downstream zero-shot benchmarks (including PIQA, HellaSwag, ARC-Easy, and WinoGrande). Our findings demonstrate that non-uniform subspace allocation unlocks latent capacity within the standard Transformer budget, enabling more effective use of model capacity.

Shubham Aggarwal

Hierarchical Representation LearningTransformer AttentionMulti-Head Attention
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Jun 25, 2026

WQ-Fusion: Dynamic Gated Attention for Cross-Domain Audio Representation

While pre-trained models excel in specialized tasks, learning universal representations across diverse acoustic domains remains challenging. To address this, we propose WQ-Fusion, a robust dual-encoder framework for cross-domain audio representation learning. Overcoming the limitations of static concatenation, WQ-Fusion integrates whisper and qwen via an Adaptive Feature Modulation module and a novel element-wise gated attention mechanism. This design enables dynamic feature selection, allowing the model to selectively emphasize relevant acoustic and semantic dimensions. Extensive experiments on the Interspeech 2026 Audio Encoder Capability Challenge (Track A) benchmark demonstrate that by effectively routing heterogeneous information, WQ-Fusion achieves a superior overall score of 0.836, significantly outperforming the strongest single-encoder baseline.

Mingda Lin, Lei Ding, Xinyue Zhou +6

School of Electronic Information, Wuhan University, Wuhan, Hubei, China · Tencent AI Lab Seattle, Seattle, USA · CIAIC, Northwestern Polytechnical University, Xi’an, Shaanxi, China +1

Audio Representation LearningGated AttentionAudio-Language ModelsTransformer AttentionFeature Fusion
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Jun 23, 2026

Emergent Capabilities Arise Randomly from Learning Sparse Attention Patterns

Neural scaling laws for transformer language models predict smooth improvements in pretraining loss with increasing parameters, but downstream capabilities such as in-context learning are known to emerge abruptly past a certain model scale. In this paper, we show that emergent capabilities arise stochastically throughout training, with larger models acquiring them earlier on average. We demonstrate that the emergence of capabilities such as pattern completion and indirect object identification corresponds to the abrupt learning of task-relevant attention patterns. To isolate this phenomenon, we train transformer models on synthetic linear map and cellular automata datasets, and we show that the difficulty of learning attention patterns depends on context length and pattern sparsity. Moreover, scaling the number of attention heads improves learning efficiency on our synthetic tasks, while increasing the head dimension yields diminishing returns past a minimum capacity. We additionally investigate architectures with alternative attention mechanisms, showing that MLP-Mixer outperforms a transformer on linear map tasks with complex attention patterns. Our findings provide a mechanistic insight into emergence, showing that downstream capabilities arise abruptly due to the intrinsic difficulty of learning sparse attention patterns in transformer models.

Vatsal Baherwani, Zixi Chen, Shikai Qiu +2

New York University

Language Model Scaling LawsTransformer AttentionSparse Attention
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Jun 23, 2026

Parallel Manifold Steering: Efficient Adaptation of Large Associative Memories via Residual Energy Shaping

Large Transformer models function as Dense Associative Memories (DAMs), retrieving knowledge via high-dimensional attractor dynamics driven by the self-attention mechanism \citep{ramsauer2020hopfield, wu2024attention}. However, adapting these frozen memory systems to new tasks presents a fundamental ``Plasticity-Stability'' dilemma. Current methods either risk catastrophic interference by modifying synaptic weights directly (e.g., LoRA) \citep{hu2021lora} or degrade associative capacity by clogging the retrieval buffer with static prompt tokens (e.g., VPT) \citep{jia2022vpt}. In this work, we propose H-Res (Hierarchical Residual Steering), a mechanism that modulates the effective energy landscape of the Transformer without altering its global equilibrium or expanding its sequence length. By formulating adaptation as a control problem on the activation manifold \citep{chen2018neuralode}, H-Res learns a state-dependent vector field that steers token trajectories into task-specific basins of attraction. We formally prove that H-Res preserves the attention entropy of the foundation model and facilitates Neural Collapse \citep{papyan2020prevalence}. Empirically, Manifold Steering outperforms global weight modification by 26% on associative retrieval tasks and eliminates the computational overhead of prompt-based methods, scaling effectively to structured domains \citep{zha2023vtab}.

Kanishk Awadhiya

Independent Researcher

Memory-Augmented Neural NetworksTransformer AttentionActivation SteeringAssociative MemoryParameter-Efficient Fine-Tuning
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Jun 23, 2026

Progressive Pixel-Neighborhood Deformable Cross-Attention for Multispectral Object Detection

Effective cross-modal feature alignment and interaction are central challenges in multispectral object detection. Although global cross-attention provides strong long-range modeling ability, its quadratic complexity with respect to feature size limits deployment on resource-constrained platforms. We therefore propose Progressive Pixel-Neighborhood Deformable Cross-Attention for multispectral feature fusion, termed PNAFusion. The proposed framework is motivated by two observations: weak misalignment between visible and thermal images is usually concentrated around local neighborhoods, and semantic correspondence across modalities often follows non-linear spatial mappings that fixed receptive fields cannot model well. To address these issues, PNAFusion incorporates local spatial priors into its architectural design to concentrate feature interaction and alignment on the most relevant neighborhoods. Specifically, a Pixel-Neighborhood Cross-Attention (PNCA) module is introduced to avoid redundant global feature matching and suppress background noise. Meanwhile, an Adaptive Deformable Alignment (ADA) module captures non-linear spatial correspondences through learned pixel-wise offsets. These components are further integrated through an iterative feedback mechanism to progressively refine cross-modal feature alignment. Experiments on FLIR, M3FD, and DroneVehicle show that PNAFusion achieves 84.2, 90.5, and 85.5 [email protected], respectively, under the YOLOv5 detector, and further reaches 86.8 [email protected] on FLIR and 90.8 [email protected] on M3FD when transferred to Co-DETR. Efficiency analysis indicates that PNAFusion reduces allocated GPU memory by 33.0% compared with ICAFusion and reduces theoretical FLOPs from 194.8 G to 156.4 G, although the deformable sampling and iterative refinement introduce additional latency. Our code will be available at https://github.com/DanielQiuTian/PNAFusion.

Tian Qiu, Jifeng Shen, Xin Zuo

School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, 212013, China · School of Computer Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

Multispectral Object DetectionCross-Modal AlignmentTransformer AttentionCross-Modal AttentionDeformable AttentionMultimodal Fusion
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Jun 18, 2026

Grouped Query Experts: Mixture-of-Experts on GQA Self-Attention

Self-attention is central to Transformer performance and is often the most expensive part of the Transformer at long context lengths because its pairwise token interactions scale quadratically with sequence length. Standard dense attention also applies the same set of attention heads to every token regardless of token difficulty or information content. This uniform activation can waste compute, especially as sequences grow longer and attention cost increases rapidly. We propose Grouped Query Experts (GQE), a mixture-of-experts layer on top of grouped-query attention (GQA). Within each GQA group, a router selects k query-head experts per token while all key-value (KV) heads remain dense and unchanged. Thus, GQE keeps the KV cache benefits of GQA and reduces only the active query-head computation. On a fixed 30B token budget at the 250M parameter scale, GQE matches the all-active GQA baseline in downstream accuracy while activating half the query heads per token.

Vishesh Tripathi, Abhay Kumar

FrontiersMind

Grouped-Query AttentionTransformer AttentionEfficient AttentionMixture-of-Experts ModelsMulti-Head Attention
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Jun 17, 2026

ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

Convolutional networks, recurrent networks, and transformers each encode different inductive biases -- locality, sequential memory, and content-dependent pairwise interaction -- and have remained mathematically distinct since their inception. We show that this fragmentation reflects not a fundamental diversity in how signals should be processed, but rather incomplete views of a single underlying mathematical object: a learnable integral transform. We introduce the Integral Transform Network (ITNet), a unified architecture built around a learnable kernel that depends jointly on positions and features. This kernel is implemented as a small neural network, specifically an MLP, that models pairwise interactions, enabling the model to adapt its behavior from data. We show that convolution, self-attention (including multi-head), and autoregressive recurrence (including LSTM, GRU, S4, and Mamba) arise as special cases under appropriate parameterizations, and that ITNet is a universal approximator of continuous operators. To make this practical, we develop tiled kernel fusion, importance-weighted Monte Carlo integration, and learned low-rank factorization, enabling efficient and scalable computation. A single ITNet architecture with a shared operator and lightweight modality-specific encoders matches or exceeds specialized baselines on ImageNet-1K , GLUE, ModelNet40, VQA,v2 and NLVR2. The results demonstrate that a single learned interaction mechanism can recover the behavior of all three architectural families from data.

Ashim Dhor, Rasel Mondal, Pin-Yu Chen

Indian Institute of Science Education and Research Bhopal · IBM Research

Transformer AttentionConvolutional Neural NetworksNeural Operators
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Jun 17, 2026

Complementary Attention Head Pruning for Efficient Transformers

The remarkable success of Transformer-based models in natural language processing stems from architectural scaling, which leads to a large number of parameters and hinders deployment in resource-constrained environments. While structured pruning offers a pathway to compression, existing state-of-the-art methods often rely on gradient-based importance ranking or stochastic gating, which suffer from instability, structural degeneration, and the need for extensive manual hyperparameter tuning. In this paper, we introduce CAHP (Complementary Attention Head Pruning), a novel post-hoc framework that redefines head selection as a global graph-theoretical problem. Rather than evaluating heads in isolation, CAHP utilizes graph-based clustering combined with information-theoretic distance measures to identify and preserve a topologically diverse subset of complementary attention heads. Without requiring a predefined sparsity level or pruning ratio, the framework automatically determines the number of selected attention heads across layers by identifying a diminishing marginal performance curve, where pruning additional heads leads to a sharp degradation in performance, as determined by the chosen polynomial degree. Extensive evaluations on the SST-5 and MNLI benchmarks, across different Transformer model scales, demonstrate that CAHP consistently outperforms competitive baselines, particularly in high-compression regimes. Furthermore, our structural analysis shows that CAHP avoids the "proximity bias" of gradient-based pruning methods, which tend to preserve heads mainly in layers close to the output, and instead retains a functionally critical set of attention heads in the model's intermediate layers.

Yaniv Livertovsky, Shahar Somin, Gonen Singer

Bar-Ilan University Ramat Gan, Israel

Model CompressionTransformer AttentionAttention Head PruningNeural Network Pruning
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Jun 17, 2026

Dual Dimensionality for Local and Global Attention

Decoder-only Transformers compute attention over the KV cache of preceding tokens. Keys (and Values) are typically represented with the same dimensionality, regardless of its distance from the prediction target. In natural language, however, the next word is most strongly influenced by the immediately preceding tokens. We hypothesize that local and distant tokens impose asymmetric demands on representational capacity: local tokens are more critical for predicting immediate outputs and thus require richer representations, whereas distant tokens primarily serve as long-range memory, for which lower-dimensional representations may suffice. We formalize this idea as Distance-Adaptive Representation (DAR), implemented in a controlled setting that preserves full-dimensional representations within a local context window while assigning reduced-dimensional representations (e.g. 1/4 of the original dimensionality) to tokens beyond that window. Across multiple pretraining scales (70M to 410M parameters), as well as continued supervised fine-tuning on a 1B-scale model, this approach closely matches the performance of full-dimensional baselines. In contrast, uniformly reducing dimensionality across all token positions leads to worse performance. These results challenge the common assumption that key and value dimensionality should be uniform across token positions. Our findings suggest a new direction for designing attention architectures that adaptively allocate representational capacity across sequences, enabling further reductions in KV cache during inference.

Zhiyuan Wang, Xuan Luo, Sirui Zeng +1

UC Santa Barbara

LLM CompressionDecoder-Only Language ModelsTransformer AttentionKV-Cache Compression
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Jun 15, 2026

Communication-Efficient Verifiable Attention for LLM Inference

Computation integrity of remote large language model (LLM) serving can be questionable. For conventional deep neural networks (DNNs), the existing TEE-shielded DNN partitioning (TSDP) approach uses Trusted Execution Environment (TEE) to compute non-linear components and verify the integrity of linear components offloaded to an untrusted GPU. However, directly applying TSDP to Transformer-based LLMs incurs significant TEE computation and TEE-GPU communication overhead. This paper presents Communication-efficient TEE-GPU Attention (VeriAttn) for accelerating verifiable LLM inference. VeriAttn offloads both linear and non-linear computations of attention to the GPU, while TEE performs verification. Moreover, for prefill, VeriAttn uses a two-level pipeline to overlap data movement, TEE pre-/post-processing, and GPU computation. For decoding, when the key-value cache exceeds available GPU memory, VeriAttn partitions attention across TEE and GPU to reduce repeated key-value transfers. Evaluation on an Intel TDX platform shows that VeriAttn achieves 2.60-3.38×\times and 3.86-5.42×\times acceleration over TSDP for 6k-token prompts and 10k-token outputs during prefill and decoding, respectively.

Ziqun Chen, Ming Wu, Michael Heinrich +4

Nanyang Technological University · Singapore · Zero Gravity Labs +1

LLM InferenceTrusted Execution EnvironmentsTransformer AttentionLLM Inference Acceleration
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Jun 15, 2026

QK-Normed MLA: QK normalization without full key caching

Query-key (QK) normalization stabilizes attention by controlling the scale of queries and keys before the dot product, but is not immediately compatible with Multi-head Latent Attention (MLA). MLA achieves efficient decoding by caching low-dimensional latent states instead of full keys, whereas post-projection QK RMSNorm appears to require the fully projected key for every cached token. We show this apparent incompatibility is an implementation artifact, not an architectural constraint. RMSNorm decomposes into a static affine weight and a dynamic scalar RMS statistic. The static key-side weight can be absorbed into the MLA query-side projection; the dynamic key statistic reduces to one inverse-RMS scalar per token and KV group. The resulting formulation is exactly equivalent to explicit post-projection QK RMSNorm in exact arithmetic and preserves MLA's latent decode path. In our 400M runs trained for up to 100B tokens, QK-Normed MLA achieves lower training loss and better downstream accuracy than QK clipping, while H800 decode benchmarks show less than 2% latency overhead up to 256k context. These results make QK normalization a practical stabilization option for MLA models without requiring full-key caching.

Yizhou Han, Yao Zhao, Jun Zhou +2

School of Data Science, The Chinese University of Hong Kong, Shenzhen.

KV CachingTransformer AttentionLLM Inference AccelerationAttention MechanismsMulti-Head AttentionMulti-Head Latent Attention
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Jun 14, 2026

Formalizing and Mitigating Structural Distortion in LLM Attention for Graph Reasoning

Large Language Models (LLMs) have shown promise for reasoning over Text-Attributed Graphs (TAGs). However, applying LLMs to graphs requires linearizing their structure into sequences, introducing distortion rooted in the graph bandwidth problem. While this distortion has been shown to degrade performance, it is often attributed to prompt design or model scale, leaving the underlying mechanism unclear. In this work, we show how rotary positional embeddings turn graph linearization into bandwidth-dependent attention decay, suppressing attention between graph-adjacent nodes that are forced far apart in the serialized sequence. This shifts the focus of LLM-based graph reasoning from prompt engineering and scaling toward correcting attention misalignment. Motivated by this analysis, we propose Graph-aligned Language Attention (GaLA), a lightweight, inference-time modification for LLMs. GaLA biases attention toward graph-adjacent nodes while preserving the LLM's sequential inductive biases. Across TAG benchmarks, GaLA improves performance with negligible overhead, demonstrating that distortion is a correctable bottleneck in LLM-based graph reasoning.

Donald Loveland, Puja Trivedi, Ari Weinstein +2

University of Michigan Ann Arbor, MI, USA · Amazon Palo Alto, CA, USA

LLM Reasoning with GraphsTransformer AttentionText-Attributed Graph LearningLLM ReasoningLLMs for Graph Learning
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Jun 12, 2026

Listening with Attention: Entropy-Guided Explainability for Transformer-Based Audio Models

Transformer-based automatic speech recognition (ASR) models such as Whisper are highly accurate, but their predictions remain difficult to interpret. Existing explainable AI (XAI) methods often lack faithfulness and precise temporal grounding. We propose Listening with Entropy-guided Attention for Faithful explainability (LEAF-X), a model-intrinsic XAI framework for transformer-based ASR. LEAF-X combines entropy-guided attention weighting, multi-layer attention rollout, and optional causal ablations to identify low-entropy, high-impact heads and layers, producing sparse token-to-frame attributions. Unlike perturbation-based explainers or raw attention maps, LEAF-X exploits the internal structure of encoder-decoder and speech-augmented decoder-only models to generate explanations that better reflect model computation. Results show 32% improved faithfulness, 35-39% stronger locality/sparsity, and the most stable attributions, supporting more transparent and auditable ASR.

Ravi Ranjan, Utkarsh Grover, Xiaomin Lin +1

Florida International University · Miami, USA · University of South Florida +1

Transformer InterpretabilityExplainable Artificial IntelligenceAutomatic Speech RecognitionTransformer Attention
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Jun 12, 2026

FAConformer: Frequency-Aware Convolutional Transformer for Auditory Attention Decoding

Auditory attention decoding (AAD) aims to infer the attended speaker from neural responses in multi-speaker acoustic environments and is a key problem for neuro-steered hearing systems. Although recent studies have achieved encouraging progress, existing AAD models still do not fully exploit frequency domain electroencephalography (EEG) information. In particular, most approaches introduce multi-band information through handcrafted feature extraction or direct cross-band feature concatenation, which mainly exploit frequency information at a shallow level and may overlook band-specific patterns and cross-band interactions. To address these limitations, this paper proposes FAConformer, a frequency-aware CNN-Transformer framework for AAD that explicitly integrates band-specific encoding and adaptive cross-band interaction. Specifically, FAConformer first decomposes EEG signals into multiple frequency bands and assigns each band to an independent CNN-Transformer encoder for band-specific modeling. The resulting band-wise features are then adaptively fused by a carefully designed frequency-aware attention (FAA) module that models cross-band dependencies by treating band-wise features as tokens. Further, band-wise auxiliary supervision (BAS) is introduced to prevent weakly contributing branches from being under-optimized during joint training. In this way, FAConformer performs frequency-aware modeling that more effectively exploits frequency domain information. Extensive experiments on two public AAD datasets with three decision-window lengths demonstrated that FAConformer consistently outperformed 12 competitive baselines, surpassing the current state-of-the-art model by 4.9%. Further analyses of band importance, ablation, and parameter sensitivity verify the effectiveness, robustness, and interpretability of the proposed framework. Code is available at https://github.com/wzwvv/FAConformer.

Ziwei Wang, Xingyi He, Tianwang Jia +2

Hubei Key Laboratory of Brain-inspired Intelligent Systems, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Hybrid CNN-Transformer ArchitecturesNeural DecodingEEG DecodingFrequency-Domain Feature LearningTransformer Attention
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Jun 10, 2026

Attention by Synchronization in Coupled Oscillator Networks

We address transformer attention on energy-constrained physical substrates. Softmax attention requires exponentiation and global reduction, operations with high energy cost on von Neumann hardware and no natural physical analog. We show that Kuramoto synchronization dynamics (which arise in electrical, mechanical, superconducting, and charge-density-wave oscillator arrays, among other physical systems) implement a well-defined attention operation. The resulting mechanism, fixed-query oscillator attention, replaces softmax's arithmetic with the equilibration of a gradient flow on the sphere: queries are learned anchors fixed on the sphere, and free oscillators evolve under Kuramoto--Lohe dynamics until they settle at positions encoding attention weights via cosine similarity. Because the computation is equilibration, no global exponential normalization is needed. The fixed point is provably unique and globally attractive from almost every initial condition, a guarantee that holds across every physical realization. Empirically, at the minimal hardware configuration (oscillator dimension dosc=2d_{\mathrm{osc}} = 2), oscillator attention matches softmax on keyword spotting, and on subject-verb agreement it trains more reliably while reaching softmax's accuracy. Softmax retains an advantage on causal language modeling, but the gap decays as a power law in doscd_{\mathrm{osc}}. The main objective of this work is not to replace softmax in software but to provide a mathematically grounded blueprint for accurate attention on physical substrates.

Fabio Pasqualetti, Taosha Guo

Electrical Engineering and Computer Science University of California, Irvine

Softmax AttentionDynamical SystemsTransformer AttentionAttention Mechanisms
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Jun 10, 2026

Boltzmann Attention: Learnable Ising Couplings for Cooperative Attention

Attention mechanisms are central to modern sequence models, yet standard attention computes relevance primarily through individual query--key similarities. Although softmax normalization introduces competition among positions, a standard attention layer does not explicitly parameterize learnable interactions between attention decisions. This limits its ability to directly model cooperative or antagonistic co-attention structure within the attention mechanism itself. We propose Boltzmann attention, an energy-based generalization in which attention patterns are governed by an interacting Ising model. The method augments the usual data-dependent local fields with learnable pairwise couplings, allowing the model to represent inter-position correlations beyond those captured by softmax or sigmoid attention. Experiments on character-level language modeling and synthetic bracket matching show that Boltzmann attention consistently improves over standard softmax attention within a standard Transformer architecture, with the advantage becoming more pronounced as sequence length increases. A four-way ablation confirms that the improvement arises from the learnable pairwise couplings. These results suggest that explicit inter-position interactions provide a principled enhancement for attention-based sequence modeling. Moreover, the Ising formulation opens a natural path toward quantum-computing-based sampling strategies: we demonstrate that diabatic quantum annealing provides a practical training method while maintaining competitive performance with exact Boltzmann computation.

Gilhan Kim, Daniel K. Park

Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea · Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea · Department of Quantum Information, Yonsei University, Seoul 03722, Republic of Korea

Quantum AnnealingIsing ModelTransformer AttentionAttention Mechanisms
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