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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Mar 3, 2026

From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs

Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural operators have emerged as powerful data-driven alternatives, they conventionally treat all discretized spatial points as uniform, independent tokens. This monolithic approach ignores the intrinsic scale separation of physical fields, applying computationally prohibitive global attention that redundantly mixes smooth large-scale dynamics with high-frequency fluctuations. Rethinking Transformers through the lens of complex dynamics, we propose DynFormer, a novel dynamics-informed neural operator. Rather than applying a uniform attention mechanism across all scales, DynFormer explicitly assigns specialized network modules to distinct physical scales. It leverages a Spectral Embedding to isolate low-frequency modes, enabling a Kronecker-structured attention mechanism to efficiently capture large-scale global interactions with reduced complexity. Concurrently, we introduce a Local-Global-Mixing transformation. This module utilizes nonlinear multiplicative frequency mixing to implicitly reconstruct the small-scale, fast-varying turbulent cascades that are slaved to the macroscopic state, without incurring the cost of global attention. Integrating these modules into a hybrid evolutionary architecture ensures robust long-term temporal stability. Extensive memory-aligned evaluations across four PDE benchmarks demonstrate that DynFormer achieves up to a 95% reduction in relative error compared to state-of-the-art baselines, while significantly reducing GPU memory consumption. Our results establish that embedding first-principles physical dynamics into Transformer architectures yields a highly scalable, theoretically grounded blueprint for PDE surrogate modeling.

Pengyu Lai, Yixiao Chen, Dewu Yang +3

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

PDE Surrogate ModelingNeural OperatorsPhysics-Informed Neural OperatorsTransformer AttentionAttention Mechanisms
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Mar 3, 2026

On the Expressive Power of Transformers for Maxout Networks and Continuous Piecewise Linear Functions

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of Transformer architectures. We first establish an explicit approximation of maxout networks by Transformer networks while preserving comparable model complexity. As a consequence, Transformers inherit the universal approximation capability of ReLU networks under similar complexity constraints. Building on this connection, we develop a framework to analyze the approximation of continuous piecewise linear functions by Transformers and quantitatively characterize their expressivity via the number of linear regions, which grows exponentially with depth. Our analysis establishes a theoretical bridge between approximation theory for standard feedforward neural networks and Transformer architectures. It also yields structural insights into Transformers: self-attention layers implement max-type operations, while feedforward layers realize token-wise affine transformations.

Linyan Gu, Lihua Yang, Feng Zhou

School of Mathematics, Sun Yat-sen University · School of Information Science, Guangdong University of Finance and Economics

Transformer ExpressivityNeural Network Approximation TheoryTransformer Attention
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Feb 28, 2026

Self-Correction Inside the Model: Leveraging Layer Attention to Mitigate Hallucinations in Large Vision Language Models

Although Large Vision-Language Models (LVLMs) have made substantial progress, hallucination, where generated text is not grounded in the visual input, remains a challenge. As LVLMs become stronger, previously reported hallucination patterns, such as linguistic bias and overthinking phenomenon, become far less consistent, making the corresponding mitigation techniques substantially less effective. In this paper, we introduce an Internal self-Correction mechanism utilizing Layer Attention (ICLA) that operates directly on hidden states during generation. Each layer selectively retrieves information from all preceding layers through a diagonal cross-layer attention mechanism, enabling self-refinement without any external correction signals. With introducing and training only 0.2M and 0.1M additional parameters on LLaVA1.5-7B and Qwen2.5-VL-7B, \ours consistently improves visual grounding across multiple hallucination benchmarks, demonstrating its effectiveness for more advanced LVLMs.

April Fu

Independent Researcher

VLM Hallucination MitigationVision-Language ModelsLarge Vision-Language ModelsTransformer Attention
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Feb 27, 2026

Transformers are Stateless Differentiable Neural Computers

Differentiable Neural Computers (DNCs) were introduced as recurrent architectures equipped with an addressable external memory supporting differentiable read and write operations. Transformers, in contrast, are nominally feedforward architectures based on multi-head self-attention. In this work we give a formal derivation showing that a causal Transformer layer is exactly a stateless Differentiable Neural Computer (sDNC) where (1) the controller has no recurrent internal state, (2) the external memory is a write-once matrix of value vectors, (3) content-based addressing via keys implements attention, and (4) multi-head attention corresponds to multiple parallel read heads. We further extend this equivalence to cross-attention, showing that encoder-decoder Transformers are precisely sDNCs with distinct read-from and write-to memories. Our results provide a unified memory-centric interpretation of Transformers and contribute to the ongoing effort to place modern large language models in a principled computational framework.

Bo Tang, Weiwei Xie

Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609 · Department of Data Science, Worcester Polytechnic Institute, Worcester, MA 01609

TransformerMemory-Augmented Neural NetworksTransformer AttentionDifferentiable Programming
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Feb 26, 2026

Affine-Scaled Attention: Towards Flexible and Stable Transformer Attention

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

Jeongin Bae, Baeseong Park, Gunho Park +7

NAVER Cloud

Transformer AttentionAttention MechanismsSoftmax Attention
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Feb 22, 2026

Incremental Learning of Sparse Attention Patterns in Transformers

This paper studies simple transformers trained on a high-order Markov chain, where the model must incorporate information from multiple past positions, each with different statistical importance. We show that transformers learn the task incrementally, with each stage corresponding to learning how to copy information from a subset of positions via a sparse attention pattern. Notably, the learning dynamics transition from a competitive phase, where all heads focus on the statistically most important positions, to a cooperative phase, where different heads specialize in different patterns. We model these dynamics with simplified differential equations and prove stage-wise convergence of the resulting system. Functionally, these stages correspond to a sequence of increasingly expressive misspecified models, with the full model class reached only at the end. Overall, we give a theoretical account of how structured attention patterns and head specialization emerge in stages without an explicit curriculum, with implications for generalization in sequential tasks.

Oğuz Kaan Yüksel, Rodrigo Alvarez Lucendo, Nicolas Flammarion

TML Lab, EPFL

Self-AttentionTransformer AttentionSparse AttentionIncremental LearningAttention MechanismsNeural Network Training Dynamics+2
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Feb 21, 2026

Toward Manifest Relationality in Transformers via Symmetry Reduction

Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly breaking symmetry, we propose a complementary framework based on symmetry reduction. We reformulate representations, attention mechanisms, and optimization dynamics in terms of invariant relational quantities, eliminating redundant degrees of freedom by construction. This perspective yields architectures that operate directly on relational structures, providing a principled geometric framework for reducing parameter redundancy and analyzing optimization.

J. François, L. Ravera

Mons University (UMONS), 20 Place du Parc, 7000 Mons, Belgium. · Grupo de Investigación en Física Teórica, Universidad Católica De La Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile.

TransformerTransformer AttentionInvariant Representation LearningNeural Representation Geometry
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Feb 21, 2026

Rank-Aware Spectral Bounds on Attention Logits for Stable Low-Precision Training

Attention scores in transformers are bilinear forms Sij=xi⊤Mxj/dhS_{ij} = x_i^\top M x_j / \sqrt{d_h} whose maximum magnitude governs overflow risk in low-precision training. We derive a rank-aware concentration inequality: when the interaction matrix M=WQWK⊤M = W^Q W^{K\top} has rank r≪dr \ll d, tail probabilities for max⁡i,j∣Sij∣\max_{i,j}|S_{ij}| decay as exp⁡(−d2α2/(γr))\exp(-d^{2}α^{2}/(γr)) rather than exp⁡(−dα2)\exp(-dα^{2}), where γ>1γ> 1 is a typicality parameter. For transformer attention where r=dhr = d_h, this yields 88--28×28\times tighter concentration than rank-agnostic bounds in modern architectures. We apply this result to FP8 training, deriving geometry-aware scale factors that provide principled overflow guarantees without observing activations. The method computes per-layer scales from the spectral norm ∥WQWK⊤∥2\|W^Q W^{K\top}\|_2 via implicit power iteration, includes a grouped query attention formulation that avoids key expansion, and remains compatible with fused attention kernels. Across GPT-2 XL to Llama-2-70B, geometry-aware scaling eliminates overflows in transient scenarios where delayed scaling fails, while achieving comparable downstream MMLU accuracy.

Seyed Morteza Emadi

UNC-Chapel Hill, Kenan-Flagler Business School, Chapel Hill, NC, USA

Transformer AttentionAttention QuantizationQuantization-Aware TrainingMixed-Precision Quantization
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Feb 21, 2026

Exact Attention Sensitivity and the Geometry of Transformer Stability

We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation. Our main result is the exact identity ∥Jτ(u)∥∞→1=θ(p)/τ\|J_τ(u)\|_{\infty\to1}=θ(p)/τ for the Jacobian Jτ(u)J_τ(u) of the tempered softmax u↦softmax(u/τ)u\mapsto\mathrm{softmax}(u/τ), where θ(p)=4max⁡S⊆[L]p(S)(1−p(S))θ(p)=4\max_{S\subseteq[L]}p(S)(1-p(S)) measures how evenly the attention distribution can be bisected rather than how concentrated it is. We combine this identity with a block-∞\infty/RMS norm under which row-stochastic attention mixing is nonexpansive. This yields a distribution-aware local Jacobian bound for multi-head attention and a sequence-length-independent Lipschitz bound on bounded input sets, with explicit dependence on width, input magnitude, temperature, and projection norms. We also identify a structural distinction between normalization placements: a pre-LN residual-sublayer Jacobian contains an additive identity term, whereas a post-LN residual-sublayer Jacobian does not. A LayerNorm projection lemma gives a sufficient condition under which the LayerNorm-only term in the post-LN expansion contracts geometrically; the condition is not tested by our experiments. Across three Pre-LN early-training runs of 774774M-parameter models, attention becomes substantially more concentrated while the median lower-bound certificate for θ(p)θ(p) remains near one at every sampled layer and checkpoint. This certifies near-maximal exact sensitivity for at least half of the sampled rows within each layer. A minority of rows enters a dominant-atom regime with lower exact sensitivity, consistent with the deterministic relationship between pmax⁡p_{\max} and θ(p)θ(p).

Seyed Morteza Emadi

UNC-Chapel Hill, Kenan-Flagler Business School Chapel Hill, NC, USA

Transformer AttentionSoftmax AttentionSensitivity Analysis
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Feb 19, 2026

LORA-CRAFT: Cross-layer Rank Adaptation via Frozen Tucker Decomposition of Pre-trained Attention Weights

We introduce LoRA-CRAFT (Cross-layer Rank Adaptation via Frozen Tucker), abbreviated CRAFT throughout, an extremely parameter-efficient fine-tuning (PEFT) method that applies Tucker tensor decomposition to pre-trained attention weight matrices stacked across transformer layers and trains only small square adaptation matrices on the resulting frozen Tucker factors. Existing tensor-based PEFT methods decompose gradient updates: LoTR applies Tucker decomposition with shared factor matrices, while SuperLoRA groups and reshapes ΔWΔW across layers before applying Tucker decomposition. Separately, methods such as PiSSA apply SVD to pre-trained weights but operate independently per layer. CRAFT bridges these two lines of work: it performs full Tucker decomposition via Higher-Order SVD (HOSVD) directly on pre-trained weights organized as cross-layer 3D tensors, freezes all resulting factors, and adapts the model through lightweight trainable transformations applied to each factor matrix. Experiments on the GLUE benchmark using RoBERTa-base and RoBERTa-large, as well as commonsense reasoning benchmarks using LLaMA2-7B and LLaMA3-8B, demonstrate that CRAFT achieves competitive performance with existing methods while requiring only \rev{extremely low Tucker adaptation parameters}. \fixw{On LLaMA3-8B, CRAFT} \rev{exceeds the average accuracy of LoRA} using hundreds of times fewer parameters\fixw{; on LLaMA2-7B the same holds at a 0.2520.252M budget}. Our results suggest that CRAFT's efficiency advantage grows with model scale, as the frozen Tucker factors better capture the richer cross-layer structure of larger pre-trained models.

Kasun Dewage, Marianna Pensky, Shankadeep Mondal +1

University of Central Florida Orlando, FL 32816, USA

Tensor DecompositionLow-Rank AdaptationTransformer AttentionParameter-Efficient Fine-Tuning
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Feb 19, 2026

In-Context Learning in Linear vs. Quadratic Attention Models: An Empirical Study on Regression Tasks

Recent work has demonstrated that transformers and linear attention models can perform in-context learning (ICL) on simple function classes, such as linear regression. In this paper, we empirically study how these two attention mechanisms differ in their ICL behavior on the canonical linear-regression task of Garg et al. We evaluate learning quality (MSE), convergence, and generalization behavior of each architecture. We also analyze how increasing model depth affects ICL performance. Our results illustrate both the similarities and limitations of linear attention relative to quadratic attention in this setting.

Ayush Goel, Arjun Kohli, Sarvagya Somvanshi

University of California, Berkeley

In-Context LearningTransformer AttentionLinear Attention
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Feb 16, 2026

Selective Synchronization Attention

The Transformer architecture has become the foundation of modern deep learning, yet its core self-attention mechanism suffers from quadratic computational complexity and lacks grounding in biological neural computation. We propose Selective Synchronization Attention (SSA), a novel attention mechanism that replaces the standard dot-product self-attention with a closed-form operator derived from the steady-state solution of the Kuramoto model of coupled oscillators. In SSA, each token is represented as an oscillator characterized by a learnable natural frequency and phase; the synchronization strength between token pairs, determined by a frequency-dependent coupling and phase-locking condition, serves as the attention weight. This formulation provides three key advantages: (i) natural sparsity arising from the phase-locking threshold, whereby tokens with incompatible frequencies automatically receive zero attention weight without explicit masking; (ii) unified positional-semantic encoding through the natural frequency spectrum, eliminating the need for separate positional encodings; and (iii) a single-pass, closed-form computation that avoids iterative ODE integration, with all components (coupling, order parameter, synchronization) derived from the oscillatory framework. We instantiate SSA within the Oscillatory Synchronization Network (OSN), a drop-in replacement for the Transformer block. Analysis of the synchronization matrices reveals non-uniform, head-diverse coupling patterns even at initialization, demonstrating a stronger architectural inductive bias than the approximately uniform attention produced by randomly initialized Transformers.

Hasi Hays

Department of Chemical Engineering, University of Arkansas, Fayetteville, AR 72701, USA

Self-AttentionTransformer AttentionSparse Attention
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Feb 9, 2026

Central Dogma Transformer II: An AI Microscope for Understanding Cellular Regulatory Mechanisms

Motivation: Interpretability is not optional in biology: understanding gene regulation requires models whose learned structure can be directly interrogated, not merely accurate predictors whose internals resist mapping onto regulatory relationships. We ask whether an architecture mirroring the central dogma yields attention and gradient maps that recover known regulatory elements and networks in inspectable form. Results: Central Dogma Transformer II (CDT-II) mirrors the central dogma in its architecture -- DNA self-attention, RNA self-attention, and DNA-to-RNA cross-attention -- requiring only genomic embeddings and raw per-cell expression. On K562 CRISPR interference (CRISPRi) data with five genes held out entirely, CDT-II predicts perturbation effects (per-gene mean r = 0.84), recovers the GFI1B regulatory network (6.6-fold enrichment, P = 3.5 x 10^-17), and concentrates cross-attention on ENCODE regulatory elements including CTCF sites (mean 7.67x across 28 target genes, P < 0.001). Gradient attribution predicts consequences of perturbing therapeutic targets (mean r = 0.82). For TFRC, target of the anti-TfR1 antibody PPMX-T003, it identifies erythrocyte-structure, iron-dependent DNA-synthesis and oxidative-stress genes, matching anemia and ferroptosis reported clinically and preclinically -- without clinical data as input. CDT-II acts as an AI microscope, surfacing clinically relevant regulatory structure from perturbation experiments alone. Availability: Source code is available at https://github.com/nobusama/CDT2. Pre-computed embeddings, training data, and model weights are available at https://huggingface.co/datasets/nobusama17/CDT2-data.

Nobuyuki Ota

Independent Researcher, Burlingame, CA, USA

Transformer InterpretabilitySingle-Cell Perturbation ModelingTransformer AttentionGene Regulatory Network InferenceGenomics
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Feb 6, 2026

Quantum Attention by Overlap Interference: Predicting Classical and Many-Body Quantum Sequences

We propose a variational quantum implementation of self-attention (QSA)-the core operation in transformers and large language models-which predicts future elements of a sequence by forming overlap-weighted combinations of past data. At variance with previous approaches, our QSA realizes the required nonlinearity through interference of state overlaps and a degree-kk polynomial kernel, and estimates a loss based on Rényi-1/21/2 entropic functionals via two observables' expectation values, avoiding the decoding of amplitude-encoded predictions into classical probabilities. QSA also accommodates a constrained, trainable data-embedding tying state overlaps to data-level similarities. Its dominant end-to-end training complexity scales as O(μ−1k2Td)O\left(μ^{-1}k^2Td\right), versus O(Tdk+1)O\left(T d^{k+1}\right) of the fairest classical comparison, with μμ a training signal; we show numerically that this allows a complexity advantage in the regime where sequence length TT dominates the embedding size dd. In simulations, our QSA-based quantum transformer learns sequence prediction on classical data and on many-body transverse-field Ising trajectories-establishing trainable attention as a practical primitive for quantum dynamical modeling.

Alessio Pecilli, Matteo Rosati

Dipartimento di Ingegneria Civile, Informatica e delle Tecnologie Aeronautiche, Universit`a degli Studi Roma Tre, Via della Vasca Navale 79, 00146 Rome, Italy

Self-AttentionTransformer AttentionVariational Quantum CircuitsAttention MechanismsSequence ModelingQuantum Neural Networks
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Feb 2, 2026

Poly-attention: a general scheme for higher-order self-attention

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

Sayak Chakrabarti, Toniann Pitassi, Josh Alman

Computer Science, Columbia University, New York, NY 10027.

Self-AttentionCompositional ReasoningTransformer AttentionAttention MechanismsNeural Network Expressivity
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Jan 11, 2026

Garbage Attention in Large Language Models: BOS Sink Heads and Sink-aware Pruning

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

Jaewon Sok, Jewon Yeom, Seonghyeon Park +2

Department of Rural Systems Engineering, Seoul National University · Graduate School of Data Science, Seoul National University · Department of Aerospace Engineering, Seoul National University

LLM PruningAttention Head AnalysisSelf-AttentionTransformer AttentionAttention SinksAttention Mechanisms+2
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Jan 10, 2026

Architecture Before the Formula: Training-Dependent Computational Semantics in Transformers

An operation's input-output function does not, by itself, determine its computational role within a represented process. That role also depends on the processes producing its inputs and receiving its outputs, a philosophical stance termed deep learning externalism (DLE). We develop a mathematical account of represented computation that distinguishes functional equivalence, retained predecessor distinctions, restricted receiver capability, and context-dependent effective architectures. The resulting equivalences depend on which computational relations a scientific description must preserve. We prove that two injective producer contexts can preserve every predecessor distinction while changing whether fixed local and attention receiver families are equivalent. We investigate these relations in a dimension-labelled PreNorm Transformer and their evolution under training. Residual bypasses restrict complete-state information identifications to two merges per block, while finer branches can change receiver accessibility. Exact gradient-descent models yield covariance-dependent geometric attenuation under learned producer routing and algebraic (t−1/2)(t^{-1/2}) attenuation under Q/K-softmax training, with optimal bounded-receiver recovery errors derived in both cases. Coupled producer-attention dynamics establish how learning jointly reorganizes the presented features and receiver allocation. Finally, present functional or receiver-profile equivalence need not determine future behavior under an optimizer. In an input-conditioned attention model, two accessibility measurements form an exact reduced predictive state, whereas one alone does not.

Luis F. Rosario Freytes

Transformer AttentionNeural Network InterpretabilityNeural Network Training Dynamics
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Dec 23, 2025

GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer

We present GeoTransolver, a multiscale geometry-aware physics attention transformer for Computer Aided Engineering (CAE). GeoTransolver extends the Transolver backbone with GALE (Geometry-Aware Latent Embeddings) attention, which pairs physics-aware self-attention on learned state slices with cross-attention to a shared geometry and global context computed via multi-scale ball queries (inspired by Domino) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry and global parameters, into physical state spaces to anchor computations to domain structure and operating regimes. We benchmark on DrivAerML, SHIFT-SUV, and SHIFT-Wing against Domino, Transolver (PhysicsNeMo implementation), and literature-reported AB-UPT, evaluating drag/lift R2 and relative L1 errors on field variables. As an additional nonlinear structural mechanics application, we also report Transolver and GeoTransolver results on bumper-beam and full-vehicle Body-in-White (BIW) crash-dynamics benchmarks, evaluating relative L2 trajectory error and probe-level kinematic MSE. GeoTransolver delivers improved accuracy, robustness to geometry and regime shifts, and favorable data efficiency; we include DrivAerML ablations and qualitative contour and design-trend results, advancing operator learning for high-fidelity surrogates on complex, irregular, non-linear domains.

Corey Adams, Rishikesh Ranade, Ram Cherukuri +1

NVIDIA Corporation, Santa Clara, US

Neural Surrogate ModelingStructural MechanicsTransformer AttentionNeural OperatorsComputational Fluid Dynamics
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Nov 24, 2025

Phase-Aligned RoPE for Mixed-Resolution Diffusion Transformer

Rotary positional embeddings (RoPE) are widely used in diffusion transformers (DiTs) to encode spatial relationships, yet their behavior with mixed-resolution tokens remains underexplored. A natural approach is to rescale token positions from different resolutions into a unified coordinate system before attention, but we show this fails. Our analysis shows that with RoPE, the attention similarity score is a highly structured and periodic function of token distance, so rescaling distances across resolutions moves token pairs to different regions of this periodic function, leading to incorrect attention scores. Motivated by this, we introduce Phase-Aligned Mixed-Resolution Attention (PMA), a training-free mechanism that stabilizes mixed-resolution attention. PMA modifies the RoPE position mapping to enforce a consistent positional scale for every query-key pair, ensuring that relative distances are evaluated under a single reference scale. To further improve local coherence near resolution transitions, we incorporate a lightweight boundary refinement module that softly exchanges features across adjacent scales. Experiments on image and video diffusion models validate our analysis and demonstrate consistent improvements in visual fidelity and computational efficiency.

Haoyu Wu, Jingyi Xu, Qiaomu Miao +2

Stony Brook University, NY, USA · UNC-Charlotte, NC, USA

Rotary Positional EmbeddingsVideo Diffusion ModelsDiffusion TransformerTransformer Attention
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Nov 7, 2025

Controllably Efficient Language Models

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

Jatin Prakash, Aahlad Puli, Rajesh Ranganath

New York University

Efficient Transformer InferenceLong-Context Language ModelingTransformer AttentionAttention Mechanisms
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Oct 28, 2025

A Unified Geometric Space for Topological Alignment Between Transformer-Based Models and Human Brain Networks

Whether artificial neural networks organize information comparably to the human brain remains unclear. Prior brain--AI alignment studies are constrained by specific inputs and tasks, limiting cross-modal comparison. Here we introduce a brain--model topological alignment space, mapping Transformer attention topology onto human intrinsic connectivity networks (ICNs) to enable task-free, modality-agnostic comparison. Analyzing 151 Transformer-based models with 62,480 attention head graphs, we observe a continuous arc-shaped distribution reflecting varying alignment. Models optimized for global semantics aligned with higher-order ICNs, while local-detail models aligned with sensory ICNs. Non-intuitive findings include reduced alignment in DINOv2 compared to its predecessors and a counterintuitive scaling inversion in distilled DeiT models, while fine-tuning and instruction tuning had limited effect. Alignment scores showed no significant correlation with ImageNet accuracy (r = 0.266, p = 0.156). This work offers a quantitative framework for comparing the organizational principles of artificial and biological systems.

Silin Chen, Yuzhong Chen, Caiwei Wang +9

The Clinical Hospital of Chengdu Brain Science Institute, MOE-K Lab for NeuroInformation, Brain-Apparatus Communication Institute, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu. 611731, China. · School of Automation, Northwestern Polytechnical University, Xi’an 710072, China. · Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA. +1

Neural Representation GeometryTransformer AttentionBrain Network Analysis
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Oct 21, 2025

Higher Embedding Dimension Creates a Stronger World Model for a Simple Sorting Task

We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small embedding dimensions, but larger dimensions yield more faithful, consistent, and robust internal representations. In particular, higher embedding dimensions strengthen the formation of structured internal representation and lead to better interpretability. After hundreds of experiments, we observe two consistent mechanisms: (1) the last row of the attention weight matrix monotonically encodes the global ordering of tokens; and (2) the selected transposition aligns with the largest adjacent difference of these encoded values. Our results provide quantitative evidence that transformers build structured internal world models and that model size improves representation quality in addition to end performance. We release our metrics and analyses, which can be used to probe similar algorithmic tasks.

Brady Bhalla, Honglu Fan, Nancy Chen +1

California Institute of Technology · Pasadena, CA 91125 · Google DeepMind +3

Transformer InterpretabilityRepresentation LearningWorld Model LearningTransformer-Based RLTransformer AttentionAlgorithmic Reasoning
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Oct 13, 2025

Qubit-centric Transformer for Surface Code Decoding

For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based decoders have emerged as a promising approach to improve the reliability of QEC. We propose the qubit-centric transformer (QCT), a novel and universal QEC decoder based on a transformer architecture with a qubit-centric attention mechanism. Our decoder transforms input syndromes from the stabilizer domain into qubit-centric tokens via a specialized embedding strategy. These qubit-centric tokens are processed through attention layers to effectively identify the underlying logical error. Furthermore, we introduce a graph-based masking method that incorporates the topological structure of quantum codes, enforcing attention toward relevant qubit interactions. Across various code distances for surface codes, QCT achieves state-of-the-art decoding performance, significantly outperforming existing neural decoders and the belief propagation (BP) with ordered statistics decoding (OSD) baseline. Notably, QCT achieves a high threshold of 18.1% under depolarizing noise, which closely approaches the theoretical bound of 18.9% and surpasses both the BP+OSD and the minimum-weight perfect matching (MWPM) thresholds. This qubit-centric approach provides a scalable and robust framework for surface code decoding, advancing the path toward fault-tolerant quantum computing.

Seong-Joon Park, Hee-Youl Kwak, Yongjune Kim

Samsung Electronics Company, Ltd., Suwon 16677, South Korea · Institute of Artificial Intelligence, Pohang University of Science and Technology (POSTECH), Pohang 37673, South Korea · Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Ulsan 44610, South Korea +1

Neural DecodingQuantum Error CorrectionTransformer Attention
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Oct 2, 2025

Accelerating Attention with Basis Decomposition

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

Jialin Zhao

Department of Computer Science Tsinghua University

Self-AttentionTransformer AttentionLLM Inference AccelerationEfficient AttentionAttention MechanismsMulti-Head Attention
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Sep 12, 2025

Multipole Semantic Attention: A Fast Approximation of Softmax Attention for Pretraining

Pretraining transformers on long sequences (entire code repositories, collections of related documents) is bottlenecked by quadratic attention costs. We present Multipole Semantic Attention (MuSe), which accelerates 64k-context pretraining by 36% while matching baseline loss, requiring no architectural changes. MuSe clusters queries and keys separately in representation space. This yields query-specific summaries that substantially outperform spatial blocking at matched sparsity, while also enabling drop-in compatibility with existing pretrained models; we validate on Llama 3.1-8B and 3.2-1B without retraining. We pretrain language models up to 1B parameters at 64k context on code and scientific documents, confirming that MuSe preserves quality and long-context utilization during training.

Rupert Mitchell, Kristian Kersting

Department of Computer Science, TU Darmstadt, Darmstadt, Germany · Hessian Center for AI (hessian.AI), Darmstadt, Germany · German Research Center for Artificial Intelligence (DFKI), Darmstadt, Germany +1

Language Model PretrainingSoftmax AttentionSelf-AttentionLong-Context Language ModelingTransformer AttentionSparse Attention+1
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Sep 4, 2025

Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation

We introduce Robust Filter Attention (RFA), a formulation of self-attention as a robust state estimator. Each token is treated as a noisy observation of a latent trajectory governed by a linear stochastic differential equation (SDE), and attention weights are determined by consistency under this model rather than static feature similarity. Under isotropic noise and decay assumptions, RFA matches the computational complexity of standard attention. On language modeling benchmarks, RFA achieves lower perplexity than RoPE within the training window while remaining stable under zero-shot extrapolation to longer contexts. The framework also provides a dynamical interpretation of standard positional mechanisms, connecting rotational embeddings and recency biases to transport and uncertainty propagation induced by stochastic dynamics.

Peter Racioppo

Independent Researcher, Los Angeles, CA, USA.

Self-AttentionLong-Context Language ModelingAutoregressive Language ModelingTransformer AttentionAttention Mechanisms
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Jul 21, 2025

Inexact calculus of variations on the hyperspherical tangent bundle with connections to the attention mechanism

We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential structure. Our methods can be categorized as inexact since our methods are projection-based and since we will perturb the functional optimization with epsilon-type quantities. We draw connections to the attention mechanism and the Transformer since it exists as a flow map in the tangent fiber for each token along the high-dimensional unit sphere. Our motivation for this work is primarily twofold: we study the attention mechanism under its flow map and its relations to traditional calculus of variations and Lagrangian optimization; and we study several calculus problems of variations on the unit hypersphere that appeal to a broader mathematical lens in approximating, variational contexts.

Andrew Gracyk

Riemannian OptimizationTransformer Attention
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Jul 17, 2025

NABLA: Neighborhood Adaptive Block-Level Attention

Recent progress in transformer-based architectures has demonstrated remarkable success in video generation tasks. However, the quadratic complexity of full attention mechanisms remains a critical bottleneck, particularly for high-resolution and long-duration video sequences. In this paper, we propose NABLA, a novel Neighborhood Adaptive Block-Level Attention mechanism that dynamically adapts to sparsity patterns in video diffusion transformers (DiTs). By leveraging block-wise attention with adaptive sparsity-driven threshold, NABLA reduces computational overhead while preserving generative quality. Our method does not require custom low-level operator design and can be seamlessly integrated with PyTorch's Flex Attention operator. Experiments demonstrate that NABLA achieves up to 2.7x faster training and inference compared to baseline almost without compromising quantitative metrics (CLIP score, VBench score, human evaluation score) and visual quality drop. The code and model weights are available here: https://github.com/gen-ai-team/Wan2.1-NABLA

Dmitrii Mikhailov, Aleksey Letunovskiy, Maria Kovaleva +6

Kandinsky Lab, Moscow, Russia

Video Diffusion ModelsDiffusion TransformerTransformer AttentionSparse AttentionDiffusion Model AccelerationBlock-Sparse Attention
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Jun 25, 2025

A foundation model with multi-variate parallel attention to generate neuronal activity

Learning from multi-variate time-series with heterogeneous channel configurations remains a fundamental challenge for deep neural networks, particularly in clinical domains such as intracranial electroencephalography (iEEG), where channel setups vary widely across subjects. In this work, we introduce multi-variate parallel attention (MVPA), a novel self-attention mechanism that disentangles content, temporal, and spatial attention, enabling flexible, generalizable, and efficient modeling of time-series data with varying channel counts and configurations. We use MVPA to build MVPFormer, a generative foundation model for human electrophysiology, trained to predict the evolution of iEEG signals across subjects. To support this and future efforts by the community, we release the SWEC iEEG dataset, the largest publicly available iEEG dataset to date, comprising nearly 10,000 hours of recordings from heterogeneous clinical sources. MVPFormer leverages MVPA to achieve strong generalization across subjects, demonstrating expert-level performance in several iEEG tasks. MVPFormer surpasses state-of-the-art (SOTA) Transformer baselines in seizure detection across the SWEC, the MAYO, and the FNUSA datasets, while also achieving SOTA performance on four Brain TreeBank iEEG decoding tasks (volume, pitch, onset, and speech). We further validate MVPA on standard time-series forecasting and classification tasks, where it matches or exceeds the performance of existing attention-based models. Together, our contributions establish MVPA as a general-purpose attention mechanism for heterogeneous time-series and MVPFormer as the first open-source, open-weights, and open-data iEEG foundation model with SOTA clinical performance. The code is available at https://github.com/IBM/multi-variate-parallel-transformer. The SWEC iEEG dataset is available at https://huggingface.co/datasets/NeuroTec/SWEC_iEEG_Dataset.

Francesco Carzaniga, Michael Hersche, Abu Sebastian +2

IBM Research – Zurich, Rüschlikon, Switzerland · Department of Neurology, Inselspital, Sleep-Wake-Epilepsy-Center, Bern University Hospital, Bern University, Bern, Switzerland

ElectroencephalographyEEG DecodingTransformer AttentionEEG Foundation Models
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Apr 13, 2025

Ordinary Least Squares as an Attention Mechanism

I show that ordinary least squares (OLS) predictions can be rewritten as the output of a restricted attention module, akin to those forming the backbone of large language models. The connection comes from viewing OLS as a similarity-based prediction rule in a learned embedding space. In this representation, least squares does not estimate coefficients per se. Instead, it selects an embedding that minimizes squared prediction error by matching training and test vectors through inner products. This maps directly onto the query-key-value structure of attention mechanisms. I then discuss extensions to dimensionality reduction, nonlinearity, and time series econometrics. Monte Carlo simulations and real-data experiments on UCI/OpenML benchmarks show that nonlinear Attention Regression performs competitively against standard machine learning baselines. In the reverse direction, I replace the attention sublayer of a transformer for tabular data with an explicit regression on polynomial features. The resulting model performs comparably to the standard transformer at a fraction of its parameter count.

Philippe Goulet Coulombe

Département des Sciences Économiques, Université du Québec à Montréal

Transformer AttentionLinear RegressionAttention MechanismsTabular Regression
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