Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kernel
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Abstract (arXiv)
Transformer is a powerful architecture that achieves superior performance on various sequence learning tasks, including neural machine translation, language understanding, and sequence prediction. At the core of the Transformer is the attention mechanism, which concurrently processes all inputs in the streams. In this paper, we present a new formulation of attention via the lens of the kernel. To be more precise, we realize that the attention can be seen as applying kernel smoother over the inputs with the kernel scores being the similarities between inputs. This new formulation gives us a better way to understand individual components of the Transformer's attention, such as the better way to integrate the positional embedding. Another important advantage of our kernel-based formulation is that it paves the way to a larger space of composing Transformer's attention. As an example, we propose a new variant of Transformer's attention which models the input as a product of symmetric kernels. This approach achieves competitive performance to the current state of the art model with less computation. In our experiments, we empirically study different kernel construction strategies on two widely used tasks: neural machine translation and sequence prediction.
Key facts. Cited by 211 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Aug 2019.
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Citing papers per year: 2021: 22; 2022: 27; 2023: 40; 2024: 44; 2025: 45; 2026: 33.
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- 2021CoAtNet: Marrying Convolution and Attention for All Data Sizescited by 566
- 2021Linear Transformers Are Secretly Fast Weight Programmerscited by 471
- 2021A Survey of Transformerscited by 399
- 2021Random Feature Attentioncited by 350
- 2021Choose a Transformer: Fourier or Galerkincited by 333
- 2023The Impact of Positional Encoding on Length Generalization in Transformerscited by 319
- 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
- 2022cosFormer: Rethinking Softmax in Attentioncited by 212
- 2021GraphiT: Encoding Graph Structure in Transformerscited by 146
- 2022ETSformer: Exponential Smoothing Transformers for Time-series Forecastingcited by 146
- 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
- 2024The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicrycited by 119
38 more
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- 2023Fast Attention Requires Bounded Entriescited by 102
- 2021Finetuning Pretrained Transformers into RNNscited by 94
- 2022Learning Operators with Coupled Attentioncited by 88
- 2022KERPLE: Kernelized Relative Positional Embedding for Length Extrapolationcited by 84
- 2024Get More with LESS: Synthesizing Recurrence with KV Cache Compression for Efficient LLM Inferencecited by 75
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- 2025Test-time regression: a unifying framework for designing sequence models with associative memorycited by 63
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- 2022Real-time Online Video Detection with Temporal Smoothing Transformerscited by 58
- 2021Stable, Fast and Accurate: Kernelized Attention with Relative Positional Encodingcited by 50
- 2022The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attentioncited by 45
- 2024Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscapecited by 43
- 2024Continuum Attention for Neural Operatorscited by 39
- 2025MesaNet: Sequence Modeling by Locally Optimal Test-Time Trainingcited by 37
- 2021Relative Positional Encoding for Transformers with Linear Complexitycited by 36
- 2023PolySketchFormer: Fast Transformers via Sketching Polynomial Kernelscited by 33
- 2023Length Extrapolation of Transformers: A Survey from the Perspective of Positional Encodingcited by 32
- 2024Conv-Basis: A New Paradigm for Efficient Attention Inference and Gradient Computation in Transformerscited by 32
- 2023Mitigating Over-smoothing in Transformers via Regularized Nonlocal Functionalscited by 31
- 2022(2.5+1)D Spatio-Temporal Scene Graphs for Video Question Answeringcited by 29
- 2021Improving Transformers with Probabilistic Attention Keyscited by 28
- 2023Primal-Attention: Self-attention through Asymmetric Kernel SVD in Primal Representationcited by 28
- 2025Tensor Product Attention Is All You Needcited by 27
- 2024Understanding the differences in Foundation Models: Attention, State Space Models, and Recurrent Neural Networkscited by 26
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- 2022Exploring the Relationship between Architecture and Adversarially Robust Generalizationcited by 23
- 2022Neural Integral Equationscited by 23
- 2023Latent Positional Information is in the Self-Attention Variance of Transformer Language Models Without Positional Embeddingscited by 23
- 2023QKSAN: A Quantum Kernel Self-Attention Networkcited by 23
- 2022Transformer Meets Boundary Value Inverse Problemscited by 22
- 2024In-Context Learning with Transformers: Softmax Attention Adapts to Function Lipschitznesscited by 22
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- 2023Calibrating Transformers via Sparse Gaussian Processescited by 21
- 2024Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannotcited by 21
- 2025Efficient Attention Mechanisms for Large Language Models: A Surveycited by 21
- 2023Practical Computational Power of Linear Transformers and Their Recurrent and Self-Referential Extensionscited by 20
- 2024Small Singular Values Matter: A Random Matrix Analysis of Transformer Modelscited by 20
50 most cited of 211 All 211 (JSON)
- 2026Attention Function as an Intrinsic Inductive Bias: How Models' Behavior Diverges in Novel Contexts30 Sep 2026
- 2026Quasi Linear Kernel Attention with Infinite Capacity28 Sep 2026
- 2026Manifold Projection and Iterative Autoencoder Refinement for Masked Language Modeling9 Sep 2026
- 2026One-Layer Transformer Provably Learns Multiclass One-Nearest Neighbor in Context1 Sep 2026
- 2026Mahalanobis-Based Multi-Head Attention for Complex State Propagation25 Aug 2026
- 2026Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing21 Aug 2026
- 2026A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex11 Aug 2026
- 2026Training-Free Universal Approximation by Prompting Random Transformers10 Aug 2026
- 2026A Coulomb Particle Model for Learning Kernel Attention in Transformers26 Jul 2026
- 2026Higher-Order Token Interactions via Quantum Attention10 Jun 2026
- 2026Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization8 Jun 2026
- 2026DN-Hypo-Pipeline: An AI-Driven Workflow for Generating Hypotheses using Large Language Models and Scientific Explanations7 Jun 2026
38 more
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- 2026Multi-Head Attention as Ensemble Nadaraya-Watson Estimation: Variance Reduction, Decorrelation, and Optimal Head Diversity18 May 2026
- 2026Support-Conditioned Flow Matching Is Kernel Smoothing13 May 2026
- 2026Rethinking Random Transformers as Adaptive Sequence Smoothers for Sleep Staging11 May 2026
- 2026The Transformer as a Polar State Estimator10 May 2026
- 2026One for All: A Non-Linear Transformer can Enable Cross-Domain Generalization for In-Context Reinforcement Learning10 May 2026
- 2026RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics30 Apr 2026
- 2026Transformer as an Euler Discretization of Score-based Variational Flow26 Apr 2026
- 2026Hierarchical Kernel Transformer: Multi-Scale Attention with an Information-Theoretic Approximation Analysis10 Apr 2026
- 2026Cactus: Accelerating Auto-Regressive Decoding with Constrained Acceptance Speculative Sampling5 Apr 2026
- 2026Transformers Can Learn Rules They've Never Seen: Proof of Computation Beyond Interpolation17 Mar 2026
- 2026GIST: Gauge-Invariant Spectral Transformers for Scalable Graph Neural Operators17 Mar 2026
- 2026Gated Differential Linear Attention: A Linear-Time Decoder for High-Fidelity Medical Segmentation3 Mar 2026
- 2026Krause Synchronization Transformers12 Feb 2026
- 2026WildCat: Near-Linear Attention in Theory and Practice10 Feb 2026
- 2026Diffusion-Inspired Reconfiguration of Transformers for Uncertainty Calibration9 Feb 2026
- 2026Universal Redundancies in Time Series Foundation Models2 Feb 2026
- 2026Sparse Attention as Compact Kernel Regression30 Jan 2026
- 2026Sensoformer: Robust Sim-to-Real Inference on Variable-Geometry Sensor Sets via Physics-Structured Randomization9 Jan 2026
- 2025Deep learning for pedestrians: backpropagation in Transformers29 Dec 2025
- 2025Modality Alignment across Trees on Heterogeneous Hyperbolic Manifolds31 Oct 2025
- 2025Translution: Unifying Self-attention and Convolution for Adaptive and Relative Modeling11 Oct 2025
- 2025Design Principles for Sequence Models via Coefficient Dynamics10 Oct 2025
- 2025Decoupled-Value Attention for Prior-Data Fitted Networks: GP Inference for Physical Equations25 Sep 2025
- 2025Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation4 Sep 2025
- 2025Attention as Conditioning: What Classical Learning Theory Predicts About Linear Transformers5 Aug 2025
- 2025Graded Transformers27 Jul 2025
- 2025Efficient Attention Mechanisms for Large Language Models: A Survey25 Jul 2025
- 2025PGKET: A Photonic Gaussian Kernel Enhanced Transformer25 Jul 2025
- 2025Attention (as Discrete-Time Markov) Chains23 Jul 2025
- 2025SAS: Simulated Attention Score10 Jul 2025
- 2025Position: We Need An Algorithmic Understanding of Generative AI10 Jul 2025
- 2025Relational inductive biases on attention mechanisms5 Jul 2025
- 2025A unified framework for establishing the universal approximation of transformer-type architectures30 Jun 2025
- 2025Transformer Circuits Can Realize Clustering Algorithms23 Jun 2025
- 2025Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods12 Jun 2025
50 newest of 211 All 211 (JSON)
- 2022cosFormer: Rethinking Softmax in Attentioncited by 212
- 2024KnowFormer: Revisiting Transformers for Knowledge Graph Reasoningcited by 5
- 2024KnowFormer: Revisiting Transformers for Knowledge Graph Reasoning19 Sep 2024
- 2022cosFormer: Rethinking Softmax in Attention17 Feb 2022
- 2021CoAtNet: Marrying Convolution and Attention for All Data Sizescited by 566
- 2021Linear Transformers Are Secretly Fast Weight Programmerscited by 471
- 2021A Survey of Transformerscited by 399
- 2021Random Feature Attentioncited by 350
- 2021Choose a Transformer: Fourier or Galerkincited by 333
- 2023The Impact of Positional Encoding on Length Generalization in Transformerscited by 319
- 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
- 2021GraphiT: Encoding Graph Structure in Transformerscited by 146
- 2022ETSformer: Exponential Smoothing Transformers for Time-series Forecastingcited by 146
- 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
- 2024The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicrycited by 119
- 2022Transformer for Graphs: An Overview from Architecture Perspectivecited by 107
12 most cited of 199 All 199 (JSON)
- 2026Attention Function as an Intrinsic Inductive Bias: How Models' Behavior Diverges in Novel Contexts30 Sep 2026
- 2026Quasi Linear Kernel Attention with Infinite Capacity28 Sep 2026
- 2026Manifold Projection and Iterative Autoencoder Refinement for Masked Language Modeling9 Sep 2026
- 2026One-Layer Transformer Provably Learns Multiclass One-Nearest Neighbor in Context1 Sep 2026
- 2026Mahalanobis-Based Multi-Head Attention for Complex State Propagation25 Aug 2026
- 2026Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing21 Aug 2026
- 2026A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex11 Aug 2026
- 2026Training-Free Universal Approximation by Prompting Random Transformers10 Aug 2026
- 2026A Coulomb Particle Model for Learning Kernel Attention in Transformers26 Jul 2026
- 2026Higher-Order Token Interactions via Quantum Attention10 Jun 2026
- 2026Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization8 Jun 2026
- 2026DN-Hypo-Pipeline: An AI-Driven Workflow for Generating Hypotheses using Large Language Models and Scientific Explanations7 Jun 2026
12 newest of 199 All 199 (JSON)