A Regularized Framework for Sparse and Structured Neural Attention
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Abstract (arXiv)
Modern neural networks are often augmented with an attention mechanism, which tells the network where to focus within the input. We propose in this paper a new framework for sparse and structured attention, building upon a smoothed max operator. We show that the gradient of this operator defines a mapping from real values to probabilities, suitable as an attention mechanism. Our framework includes softmax and a slight generalization of the recently-proposed sparsemax as special cases. However, we also show how our framework can incorporate modern structured penalties, resulting in more interpretable attention mechanisms, that focus on entire segments or groups of an input. We derive efficient algorithms to compute the forward and backward passes of our attention mechanisms, enabling their use in a neural network trained with backpropagation. To showcase their potential as a drop-in replacement for existing ones, we evaluate our attention mechanisms on three large-scale tasks: textual entailment, machine translation, and sentence summarization. Our attention mechanisms improve interpretability without sacrificing performance; notably, on textual entailment and summarization, we outperform the standard attention mechanisms based on softmax and sparsemax.
Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 May 2017.
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Citing papers per year: 2021: 9; 2022: 9; 2023: 5; 2024: 6; 2025: 5; 2026: 4.
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- 2021Efficient and Modular Implicit Differentiationcited by 199
- 2023Neurons in Large Language Models: Dead, N-gram, Positionalcited by 88
- 2021A Survey on Green Deep Learningcited by 52
- 2021Sparse Attention with Linear Unitscited by 41
- 2021SPECTRA: Sparse Structured Text Rationalizationcited by 19
- 2021Trilevel Neural Architecture Search for Efficient Single Image Super-Resolutioncited by 15
- 2024Attention layers provably solve single-location regressioncited by 15
- 2024Sparse and Structured Hopfield Networkscited by 13
- 2022Towards Self-Supervised Learning of Global and Object-Centric Representationscited by 11
- 2021Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyondcited by 10
- 2022Leveraging Smooth Attention Prior for Multi-Agent Trajectory Predictioncited by 9
- 2022Learning Self-Modulating Attention in Continuous Time Space with Applications to Sequential Recommendationcited by 8
26 more
- 2023Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUscited by 8
- 2021Evidential Softmax for Sparse Multimodal Distributions in Deep Generative Modelscited by 6
- 2022A Unified Perspective on Value Backup and Exploration in Monte-Carlo Tree Searchcited by 6
- 2024DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Contextcited by 6
- 2024MultiMax: Sparse and Multi-Modal Attention Learningcited by 5
- 2023Give Me More Details: Improving Fact-Checking with Latent Retrievalcited by 4
- 2021Yet Another Representation of Binary Decision Trees: A Mathematical Demonstrationcited by 2
- 2022Learning with Latent Structures in Natural Language Processing: A Surveycited by 2
- 2022Adaptive Sparse and Monotonic Attention for Transformer-based Automatic Speech Recognitioncited by 2
- 2022Convolution-enhanced Evolving Attention Networkscited by 2
- 2023Dual-Attention Neural Transducers for Efficient Wake Word Spotting in Speech Recognitioncited by 2
- 2023Learning Hierarchical Relational Representations through Relational Convolutionscited by 2
- 2024MGHF: Multi-Granular High-Frequency Perceptual Loss for Image Super-Resolutioncited by 2
- 2026Entropy-Generated Attention Beyond Softmax and Entmax: Kaniadakis and Reciprocal-Symmetric Abe Operatorscited by 2
- 2022Modeling Semantic Composition with Syntactic Hypergraph for Video Question Answeringcited by 1
- 2025Bregman Conditional Random Fields: Sequence Labeling with Parallelizable Inference Algorithmscited by 1
- 2026Geometric Analysis of Token Selection in Multi-Head Attentioncited by 1
- 2021Decision Machines: Congruent Decision Treescited by 0
- 2022Mortality Prediction Models with Clinical Notes Using Sparse Attention at the Word and Sentence Levelscited by 0
- 2024Double Momentum Method for Lower-Level Constrained Bilevel Optimizationcited by 0
- 2025FDCT: Frequency-Aware Decomposition and Cross-Modal Token-Alignment for Multi-Sensor Target Classificationcited by 0
- 2025Smooth Quadratic Prediction Marketscited by 0
- 2025Understanding Sensitivity of Differential Attention through the Lens of Adversarial Robustnesscited by 0
- 2025Fairness Meets Privacy: Integrating Differential Privacy and Demographic Parity in Multi-class Classificationcited by 0
- 2026Empty SPACE: Cross-Attention Sparsity for Concept Erasure in Diffusion Modelscited by 0
- 2026Local Evidence and Geometric Readout Repair in Trained GNNscited by 0
- 2026Local Evidence and Geometric Readout Repair in Trained GNNs22 Sep 2026
- 2026Empty SPACE: Cross-Attention Sparsity for Concept Erasure in Diffusion Models11 May 2026
- 2026Entropy-Generated Attention Beyond Softmax and Entmax: Kaniadakis and Reciprocal-Symmetric Abe Operators9 Feb 2026
- 2026Geometric Analysis of Token Selection in Multi-Head Attention2 Feb 2026
- 2025Fairness Meets Privacy: Integrating Differential Privacy and Demographic Parity in Multi-class Classification24 Nov 2025
- 2025Understanding Sensitivity of Differential Attention through the Lens of Adversarial Robustness1 Oct 2025
- 2025Bregman Conditional Random Fields: Sequence Labeling with Parallelizable Inference Algorithms31 May 2025
- 2025Smooth Quadratic Prediction Markets5 May 2025
- 2025FDCT: Frequency-Aware Decomposition and Cross-Modal Token-Alignment for Multi-Sensor Target Classification12 Mar 2025
- 2024MGHF: Multi-Granular High-Frequency Perceptual Loss for Image Super-Resolution20 Nov 2024
- 2024Attention layers provably solve single-location regression2 Oct 2024
- 2024Double Momentum Method for Lower-Level Constrained Bilevel Optimization25 Jun 2024
26 more
- 2024MultiMax: Sparse and Multi-Modal Attention Learning3 Jun 2024
- 2024DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Context8 May 2024
- 2024Sparse and Structured Hopfield Networks21 Feb 2024
- 2023Learning Hierarchical Relational Representations through Relational Convolutions5 Oct 2023
- 2023Neurons in Large Language Models: Dead, N-gram, Positional9 Sep 2023
- 2023Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUs29 Aug 2023
- 2023Give Me More Details: Improving Fact-Checking with Latent Retrieval25 May 2023
- 2023Dual-Attention Neural Transducers for Efficient Wake Word Spotting in Speech Recognition3 Apr 2023
- 2022Convolution-enhanced Evolving Attention Networks16 Dec 2022
- 2022Mortality Prediction Models with Clinical Notes Using Sparse Attention at the Word and Sentence Levels12 Dec 2022
- 2022Adaptive Sparse and Monotonic Attention for Transformer-based Automatic Speech Recognition30 Sep 2022
- 2022Modeling Semantic Composition with Syntactic Hypergraph for Video Question Answering13 May 2022
- 2022Learning Self-Modulating Attention in Continuous Time Space with Applications to Sequential Recommendation30 Mar 2022
- 2022Towards Self-Supervised Learning of Global and Object-Centric Representations11 Mar 2022
- 2022Leveraging Smooth Attention Prior for Multi-Agent Trajectory Prediction8 Mar 2022
- 2022A Unified Perspective on Value Backup and Exploration in Monte-Carlo Tree Search11 Feb 2022
- 2022Learning with Latent Structures in Natural Language Processing: A Survey3 Jan 2022
- 2021A Survey on Green Deep Learning8 Nov 2021
- 2021Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyond27 Oct 2021
- 2021Evidential Softmax for Sparse Multimodal Distributions in Deep Generative Models27 Oct 2021
- 2021SPECTRA: Sparse Structured Text Rationalization9 Sep 2021
- 2021Efficient and Modular Implicit Differentiation31 May 2021
- 2021Sparse Attention with Linear Units14 Apr 2021
- 2021Decision Machines: Congruent Decision Trees27 Jan 2021
- 2021Yet Another Representation of Binary Decision Trees: A Mathematical Demonstration18 Jan 2021
- 2021Trilevel Neural Architecture Search for Efficient Single Image Super-Resolution17 Jan 2021
- 2021Efficient and Modular Implicit Differentiationcited by 199
- 2023Neurons in Large Language Models: Dead, N-gram, Positionalcited by 88
- 2021A Survey on Green Deep Learningcited by 52
- 2021Sparse Attention with Linear Unitscited by 41
- 2021SPECTRA: Sparse Structured Text Rationalizationcited by 19
- 2021Trilevel Neural Architecture Search for Efficient Single Image Super-Resolutioncited by 15
- 2024Attention layers provably solve single-location regressioncited by 15
- 2024Sparse and Structured Hopfield Networkscited by 13
- 2022Towards Self-Supervised Learning of Global and Object-Centric Representationscited by 11
- 2021Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyondcited by 10
- 2022Leveraging Smooth Attention Prior for Multi-Agent Trajectory Predictioncited by 9
- 2022Learning Self-Modulating Attention in Continuous Time Space with Applications to Sequential Recommendationcited by 8
12 most cited of 37 All 37 (JSON)
- 2026Local Evidence and Geometric Readout Repair in Trained GNNs22 Sep 2026
- 2026Entropy-Generated Attention Beyond Softmax and Entmax: Kaniadakis and Reciprocal-Symmetric Abe Operators9 Feb 2026
- 2026Geometric Analysis of Token Selection in Multi-Head Attention2 Feb 2026
- 2025Fairness Meets Privacy: Integrating Differential Privacy and Demographic Parity in Multi-class Classification24 Nov 2025
- 2025Understanding Sensitivity of Differential Attention through the Lens of Adversarial Robustness1 Oct 2025
- 2025Bregman Conditional Random Fields: Sequence Labeling with Parallelizable Inference Algorithms31 May 2025
- 2025Smooth Quadratic Prediction Markets5 May 2025
- 2025FDCT: Frequency-Aware Decomposition and Cross-Modal Token-Alignment for Multi-Sensor Target Classification12 Mar 2025
- 2024MGHF: Multi-Granular High-Frequency Perceptual Loss for Image Super-Resolution20 Nov 2024
- 2024Attention layers provably solve single-location regression2 Oct 2024
- 2024Double Momentum Method for Lower-Level Constrained Bilevel Optimization25 Jun 2024
- 2024MultiMax: Sparse and Multi-Modal Attention Learning3 Jun 2024
12 newest of 37 All 37 (JSON)