Structured Prediction Energy Networks
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Abstract (arXiv)
We introduce structured prediction energy networks (SPENs), a flexible framework for structured prediction. A deep architecture is used to define an energy function of candidate labels, and then predictions are produced by using back-propagation to iteratively optimize the energy with respect to the labels. This deep architecture captures dependencies between labels that would lead to intractable graphical models, and performs structure learning by automatically learning discriminative features of the structured output. One natural application of our technique is multi-label classification, which traditionally has required strict prior assumptions about the interactions between labels to ensure tractable learning and prediction. We are able to apply SPENs to multi-label problems with substantially larger label sets than previous applications of structured prediction, while modeling high-order interactions using minimal structural assumptions. Overall, deep learning provides remarkable tools for learning features of the inputs to a prediction problem, and this work extends these techniques to learning features of structured outputs. Our experiments provide impressive performance on a variety of benchmark multi-label classification tasks, demonstrate that our technique can be used to provide interpretable structure learning, and illuminate fundamental trade-offs between feed-forward and iterative structured prediction.
Key facts. Cited by 59 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Nov 2015.
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Citing papers per year: 2020: 1; 2021: 14; 2022: 15; 2023: 8; 2024: 4; 2025: 6; 2026: 11.
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- 2022On Reinforcement Learning and Distribution Matching for Fine-Tuning Language Models with no Catastrophic Forgettingcited by 82
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- 2023A Block Metropolis-Hastings Sampler for Controllable Energy-based Text Generationcited by 6
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- 2025Introducing Verification Task of Set Consistency with Set-Consistency Energy Networkscited by 2
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- 2022SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Modelscited by 1
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- 2025Incorporating Inductive Biases to Energy-based Generative Modelscited by 1
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50 most cited of 59 All 59 (JSON)
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- 2026Contrastive Energy Fields for Inference-Time Procedure Planning in Instructional Videos17 Aug 2026
- 2026KVpop -- Key-Value Cache Compression with Predictive Online Pruning6 Jul 2026
- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers16 Jun 2026
- 2026AURA: Active-Response Attribution under Treatment Ambiguity in Bacterial Cytological Profiling15 Jun 2026
- 2026SAVER: Selective As-Needed Vision Evidence for Multimodal Information Extraction20 May 2026
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- 2026Learning Dynamic Belief Graphs for Theory-of-mind Reasoning20 Mar 2026
- 2026SEAL-pose: Enhancing 3D Human Pose Estimation via a Learned Loss for Structural Consistency23 Feb 2026
- 2026DCER: Dual-Stage Compression and Energy-Based Reconstruction3 Feb 2026
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38 more
- 2025Sparse Latent Factor Forecaster (SLFF) with Iterative Inference for Transparent Multi-Horizon Commodity Futures Prediction11 May 2025
- 2025Incorporating Inductive Biases to Energy-based Generative Models2 May 2025
- 2025Introducing Verification Task of Set Consistency with Set-Consistency Energy Networks12 Mar 2025
- 2025LIFe-GoM: Generalizable Human Rendering with Learned Iterative Feedback Over Multi-Resolution Gaussians-on-Mesh13 Feb 2025
- 2025Convex Is Back: Solving Belief MDPs With Convexity-Informed Deep Reinforcement Learning13 Feb 2025
- 2024Differentiation Through Black-Box Quadratic Programming Solvers8 Oct 2024
- 2024Preference-Optimized Pareto Set Learning for Blackbox Optimization19 Aug 2024
- 2024Deep Sketched Output Kernel Regression for Structured Prediction13 Jun 2024
- 2024Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations25 Jan 2024
- 2023A Block Metropolis-Hastings Sampler for Controllable Energy-based Text Generation7 Dec 2023
- 2023Zero-shot Referring Expression Comprehension via Structural Similarity Between Images and Captions28 Nov 2023
- 2023Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration With Provable Guarantees16 Sep 2023
- 2023PatchCT: Aligning Patch Set and Label Set with Conditional Transport for Multi-Label Image Classification18 Jul 2023
- 2023SPEECH: Structured Prediction with Energy-Based Event-Centric Hyperspheres23 May 2023
- 2023Diffusion Probabilistic Models for Structured Node Classification21 Feb 2023
- 2023Interval Type-2 Fuzzy Neural Networks for Multi-Label Classification21 Feb 2023
- 2023Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernels20 Feb 2023
- 2022Implicit Training of Energy Model for Structure Prediction21 Nov 2022
- 2022Vector-Valued Least-Squares Regression under Output Regularity Assumptions16 Nov 2022
- 2022Autoregressive Structured Prediction with Language Models26 Oct 2022
- 2022Alternating Differentiation for Optimization Layers3 Oct 2022
- 2022Theseus: A Library for Differentiable Nonlinear Optimization19 Jul 2022
- 2022On Reinforcement Learning and Distribution Matching for Fine-Tuning Language Models with no Catastrophic Forgetting1 Jun 2022
- 2022Learning Energy Networks with Generalized Fenchel-Young Losses19 May 2022
- 2022Total Variation Optimization Layers for Computer Vision7 Apr 2022
- 2022Energy-based Latent Aligner for Incremental Learning28 Mar 2022
- 2022Structured Multi-task Learning for Molecular Property Prediction22 Feb 2022
- 2022SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Models20 Feb 2022
- 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters8 Feb 2022
- 2022Modeling Structure with Undirected Neural Networks8 Feb 2022
- 2022Tutorial on amortized optimization1 Feb 2022
- 2022Constrained Structure Learning for Scene Graph Generation27 Jan 2022
- 2021Probabilistic Tracking with Deep Factors2 Dec 2021
- 2021Gaussian Mixture Variational Autoencoder with Contrastive Learning for Multi-Label Classification2 Dec 2021
- 2021Can multi-label classification networks know what they don't know?29 Sep 2021
- 2021The State of the Art when using GPUs in Devising Image Generation Methods Using Deep Learning13 Sep 2021
- 2021Structured Prediction in NLP -- A survey31 Aug 2021
- 2021Learning Energy-Based Approximate Inference Networks for Structured Applications in NLP27 Aug 2021
50 newest of 59 All 59 (JSON)
- 2026Learning Dynamic Belief Graphs for Theory-of-mind Reasoning20 Mar 2026
- 2020Text Generation by Learning from Demonstrationscited by 64
- 2020Text Generation by Learning from Demonstrations16 Sep 2020
- 2021Can multi-label classification networks know what they don't know?cited by 100
- 2022Tutorial on amortized optimizationcited by 83
- 2022On Reinforcement Learning and Distribution Matching for Fine-Tuning Language Models with no Catastrophic Forgettingcited by 82
- 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 65
- 2022Autoregressive Structured Prediction with Language Modelscited by 43
- 2021Exposing the Implicit Energy Networks behind Masked Language Models via Metropolis--Hastingscited by 37
- 2022Energy-based Latent Aligner for Incremental Learningcited by 37
- 2024Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretationscited by 33
- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformerscited by 28
- 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
- 2022Alternating Differentiation for Optimization Layerscited by 22
- 2023PatchCT: Aligning Patch Set and Label Set with Conditional Transport for Multi-Label Image Classificationcited by 21
12 most cited of 53 All 53 (JSON)
- 2026Settling: Equilibrium Inference for Non-Convex Validity Sets9 Sep 2026
- 2026Contrastive Energy Fields for Inference-Time Procedure Planning in Instructional Videos17 Aug 2026
- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers16 Jun 2026
- 2026AURA: Active-Response Attribution under Treatment Ambiguity in Bacterial Cytological Profiling15 Jun 2026
- 2026SAVER: Selective As-Needed Vision Evidence for Multimodal Information Extraction20 May 2026
- 2026Contextual Plackett-Luce: An Efficient Neural Model for Probabilistic Sequence Selection under Ambiguity9 May 2026
- 2026SEAL-pose: Enhancing 3D Human Pose Estimation via a Learned Loss for Structural Consistency23 Feb 2026
- 2026DCER: Dual-Stage Compression and Energy-Based Reconstruction3 Feb 2026
- 2025Type-Compliant Adaptation Cascades: Adapting Programmatic LM Workflows to Data25 Aug 2025
- 2025Sparse Latent Factor Forecaster (SLFF) with Iterative Inference for Transparent Multi-Horizon Commodity Futures Prediction11 May 2025
- 2025Incorporating Inductive Biases to Energy-based Generative Models2 May 2025
- 2025Introducing Verification Task of Set Consistency with Set-Consistency Energy Networks12 Mar 2025
12 newest of 53 All 53 (JSON)