mlsanityData to 14 Oct 2026

Structured Prediction Energy Networks

arXiv 1511.06350 ↗First posted 19 Nov 2015cs.LG stat.MLcited by 59

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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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  3. 2022On Reinforcement Learning and Distribution Matching for Fine-Tuning Language Models with no Catastrophic Forgettingcited by 82
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  5. 2020Text Generation by Learning from Demonstrationscited by 64
  6. 2022Autoregressive Structured Prediction with Language Modelscited by 43
  7. 2021Exposing the Implicit Energy Networks behind Masked Language Models via Metropolis--Hastingscited by 37
  8. 2022Energy-based Latent Aligner for Incremental Learningcited by 37
  9. 2024Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretationscited by 33
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  11. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  12. 2022Alternating Differentiation for Optimization Layerscited by 22
38 more
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  5. 2021Gaussian Mixture Variational Autoencoder with Contrastive Learning for Multi-Label Classificationcited by 15
  6. 2022Structured Multi-task Learning for Molecular Property Predictioncited by 12
  7. 2021Neuro-Symbolic Constraint Programming for Structured Predictioncited by 11
  8. 2025LIFe-GoM: Generalizable Human Rendering with Learned Iterative Feedback Over Multi-Resolution Gaussians-on-Meshcited by 11
  9. 2021Energy-Based Models for Code Generation under Compilability Constraintscited by 10
  10. 2024Differentiation Through Black-Box Quadratic Programming Solverscited by 10
  11. 2021SocAoG: Incremental Graph Parsing for Social Relation Inference in Dialoguescited by 9
  12. 2022Total Variation Optimization Layers for Computer Visioncited by 8
  13. 2022Learning Energy Networks with Generalized Fenchel-Young Lossescited by 8
  14. 2023A Block Metropolis-Hastings Sampler for Controllable Energy-based Text Generationcited by 6
  15. 2022Vector-Valued Least-Squares Regression under Output Regularity Assumptionscited by 5
  16. 2023Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernelscited by 5
  17. 2021Flow-based Spatio-Temporal Structured Prediction of Motion Dynamicscited by 3
  18. 2022Constrained Structure Learning for Scene Graph Generationcited by 3
  19. 2023Diffusion Probabilistic Models for Structured Node Classificationcited by 3
  20. 2021Structured Convolutional Kernel Networks for Airline Crew Schedulingcited by 2
  21. 2023SPEECH: Structured Prediction with Energy-Based Event-Centric Hyperspherescited by 2
  22. 2024Deep Sketched Output Kernel Regression for Structured Predictioncited by 2
  23. 2024Preference-Optimized Pareto Set Learning for Blackbox Optimizationcited by 2
  24. 2025Introducing Verification Task of Set Consistency with Set-Consistency Energy Networkscited by 2
  25. 2026DCER: Dual-Stage Compression and Energy-Based Reconstructioncited by 2
  26. 2022SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Modelscited by 1
  27. 2023Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration With Provable Guaranteescited by 1
  28. 2025Incorporating Inductive Biases to Energy-based Generative Modelscited by 1
  29. 2025Type-Compliant Adaptation Cascades: Adapting Programmatic LM Workflows to Datacited by 1
  30. 2026KVpop -- Key-Value Cache Compression with Predictive Online Pruningcited by 1
  31. 2021Learning Energy-Based Approximate Inference Networks for Structured Applications in NLPcited by 0
  32. 2021The State of the Art when using GPUs in Devising Image Generation Methods Using Deep Learningcited by 0
  33. 2021Structured Prediction in NLP -- A surveycited by 0
  34. 2021Probabilistic Tracking with Deep Factorscited by 0
  35. 2022Modeling Structure with Undirected Neural Networkscited by 0
  36. 2022Implicit Training of Energy Model for Structure Predictioncited by 0
  37. 2023Interval Type-2 Fuzzy Neural Networks for Multi-Label Classificationcited by 0
  38. 2025Convex Is Back: Solving Belief MDPs With Convexity-Informed Deep Reinforcement Learningcited by 0

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