# Learning Approximate Inference Networks for Structured Prediction

arXiv: https://arxiv.org/abs/1803.03376 · HTML: https://mlsanity.com/paper/1803.03376/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2018.

## Built on by (most cited first, 13 of 13)

- [Can multi-label classification networks know what they don't know?](https://mlsanity.com/paper/2109.14162/) (2021)
- [Autoregressive Structured Prediction with Language Models](https://mlsanity.com/paper/2210.14698/) (2022)
- [Energy-based Latent Aligner for Incremental Learning](https://mlsanity.com/paper/2203.14952/) (2022)
- [Gaussian Mixture Variational Autoencoder with Contrastive Learning for Multi-Label Classification](https://mlsanity.com/paper/2112.00976/) (2021)
- [Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics](https://mlsanity.com/paper/2104.04391/) (2021)
- [Approximating CKY with Transformers](https://mlsanity.com/paper/2305.02386/) (2023)
- [Reinforcement Learning-based Semi-supervised Knowledge Distillation with LLM-as-a-Judge](https://mlsanity.com/paper/2604.02621/) (2026)
- [SPEECH: Structured Prediction with Energy-Based Event-Centric Hyperspheres](https://mlsanity.com/paper/2305.13617/) (2023)
- [Multi-Label Out-of-Distribution Detection with Spectral Normalized Joint Energy](https://mlsanity.com/paper/2405.04759/) (2024)
- [Deep Sketched Output Kernel Regression for Structured Prediction](https://mlsanity.com/paper/2406.09253/) (2024)
- [Learning Energy-Based Approximate Inference Networks for Structured Applications in NLP](https://mlsanity.com/paper/2108.12522/) (2021)
- [Structured Prediction in NLP -- A survey](https://mlsanity.com/paper/2110.02057/) (2021)
- [Implicit Training of Energy Model for Structure Prediction](https://mlsanity.com/paper/2211.11649/) (2022)

## Abstract (arXiv)

Structured prediction energy networks (SPENs; Belanger & McCallum 2016) use neural network architectures to define energy functions that can capture arbitrary dependencies among parts of structured outputs. Prior work used gradient descent for inference, relaxing the structured output to a set of continuous variables and then optimizing the energy with respect to them. We replace this use of gradient descent with a neural network trained to approximate structured argmax inference. This "inference network" outputs continuous values that we treat as the output structure. We develop large-margin training criteria for joint training of the structured energy function and inference network. On multi-label classification we report speed-ups of 10-60x compared to (Belanger et al, 2017) while also improving accuracy. For sequence labeling with simple structured energies, our approach performs comparably to exact inference while being much faster at test time. We then demonstrate improved accuracy by augmenting the energy with a "label language model" that scores entire output label sequences, showing it can improve handling of long-distance dependencies in part-of-speech tagging. Finally, we show how inference networks can replace dynamic programming for test-time inference in conditional random fields, suggestive for their general use for fast inference in structured settings.