# Deep Structured Prediction with Nonlinear Output Transformations

arXiv: https://arxiv.org/abs/1811.00539 · HTML: https://mlsanity.com/paper/1811.00539/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2018.

## Built on by (most cited first, 12 of 12)

- [Total Variation Optimization Layers for Computer Vision](https://mlsanity.com/paper/2204.03643/) (2022)
- [DeepCPCFG: Deep Learning and Context Free Grammars for End-to-End Information Extraction](https://mlsanity.com/paper/2103.05908/) (2021)
- [Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics](https://mlsanity.com/paper/2104.04391/) (2021)
- [Constrained Structure Learning for Scene Graph Generation](https://mlsanity.com/paper/2201.11697/) (2022)
- [Diffusion Probabilistic Models for Structured Node Classification](https://mlsanity.com/paper/2302.10506/) (2023)
- [Structured Convolutional Kernel Networks for Airline Crew Scheduling](https://mlsanity.com/paper/2105.11646/) (2021)
- [Deep Sketched Output Kernel Regression for Structured Prediction](https://mlsanity.com/paper/2406.09253/) (2024)
- [SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Models](https://mlsanity.com/paper/2202.09914/) (2022)
- [Heatmap Regression without Soft-Argmax for Facial Landmark Detection](https://mlsanity.com/paper/2508.14929/) (2025)
- [DIFF-ERO: A Conformance-Aware Loss for Deep Learning in Process Mining](https://mlsanity.com/paper/2606.14283/) (2026)
- [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)

## Abstract (arXiv)

Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current deep structured models are restricted by oftentimes very local neighborhood structure, which cannot be increased for computational complexity reasons, and by the fact that the output configuration, or a representation thereof, cannot be transformed further. Very recent approaches which address those issues include graphical model inference inside deep nets so as to permit subsequent non-linear output space transformations. However, optimization of those formulations is challenging and not well understood. Here, we develop a novel model which generalizes existing approaches, such as structured prediction energy networks, and discuss a formulation which maintains applicability of existing inference techniques.