# Constrained Structured Regression with Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1511.07497 · HTML: https://mlsanity.com/paper/1511.07497/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2015.

## Built on by (most cited first, 1 of 1)

- [Multi-Scale Temporal Homeostasis Enables Efficient and Robust Neural Networks](https://mlsanity.com/paper/2602.07009/) (2026)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not only able to predict a label but often predict a confidence in the form of a probability distribution over the output space. In continuous regression tasks, such a probability estimate is often lacking. We present a regression framework which models the output distribution of neural networks. This output distribution allows us to infer the most likely labeling following a set of physical or modeling constraints. These constraints capture the intricate interplay between different input and output variables, and complement the output of a CNN. However, they may not hold everywhere. Our setup further allows to learn a confidence with which a constraint holds, in the form of a distribution of the constrain satisfaction. We evaluate our approach on the problem of intrinsic image decomposition, and show that constrained structured regression significantly increases the state-of-the-art.