# Label Encoding for Regression Networks

arXiv: https://arxiv.org/abs/2212.01927 · HTML: https://mlsanity.com/paper/2212.01927/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 63 references that are in the map.
- First posted on arXiv 4 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [Fine-Grained Head Pose Estimation Without Keypoints](https://mlsanity.com/paper/1710.00925/) (2017)
- [Look at Boundary: A Boundary-Aware Face Alignment Algorithm](https://mlsanity.com/paper/1805.10483/) (2018)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [Adaptive Wing Loss for Robust Face Alignment via Heatmap Regression](https://mlsanity.com/paper/1904.07399/) (2019)
- [LUVLi Face Alignment: Estimating Landmarks' Location, Uncertainty, and Visibility Likelihood](https://mlsanity.com/paper/2004.02980/) (2020)
- [Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a Car](https://mlsanity.com/paper/1704.07911/) (2017)
- [Style Aggregated Network for Facial Landmark Detection](https://mlsanity.com/paper/1803.04108/) (2018)
- [Human pose estimation via Convolutional Part Heatmap Regression](https://mlsanity.com/paper/1609.01743/) (2016)
- [Deep Alignment Network: A convolutional neural network for robust face alignment](https://mlsanity.com/paper/1706.01789/) (2017)
- [Deep Ordinal Regression with Label Diversity](https://mlsanity.com/paper/2006.15864/) (2020)
- [Error-Correcting Output Codes with Ensemble Diversity for Robust Learning in Neural Networks](https://mlsanity.com/paper/1912.00181/) (2019)
- [AnchorFace: An Anchor-based Facial Landmark Detector Across Large Poses](https://mlsanity.com/paper/2007.03221/) (2020)
- [Efficient Loss-Based Decoding on Graphs For Extreme Classification](https://mlsanity.com/paper/1803.03319/) (2018)
- [Designing communication systems via iterative improvement: error correction coding with Bayes decoder and codebook optimized for source symbol error](https://mlsanity.com/paper/1805.07429/) (2018)

## Built on by (most cited first, 5 of 5)

- [TALENT: A Tabular Analytics and Learning Toolbox](https://mlsanity.com/paper/2407.04057/) (2024)
- [Sample Selection via Contrastive Fragmentation for Noisy Label Regression](https://mlsanity.com/paper/2502.17771/) (2025)
- [The Role of Codeword-to-Class Assignments in Error-Correcting Codes: An Empirical Study](https://mlsanity.com/paper/2302.05334/) (2023)
- [Learning Label Encodings for Deep Regression](https://mlsanity.com/paper/2303.02273/) (2023)
- [Balanced Sharpness-Aware Minimization for Imbalanced Regression](https://mlsanity.com/paper/2508.16973/) (2025)

## Abstract (arXiv)

Deep neural networks are used for a wide range of regression problems. However, there exists a significant gap in accuracy between specialized approaches and generic direct regression in which a network is trained by minimizing the squared or absolute error of output labels. Prior work has shown that solving a regression problem with a set of binary classifiers can improve accuracy by utilizing well-studied binary classification algorithms. We introduce binary-encoded labels (BEL), which generalizes the application of binary classification to regression by providing a framework for considering arbitrary multi-bit values when encoding target values. We identify desirable properties of suitable encoding and decoding functions used for the conversion between real-valued and binary-encoded labels based on theoretical and empirical study. These properties highlight a tradeoff between classification error probability and error-correction capabilities of label encodings. BEL can be combined with off-the-shelf task-specific feature extractors and trained end-to-end. We propose a series of sample encoding, decoding, and training loss functions for BEL and demonstrate they result in lower error than direct regression and specialized approaches while being suitable for a diverse set of regression problems, network architectures, and evaluation metrics. BEL achieves state-of-the-art accuracies for several regression benchmarks. Code is available at https://github.com/ubc-aamodt-group/BEL_regression.