mlsanityData to 7 Oct 2026

Improving Deep Regression with Ordinal Entropy

arXiv 2301.08915 ↗First posted 21 Jan 2023cs.CV cs.AI cs.LGcited by 44

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Abstract (arXiv)

In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the cross-entropy loss, outperforms regression with a mean squared error loss in its ability to learn high-entropy feature representations. Based on the analysis, we propose an ordinal entropy loss to encourage higher-entropy feature spaces while maintaining ordinal relationships to improve the performance of regression tasks. Experiments on synthetic and real-world regression tasks demonstrate the importance and benefits of increasing entropy for regression.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). Builds on 21 of its 31 references that are in the map. First posted on arXiv 21 Jan 2023.

Builds on

21 of 31 references.

References · 21

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2019When Does Label Smoothing Help?cited by 985
  4. 2016Stacked Hourglass Networks for Human Pose Estimationcited by 913
  5. 2018Deep Ordinal Regression Network for Monocular Depth Estimationcited by 721
  6. 2019Large-Scale Long-Tailed Recognition in an Open Worldcited by 704
  7. 2020AdaBins: Depth Estimation using Adaptive Binscited by 596
  8. 2017Opening the Black Box of Deep Neural Networks via Informationcited by 494
  9. 2017Regularizing Neural Networks by Penalizing Confident Output Distributionscited by 461
  10. 2016Deeper Depth Prediction with Fully Convolutional Residual Networkscited by 402
  11. 2019From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimationcited by 379
  12. 2018CSRNet: Dilated Convolutional Neural Networks for Understanding the Highly Congested Scenescited by 267
9 more
  1. 2019Distribution-Aware Coordinate Representation for Human Pose Estimationcited by 165
  2. 2021Delving into Deep Imbalanced Regressioncited by 157
  3. 2014Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimationcited by 129
  4. 2020A unifying mutual information view of metric learning: cross-entropy vs. pairwise lossescited by 100
  5. 2016Estimating Depth from Monocular Images as Classification Using Deep Fully Convolutional Residual Networkscited by 91
  6. 2021SimCC: a Simple Coordinate Classification Perspective for Human Pose Estimationcited by 68
  7. 2022RankSim: Ranking Similarity Regularization for Deep Imbalanced Regressioncited by 52
  8. 2022Discrete-Constrained Regression for Local Counting Modelscited by 19
  9. 2022Class Distance Weighted Cross-Entropy Loss for Ulcerative Colitis Severity Estimationcited by 17

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 16; 2025: 15; 2026: 9.

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  1. 2024Stop Regressing: Training Value Functions via Classification for Scalable Deep RLcited by 136
  2. 2024Hierarchical Classification Auxiliary Network for Time Series Forecastingcited by 26
  3. 2023Learning-to-Rank Meets Language: Boosting Language-Driven Ordering Alignment for Ordinal Classificationcited by 21
  4. 2024GraphLand: Evaluating Graph Machine Learning Models on Diverse Industrial Datacited by 20
  5. 2024Test-time Adaptation for Regression by Subspace Alignmentcited by 9
  6. 2024FGENet: Fine-Grained Extraction Network for Congested Crowd Countingcited by 7
  7. 2024On the Integration of Spatial-Temporal Knowledge: A Lightweight Approach to Atmospheric Time Series Forecastingcited by 7
  8. 2025Improve Representation for Imbalanced Regression through Geometric Constraintscited by 7
  9. 2023Semi-Supervised Crowd Counting with Contextual Modeling: Facilitating Holistic Understanding of Crowd Scenescited by 6
  10. 2023Ordinal Classification with Distance Regularization for Robust Brain Age Predictioncited by 4
  11. 2024Deep Regression Representation Learning with Topologycited by 4
  12. 2024Is Value Functions Estimation with Classification Plug-and-play for Offline Reinforcement Learning?cited by 4
32 more
  1. 2025Sample Selection via Contrastive Fragmentation for Noisy Label Regressioncited by 4
  2. 2025Rethinking Cell Counting Methods: Decoupling Counting and Localizationcited by 4
  3. 2023SupReMix: Supervised Contrastive Learning for Medical Imaging Regression with Mixupcited by 3
  4. 2024An Efficient Model-Agnostic Approach for Uncertainty Estimation in Data-Restricted Pedometric Applicationscited by 3
  5. 2024Ordinal-Aware Calibration for Ordinal Classificationcited by 3
  6. 2025AbRank: A Benchmark Dataset and Metric-Learning Framework for Antibody-Antigen Affinity Rankingcited by 3
  7. 2025TabTreeFormer: Tabular Data Generation Using Hybrid Tree-Transformercited by 2
  8. 2025Towards Depth Foundation Model: Recent Trends in Vision-Based Depth Estimationcited by 2
  9. 2026LiftFormer: Lifting and Frame Theory Based Monocular Depth Estimation Using Depth and Edge Oriented Subspace Representationcited by 2
  10. 2024Gradient Aligned Regression via Pairwise Lossescited by 1
  11. 2024Adaptive Random Feature Regularization on Fine-tuning Deep Neural Networkscited by 1
  12. 2024Leveraging Group Classification with Descending Soft Labeling for Deep Imbalanced Regressioncited by 1
  13. 2024MetricDepth: Enhancing Monocular Depth Estimation with Deep Metric Learningcited by 1
  14. 2025ACCon: Angle-Compensated Contrastive Regularizer for Deep Regressioncited by 1
  15. 2025Improving Deep Regression with Tightnesscited by 1
  16. 2025Balanced Sharpness-Aware Minimization for Imbalanced Regressioncited by 1
  17. 2024F2Depth: Self-supervised Indoor Monocular Depth Estimation via Optical Flow Consistency and Feature Map Synthesiscited by 0
  18. 2024Generalized Robust Fundus Photography-based Vision Loss Estimation for High Myopiacited by 0
  19. 2025AdaPRL: Adaptive Pairwise Regression Learning with Uncertainty Estimation for Universal Regression Taskscited by 0
  20. 2025Improving Value-based Process Verifier via Structural Prior Injectioncited by 0
  21. 2025DLA-Count: Dynamic Label Assignment Network for Dense Cell Distribution Countingcited by 0
  22. 2025Mixture Experts with Test-Time Self-Supervised Aggregation for Tabular Imbalanced Regressioncited by 0
  23. 2025Highly Imbalanced Regression with Tabular Data in SEP and Other Applicationscited by 0
  24. 2025Contrastive Learning for Semi-Supervised Deep Regression with Generalized Ordinal Rankings from Spectral Seriationcited by 0
  25. 2026Stabilizing Test-Time Adaptation of High-Dimensional Simulation Surrogates via D-Optimal Statisticscited by 0
  26. 2026Hierarchical Awareness Adapters with Hybrid Pyramid Feature Fusion for Dense Depth Predictioncited by 0
  27. 2026Semi-Supervised Gaze Estimation via Disentangled Subspace Contrastive Learningcited by 0
  28. 2026Your Data Manifold is Secretly a Reward Model: Shell-LCC for Text-to-Video Generationcited by 0
  29. 2026Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Datacited by 0
  30. 2026Contrastive Order Learning: A General Framework for Ordinal Regressioncited by 0
  31. 2026Inferring Urban Mobility Interactions from Aggregated Dynamicscited by 0
  32. 2026Exposing Blind Spots in Deep Imbalanced Regression Evaluationcited by 0