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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.","url_abs":"https://arxiv.org/abs/2301.08915v3","url_pdf":"https://arxiv.org/pdf/2301.08915v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"improving-deep-regression-with-ordinal","repo_url":"https://github.com/needylove/ordinalentropy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"crowd-counting","task_name":"Crowd Counting"},{"task_slug":"depth-estimation","task_name":"Depth Estimation"},{"task_slug":"monocular-depth-estimation","task_name":"Monocular Depth Estimation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/crowd-counting-on-shanghaitech-a","task":"Crowd Counting","dataset":"ShanghaiTech A","model":"OrdinalEntropy","rank_in_archive_order":20,"of":35,"metrics":{"MAE":"65.6","MSE":"105.0"},"uses_additional_data":false},{"leaderboard":"/sota/crowd-counting-on-shanghaitech-b","task":"Crowd Counting","dataset":"ShanghaiTech B","model":"OrdinalEntropy","rank_in_archive_order":20,"of":32,"metrics":{"MAE":"9.1","MSE":"14.5"},"uses_additional_data":false},{"leaderboard":"/sota/monocular-depth-estimation-on-nyu-depth-v2","task":"Monocular Depth Estimation","dataset":"NYU-Depth V2","model":"OrdinalEntropy","rank_in_archive_order":37,"of":85,"metrics":{"Delta < 1.25":"0.932","RMSE":"0.321","absolute relative error":"0.089","log 10":"0.039"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.08915","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.08915"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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