title: Improve Representation for Imbalanced Regression through Geometric
    Constraints
summary: In representation learning, uniformity refers to the uniform feature
  distribution in the latent space (i.e., unit hypersphere). Previous work has
  shown that improving uniformity contributes to the learning of
  under-represented classes. However, most of the previous work focused on
  classification; the representation space of imbalanced regression remains
  unexplored. Classification-based methods are not suitable for regression tasks
  because they cluster features into distinct groups without considering the
  continuous and ordered nature essential for regression. In a geometric aspect,
  we uniquely focus on ensuring uniformity in the latent space for imbalanced
  regression through two key losses: enveloping and homogeneity. The enveloping
  loss encourages the induced trace to uniformly occupy the surface of a
  hypersphere, while the homogeneity loss ensures smoothness, with
  representations evenly spaced at consistent intervals. Our method integrates
  these geometric principles into the data representations via a Surrogate-driven
  Representation Learning (SRL) framework. Experiments with real-world regression
  and operator learning tasks highlight the importance of uniformity in
  imbalanced regression and validate the efficacy of our geometry-based loss
  functions.
paper_authors._id: 67c8502f4b773d4f539fb5ac
paper_authors.name: Zijian Dong
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-03-05T14:44:22.495Z
paper_authors._id: 651c000fc4db16814c03d86a
paper_authors.avatarUrl: /avatars/f1d61d5f9ffde4bb43402ff7b3c75332.svg
paper_authors.fullname: Zijian Dong
paper_authors.type: user
paper_authors.user: ZijianDD
paper_authors._id: 67c8502f4b773d4f539fb5ad
paper_authors.name: Yilei Wu
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-03-05T14:44:30.902Z
paper_authors._id: 651c0afb26b2dee1ed2dfab8
paper_authors.avatarUrl: /avatars/14a69bc1f0b877106cc39a19fcc9acdb.svg
paper_authors.fullname: yilei wu
paper_authors.type: user
paper_authors.user: yilei-nus
paper_authors._id: 67c8502f4b773d4f539fb5ae
paper_authors.name: Chongyao Chen
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-03-05T14:44:44.533Z
paper_authors._id: 66af930bfd80ab874984b511
paper_authors.avatarUrl: /avatars/ed81bdc7a21e83462572ac731ab85a89.svg
paper_authors.fullname: chenchongyao
paper_authors.type: user
paper_authors.user: ccyhaha2
paper_authors._id: 67c8502f4b773d4f539fb5af
paper_authors.name: Yingtian Zou
paper_authors._id: 67c8502f4b773d4f539fb5b0
paper_authors.name: Yichi Zhang
paper_authors._id: 67c8502f4b773d4f539fb5b1
paper_authors.name: Juan Helen Zhou
paper_title: Improve Representation for Imbalanced Regression through Geometric
    Constraints
paper_summary: In representation learning, uniformity refers to the uniform feature
  distribution in the latent space (i.e., unit hypersphere). Previous work has
  shown that improving uniformity contributes to the learning of
  under-represented classes. However, most of the previous work focused on
  classification; the representation space of imbalanced regression remains
  unexplored. Classification-based methods are not suitable for regression tasks
  because they cluster features into distinct groups without considering the
  continuous and ordered nature essential for regression. In a geometric aspect,
  we uniquely focus on ensuring uniformity in the latent space for imbalanced
  regression through two key losses: enveloping and homogeneity. The enveloping
  loss encourages the induced trace to uniformly occupy the surface of a
  hypersphere, while the homogeneity loss ensures smoothness, with
  representations evenly spaced at consistent intervals. Our method integrates
  these geometric principles into the data representations via a Surrogate-driven
  Representation Learning (SRL) framework. Experiments with real-world regression
  and operator learning tasks highlight the importance of uniformity in
  imbalanced regression and validate the efficacy of our geometry-based loss
  functions.
paper_ai_keywords: latent space uniform feature distribution unit hypersphere under-represented classes imbalanced regression classification-based methods continuous and ordered nature enveloping loss homogeneity loss induced trace smoothness evenly spaced consistent intervals Surrogate-driven Representation Learning (SRL) framework geometry-based loss functions