Improve Representation for Imbalanced Regression through Geometric
  Constraints
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.
67c8502f4b773d4f539fb5ac
Zijian Dong
admin_assigned
2025-03-05T14:44:22.495Z
651c000fc4db16814c03d86a
/avatars/f1d61d5f9ffde4bb43402ff7b3c75332.svg
Zijian Dong
user
ZijianDD
67c8502f4b773d4f539fb5ad
Yilei Wu
admin_assigned
2025-03-05T14:44:30.902Z
651c0afb26b2dee1ed2dfab8
/avatars/14a69bc1f0b877106cc39a19fcc9acdb.svg
yilei wu
user
yilei-nus
67c8502f4b773d4f539fb5ae
Chongyao Chen
admin_assigned
2025-03-05T14:44:44.533Z
66af930bfd80ab874984b511
/avatars/ed81bdc7a21e83462572ac731ab85a89.svg
chenchongyao
user
ccyhaha2
67c8502f4b773d4f539fb5af
Yingtian Zou
67c8502f4b773d4f539fb5b0
Yichi Zhang
67c8502f4b773d4f539fb5b1
Juan Helen Zhou
Improve Representation for Imbalanced Regression through Geometric
  Constraints
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.
Ensuring uniform feature distribution in the latent space for imbalanced regression through geometric losses improves representation learning and model performance.
representation learning uniformity latent space hypersphere enveloping loss homogeneity loss Surrogate-driven Representation Learning (SRL) regression operator learning