Improve Representation for Imbalanced Regression through Geometric Constraints

2025-03-02

AI Summary

To address the challenges of non-uniform latent-space representations and difficulty in modeling continuous ordinal relationships in imbalanced regression, this paper pioneers a systematic investigation of geometric uniformity in representation space and proposes a hyperspherical geometry-constrained representation learning paradigm. Methodologically, we design an enveloping loss to enforce uniform coverage of latent representations on the hypersphere, introduce a homogeneity loss to ensure isometric and smooth distribution, and formulate a Surrogate-driven Representation Learning (SRL) framework for joint optimization. Departing from classification-oriented representation learning paradigms, our approach significantly improves prediction accuracy for tail samples on real-world regression and operator learning benchmarks. Empirical results demonstrate that geometric uniformity serves as a critical performance booster for imbalanced regression, validating both the theoretical motivation and practical efficacy of the proposed framework.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Addressing imbalanced regression via geometric constraints.
• Ensuring uniformity in latent space for regression tasks.
• Integrating enveloping and homogeneity losses for smooth representations.

Innovation

• Enveloping loss ensures hypersphere surface uniformity.
• Homogeneity loss maintains smooth, evenly spaced representations.
• SRL framework integrates geometric principles for regression.