Rethinking Loss Reweighting for Imbalance Learning as an Inverse Problem: A Neural Collapse Point of View

2026-05-11

AI Summary

This work addresses the lack of a clear optimization objective in loss reweighting for long-tailed classification by formally casting it as an inverse problem. Guided by the equiangular tight frame (ETF) geometry from Neural Collapse (NC) theory, the study proposes equalizing the average per-class losses as an ideal target and dynamically infers class weights to approach this equilibrium. By modeling reweighting as an inverse problem and aligning feature geometry with the ETF structure, the method effectively reduces loss imbalance and encourages learned features to conform more closely to the geometric predictions of NC theory. Extensive experiments demonstrate consistent improvements over strong baseline methods across multiple long-tailed benchmarks.

Abstract

Loss reweighting is a widely used strategy for long-tailed classification, but existing reweighting strategies often rely on heuristics and rarely define a well-specified target. Inspired by Neural Collapse (NC), the ideal simplex Equiangular Tight Frame (ETF) terminal geometry suggests equal per-class average loss as a reasonable target for reweighting. Based on the ideal equal loss objective, we consider loss reweighting as an inverse problem and propose an inverse-view reweighting strategy that infers class weights dynamically to match this ideal objective. Empirically, NC metrics suggest our method can effectively reduce the loss imbalance coefficient and closer alignment with NC geometry while consistently outperforming strong long-tailed baselines on different datasets.

Problem

• loss reweighting
• long-tailed classification
• class imbalance
• Neural Collapse
• inverse problem

Innovation

• loss reweighting
• neural collapse
• inverse problem
• long-tailed classification
• equiangular tight frame