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

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 achieve closer alignment with NC geometry while consistently outperforming strong long-tailed baselines on different datasets. Our code is publicly available at: https://github.com/tongzixin716716/Inverse-Loss-Reweighting.

Real-world datasets are often imbalanced: some categories have many training samples, while others have only a few. This makes machine learning models biased toward common categories and less reliable on rare ones. Loss reweighting is a common solution that assigns different importance to different categories during training, but many existing weighting rules are still heuristic. Our paper rethinks reweighting from an inverse perspective. Instead of manually choosing class weights, we ask what weights can guide the model toward a more balanced final structure. We use Neural Collapse as an ideal target because it characterizes the simple and symmetric terminal geometry of well-trained classifiers. Based on this idea, we propose a dynamic reweighting method for long-tailed classification, helping the model learn more balanced representations.