Beyond Static Costs: Learning-Dynamics Aware Loss Functions for Long-Tailed Classification

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.

Deep learning models using traditional softmax classifiers have achieved remarkable success in various classification tasks. However, their performance degrades significantly on imbalanced datasets. Although Balanced Softmax is widely adopted as a state-of-the-art rebalancing method, it possesses inherent limitations, such as yielding disproportionately lower testing accuracy for tail classes. To mitigate these shortcomings, we propose the Class-Balanced Softmax (CBS). Rooted in a theoretical Bayesian framework and a heuristic power-law assumption, the CBS is a simple logit adjustment that is computationally inexpensive and easily integrated into existing pipelines. Furthermore, we characterise a fundamental phenomenon in models trained on imbalanced data, termed the preference issue, wherein models exhibit higher training error and a larger generalisation gap for classes with limited data. To quantify this issue, we introduce a novel metric and demonstrate that CBS effectively mitigates the preference issue. Extensive experiments on large-scale benchmarks show that CBS is highly scalable and outperforms existing methods, including Balanced Softmax.

Long-tailed recognition suffers from a persistent head--tail trade-off: improving tail performance often degrades head accuracy and can increase training instability. Despite strong empirical results from re-weighting, decoupled training, and multi-expert methods, key design choices about representation sharing between head and tail classes and supervision weighting across class groups remain largely heuristic. In this work, we propose OSDTW, a principled task-decomposition framework that partitions the original single-label recognition problem into a head task and a tail task, implemented with a shared encoder and task-specific decoders. To handle the mutual exclusivity and statistical dependence between the two label groups, we introduce a factorized model and show that the resulting Kullback--Leibler divergence-based generalization error can be written as the sum of task-wise terms up to an additive constant, yielding a well-defined task-wise objective. We further develop a three-stage training pipeline: independent task training to estimate task-wise optima and the Fisher information matrix, weighted joint training to learn a shared encoder, and branch assembly to construct the final decoupled model. Under a block-diagonal Fisher approximation, we derive a computable second-order expansion of the expected generalization error, decomposing it into encoder variance, encoder bias, and decoder variance. This bias--variance decomposition provides a computable proxy to select the shared depth and task weights, enabling efficient hyper-parameter search. Experiments on standard long-tailed benchmarks demonstrate the effectiveness of the proposed approach over strong baselines.