Generalised Balanced Softmax: A Finite-Data Perspective on Logit Adjustment for Long-Tailed Recognition

Models trained on long-tailed data using standard softmax tend to exhibit higher training error and a larger generalisation gap for classes with fewer training samples. We characterise this class-wise disparity as the preference issue and quantify it using a new metric, the model imbalance level $I$. To understand this issue, we analyse how imbalanced training data adversely affects class-wise gradients under standard softmax training. This paper then develops a finite-data Generalised Balanced Softmax (GBS) framework for analysing and mitigating the preference issue. The framework uses the training-time logit adjustment $z_{nc}+β\log|N_c|$, which is algebraically identical to the training-time logit-adjusted loss of Menon et al. (2021) when $τ=β$. The case $β=1$ also coincides with Balanced Softmax and with the unit adjustment supported by the Fisher-consistency argument under the true data distribution, corresponding to an idealised infinite-data setting. Building on this existing loss family, this paper uses a heuristic power-law assumption to motivate the adjustable coefficient and studies how $β$ affects trained models. Across the evaluated long-tailed benchmarks, $β=1$ does not attain the highest average testing recall on most datasets, showing that a different coefficient can be preferable when training on finite data. The selected values of $β$ reduce $I$ and improve average testing recall relative to the $β=1$ reference, while retaining negligible computational overhead and compatibility with existing representation-learning frameworks.