Multiplicative Logit Adjustment Approximates Neural-Collapse-Aware Decision Boundary Adjustment

Naoya Hasegawa, Issei Sato

Keywords: long-tailed recognition, imbalanced learning, neural collapse, logit adjustment, multiplicative logit adjustment, machine learning, learning theory

TL;DR: We establish a theoretical basis for understanding the effectiveness of multiplicative logit adjustment in long-tailed recognition.

Abstract:

Real-world data distributions are often highly skewed. This has spurred a growing body of research on long-tailed recognition, aimed at addressing the imbalance in training classification models. Among the methods studied, multiplicative logit adjustment (MLA) stands out as a simple and effective method. What theoretical foundation explains the effectiveness of this heuristic method?
We provide a justification for the effectiveness of MLA with the following two-step process. First, we develop a theory that adjusts optimal decision boundaries by estimating feature spread on the basis of neural collapse. Second, we demonstrate that MLA approximates this optimal method. Additionally, through experiments on long-tailed datasets, we illustrate the practical usefulness of MLA under more realistic conditions. We also offer experimental insights to guide the tuning of MLA hyperparameters.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 3636