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

TL;DR

This paper provides a theoretical justification for multiplicative logit adjustment (MLA) in long-tailed recognition, showing it approximates neural-collapse-aware decision boundary adjustment and demonstrating its practical effectiveness.

Contribution

The paper develops a theory connecting MLA with neural collapse and decision boundary adjustment, offering a new understanding of MLA's effectiveness.

Findings

MLA approximates neural-collapse-aware decision boundary adjustment.

Experimental results confirm MLA's effectiveness on long-tailed datasets.

Guidelines for tuning MLA hyperparameters are provided.

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.