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

arXiv: https://arxiv.org/abs/2409.17582 · HTML: https://mlsanity.com/paper/2409.17582/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 67 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (2020)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Well-tuned Simple Nets Excel on Tabular Datasets](https://mlsanity.com/paper/2106.11189/) (2021)
- [Feature Space Augmentation for Long-Tailed Data](https://mlsanity.com/paper/2008.03673/) (2020)
- [Targeted Supervised Contrastive Learning for Long-Tailed Recognition](https://mlsanity.com/paper/2111.13998/) (2021)
- [Deep Representation Learning on Long-tailed Data: A Learnable Embedding Augmentation Perspective](https://mlsanity.com/paper/2002.10826/) (2020)
- [Retrieval Augmented Classification for Long-Tail Visual Recognition](https://mlsanity.com/paper/2202.11233/) (2022)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)
- [CODA: A Real-World Road Corner Case Dataset for Object Detection in Autonomous Driving](https://mlsanity.com/paper/2203.07724/) (2022)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [Identifying and Compensating for Feature Deviation in Imbalanced Deep Learning](https://mlsanity.com/paper/2001.01385/) (2020)
- [A Survey on Long-Tailed Visual Recognition](https://mlsanity.com/paper/2205.13775/) (2022)

## Built on by (most cited first, 1 of 1)

- [AdaPCLA: Adaptive Prior-Calibrated Logit Adjustment for Long-Tailed Longitudinal EHR Generation](https://mlsanity.com/paper/2607.12645/) (2026)

## Abstract (arXiv)

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.