Unpacking Softmax: How Temperature Drives Representation Collapse, Compression, and Generalization

TL;DR

This paper investigates how the softmax function's temperature parameter influences neural network representations, revealing a rank deficit bias and demonstrating how temperature tuning can improve compression and out-of-distribution generalization.

Contribution

It introduces the concept of rank deficit bias caused by softmax temperature and shows how to leverage temperature tuning for better representation compression and robustness.

Findings

Softmax temperature affects the rank of learned representations.

Adjusting temperature can improve out-of-distribution performance.

Softmax dynamics can be exploited for representation compression.

Abstract

The softmax function is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven effectiveness, its influence on learning dynamics and learned representations remains poorly understood, limiting our ability to optimize model behavior. In this paper, we study the pivotal role of the softmax function in shaping the model's representation. We introduce the concept of rank deficit bias - a phenomenon in which softmax-based deep networks find solutions of rank much lower than the number of classes. This bias depends on the softmax function's logits norm, which is implicitly influenced by hyperparameters or directly modified by softmax temperature. Furthermore, we demonstrate how to exploit the softmax dynamics to learn compressed representations or to enhance their performance on out-of-distribution data. We validate our findings across diverse architectures and real-world datasets, highlighting the broad applicability of temperature tuning in improving model performance. Our work provides new insights into the mechanisms of softmax, enabling better control over representation learning in deep neural networks.