Bias in Motion: Theoretical Insights into the Dynamics of Bias in SGD Training

Anchit Jain, Rozhin Nobahari, Aristide Baratin, Stefano Sarao Mannelli

Keywords: learning dynamics, online learning, stochastic gradient descent, analytical model, fairness, spurious correlation

TL;DR: We propose a completely analytically tractable framework for studying the evolution of bias of a classifier during training

Abstract:

Machine learning systems often acquire biases by leveraging undesired features in the data, impacting accuracy variably across different sub-populations. This paper explores the evolution of bias in a teacher-student setup modeling different data sub-populations with a Gaussian-mixture model, by providing an analytical description of the stochastic gradient descent dynamics of a linear classifier in this
setting. Our analysis reveals how different properties of sub-populations influence bias at different timescales, showing a shifting preference of the classifier during training. We empirically validate our results in more complex scenarios by training deeper networks on real datasets including CIFAR10, MNIST, and CelebA.

Is Neurips Submission: Yes

Submission Number: 19