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

Over the past decade, the problem of assessing the fairness of classifiers has garnered significant attention, revealing that machine learning (ML) systems not only reproduce existing biases in the data but also tend to amplify them [1, 2, 3]. Given the complexity of the ML pipeline, isolating and characterising the key drivers of this amplification is challenging. Recent studies have begun to disentangle the contributions from architectural design choices, including overparameterisation [4], model complexity, activation functions [5, 6], learning protocols [7, 8], post-processing practices such as pruning [9], and intrinsic aspects of the data like its geometrical properties [10]. Theoretical results in this area (e.g., [4, 10]) are mostly based on asymptotic analysis, leaving the transient learning regime poorly understood. Due to limitations on computational resources, a trained ML system may operate far from the asymptotic regime and hence existing results may not always apply. Insights from class imbalance literature [7, 6] indicate that classifiers converge faster for classes with more data, but how this applies to fairness, where datasets might be balanced by label but imbalanced by demographics, remains unclear.