Machine learning systems often acquire biases by leveraging undesired
features in the data, impacting accuracy variably across different
sub-populations. Current understanding of bias formation mostly focuses on the
initial and final stages of learning, leaving a gap in knowledge regarding the
transient dynamics. To address this gap, this paper explores the evolution of
bias in a teacher-student setup modeling different data sub-populations with a
Gaussian-mixture model. We provide an analytical description of the stochastic
gradient descent dynamics of a linear classifier in this setting, which we
prove to be exact in high dimension. Notably, our analysis reveals how
different properties of sub-populations influence bias at different timescales,
showing a shifting preference of the classifier during training. Applying our
findings to fairness and robustness, we delineate how and when heterogeneous
data and spurious features can generate and amplify bias. We empirically
validate our results in more complex scenarios by training deeper networks on
synthetic and real datasets, including CIFAR10, MNIST, and CelebA.

机器学习系统通常通过利用数据中的不希望的特征获得偏差，对不同的亚群体造成不同程度的精确度影响。本文探讨了在教师 - 学生模型中，模拟不同数据亚群体的高斯混合模型，偏差如何演化的问题。我们提供了这种设置下线性分类器随机梯度下降动力学的解析描述，该描述在高维度下被证明是准确的。值得注意的是，我们的分析揭示了亚群体的不同属性在不同时间尺度上如何影响偏差，展示了分类器在训练过程中偏好的转变。将我们的发现应用于公平性和鲁棒性，我们阐述了异质数据和虚假特征如何生成和放大偏差的时间与方式。通过在合成数据集和真实数据集（包括 CIFAR10，MNIST 和 CelebA）上训练更深层次的网络来经验性地验证我们的结果。