Classical wisdom in machine learning holds that the generalization error can
be decomposed into bias and variance, and these two terms exhibit a
\emph{trade-off}. However, in this paper, we show that for an ensemble of deep
learning based classification models, bias and variance are \emph{aligned} at a
sample level, where squared bias is approximately \emph{equal} to variance for
correctly classified sample points. We present empirical evidence confirming
this phenomenon in a variety of deep learning models and datasets. Moreover, we
study this phenomenon from two theoretical perspectives: calibration and neural
collapse. We first show theoretically that under the assumption that the models
are well calibrated, we can observe the bias-variance alignment. Second,
starting from the picture provided by the neural collapse theory, we show an
approximate correlation between bias and variance.

机器学习的经典智慧认为泛化误差可以从偏差和方差两个方面进行分解，并且这两个术语之间存在一种权衡关系。然而，在本文中，我们展示了对于由深度学习为基础的分类模型集合，偏差和方差在样本级别上是一致的，其中对于正确分类的样本点，平方偏差近似等于方差。我们通过实证证据在多种深度学习模型和数据集上验证了这一现象。此外，我们从两个理论角度研究了这一现象：校准和神经坍缩。我们首先理论上证明在模型被很好地校准的假设下，我们可以观察到偏差 - 方差一致性。其次，从神经坍缩理论提供的视角出发，我们展示了偏差和方差之间的近似相关性。