Multicalibration is a notion of fairness that aims to provide accurate predictions across a large set of groups. Multicalibration is known to be a different goal than loss minimization, even for simple predictors such as linear functions. In this note, we show that for (almost all) large neural network sizes, optimally minimizing squared error leads to multicalibration. Our results are about representational aspects of neural networks, and not about algorithmic or sample complexity considerations. Previous such results were known only for predictors that were nearly Bayes-optimal and were therefore representation independent. We emphasize that our results do not apply to specific algorithms for optimizing neural networks, such as SGD, and they should not be interpreted as "fairness comes for free from optimizing neural networks".

翻译：多重校准是一种公平性概念，旨在跨大量群体提供准确预测。已知多重校准与损失最小化是不同的目标，即使对于线性函数等简单预测器也是如此。本文表明，对于（几乎所有）大神经网络规模，最优地最小化平方误差将导致多重校准。我们的结果涉及神经网络的表示方面，而非算法或样本复杂度考量。此前类似结果仅适用于接近贝叶斯最优的预测器，因此与表示无关。需强调的是，我们的结果不适用于优化神经网络的具体算法（如SGD），也不应被解读为“通过优化神经网络可免费获得公平性”。