Humans and animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. Several recent works argue that the brain supports these abilities by forming neural representations that encode such latent structures in flexible, generalizable ways. However, it remains unclear what aspects of neural population activity are contributing to these computational capabilities. Here, we develop an analytical theory linking the mesoscopic statistics of a neural population's activity to generalization performance on a multi-task learning problem. To do this, we rely on a generative model in which different tasks depend on a common, unobserved latent structure and predictions are formed from a linear readout of a neural population's activity. We show that three geometric measures of the population activity determine generalization performance in these settings. Using this theory, we find that experimentally observed factorized (or disentangled) representations naturally emerge as an optimal solution to the multi-task learning problem. We go on to show that when data is scarce, optimal codes compress less informative latent variables, and when data is abundant, optimal codes expand this information in the state space. We validate predictions from our theory using biological and artificial neural network data. Our results therefore tie neural population geometry to the multi-task learning problem and make normative predictions of the structure of population activity in these settings.

人和动物可以认识到环境中的潜在结构，并将这些信息应用于有效地导航世界。本论文开发了一个分析理论，将神经群体活动的中等统计特性与多任务学习问题上的泛化性能相联系。利用这个理论，我们发现实验观察到的因素化（或解缠）表示自然地成为多任务学习问题的最优解，同时验证了来自生物和人工神经网络数据的理论预测。这些结果将神经群体几何学与多任务学习问题联系起来，并对这些场景中的群体活动结构进行正式预测。

神经种群几何和任务共享潜在结构的最优编码