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.

翻译：人类和动物能够识别环境中的潜在结构，并利用这些信息高效地导航世界。近期多项研究提出，大脑通过形成以灵活、可泛化方式编码这种潜在结构的神经表征来支持这些能力。然而，神经群体活动的哪些方面促成了这些计算能力仍不明确。本文建立了一个分析理论，将神经群体活动的介观统计特性与多任务学习问题上的泛化性能联系起来。为此，我们采用一个生成模型，其中不同任务依赖于共同的未观测潜在结构，且预测由神经群体活动的线性读出形成。研究表明，群体活动的三个几何度量决定了这些场景中的泛化性能。利用该理论，我们发现实验观测到的因子化（或解耦）表征自然成为多任务学习问题的最优解。进一步研究表明，当数据稀缺时，最优编码会压缩信息量较小的潜在变量；而当数据充足时，最优编码会在状态空间中扩展这些信息。我们利用生物与人工神经网络数据验证了理论预测。因此，我们的结果将神经群体几何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提出了规范性预测。