Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons, namely nonnegativity and energy efficiency in both activity and weights, promote such sought after disentangled representations by enforcing neurons to become selective for single factors of task variation. We demonstrate these constraints lead to disentanglement in a variety of tasks and architectures, including variational autoencoders. We also use this theory to explain why the brain partitions its cells into distinct cell types such as grid and object-vector cells, and also explain when the brain instead entangles representations in response to entangled task factors. Overall, this work provides a mathematical understanding of why single neurons in the brain often represent single human-interpretable factors, and steps towards an understanding task structure shapes the structure of brain representation.

翻译：大脑中的神经元通常针对特定任务变量进行精细调谐。此外，这种解缠表示在机器学习中备受追捧。本文从数学上证明，神经元上的简单生物约束——即活动与权重的非负性和能量效率——通过强制神经元对任务变异的单一因子具有选择性，从而促进这种备受追捧的解缠表示。我们证明了这些约束在多种任务和架构（包括变分自编码器）中导致了解缠。我们还利用这一理论解释了为何大脑将其细胞划分为不同功能类型（如网格细胞和物体向量细胞），并解释了何时大脑会因纠缠任务因子而产生纠缠表示。总体而言，本研究提供了关于大脑中单个神经元为何常表征单个人类可解释因子的数学理解，并推动了任务结构如何塑造大脑表征结构的认知进展。