范围，而非独立性，驱动生物启发表征中的模块化
Range, not Independence, Drives Modularity in Biologically Inspired Representations
AI总结：
本研究提出理论，证明非负能量高效网络中源变量的模块化由支持集范围而非独立性决定，并应用于神经科学数据，为混合选择性提供新解释。
摘要：
为什么生物和人工神经元有时会模块化，每个神经元编码一个有意义变量，而有时却将多个变量的表征纠缠在一起？在这项工作中，我们发展了一个理论，解释何时生物启发的网络——即那些非负且能量高效的网络——会将其对源变量（sources）的表征模块化。我们推导了关于源样本的充分必要条件，这些条件决定了最优生物启发线性自编码器中的神经元是否模块化。我们的理论适用于任何数据集，远远超出了先前工作中研究的统计独立性情形。相反，我们表明，如果源的支持集“充分分散”，它们就会模块化。基于这一理论，我们在多种实证研究中提取并验证了关于数据分布如何影响非线性前馈和循环神经网络在监督和无监督任务中训练时模块化的预测。此外，我们将这些想法应用于神经科学数据，表明范围独立性可用于理解在内嗅皮层记录中看似冲突的实验中空间和奖励信息的混合或模块化。进一步，我们利用这些结果提出了混合选择性的替代起源，超越了占主导地位的灵活非线性分类理论。总之，我们的理论规定了神经活动何时模块化的精确条件，为在脑和机器中诱导和阐明模块化表征提供了工具。
英文摘要：
Why do biological and artificial neurons sometimes modularise, each encoding a single meaningful variable, and sometimes entangle their representation of many variables? In this work, we develop a theory of when biologically inspired networks -- those that are nonnegative and energy efficient -- modularise their representation of source variables (sources). We derive necessary and sufficient conditions on a sample of sources that determine whether the neurons in an optimal biologically-inspired linear autoencoder modularise. Our theory applies to any dataset, extending far beyond the case of statistical independence studied in previous work. Rather we show that sources modularise if their support is ``sufficiently spread''. From this theory, we extract and validate predictions in a variety of empirical studies on how data distribution affects modularisation in nonlinear feedforward and recurrent neural networks trained on supervised and unsupervised tasks. Furthermore, we apply these ideas to neuroscience data, showing that range independence can be used to understand the mixing or modularising of spatial and reward information in entorhinal recordings in seemingly conflicting experiments. Further, we use these results to suggest alternate origins of mixed-selectivity, beyond the predominant theory of flexible nonlinear classification. In sum, our theory prescribes precise conditions on when neural activities modularise, providing tools for inducing and elucidating modular representations in brains and machines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
