Recently, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies or global normative approaches. However, concrete methodologies for bridging the gap between these levels of abstraction remain elusive. In this work, we investigate the internal mechanisms of neural networks through the lens of neural population geometry, aiming to provide understanding at an intermediate level of abstraction, as a way to bridge that gap. Utilizing manifold capacity theory (MCT) from statistical physics and manifold alignment analysis (MAA) from high-dimensional statistics, we probe the underlying organization of task-dependent manifolds in deep neural networks and macaque neural recordings. Specifically, we quantitatively characterize how different learning objectives lead to differences in the organizational strategies of these models and demonstrate how these geometric analyses are connected to the decodability of task-relevant information. These analyses present a strong direction for bridging mechanistic and normative theories in neural networks through neural population geometry, potentially opening up many future research avenues in both machine learning and neuroscience.

翻译：近期，对生物与人工神经网络计算机制的理解主要源于低层次机制研究或全局规范性方法。然而，跨越这两类抽象层次的具体方法论仍然难以捉摸。本研究通过神经群体几何视角探查神经网络的内在机制，旨在提供中间抽象层次的洞见以弥合上述鸿沟。我们运用统计物理中的流形容量理论和基于高维统计学的流形对齐分析，探索深度神经网络与猕猴神经记录中任务依赖流形的底层组织架构。具体而言，我们定量刻画了不同学习目标如何导致模型组织策略的差异化，并论证了这些几何分析与任务相关信息可解码性之间的关联。这些分析为通过神经群体几何连接神经网络的机制性与规范性理论开辟了强力路径，有望在机器学习与神经科学领域开拓众多未来研究方向。