Probing Biological and Artificial Neural Networks with Task-dependent Neural Manifolds
This work addresses the problem of bridging abstraction levels in neural network understanding for researchers in machine learning and neuroscience, though it appears incremental as it builds on existing geometric theories.
The authors tackled the gap between low-level mechanistic and global normative approaches in understanding neural networks by investigating internal mechanisms through neural population geometry, using manifold capacity theory and manifold alignment analysis to characterize how learning objectives affect organizational strategies in deep neural networks and macaque recordings, and connecting these geometric analyses to task-relevant information decodability.
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.