Nonlinear classification of neural manifolds with contextual information

Area of Science:

• Computational neuroscience
• Machine learning
• Neural systems analysis

Background:

• Neural systems efficiently process information using distributed representations.
• Manifold capacity links population geometry to neural manifold separability but is limited to linear readouts.
• Understanding context-dependent computation is crucial for neuroscience and AI.

Purpose of the Study:

• To develop a theoretical framework for context-dependent manifold capacity.
• To extend manifold capacity analysis beyond linear readouts.
• To capture representation reformatting in deep neural networks.

Main Methods:

• Leveraging latent directions in input space to incorporate contextual information.
• Deriving an exact formula for context-dependent manifold capacity.
• Validating the framework on synthetic and real neural data.

Main Results:

• The new framework accurately models context-dependent manifold capacity.
• It reveals representation reformatting in early layers of deep networks.
• The approach is applicable across various scales, datasets, and models.

Conclusions:

• The developed framework provides a powerful tool for analyzing context-dependent neural computation.
• It bridges the gap between population geometry and task implementation in neural systems.
• This work advances our understanding of how neural networks, both artificial and biological, process information dynamically.