Generalized Shape Metrics on Neural Representations.

Area of Science:

• Computational Neuroscience
• Machine Learning
• Systems Neuroscience

Background:

• Understanding biological and artificial neural networks is crucial but challenging.
• Comparing network representations across different architectures and organisms requires standardized tools.
• Network-level factors like architecture and brain region influence neural representations.

Purpose of the Study:

• To provide a rigorous framework for analyzing representational dissimilarity in neural networks.
• To develop standardized analysis tools for comparing neural representations across diverse systems.
• To investigate how network-level covariates impact neural representations.

Main Methods:

• Defined a family of metric spaces to quantify representational dissimilarity.
• Modified existing representational similarity measures (canonical correlation analysis, centered kernel alignment) to satisfy the triangle inequality.
• Formulated a novel metric for convolutional layers and developed approximate Euclidean embeddings for integrating network representations into machine learning methods.

Main Results:

• Demonstrated the developed methods on large-scale biological (Allen Institute Brain Observatory) and deep learning (NAS-Bench-101) datasets.
• Identified relationships between neural representations that are interpretable.
• Showcased how anatomical features and model performance relate to neural representations.

Conclusions:

• The proposed metric space framework offers a robust foundation for analyzing neural representations.
• The developed tools enable standardized comparison of neural representations across biological and artificial networks.
• These methods facilitate a deeper understanding of information processing in both brains and artificial systems.