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Representations and generalization in artificial and brain neural networks.

Qianyi Li1,2, Ben Sorscher3, Haim Sompolinsky2,4

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Summary

Biological and artificial deep neural networks (DNNs) show varying generalization capabilities. Geometric properties of neural manifolds and learning theory in DNNs offer insights into how DNNs can improve generalization from limited data.

Keywords:
deep neural networksfew-shot learningneural manifoldsrepresentational driftvisual cortex

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Area of Science:

  • Neuroscience
  • Machine Learning
  • Cognitive Science

Background:

  • Humans and animals generalize effectively from limited data, a feat not yet matched by artificial intelligence.
  • Generalization in biological and artificial deep neural networks (DNNs) is crucial for real-world applications, encompassing both in-distribution and out-of-distribution scenarios.

Purpose of the Study:

  • To investigate generalization in biological and artificial deep neural networks (DNNs).
  • To propose hypotheses linking neural manifold geometry and DNN learning theory to generalization capabilities.
  • To bridge neuroscience, machine learning, and cognitive science through a unified methodology.

Main Methods:

  • Overviewing recent progress in studying the geometry of neural manifolds, particularly in visual object recognition.
  • Discussing theories connecting manifold dimension and radius to generalization capacity.
  • Exploring the theory of learning in wide DNNs, including the role of weight norm regularization, network architecture, and hyperparameters.

Main Results:

  • Neural manifold geometry, specifically its geometric properties, acts as an order parameter linking neural substrates to generalization.
  • Theories of learning in wide DNNs provide mechanistic insights into generating desired neural representational geometries and generalization.
  • Weight norm regularization, network architecture, and hyperparameters play significant roles in DNN generalization.

Conclusions:

  • Geometric properties of neural manifolds are key to understanding generalization in both biological and artificial systems.
  • The theory of learning in wide DNNs offers a mechanistic framework for improving generalization capabilities.
  • Further research into representational drift and learning dynamics is essential for advancing AI generalization.