Representations and generalization in artificial and brain neural networks

Humans and animals excel at generalizing from limited data, a capability yet to be fully replicated in artificial intelligence. This perspective investigates generalization in biological and artificial deep neural networks (DNNs), in both in-distribution and out-of-distribution contexts. We introduce two hypotheses: First, the geometric properties of the neural manifolds associated with discrete cognitive entities, such as objects, words, and concepts, are powerful order parameters. They link the neural substrate to the generalization capabilities and provide a unified methodology bridging gaps between neuroscience, machine learning, and cognitive science. We overview recent progress in studying the geometry of neural manifolds, particularly in visual object recognition, and discuss theories connecting manifold dimension and radius to generalization capacity. Second, we suggest that the theory of learning in wide DNNs, especially in the thermodynamic limit, provides mechanistic insights into the learning processes generating desired neural representational geometries and generalization. This includes the role of weight norm regularization, network architecture, and hyper-parameters. We will explore recent advances in this theory and ongoing challenges. We also discuss the dynamics of learning and its relevance to the issue of representational drift in the brain.