Nigel Goldenfeld and Brian Keating discuss the idea that larger systems can exhibit qualitatively new behavior, using correlations in solids and magnets as examples. Emergent properties do not mean that the underlying physical laws have been violated.
Nigel Goldenfeld and Brian Keating use cross-linked polymer chains to explain how a loose collection can acquire rigidity. They connect this reasoning to the puzzle of highly parameterized learning systems that appear capable of generalizing despite the risk of fitting noise.
Nigel Goldenfeld and Brian Keating examine a simplified mathematical model and the distinction between sharp transitions in infinite systems and rounded behavior in finite ones. The physics analogy provides an explanatory research direction, not a proof that every neural network follows the same mechanism.
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