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arxiv

Dynamical coarse-graining of neural-network training

Dynamical coarse-graining of neural networks gives macroscopic observables and enables training to be predicted, and controlled in a state space far smaller than the parameter space. In this paper,…

machine-learning
arxiv

Symmetry Breaking Is the Price of Finite Capacity

If rotating a problem never changes its answer, one might expect its best model to be rotation-invariant; we show that this fails, predictably and by an exact amount, when capacity is limited. A…

deep-learning
arxiv

Game theory of academic effort and hiring in the age of AI

Many academic disciplines (in particular, mathematics and the theoretical sciences) face difficult questions about how to adapt their practices to the rise of highly capable artificial intelligence…

machine-learning