Preprint in the OpenAI Math release
The free energy of the spherical random perceptron
OpenAI
Abstract
We prove an exact variational formula for the limiting pressure of the spherical random perceptron with an arbitrary bounded continuous single-pattern potential. The formula holds at every fixed positive density and inverse temperature, with convergence in expectation and in probability.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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