# Gardner formula for Ising perceptron models at small densities

@inproceedings{Bolthausen2021GardnerFF, title={Gardner formula for Ising perceptron models at small densities}, author={Erwin Bolthausen and Shuta Nakajima and Nike Sun and Chang Xu}, booktitle={Annual Conference Computational Learning Theory}, year={2021} }

We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-sided threshold function, it was shown by Talagrand (2000, 2011) that for small densities alpha, the free energy of the model converges in the large-N limit to the replica symmetric formula conjectured in the physics literature (Krauth--Mezard 1989, see also Gardner--Derrida 1988). We give a new proof of this result…

## 8 Citations

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