Variational Bounds for Perceptron Learning from Structured Data
We introduce a variational approach to a finite-temperature continuous-spin perceptron trained on a Gaussian mixture. The model allows for a broad class of concave utilities and log-concave separable prior measures on the spins. By combining the interpolation method with log-concavity and concentration estimates, we derive lower and upper minimax variational bounds for the limiting quenched pressure. Remarkably, the two bounds differ only in the order of optimization of two variational parameters, while all remaining extrema are controlled by the concave--convex structure of the variational potential. Whenever the two optimizations commute, the two bounds match and identify the solution o...
| Authors | Francesco Camilli, Pierluigi Contucci, Federica Gerace et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 August 2026 |
| Last updated at source | 5 August 2026 |
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