4 papers
Quantitative Gaussian-Process limits of Tensor Programs
Andrea Agazzi, Eloy Mosig García, Dario Trevisan
We study the infinite-width Gaussian-process limit of random neural networks through the lens of tensor programs, and we provide a quantitative convergence theory in Wasserstein di…
Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
Andrea Agazzi, Giuseppe Bruno, Eloy Mosig García +2
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time st…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
Quantitative convergence of trained single layer neural networks to Gaussian processes
Eloy Mosig, Andrea Agazzi, Dario Trevisan
In this paper, we study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit. Whi…