4 papers
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…
Effective continuous equations for adaptive SGD: a stochastic analysis view
Luca Callisti, Marco Romito, Francesco Triggiano
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations fram…
Non-uniqueness of weak solutions for a logarithmically supercritical hyperdissipative Navier-Stokes system
Marco Romito, Francesco Triggiano
The existence of non-unique solutions of finite kinetic energy for the three dimensional Navier-Stokes equations is proved in the slightly supercritical hyper-dissipative setting i…
Gaussian processes based data augmentation and expected signature for time series classification
Marco Romito, Francesco Triggiano
The signature is a fundamental object that describes paths (that is, continuous functions from an interval to a Euclidean space). Likewise, the expected signature provides a statis…