6 papers
Score-Based Diffusion Models in Infinite Dimensions: A Malliavin Calculus Perspective
Ehsan Mirafzali, Frank Proske, Daniele Venturi +1
We study score-based diffusion modelling in infinite-dimensional separable Hilbert spaces through Malliavin calculus, extending the analysis of generative models beyond the finite-…
Holographic generative flows with AdS/CFT
Ehsan Mirafzali, Sanjit Shashi, Sanya Murdeshwar +3
We present a framework for generative machine learning that leverages the holographic principle of quantum gravity, or to be more precise its manifestation as the anti-de Sitter/co…
Generative forecasting with joint probability models
Patrick Wyrod, Ashesh Chattopadhyay, Daniele Venturi
Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited…
Malliavin Calculus for Score-based Diffusion Models
Ehsan Mirafzali, Utkarsh Gupta, Patrick Wyrod +3
We introduce a new framework based on Malliavin calculus to derive exact analytical expressions for the score function , i.e., the gradient of the log-density a…
A Malliavin calculus approach to score functions in diffusion generative models
Ehsan Mirafzali, Frank Proske, Utkarsh Gupta +2
Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which de…
Uncertainty propagation in feed-forward neural network models
Jeremy Diamzon, Daniele Venturi
We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vecto…