7 papers
Uncertainty propagation in auto-regressive random neural network models
Janice Adams, Daniele Venturi
We develop analytical and particle-based methods for uncertainty propagation in random neural network models, where both the inputs and network parameters are allowed to be random.…
Holographic generative flows with AdS/CFT
Ehsan Mirafzali, Sanjit Shashi, Sanya Murdeshwar +3
Holography, in the form of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, offers a natural setting for generative modelling. Data on a boundary manifold lifts…
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…
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-…
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…
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…