2 citations · 3 across the 9 of their papers we have counts for
10 papers
Measure Neural Mappings
Ricardo Baptista, Edoardo Calvello, Bohan Chen +2
We introduce and define measure neural mappings (MNMs), which combine measure-dependent neural transport with ensemble consistency for learning operators on probability measures. E…
Expressivity In Multimodal Contrastive Learning
Andrew Stuart, Florian Wolf
Contrastive learning has become a cornerstone of modern representation learning, powering CLIP-style models that underpin text-to-image generation, vision-language models, and retr…
Learning Probabilistic Filters with Strictly Proper Scoring Rules
Eviatar Bach, Ricardo Baptista, Jochen Bröcker +2
Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system given observations, i…
Large Language Models: A Mathematical Formulation
Ricardo Baptista, Andrew Stuart, Son Tran
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writi…
A Mathematical Perspective On Contrastive Learning
Ricardo Baptista, Andrew M. Stuart, Son Tran
Multimodal contrastive learning is a methodology for linking different data modalities; the canonical example is linking image and text data. The methodology is typically framed as…
Learning Enhanced Ensemble Filters
Eviatar Bach, Ricardo Baptista, Edoardo Calvello +2
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates thi…
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
Ricardo Baptista, Edoardo Calvello, Matthieu Darcy +3
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forc…
Memorization and Regularization in Generative Diffusion Models
Ricardo Baptista, Agnimitra Dasgupta, Nikola B. Kovachki +2
Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities fo…
Machine Learning for Inverse Problems and Data Assimilation
Eviatar Bach, Ricardo Baptista, Daniel Sanz-Alonso +1
The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is…
Learning Optimal Filters Using Variational Inference
Eviatar Bach, Ricardo Baptista, Enoch Luk +1
Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and en…