Geometric Foundations of AI with Applications to Finance, Control, and PDEs

Applications to: Reasoning, Finance, and PDEs

We investigate the structures underpinning the analytic and statistical foundations of AI, and using mathematics as a guide we optimize the inductive bias of these models towards applications in finance, reasoning, PDEs, and control.

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A dynamically updated directed map of publications and preprints, organized by arXiv subjects, title keywords, and the high-level AI Theory / Applications hierarchy.

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We run the Fields Institute's AI Theory Seminar

We organize the Fields Institute's AI Theory Seminar, focused on mathematical foundations of AI, approximation and learning theory, reasoning, stochastic analysis, control, games, PDEs, and finance.

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Geometric Foundations of AI

Applications to: Reasoning, Finance, and PDEs

Research Map

Click a paper node to read its title here.

Who we are

We run the Fields Institute's AI Theory Seminar

Upcoming Talk We've Organized

Hot off the press

Select Publications

Geometric Foundations of AI

Applications to: Reasoning, Finance, and PDEs

Research Map

Click a paper node to read its title here.

Who we are

Small Transformers Compute Universal Metric Embeddings

Designing Universal Causal Deep Learning Models: The Geometric (Hyper) Transformer

Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?

Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity

Filtered not Mixed: Stochastic Filtering-Based Online Gating for Mixture of Large Language Models

Neural Spacetimes for DAG Representation Learning

A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression

Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization

Optimizing Optimizers: Regret-optimal gradient descent algorithms

Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis

NEU: A meta-algorithm for universal uap-invariant feature representation

Universal Approximation Under Constraints is Possible with Transformers

Learning Sub-Patterns in Piece-Wise Continuous Functions

Instance-Dependent Generalization Bounds via Optimal Transport

Universal Regular Conditional Distributions

Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices

We run the Fields Institute's AI Theory Seminar

Upcoming Talk We've Organized

Hot off the press

Select Publications