Tona

Tonatiuh Matos Wiederhold

I'm a mathematician and researcher who builds AI systems, optimization tools, and the mathematical theory that makes them work.

I care deeply about using my programming skills to solve hard problems and build tools that make abstract ideas useful.

QuantGPT

An agentic AI framework that incorporates knowledge-graph reasoning with cryptographic vulnerability scanning through large language models (LLMs) to identify potential post-quantum security threats.

Developed for 8 months as Visiting Scholar at the Fields Institute for Mathematical Sciences, in partnership with a major Canadian bank. Presented at an internal conference to over 300 people.

Merton Jump Diffusion Model Calibration with Machine Learning

Extended the Black-Scholes / geometric Brownian motion model by adding Poisson jumps to capture sudden market moves; calibrated the parameters on historical stock price data using a limited-memory BFGS optimization algorithm, using finite differences to estimate the Merton deltas; and compared hedging strategies across multiple assets, finding improved performance on jumpy stocks.

Project website

Border Tracer

A new border-tracing algorithm that generalizes classical image segmentation techniques from pixel-based grids to arbitrary polygonal tilings in abstract adjacency graphs.

Project website | Published paper

Fer Group

A comprehensive object-oriented framework for the study of graph automorphism groups and more, including an optimally indexed SQL database for statistical inference and hypothesis testing.

Project website | Published paper

Neuro Shannon

We leveraged recent advancements in Graph Neural Networks to optimize a noisy communication network to estimate its Shannon capacity.

Deep Computations

A unified framework linking machine learning and compactness, exemplifying how the topology of function spaces encodes the algorithmic and epistemic limits of prediction.

Preprint

Set Theory Forces Probability

Take the naturals as vertices of an infinite graph and flip a coin to decide whether each pair is an edge or not. Do this twice and you obtain two different infinite graphs. What is the probability that they are isomorphic? In this published paper I give a new proof that the answer is, surprisingly, 100%.