Our paper on Short Time Fourier Transform (STFT) phase retrieval was recently published at the 34th European Signal Processing Conference! We showed that neural networks can perform speech phase retreival given far fewer samples than what is mathematically required. Read it here.

I participated in the super exciting Mathematical Research Community (MRC) on Explainable, Interpretable, and Adversarial AI at Beaver Hollow, NY! A lot of things were discussed–including the capabilities of transformers, latent geometries of language models, and neural collapse. You can hear more on these matters at the upcoming Joint Math Meetings in Seattle at the special session for this MRC.

‘Tis the season to drop preprints! My work titled Sharp error estimates for target measure diffusion maps with applications to the committor problem with Dr. Maria Cameron and Luke Evans is submitted and up on arXiv. This paper is about leveraging the approximation theory of diffusion maps to gain concrete speedups in accuracy for applications in molecular dynamics.

I attended the Measure Transport, Diffusion Processes and Sampling Workshop at the Flatiron Institute! My poster featured new results on Target Measure Diffusion Maps (TMDmap), including a stability estimate for Dirichlet BVPs using TMDmaps and an application to machine learning-based rare event quantification in the butane molecule.

I recently presented a poster titled Error analysis of Target Measure Diffusion Maps and applications to transition path theory at the Optimal Transport for Data Science workshop at ICERM, Brown University!

Next meeting: December 4th, 3:00 pm, Kirwan Hall 1310. Speaker: Meenakshi Krishnan

I spent last week attending the Applied Harmonic Analysis and Machine Learning Summer School at the Machine Learning Genoa Center in Genova, Italy!

I worked on creating and implementing a new algorithm for using information theory to make phylogenetic trees from aligned DNA sequences at the Cummings Lab in UMD.

This project motivated many interesting biological questions, but here is a mathematical one that caught my fancy: Given a function \(f: \{0,1\}^n \to \mathbb{R}\), can one find a polynomial time algorithm to compute the global maximum of \(f\)? One might be tempted to say “ah this is just integer programming” but what happens when there is no meaningful extension of \(f\) to \([0,1]^n\)? This problem arises in computing the optimal split in a tree, where we must maximize the function \(\vert A \vert H(A) + \vert A^c \vert H(A^c)\) over all possible partitions \(A \sqcup A^c = X\) of a finite set \(X\). Here \(H(A)\) is the (empirical) entropy of \(A\). Email me if you have suggestions and find out more about this project here.

The initial commit of projects is in (hopefully with many more to come). Particular highlights include my undergraduate thesis, code for a couple of projects, and a stash of notes meant for the cramming undergraduate (aka me 2 years ago). Check them out here.

Finally the website is up! It looks a bit minimal, but that’s kind of the style I meant to go for. I used this template designed by Marc Weitz to start with. The wonders of open source never cease to amaze.