Michigan State University
College of Natural Science
College of Engineering
I am a mathematician working at the interface of harmonic analysis, data science and machine learning, and I am the scientific leader of the CEDAR Team at Michigan State University. Please navigate below for information on various projects, or use the menu above to find information on papers, talks, code, teaching, and other things. If you are a graduate student or postdoc interested in working with me, please contact me utilizing the information in the Contact page.
[November 15, 2020] I am very pleased to announce that my paper with CEDAR team members Paul Sinz and Xavier Brumwell on Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties has been published in the Journal of Chemical Physics; the paper was a joint effort with Prof. Yue Qi (formerly of the ChEMS department at MSU, now at Brown) and some members in her group, namely Michael Swift, Jialin Liu, and Kwang Jin Kim. In this paper we introduce three-dimensional periodic wavelet scattering networks using atomic orbital wavelets as a feature extractor for periodic atomic systems, which are often used to model materials. Using amorphous lithium silicon as a testbed, we show that linear regressions based on 3D wavelet scattering representations of periodic atomic systems not only achieve interpolation errors for the ground state formation energy on par with neural networks, but wavelet scattering models can also extrapolate to larger atomic systems, predict energies along diffusion barrier paths, and accurately calculate the bulk modulus elastic property.
[September 14, 2020] I am pleased to say that former ACRES REU student and CEDAR Team member Muawiz Chaudhary and I are co-authors on the paper Kymatio: Scattering Transforms in Python, which was a large, international effort and appears in the Journal of Machine Learning Research. In this paper we present the Kymatio software package, an easy-to-use, high-performance Python implementation of the wavelet scattering transform in 1D, 2D, and 3D that is compatible with modern deep learning frameworks, including PyTorch and TensorFlow/Keras. The transforms are implemented on both CPUs and GPUs, the latter offering a significant speedup over the former. The package also has a small memory footprint. Source code, documentation, and examples are available under a BSD license at https://www.kymat.io.
[July 16, 2020] My paper with Anna Little entitled Wavelet invariants for statistically robust multi-reference alignment has been accepted to Information and Inference. This is Anna’s and my first paper on the multi-reference alignment problem, which we were introduced to by a very nice talk at MSU by Amit Singer a few years back. After seeing his talk we were inspired to look into the problem in more detail, and decided to consider a modified and more difficult version of the problem. In the usual MRA problem one tries to recover a signal from random translates of the signal that have also been corrupted by additive white noise. In our modified version of the problem, we keep the random translations and additive white noise, but also corrupt the signals by random dilations, which can be used to model random stretching of molecules or random zoom in images. We worked really hard on this paper and are quite pleased with the results, so please check it out! UPDATE [September 14, 2020]: The paper now appears online on the Information and Inference website here!
[June 28, 2020] I am very pleased to announce that my paper with Michael Perlmutter, Feng Gao, and Guy Wolf entitled Geometric Scattering Networks on Compact Riemannian Manifolds has been accepted to the Mathematical and Scientific Machine Learning (MSML) conference. This is the first edition of the MSML conference, and we are very excited to be a part of it. In this paper we extend the wavelet scattering transform to compact Riemannian manifolds and use this extension as a model for deep networks on such manifolds. We prove that these networks are provably invariant to isometry group actions, and stable to diffeomorphism actions on input signals supported on the manifold. This paper is part of a series of works on geometric wavelet scattering networks on graphs and manifolds, but is our first comprehensive manifold-based paper (there was a preliminary version of this work in NeurIPS workshop in 2018). UPDATE [September 14, 2020]: The paper has been published in the Proceedings of Machine Learning Research, and is available here!
[June 14, 2020] Guy Wolf and I are organizing an online SIAM MDS mini-symposium on “Deep thoughts on geometric learning & exploration of non-Euclidean data.” It will be held June 17 and June 24 and we have a great list of speakers. Anyone can join via Zoom – more information here. UPDATE [June 27, 2020]: The mini-symposium has concluded! Slides from the talks can be found on the mini-symposium page.
[April 27, 2020] There is an exciting online seminar series on the Mathematics of INformation, Data, and Signals (MINDS), with a really great list of speakers. Anyone can join virtually through Zoom, you just need to sign up through the Google form here.