Department of Mathematics

Matthew John Hirn

Picture of Matthew John Hirn

Assistant Professor (joint with CMSE)

  • Ph.D., University of Maryland, 2009

  •  2507F Engineering Bldg
  •  517-432-0611

Currently Teaching
Research Interests

My research is in pure, applied, and computational harmonic analysis, motivated in large part by a desire to rigorously understand the mathematical underpinnings of machine learning algorithms. This understanding in turn leads to the development of new machine learning paradigms, particularly for the analysis of high dimensional data. Finally, these methods are leveraged to open up new avenues for scientific breakthroughs, either by circumventing prohibitively costly computations or by revealing unforeseen patterns in complex data. 

My primary interests range over pure and applied topics, but can be loosely summarized as:

- Mathematical foundations of deep learning 
   (scattering transforms, convolutional neural networks, generative models)
- Machine learning and multiscale physics 
   (quantum chemistry, materials science, turbulence)
- Geometric and graphical models for high dimensional data analysis 
   (manifold learning, graph learning, geometric deep learning, biomedical data)
- Smooth extension, interpolation, and regression of data, with efficient algorithms
   (Whitney extensions, statistical learning theory)

Selected Publications
  • Geometric Scattering for Graph Data Analysis. With Feng Gao and Guy Wolf. In Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research (PMLR), volume 97, pages 2122-2131, 2019.  Open
  • Time Coupled Diffusion Maps. With Nicholas Marshall. Applied and Computational Harmonic Analysis, volume 45, issue 3, pages 709-728, 2018.  Open
  • Solid Harmonic Wavelet Scattering. With Michael Eickenberg, Georgios Exarchakis and Stéphane Mallat. In Advances in Neural Information Processing Systems 30, pages 6543-6552, 2017.  Open
  • Wavelet Scattering Regression of Quantum Chemical Energies. With Stéphane Mallat and Nicolas Poilvert. Multiscale Modeling and Simulation, volume 15, issue 2, pages 827-863, 2017.  Open
  • Computing minimal interpolants in C^{1,1}(R^d). With Ariel Herbert-Voss and Frederick McCollum. Revista Matemática Iberoamericana, volume 33, issue 1, pages 29-66, 2017.  Open
  • A general theorem of existence of quasi absolutely minimal Lipschitz extensions. With Erwan Le Gruyer. Mathematische Annalen, volume 359, issue 3-4, pages 595-628, August 2014.  Open
  • Diffusion maps for changing data. With Ronald R. Coifman. Applied and Computational Harmonic Analysis, volume 36, issue 1, pages 79-107, January 2014.  Open