home · research · notes & code

Research

	Neural collapse in the orthoplex regime James Alcala, Rayna Andreeva, Vladimir A. Kobzar, Dustin G. Mixon, Sanghoon Na, Shashank Sule, Yangxinyu Xie. arXiv, 2026 arXiv / Neural collapse is a phenomenon in deep learning where features of a classifier converge to the vertices of a simplex as training progresses. We studied this phenomenon where the number of classes exceeds the dimension.
	Input layer regularization and automated regularization hyperparameter tuning for myelin water estimation using deep learning Mirage Modi, Shashank Sule, Jonathan Palumbo, Michael Rozowski, Griffin S. Hampton, Mustapha Bouhrara, Wojciech Czaja, Richard G. Spencer. NMR in Biomedicine, 2026 journal / arXiv / code / We study how much information classical statistical estimators hold about underlying random variables in myelin water imaging, and show that input layer regularization with automated hyperparameter tuning can outperform copious deep learning alone.
	Learning collective variables that respect permutational symmetry Jiaxin Yuan, Shashank Sule, Yeuk Yim Lam, Maria Cameron. J. Chem. Phys., 2025 arXiv / We propose algorithms for learning collective variables that respect permutational symmetry, with case studies on Lennard-Jones clusters using quantitative coarse-graining theory and tools from geometric data science.
	Learning collective variables that preserve transition rates Shashank Sule, Arnav Mehta, Maria Cameron. SIAM Multiscale Modeling and Simulation, 2025 arXiv / code / We turn Legoll and Lelievre’s quantitative coarse-graining theory into an algorithm for learning collective variables that preserve transition rates in molecular systems, with a case study on butane.
	Neumann eigenmaps for landmark embedding Shashank Sule, Wojciech Czaja. Sampling Theory and Applications (Oral), 2025 arXiv / We propose a new dimensionality reduction technique termed Neumann eigenmaps which uses landmarks to enhance standard spectral embedddings, while preserving an isometry property of diffusion maps.
	Sharp estimates for target measure diffusion maps and applications to the committor problem Shashank Sule, Luke Evans, Maria Cameron. Applied and Computational Harmonic Analysis, 2025 arXiv / We leverage the approximation theory of target measure diffusion maps to obtain sharp error estimates with explicit prefactors, yielding concrete accuracy gains for rare-event quantification via the committor problem in molecular dynamics.
	On the limits of neural network explainability via descrambling Shashank Sule, Richard G. Spencer, Wojciech Czaja. Applied and Computational Harmonic Analysis, 2025 We study fundamental limits on explaining neural network decisions through descrambling methods, identifying when such approaches can and cannot recover meaningful structure from learned representations.
	Neural network-based speech reconstruction from undersampled STFT magnitude data Wojciech Czaja, Matthias Wellershoff, Shashank Sule, Canran Ji. EUSIPCO 2024, 2024 We show that neural networks can reconstruct speech from undersampled Short Time Fourier Transform magnitude measurements, recovering phase information from far fewer samples than classical methods require.
	Sobolev Orthogonal Polynomials on the Sierpinski Gasket Qingxuan Jiang, Tian Lan, Kasso Okoudjou, Robert Strichartz, Shashank Sule, Sreeram Venkat. J. Fourier Analysis and Appl., 2021 journal / arXiv / code / We construct and analyze Sobolev orthogonal polynomials on the Sierpinski gasket, extending classical orthogonal polynomial theory to fractal domains.