About me

I am a Postdoc at Mila-Quebec AI Institute. I am working with groups of Guy Wolf (Mila), Smita Krishnaswamy (Krishnaswamy Lab, Yale University) and Bastian Rieck (AIDOS, Helmholtz Munich). I received my Ph.D. in Mathematics from Queen's University under the supervision of Professor Andrew Lewis.

My research centers on developing novel machine learning (ML) methodologies informed by tools from advanced mathematics, with a focus on applications in biomedical discovery. Despite our abilities to train ever-larger models, fundamental insights into how ML models work in biomedical contexts remain limited. My goal is to deepen our understanding of these models and address some of the core challenges they present.

Specifically, I am interested in integrating ideas from (1) optimal transport, generative modeling, and deep learning to explore cellular development and responses to varying conditions; (2) diffusion geometry, manifold learning, and geometry-regularized Variational Autoencoders (VAEs) to analyze high-dimensional data in lower dimensions for trajectory inference, data generation, and causality discovery; (3) graph signal processing and partial differential equations to predict molecular and protein structures; and (4) representation learning and graph scattering to investigate neural activity in the brain.

Publications & Preprints

* denotes equal contribution

Bhaskar, D.*, Zhang, Y*., Moore, J.*, Gao, F., Rieck, B., Wolf, Khasawneh, F., Munch, E., Noah, J. Adam, Pushkarskaya, H., Pittenger, C., Greco, V., Krishnaswamy, S. (2024). "Neurospectrum: A Geometric and Topological Deep Learning Framework for Uncovering Spatiotemporal Signatures in Neural Activity", bioRxiv, DOI: 10.1101/2023.03.22.533807, (Nature Computational Science (Under Review), 2025, pdf).
Singh, R., Zhang, Y., Bhaskar, D., Srihari, V., Tek, C., Zhang, X., Noah, J. A., Krishnaswamy, S., and Hirsch, J. "Deep Multimodal Representations and Classification of First-Episode Psychosis via Live Face Processing", Frontiers in Psychiatry Schizophrenia, 2025 (pdf).
Zhang, Y., Mezrag, L., Sun, X., Xu, C., Macdonald, K., Bhaskar, D., Krishnaswamy, S., Wolf, G., Rieck, B. "Principal Curvatures Estimation with Applications to Single Cell Data", The 50th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2025, (pdf).
Viswanath, S., Singh, R., Zhang, Y., J Adam Noah, Joy Hirsch, Smita Krishnaswamy. "SlepNet: Spectral Subgraph Representation Learning for Neural Dynamics", arXiv preprint arXiv:2506.16602, 2025 (Submitted to NeurIPS 2025, pdf)
Gomes, D. M., Zhang, Y., Belilovsky, E., Wolf, G., and Hosseini, M. S. "AdaFisher: Adaptive Second Order Optimization via Fisher Information", The Thirteenth International Conference on Learning Representations (ICLR), 2025. (Accepted, pdf)
Sun, X., Liao, D., MacDonald, K., Zhang, Y., Liu, C., Huguet, G., Wolf, G., Adelstein, I., Rudner, T. G. J., and Krishnaswamy, S. "Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds", International Conference on Artificial Intelligence and Statistics (AISTATS), 2025. (Accepted, pdf)

Bhaskar*, D., Zhang*, Y., Xu*, C., Sun, X., Fasina, O., Wolf, G., Nickel, M., Perlmutter, M., and Krishnaswamy, "Graph Topological Property Recovery with Heat and Wave Dynamics-based Features on Graphs" (submitted to NeurIPS 2025, pdf)

Zhang, Y., Huguet, G., Brouwer, E.D., Fasina, O., Tong, A., Ricky T. Q. Chen, Wolf, G., Nickel, M., Adelstein, I., Smita Krishnaswamy. “Neural FIM for learning Fisher information metrics from point cloud data”, September, 2025. (Journal Version, submitted to IEEE TPAMI)

Fasina, O., Huguet, G., Tong, A., Zhang, Y., Wolf, G., Nickel, M., Adelstein, I., and Krishnaswamy, S., "Neural FIM for learning Fisher information metrics from point cloud data", International Conference on Machine Learning (ICML), 2023. (Conference Paper, pdf)

Huguet, G., Tong, A., Brouwer, E. D., Zhang, Y., Wolf, G., Adelstein, I., and Krishnaswamy, S., "A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction", Neural Information Processing Systems (NeurIPS), 2023. (pdf)
(Conference Paper) Bhaskar, D., MacDonald, K., Fasina, O., Thomas, D., Rieck, B., Adelstein, I., and Krishnaswamy, S. "Diffusion Curvature for Estimating Local Curvature in High Dimensional Data", Neural Information Processing Systems (NeurIPS), 2022.

(Journal Version) MacDonald, K., Bhaskar, D., Zhang, Y., Ian Adelstein, Smita Krishnaswamy. “Diffusion Curvature for Estimating Local Curvature in High Dimensional Data” .

Tong, A., Malkin, N., Fatras, K., Atanackovic, L., Zhang, Y., Huguet, G., Wolf, G., and Bengio, Y. "Simulation-free Schrödinger bridges via score and flow matching", International Conference on Artificial Intelligence and Statistics (AISTATS), 2023. (pdf)

Tong, A., Malkin, N., Huguet, G., Zhang, Y., Rector-Brooks, J., FATRAS, K., Wolf, G., and Bengio, Y., "Improving and Generalizing Flow-Based Generative Models with Minibatch Optimal Transport", Presented in Frontiers4LCD Workshop @ ICML, 2023. (pdf)
Tong, A., Malkin, N., Huguet, G., Zhang, Y., Rector-Brooks, J., FATRAS, K., Wolf, G., and Bengio, Y. "Improving and Generalizing Flow-Based Generative Models with Minibatch Optimal Transport", Transactions on Machine Learning Research (TMLR), 2023. (pdf).
Lewis, A., and Zhang, Y., ''Topologies for geometric flows and continuous dependence on parameters'', (Submitted to EJDE), 2023. (pdf)

Zhang, Y., ''The exponential map for time-varying vector fields'', (pdf), 2022.

Zhang, Y., Feng, W., and Abdella, K., "Positive solutions for second-order differential equations with singularities and separated integral boundary conditions", Electron J. Qual. Theory of Differ. Equ., no. 75, pp. 1–12, 2020. (pdf)

Kang, S., Zhang, Y., and Feng, W., "Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators", Mathematics, vol. 9, no. 3, 2021. (pdf)

Teaching

Summer School (at Yale University)

- SUMRY (Summer Undergraduate Math Research at Yale) 2024 Summer (Webpage)

Instructor (at Mila)

– MATH 6493: Geometric Data Analysis (Graduate Course) 2023 Fall (Webpage)

– MATH 6493: Geometric Data Analysis (Graduate Course) 2025 Fall (Webpage)

Instructor (at Queen's)

– MATH 228: Complex Analysis (Core Course) 2021 Winter (Lecture Videos)

– MTHE 235: Introduction to Differential Equations (Core Course) 2021 Fall (class of size 267, in person)

– MATH 228: Complex Analysis (Core Course) 2022 Winter (In person classes)

Teaching Assistant (at Queen's)

Seminars & Tutorials

– MATH 110: Linear Algebra (2017, 2018 Fall)

– MATH 120: Differential and Integral Calculus (2018 Winter)

– MATH 126: Differential and Integral Calculus (2017, 2018 Fall & Winter)

– MATH 280: Advanced Calculus (2018, 2019 Fall)

– MTHE 224: Applied Mathematics for Civil Engineers (2017-2020 Fall)

– MATH 281: Introduction to Real Analysis (2018, 2019 Winter)

– MATH 334: Mathematical Methods for Engineering and Physics (2019, 2021 Fall)

– MATH 335: Mathematics of Engineering Systems (2020 Winter)

– MATH 341: Differential Geometry (2018 Fall)

Teaching Assistant (at Trent)

Seminars & Tutorials

– MATH 2110H: Multivariable Calculus III (2015, 2016 Fall)

– MATH 2120H: Multivariable Calculus IV (2015, 2016 Winter)

– MATH 2150: Ordinary Differential Equations (2015, 2016 Winter)

Academic Honors

Mathematics has always been my greatest passion. I was blessed to receive a few awards on the journey of pursuing the interest of mathematics.

Awards:

Honorable Mention, MCM (Mathematical Contest in Modelling, USA), 2013.
Silver Medal, National Mathematical Contest (China), 2013.
Gold Medal, National Mathematical Contest in Modelling (China), 2013.
Gold Medal, Tianjin Mathematical Contest (China), 2012.
Second Grand, National Olympic Contest in Mathematics (China), 2009.

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