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Computational Mathematics

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    Biomolecular and Biophysical Inference Bridging the gap between molecular simulations and experimental data, enabling quantitative characterization of biomolecules.

    Machine Learning and Computational Statistics Using leading-edge tools and methods to push the boundaries of computational mathematics.

    Numerical Analysis and Scientific Computing Creating fast, accurate and robust high-order solvers for many equations in complicated geometries.

    COMPASS Connecting researchers working on molecular sampling, simulation and design.

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Flatiron Institute Computational Mathematics

Computational Mathematics: Publications

Read the latest papers published by our researchers.

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  1. MoMo: Momentum Models for Adaptive Learning Rates

    Proceedings of Machine Learning Research, 2024

    Fabian Schaipp, R. Ohana, M. Eickenberg, Aaron Defazio, and R. Gower

  2. Amortized Variational Inference: When and Why?

    Uncertainty in Artificial Intelligence, arXiv:2307.11018, 2024

    C. Margossian and D. Blei

  3. Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models

    arxiv:2402.19449, 2024

    Frederik Kunstner, Robin Yadav, Alan Milligan, Mark Schmidt, and A. Bietti

  4. Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions

    Bayesian Analysis, arxiv:2110.00610, 2024

    C. Modi, A. Barnett, and B. Carpenter

  5. posteriordb: Testing, Benchmarking and Developing Bayesian Inference Algorithms

    arxiv:2407.04967, 2024

    Måns Magnusson, Jakob Torgander, Paul-Christian Bürkner, Lu Zhang, B. Carpenter, and Aki Vehtari

  6. Good Rates From Bad Coordinates: The Exponential Average Time-dependent Rate Approach

    Journal of Chemical Theory and Computation, 2024

    Nicodemo Mazzaferro, Subarna Sasmal, P. Cossio, and Glen M. Hocky

  7. AstroCLIP: a cross-modal foundation model for galaxies

    Monthly Notices of the Royal Astronomical Society, arxiv:2310.03024, 2024

    Liam Parker, et al.

  8. Learning sum of diverse features: computational hardness and efficient gradient-based training for ridge combinations

    Proceedings of Machine Learning Research, arxiv:2406.11828, 2024

    Kazusato Oko, Yujin Song, Taiji Suzuki, and D. Wu

  9. Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs

    arxiv:2403.13748, 2024

    C. Margossian, L. Pillaud-Vivien, and L. Saul

  10. How Truncating Weights Improves Reasoning in Language Models

    arxiv:2406.03068, 2024

    Lei Chen, Joan Bruna, and A. Bietti

  11. Offline supervised learning vs online direct policy optimization: A comparative study and a unified training paradigm for neural network-based optimal feedback control

    Physica D: Nonlinear Phenomena, 2024

    Yue Zhao and J. Han

  12. Contextual Counting: A Mechanistic Study of Transformers on a Quantitative Task

    arxiv:2406.02585, 2024

    Siavash Golkar, et al.

  13. Crowdsourcing with Difficulty: A Bayesian Rating Model for Heterogeneous Items

    arxiv:2405.19521, 2024

    Seong Woo Han, Ozan Adıgüzel, and B. Carpenter

  14. Neurosift: DANDI exploration and NWB visualization in the browser

    Journal of Open Source Software, 2024

    J. Magland, J. Soules, Cody Baker, and Benjamin Dichter

  15. Why is parameter averaging beneficial in SGD? An objective smoothing perspective

    Proceedings of Machine Learning Research, arxiv:2302.09376, 2024

    Atsushi Nitanda, Ryuhei Kikuchi, Shugo Maeda, and D. Wu

  16. Simulation-Based Stacking

    Proceedings of Machine Learning Research, arXiv:2310.17009, 2024

    Yuling Yao, B. Régaldo-Saint Blancard, and Justin Domke

  17. GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo

    arxiv:2404.15253, 2024

    N. Bou-Rabee, B. Carpenter, and Milo Marsden

  18. Improved statistical and computational complexity of the mean-field Langevin dynamics under structured data

    The Twelfth International Conference on Learning Representations, 2024

    Atsushi Nitanda, Kazusato Oko, Taiji Suzuki, and D. Wu

  19. Efficient convergent boundary integral methods for slender bodies

    Journal of Computational Physics, 2024

    D. Malhotra and A. Barnett

  20. Galaxy clustering analysis with SimBIG and the wavelet scattering transform

    Physical Review D, arxiv:2310.15250, 2024

    B. Régaldo-Saint Blancard, ChangHoon Hahn, Shirley Ho, Jiamin Hou, Pablo Lemos, Elena Massara, et al.

  21. Escaping saddle points efficiently with occupation-time-adapted perturbation

    Journal of Computational Mathematics and Data Science, 2024

    Xin Guo, J. Han, Mahan Tajrobehkar, and Wenpin Tang

  22. Statistical Component Separation for Targeted Signal Recovery in Noisy Mixtures

    arxiv:2306.15012, 2024

    B. Régaldo-Saint Blancard and M. Eickenberg

  23. Nonlinear spiked covariance matrices and signal propagation in deep neural networks

    Proceedings of Machine Learning Research, arxiv:2402.10127, 2024

    Zhichao Wang, D. Wu, and Zhou Fan

  24. For how many iterations should we run Markov chain Monte Carlo?

    arxiv:2311.02726, 2024

    C. Margossian and Andrew Gelman

  25. Design of Perfectly Conducting Objects That Are Invisible to an Incident Plane Wave

    IEEE Journal on Multiscale and Multiphysics Computational Techniques, 2024

    Johan Helsing, S. Jiang, and Anders Karlsson

  26. Deep reinforcement learning in finite-horizon to explore the most probable transition pathway

    Physica D: Nonlinear Phenomena, 2024

    Jin Guo, Ting Gao, Peng Zhang, J. Han, and Jinqiao Duan

  27. Envelopes of Horospheres and Weingarten Surfaces in Hyperbolic 3-Space

    arxiv:2401.12115, 2024

  28. The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

    Plasma Physics and Controlled Fusion, 2024

    John Kappel, Matt Landreman, and D. Malhotra

  29. Should Under-parameterized Student Networks Copy or Average Teacher Weights?

    Conference on Neural Information Processing Systems, arXiv:2311.01644, 2024

    B. Şimşek, Amire Bendjeddou, Wulfram Gerstner, and Johanni Brea

  30. Generalization in diffusion models arises from geometry-adaptive harmonic representations

    International Conference on Learning Representations, 2024

    Zahra Kadkhodaie, Florentin Guth, E. Simoncelli, and S. Mallat

  31. Scaling Laws for Associative Memories

    International Conference on Learning Representations, arxiv:2310.02984, 2024

    Vivien Cabannes, Elvis Dohmatob, and A. Bietti

  32. Solving the Scattering Problem for Open Wave-Guides, III: Radiation Conditions and Uniqueness

    arxiv:2401.04674, 2024

    Rafe Mazzeo

  33. Stochastic Optimal Control Matching

    Advances in Neural Information Processing Systems, 2024

    Carles Domingo-Enrich, J. Han, Brandon Amos, Joan Bruna, and Ricky T. Q. Chen

  34. Learning High-Dimensional McKean–Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence

    SIAM Journal on Numerical Analysis, arXiv:2204.11924, 2024

    J. Han, Ruimeng Hu, and Jihao Long

  35. Directional Smoothness and Gradient Methods: Convergence and Adaptivity

    Conference on Neural Information Processing Systems, arxiv:2403.04081, 2024

    Aaron Mishkin, Ahmed Khaled, Yuanhao Wang, Aaron Defazio, and R. Gower

  36. Uniform approximation of common Gaussian process kernels using equispaced Fourier grids

    Applied and Computational Harmonic Analysis, arXiv:2305.11065, 2024

    A. Barnett, Philip Greengard, Ph.D., and M. Rachh

  37. A new provably stable weighted state redistribution algorithm

    SIAM Journal on Scientific Computing, 2024

    M. Berger and A. Giuliani

  38. A new version of the adaptive fast Gauss transform for discrete and continuous sources

    SIAM Review, arXiv:2305.07165, 2024

    L. Greengard, S. Jiang, M. Rachh, and J. Wang

  39. Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation

    SIAM Journal on Scientific Computing, arXiv:2307.05816, 2024

    M. Berger and Randall J. LeVeque

  40. A high-order fast direct solver for surface PDEs

    SIAM Journal on Scientific Computing, arxiv:2210.00022, 2024

    D. Fortunato

  41. Explainable Equivariant Neural Networks for Particle Physics: PELICAN

    arXiv:2307.16506, 2023

    A. Bogatskii, Timothy Hoffman, David W. Miller, Jan T. Offermann, and Xiaoyang Liu

  42. Provable convergence guarantees for black-box variational inference

    Conference on Neural Information Processing Systems, 2023

    Justin Domke, R. Gower, and Guillaume Garrigos

  43. Sharp error estimates for target measure diffusion maps with applications to the committor problem

    arXiv:2312.14418, 2023

    Shashank Sule, L. Evans, and Maria Cameron

  44. Improving Convergence and Generalization Using Parameter Symmetries

    Conference on Neural Information Processing Systems, 2023

    Bo Zhao, R. Gower, Robin Walters, and Rose Yu

  45. Microscopic Theory, Analysis, and Interpretation of Conductance Histograms in Molecular Junctions

    Nature Communications, November 23, 2023

    Leopoldo Mejía, P. Cossio, and Ignacio Franco

  46. Bayesian spatial modelling of localised SARS-CoV-2 transmission through mobility networks across England

    PLOS Computational Biology, 2023

    Thomas Ward, Mitzi Morris, Andrew Gelman, B. Carpenter, William Ferguson, Christopher Overton, et al.

  47. Birth of a Transformer: A Memory Viewpoint

    arxiv:2306.00802, 2023

    A. Bietti, Vivien Cabannes, Diane Bouchacourt, Herve Jegou, and Leon Bottou

  48. On Learning Gaussian Multi-index Models with Gradient Flow

    arxiv:2310.19793, 2023

    A. Bietti, Joan Bruna, and L. Pillaud-Vivien

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