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41st International Conference on Machine Learning, ICML 2024

作者： Papamarkou, Theodore Skoularidou, Maria Palla, Konstantina Aitchison, Laurence Arbel, Julyan Dunson, David Filippone, Maurizio Fortuin, Vincent Hennig, Philipp Hernández-Lobato, José Miguel Hubin, Aliaksandr Immer, Alexander Karaletsos, Theofanis Khan, Mohammad Emtiyaz Kristiadi, Agustinus Li, Yingzhen Mandt, Stephan Nemeth, Christopher Osborne, Michael A. Rudner, Tim G.J. Rügamer, David Teh, Yee Whye Welling, Max Wilson, Andrew Gordon Zhang, Ruqi Department of Mathematics The University of Manchester Manchester United Kingdom Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge United States Spotify London United Kingdom Computational Neuroscience Unit University of Bristol Bristol United Kingdom Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University United States Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany Department of Computer Science Technical University of Munich Munich Germany Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge United Kingdom Department of Mathematics University of Oslo Oslo Norway Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative CA United States Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London United Kingdom Department of Computer Science UC Irvine Irvine United States Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Center for Data Science New York University New York United States Department of Statistics LMU Munich Munich Germany DeepMind London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences Center for Data Science Computer Science Department New York University New York United States Department of Computer Science Purdue University West Lafayette United States

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential. Copyright 2024 by the author(s)

关键词： Contrastive Learning

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Precise Determination of Pair Interactions from Pair Statistics of Many-Body Systems In and Out of Equilibrium

arXiv

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arXiv 2022年

作者： Torquato, Salvatore Wang, Haina Department of Chemistry Department of Physics Princeton Institute of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g2(r) or corresponding structure factor S(k) in d-dimensional Euclidean space Rd is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato conjectured that any realizable g2(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised a novel optimization algorithm to find effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g2(r) and structure factor S(k) so that the small- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point;(2) liquid under the Dzugutov potential;(3) nonequilibrium random sequential addition packing;and (4) and a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice (URL). We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L2-norm errors

关键词： Statistics

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The Manifold Scattering Transform for High-Dimensional Point Cloud Data

arXiv

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arXiv 2022年

作者： Chew, Joyce Steach, Holly R. Viswanath, Siddharth Wu, Hau-Tieng Hirn, Matthew Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael UCLA Department of Mathematics Los AngelesCA United States Yale University Department of Genetics New HavenCT United States UC Irvine Department of Computer Science IrvineCA United States Duke University Department of Mathematics DurhamNC United States Duke University Department of Statistical Science DurhamNC United States Michigan State University Department of Mathematics East Lansing United States Michigan State University Department of CMSE East Lansing United States Yale University Department of Computer Science New HavenCT United States Yale University Applied Math Program New HavenCT United States

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification *** Codes 68T07 Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

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Principal Curvatures Estimation with Applications to Single Cell Data

arXiv

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arXiv 2025年

作者： Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian Université de Montréal Dept. of Math. & Stat. QC Montréal Canada Mila – Quebec AI Institute MontréalQC Canada Yale University Dept. of Comp. Sci. New HavenCT United States Dept. of Genetics New HavenCT United States Applied Mathematics Program New HavenCT United States Université de Fribourg Department of Informatics Fribourg Switzerland Helmholtz Zentrum München Institute of AI for Health Munich Germany

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation. © 2025, CC BY.

关键词： Spatio-temporal data

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Computational design of anisotropic stealthy hyperuniform composites with engineered directional scattering properties

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Physical Review E 2023年第4期108卷 045306-045306页

作者： Wenlong Shi David Keeney Duyu Chen Yang Jiao Salvatore Torquato Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Materials Research Laboratory University of California Santa Barbara California 93106 USA Department of Physics Arizona State University Tempe Arizona 85287 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ̃V(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ̃V(k)=0 for k∈Ω, i.e., complete suppression of scattering in an “exclusion” region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions

关键词： Amorphous materials Complex materials Simulated annealing

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Developing a medical artificial intelligence course for high school students

Developing a medical artificial intelligence course for high...

引用

International Forum on Medical Imaging in Asia 2021, IFMIA 2021

作者： Huang, Chao-Jung Wu, Tinghui Lu, Jui-Ting Lin, Beatrice Chang, Dawei Wang, Pochuan Wang, Mei-Chi Lee, Peijung Wang, Weichung National Taiwan University-Stanford Joint Program Office of AI in Biotechnology Ministry of Science and Technology Joint Research Center for Artificial Intelligence Technology and All Vista Healthcare Taipei Taiwan Institute of Applied Mathematical Sciences National Taiwan University Taipei Taiwan Department of Mathematics Ecole Normale Supérieure de Lyon Lyon France Department of Computer Science and Information Engineering National Taiwan University Taipei Taiwan Department of Electronic and Computer Engineering National Taiwan University of Science and Technology Taipei Taiwan Department of Mathematics National Taiwan University Taipei Taiwan

ISBN: (数字)9781510644212

ISBN: (纸本)9781510644205

Artificial intelligence (AI) training courses often require prerequisites such as calculus or statistics. It is hence challenging to design and develop an introductory AI course for students of secondary education. This research intends to develop a medical AI course, provide high school students with an overview of deep learning applications in medical image analysis, and inspire them to pursue careers in the field of medical AI. We designed a 20-hour course, including lectures and two hands-on projects based on medical image classification. The proposed courses provided medical AI disciplines and built up their knowledge from basic to advanced levels. During the ten-day online courses, all the students were fully engaged and gave us positive feedback. The students endeavored to complete the experimental study in training, testing, and hypothesis of medical images application in the course. Their performance exceeded all expectations, for they did further analysis by tuning different hyperparameters. We designed a course evaluation form, which suggested that the students found it essential and expected to interact with the instructors. The results indicate that combining lectures with hands-on sessions would lead to evidently better achievement in terms of high school students' medical AI knowledge and positive attitudes while addressing real-world problems in the projects. Through this innovative education model, high school students regained their enthusiasm and were encouraged to cultivate their medical AI skills through self-learning while finishing the project. We conclude that this course could be successfully applied to interdisciplinary education in high school. © 2021 SPIE.

关键词： Students

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Interior electroneutrality in nernst-planck-navier-stokes systems

arXiv

引用

arXiv 2020年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States DEPARTMENT OF MATHEMATICS TEMPLE UNIVERSITY PHILADELPHIAPA19122 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions for the ionic concentrations, we prove that the ionic charge density ρ converges in time to zero in the interior of the domain, in the limit of vanishing Debye length (ǫ → 0). For the unstable regime of Dirichlet boundary conditions for the ionic concentrations, we prove bounds that are uniform in time and ǫ. We also consider electroneutral boundary conditions, for which we prove that electroneutrality ρ → 0 is achieved at any fixed ǫ > 0, exponentially fast in time in Lp, for all 1 ≤ p MSC Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Boundary conditions

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On deterministic parallel implementation of the branch-and-bound method with monotonic objects 21

On deterministic parallel implementation of the branch-and-b...

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21st Conference on Scientific Services and Internet, SSI 2019

作者： Adamovich, Alexei Klimov, Andrei Ailamazyan Program Systems Institute of RAS Peter I str. 4a selo Veskovo Pereslavl-Zalessky Yaroslavl region152021 Russia Keldysh Institute of Applied Mathematics of RAS Miusskaya sq. 4 Moscow125047 Russia

This paper continues the authors’ research into the development of a system of deterministic parallel programming and the creation of libraries of so-called monotonic classes. The system is two-level and uses two input languages: a universal object-oriented language like Java for the implementation of monotonic classes, which makes up the lower-level subsystem, and a higher-level functional language with the ability to create and use immutable and monotonic objects. The libraries of monotonic classes ensure that all programs in the higher-level language that use only monotonic classes are deterministic and idempotent when they are parallelized by asynchronous calls of all functions. An important part of the development of such a system is the creation of monotonic class libraries for various fields of application and the demonstration of solutions to several applied problems using them. This paper is devoted specifically to implementing the search for the minimum weight of paths in a graph by the branch-and-bound method. We provide a solution referred to as conditionally monotonic, where the monotonicity holds only for nonnegative edge weights. The problem of the exact implementation of the branch-and-bound method with monotonic objects is stated. Copyright © 2020 for this paper by its authors.

关键词： Branch and bound method

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SUPP & MAPP: ADAPTABLE STRUCTURE-BASED REPRESENTATIONS FOR MIR TASKS 21

SUPP & MAPP: ADAPTABLE STRUCTURE-BASED REPRESENTATIONS FOR M...

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21st International Society for Music Information Retrieval Conference, ISMIR 2020

作者： Savard, Claire Bugbee, Erin H. McGuirl, Melissa R. Kinnaird, Katherine M. Department of Physics University of Colorado Boulder United States Department of Biostatistics Brown University United States Division of Applied Mathematics Brown University United States Department of Computer Science and Program in Statistical and Data Sciences Smith College United States

ISBN: (纸本)9780981353708

Accurate and flexible representations of music data are paramount to addressing MIR tasks, yet many of the existing approaches are difficult to interpret or rigid in nature. This work introduces two new song representations for structure-based retrieval methods: Surface Pattern Preservation (SuPP), a continuous song representation, and Matrix Pattern Preservation (MaPP), SuPP’s discrete counterpart. These representations come equipped with several user-defined parameters so that they are adaptable for a range of MIR tasks. Experimental results show MaPP as successful in addressing the cover song task on a set of Mazurka scores, with a mean precision of 0.965 and recall of 0.776. SuPP and MaPP also show promise in other MIR applications, such as novel-segment detection and genre classification, the latter of which demonstrates their suitability as inputs for machine learning problems. © Claire Savard, Erin H. Bugbee, Melissa R. McGuirl, Katherine M. Kinnaird.

关键词： Information retrieval

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NERNST-PLANCK-NAVIER-STOKES SYSTEMS NEAR EQUILIBRIUM

arXiv

引用

arXiv 2020年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States DEPARTMENT OF MATHEMATICS TEMPLE UNIVERSITY PHILADELPHIAPA19122 United States PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States

The Nernst-Planck-Navier-Stokes system models electrodiffusion of ions in a fluid. We prove global existence of solutions in bounded domains in three dimensions with either blocking (no-flux) or uniform selective (special Dirichlet) boundary conditions for ion concentrations. The global existence of strong solutions is established for initial conditions that are sufficiently small perturbations of steady state solutions. The solutions remain close to equilbrium in strong norms. The main two steps of the proof are (1) the decay of the sum of relative entropies (Kullback-Leibler divergences) and (2) the control of L2 norms of deviations by the sum of relative *** Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Navier Stokes equations

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