9,093 research outputs found

    Peak Estimation of Time Delay Systems using Occupation Measures

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    This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding the maximum number of infected people in an epidemic model with a nonzero incubation period. The variables of this peak estimation problem include the stopping time and the original history (restricted to a class of admissible histories). The original nonconvex DDE peak estimation problem is approximated by an infinite-dimensional Linear Program (LP) in occupation measures, inspired by existing measure-based methods in peak estimation and optimal control. This LP is approximated from above by a sequence of Semidefinite Programs (SDPs) through the moment-Sum of Squares (SOS) hierarchy. Effectiveness of this scheme in providing peak estimates for DDEs is demonstrated with provided examplesComment: 34 pages, 14 figures, 3 table

    Improved information criteria for Bayesian model averaging in lattice field theory

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    Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for these model weights. Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analogue of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion (BPIC), and the posterior predictive information criterion (PPIC). We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data.Comment: 69 pages, 13 figures. v2: corrections to data subset formulas for BPIC and PPIC; edits for clarity. Submitted to PR

    Compressed and distributed least-squares regression: convergence rates with applications to Federated Learning

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    In this paper, we investigate the impact of compression on stochastic gradient algorithms for machine learning, a technique widely used in distributed and federated learning. We underline differences in terms of convergence rates between several unbiased compression operators, that all satisfy the same condition on their variance, thus going beyond the classical worst-case analysis. To do so, we focus on the case of least-squares regression (LSR) and analyze a general stochastic approximation algorithm for minimizing quadratic functions relying on a random field. We consider weak assumptions on the random field, tailored to the analysis (specifically, expected H\"older regularity), and on the noise covariance, enabling the analysis of various randomizing mechanisms, including compression. We then extend our results to the case of federated learning. More formally, we highlight the impact on the convergence of the covariance Cania\mathfrak{C}_{\mathrm{ania}} of the additive noise induced by the algorithm. We demonstrate despite the non-regularity of the stochastic field, that the limit variance term scales with Tr(CaniaH−1)/K\mathrm{Tr}(\mathfrak{C}_{\mathrm{ania}} H^{-1})/K (where HH is the Hessian of the optimization problem and KK the number of iterations) generalizing the rate for the vanilla LSR case where it is σ2Tr(HH−1)/K=σ2d/K\sigma^2 \mathrm{Tr}(H H^{-1}) / K = \sigma^2 d / K (Bach and Moulines, 2013). Then, we analyze the dependency of Cania\mathfrak{C}_{\mathrm{ania}} on the compression strategy and ultimately its impact on convergence, first in the centralized case, then in two heterogeneous FL frameworks

    Safe Reinforcement Learning as Wasserstein Variational Inference: Formal Methods for Interpretability

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    Reinforcement Learning or optimal control can provide effective reasoning for sequential decision-making problems with variable dynamics. Such reasoning in practical implementation, however, poses a persistent challenge in interpreting the reward function and corresponding optimal policy. Consequently, formalizing the sequential decision-making problems as inference has a considerable value, as probabilistic inference in principle offers diverse and powerful mathematical tools to infer the stochastic dynamics whilst suggesting a probabilistic interpretation of the reward design and policy convergence. In this study, we propose a novel Adaptive Wasserstein Variational Optimization (AWaVO) to tackle these challenges in sequential decision-making. Our approach utilizes formal methods to provide interpretations of reward design, transparency of training convergence, and probabilistic interpretation of sequential decisions. To demonstrate practicality, we show convergent training with guaranteed global convergence rates not only in simulation but also in real robot tasks, and empirically verify a reasonable tradeoff between high performance and conservative interpretability.Comment: 24 pages, 8 figures, containing Appendi

    Joint stochastic simulation of petrophysical properties with elastic attributes based on parametric copula models

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    The spatial stochastic co-simulation method based on copulas is a general method that allows simulating variables with any type of dependency and probability distribution functions. This flexibility comes from the use of a copula model for the representation of the joint probability distribution function. The method has been mainly implemented through a non-parametric approach using Bernstein copulas and has been successfully applied for the simulation of petrophysical properties using elastic seismic attributes as secondary variables. In the present work this method is implemented through two other approaches: parametric and semi-parametric. Specifically, for the parametric approach the family of Archimedean copulas is used. First, the parametric approach is validated against a published case, and then a comparison of the three approaches in terms of accuracy and performance is made. The results showed that the parametric approach is the one that reproduces the data statistics worse and presents greater uncertainty with a lower computational cost, while the non-parametric approach was the one that best reproduces the dependence of the data at a high computational cost. The semi-parametric approach reduces the computational cost by 10% compared to the non-parametric approach, but its accuracy is significantly degraded

    Random Function Descent

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    While gradient based methods are ubiquitous in machine learning, selecting the right step size often requires "hyperparameter tuning". This is because backtracking procedures like Armijo's rule depend on quality evaluations in every step, which are not available in a stochastic context. Since optimization schemes can be motivated using Taylor approximations, we replace the Taylor approximation with the conditional expectation (the best L2L^2 estimator) and propose "Random Function Descent" (RFD). Under light assumptions common in Bayesian optimization, we prove that RFD is identical to gradient descent, but with calculable step sizes, even in a stochastic context. We beat untuned Adam in synthetic benchmarks. To close the performance gap to tuned Adam, we propose a heuristic extension competitive with tuned Adam

    Time as a supervisor: temporal regularity and auditory object learning

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    Sensory systems appear to learn to transform incoming sensory information into perceptual representations, or “objects,” that can inform and guide behavior with minimal explicit supervision. Here, we propose that the auditory system can achieve this goal by using time as a supervisor, i.e., by learning features of a stimulus that are temporally regular. We will show that this procedure generates a feature space sufficient to support fundamental computations of auditory perception. In detail, we consider the problem of discriminating between instances of a prototypical class of natural auditory objects, i.e., rhesus macaque vocalizations. We test discrimination in two ethologically relevant tasks: discrimination in a cluttered acoustic background and generalization to discriminate between novel exemplars. We show that an algorithm that learns these temporally regular features affords better or equivalent discrimination and generalization than conventional feature-selection algorithms, i.e., principal component analysis and independent component analysis. Our findings suggest that the slow temporal features of auditory stimuli may be sufficient for parsing auditory scenes and that the auditory brain could utilize these slowly changing temporal features

    Saliency detection for large-scale mesh decimation

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    Highly complex and dense models of 3D objects have recently become indispensable in digital industries. Mesh decimation then plays a crucial role in the production pipeline to efficiently get visually convincing yet compact expressions of complex meshes. However, the current pipeline typically does not allow artists control the decimation process, just a simplification rate. Thus a preferred approach in production settings splits the process into a first pass of saliency detection highlighting areas of greater detail, and allowing artists to iterate until satisfied before simplifying the model. We propose a novel, efficient multi-scale method to compute mesh saliency at coarse and finer scales, based on fast mesh entropy of local surface measurements. Unlike previous approaches, we ensure a robust and straightforward calculation of mesh saliency even for densely tessellated models with millions of polygons. Moreover, we introduce a new adaptive subsampling and interpolation algorithm for saliency estimation. Our implementation achieves speedups of up to three orders of magnitude over prior approaches. Experimental results showcase its resilience to problem scenarios that efficiently scales up to process multi-million vertex meshes. Our evaluation with artists in the entertainment industry also demonstrates its applicability to real use-case scenarios

    Exploring QCD matter in extreme conditions with Machine Learning

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    In recent years, machine learning has emerged as a powerful computational tool and novel problem-solving perspective for physics, offering new avenues for studying strongly interacting QCD matter properties under extreme conditions. This review article aims to provide an overview of the current state of this intersection of fields, focusing on the application of machine learning to theoretical studies in high energy nuclear physics. It covers diverse aspects, including heavy ion collisions, lattice field theory, and neutron stars, and discuss how machine learning can be used to explore and facilitate the physics goals of understanding QCD matter. The review also provides a commonality overview from a methodology perspective, from data-driven perspective to physics-driven perspective. We conclude by discussing the challenges and future prospects of machine learning applications in high energy nuclear physics, also underscoring the importance of incorporating physics priors into the purely data-driven learning toolbox. This review highlights the critical role of machine learning as a valuable computational paradigm for advancing physics exploration in high energy nuclear physics.Comment: 146 pages,53 figure

    Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method

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    This work aims at deriving special types of one-dimensional Finite Elements (1D FE) for efficiently modeling heterogeneous prismatic structures, in the small strains regime, by means of reduced-order modeling (ROM) and domain decomposition techniques. The employed partitioning framework introduces “fictitious” interfaces between contiguous subdomains, leading to a formulation with both subdomain and interface fields. We propose a low-dimensional parameterization at both subdomain and interface levels by using reduced-order bases precomputed in an offline stage by applying the Singular Value Decomposition (SVD) on solution snapshots. In this parameterization, the amplitude of the fictitious interfaces play the role of coarse-scale displacement unknowns. We demonstrate that, with this partitioned framework, it is possible to arrive at a solution strategy that avoids solving the typical nested local/global problem of other similar methods (such as the FE method). Rather, in our approach, the coarse-grid cells can be regarded as special types of finite elements, whose nodes coincides with the centroids of the interfaces, and whose kinematics are dictated by the modes of the “fictitious” interfaces. This means that the kinematics of our coarse-scale FE are not pre-defined by the user, but extracted from the set of “training” computational experiments. Likewise, we demonstrate that the coarse-scale and fine-scale displacements are related by inter-scale operators that can be precomputed in the offline stage. Lastly, a hyperreduced scheme is considered for the evaluation of the internal forces, allowing us to deal with possible material nonlinearities.This work has received support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2018-000797-S)”. A. Giuliodori also gratefully acknowledges the support of “Secretaria d’Universitats i Recerca de la Generalitat de Catalunya i del Fons Social Europeu” through the FI grant (00939/2020), and J.A. Hernández the support of, on the one hand, the European High-Performance Computing Joint Undertaking (JU) under grant agreement No. 955558 (the JU receives, in turn, support from the European Union’s Horizon 2020 research and innovation program and from Spain, Germany, France, Italy, Poland, Switzerland, Norway), and the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 952966 (project FIBREGY).Peer ReviewedPostprint (published version
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