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Tag: stochastic

  • Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation

    Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation arXiv:2602.15925v1 Announce Type: new Abstract: Stochastic-gradient MCMC methods enable scalable Bayesian posterior sampling but often suffer from sensitivity to minibatch size and gradient noise. To address this, we propose Stochastic Gradient Lattice Random Walk (SGLRW), an extension of the Lattice Random Walk discretization. Unlike conventional Stochastic…

  • High-Dimensional Limit of Stochastic Gradient Flow via Dynamical Mean-Field Theory

    High-Dimensional Limit of Stochastic Gradient Flow via Dynamical Mean-Field Theory arXiv:2602.06320v1 Announce Type: new Abstract: Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for describing the high-dimensional asymptotic behavior of multi-pass…

  • Low-Dimensional Adaptation of Rectified Flow: A New Perspective through the Lens of Diffusion and Stochastic Localization

    Low-Dimensional Adaptation of Rectified Flow: A New Perspective through the Lens of Diffusion and Stochastic Localization arXiv:2601.15500v1 Announce Type: new Abstract: In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…

  • Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data

    Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data arXiv:2601.05227v1 Announce Type: new Abstract: I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach, termed Stochastic Latent Differential Inference (SLDI), embeds…

  • Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators

    Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators arXiv:2512.24106v1 Announce Type: new Abstract: In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well…

  • Riemannian Stochastic Interpolants for Amorphous Particle Systems

    Riemannian Stochastic Interpolants for Amorphous Particle Systems arXiv:2512.16607v1 Announce Type: new Abstract: Modern generative models hold great promise for accelerating diverse tasks involving the simulation of physical systems, but they must be adapted to the specific constraints of each domain. Significant progress has been made for biomolecules and crystalline materials. Here, we address amorphous materials…

  • Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks

    Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks arXiv:2511.02258v1 Announce Type: new Abstract: This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD) for single-layer networks. Building on the seminal work of Saad and Solla, which analyzed the deterministic (ballistic) scaling limits of SGD corresponding to the gradient flow of…

  • Effective continuous equations for adaptive SGD: a stochastic analysis view

    Effective continuous equations for adaptive SGD: a stochastic analysis view arXiv:2509.21614v1 Announce Type: new Abstract: We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective continuous stochastic dynamics for these methods.…

  • Batched Stochastic Matching Bandits

    Batched Stochastic Matching Bandits arXiv:2509.04194v1 Announce Type: new Abstract: In this study, we introduce a novel bandit framework for stochastic matching based on the Multi-nomial Logit (MNL) choice model. In our setting, $N$ agents on one side are assigned to $K$ arms on the other side, where each arm stochastically selects an agent from its…

  • Stochastic Differential Equations and Temperature — NASA Climate Data pt. 2

    Stochastic Differential Equations and Temperature — NASA Climate Data pt. 2 The Ornstein-Uhlenbeck process in Python The post Stochastic Differential Equations and Temperature — NASA Climate Data pt. 2 appeared first on Towards Data Science. Marco Hening Tallarico Go to original source

  • Stochastic Gradients under Nuisances

    Stochastic Gradients under Nuisances arXiv:2508.20326v1 Announce Type: new Abstract: Stochastic gradient optimization is the dominant learning paradigm for a variety of scenarios, from classical supervised learning to modern self-supervised learning. We consider stochastic gradient algorithms for learning problems whose objectives rely on unknown nuisance parameters, and establish non-asymptotic convergence guarantees. Our results show that, while…

  • Nonparametric learning of stochastic differential equations from sparse and noisy data

    Nonparametric learning of stochastic differential equations from sparse and noisy data arXiv:2508.11597v1 Announce Type: new Abstract: The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift, our goal here is to learn the entire…

  • Stochastic dynamics learning with state-space systems

    Stochastic dynamics learning with state-space systems arXiv:2508.07876v1 Announce Type: new Abstract: This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space systems, a central model class in time series learning, and establish…

  • Flow Stochastic Segmentation Networks

    Flow Stochastic Segmentation Networks arXiv:2507.18838v1 Announce Type: cross Abstract: We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank parameterisation of previous methods and show that Flow-SSNs can estimate arbitrarily high-rank pixel-wise covariances without assuming the rank…

  • Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains

    Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains arXiv:2507.15990v1 Announce Type: new Abstract: Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in…

  • Sampling conditioned diffusions via Pathspace Projected Monte Carlo

    Sampling conditioned diffusions via Pathspace Projected Monte Carlo arXiv:2506.15743v1 Announce Type: new Abstract: We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that…

  • The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations

    The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations arXiv:2505.11622v1 Announce Type: new Abstract: We present a novel kernel-based method for learning multivariate stochastic differential equations (SDEs). The method follows a two-step procedure: we first estimate the drift term function, then the (matrix-valued) diffusion function given the drift. Occupation kernels are integral functionals…

  • Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling

    Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling arXiv:2504.13333v1 Announce Type: new Abstract: We present a novel data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation-Dissipation Theorem (GFDT) links the unperturbed steady-state distribution to the system’s linear response.…

  • A stochastic gradient descent algorithm with random search directions

    A stochastic gradient descent algorithm with random search directions arXiv:2503.19942v1 Announce Type: new Abstract: Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining coordinates. However, this approach is usually restricted…

  • Advancing calibration for stochastic agent-based models in epidemiology with Stein variational inference and Gaussian process surrogates

    Advancing calibration for stochastic agent-based models in epidemiology with Stein variational inference and Gaussian process surrogates arXiv:2502.19550v1 Announce Type: new Abstract: Accurate calibration of stochastic agent-based models (ABMs) in epidemiology is crucial to make them useful in public health policy decisions and interventions. Traditional calibration methods, e.g., Markov Chain Monte Carlo (MCMC), that yield a…

  • New Lower Bounds for Stochastic Non-Convex Optimization through Divergence Composition

    New Lower Bounds for Stochastic Non-Convex Optimization through Divergence Composition arXiv:2502.14060v1 Announce Type: new Abstract: We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the convergence properties of standard algorithms are well-understood in deterministic regimes,…

  • Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve

    Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve arXiv:2501.08288v1 Announce Type: new Abstract: Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely $x=a+b$ or $x = ab$. For…

  • Projected gradient methods for nonconvex and stochastic optimization: new complexities and auto-conditioned stepsizes

    Projected gradient methods for nonconvex and stochastic optimization: new complexities and auto-conditioned stepsizes arXiv:2412.14291v1 Announce Type: cross Abstract: We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the “vanilla” PG method, achieving the…

  • Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

    Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations arXiv:2412.07265v1 Announce Type: new Abstract: In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of…