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Decentralized stochastic optimization is the basic building block of modern collaborative machine learning, distributed estimation and control, and large-scale sensing. Since involved data usually contain sensitive information like user…

Selective State Space Models (SSMs) achieve linear-time inference, yet their gradient-based sensitivity analysis remains bottlenecked by O(L) memory scaling during backpropagation. This memory constraint precludes genomic-scale modeling (L…

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's…

In this paper, we propose an efficient implementation of deep policy gradient method (PGM) for optimal control problems in continuous time. The proposed method has the ability to manage the allocation of computational resources, number of…

We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems, a grand challenge in computational science. State-of-the-art methods for these problems are severely limited…

Large-batch stochastic gradient descent (SGD) is widely used for training in distributed deep learning because of its training-time efficiency, however, extremely large-batch SGD leads to poor generalization and easily converges to sharp…

Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class…

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In…

The plain stochastic gradient descent and momentum stochastic gradient descent have extremely wide applications in deep learning due to their simple settings and low computational complexity. The momentum stochastic gradient descent uses…

Stochastic Gradient (SG) Markov Chain Monte Carlo algorithms (MCMC) are popular algorithms for Bayesian sampling in the presence of large datasets. However, they come with little theoretical guarantees and assessing their empirical…

Gradient tracking (GT) is an algorithm designed for solving decentralized optimization problems over a network (such as training a machine learning model). A key feature of GT is a tracking mechanism that allows to overcome data…

Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often…

Efficient continuous time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state-of-the-art for most discrete quantum models. They have not been widely used yet for fermionic quantum…

Significant success has been realized recently on applying machine learning to real-world applications. There have also been corresponding concerns on the privacy of training data, which relates to data security and confidentiality issues.…

This paper develops asymptotic theory for quantile estimation via stochastic gradient descent (SGD) with a constant learning rate. The quantile loss function is neither smooth nor strongly convex. Beyond conventional perspectives and…

The optimisation of scenarios and design of real-time-control in tokamaks, especially for machines still in design phase, requires a comprehensive exploration of solutions to the Grad-Shafranov (GS) equation over a high-dimensional space of…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…