Related papers: Localised distributions in complex Langevin dynami…
We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian Ansatz. We find that the Gaussian Ansatz captures the essential and even quantitative…
We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of…
Colloidal particles that experience perfectly elastic collisions can be modelled using Langevin processes with specular reflection conditions. The article presents a discretisation scheme and offers a conjecture for the rate of convergence…
We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is…
Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the…
Langevin integrators based on operator splitting are widely used in molecular dynamics. This work examines Langevin splitting schemes from the perspective of their internal trajectories and observation points, complementing existing…
In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [WT11], that incorporates a stochastic sampling step inside the traditional over-damped Langevin diffusion. This method is…
This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct…
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…
There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed…
We demonstrate analytically that complex Langevin dynamics can solve the sign problem in one-dimensional QCD in the thermodynamic limit. In particular, it is shown that the contributions from the complex and highly oscillating spectral…
Non-Markovian stochastic Langevin-like equations of motion are compared to their corresponding Markovian (local) approximations. The validity of the local approximation for these equations, when contrasted with the fully nonlocal ones, is…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…
We study stochastic optimization in the context of performative shifts, where the data distribution changes in response to the deployed model. We demonstrate that naive retraining can be provably suboptimal even for simple distribution…
This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary. It shows that the polynomial collocation towards a lognormal distribution does not work well. Then, the potentials issues of…
We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the…
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…
Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization. We appropriately add tractable noise to the…
We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a…