arXiv research

Enhanced Gaussian process regression for multi-fidelity data fusion.

New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.

Anomalous diffusion in SGD reveals interactions between hyperparameters and Hessian.

Study on convergence of SDEs using entropy methods.

We develop underdamped diffusion bridges for sampling from unnormalized densities.

Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…

Error estimates found between SGD with momentum and Langevin diffusion.

New method optimizes non-linear functionals over probability measures.

Study on Langevin dynamics convergence rates and their application to GAN training.

New method controls bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin.

We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves $\varepsilon$ error (in 2-Wasserstein distance) in $\mathcal{O}(\sqrt{d}/\varepsilon)$ steps. This is a significant improv…

New method proves dimension-free convergence for ULD in KL divergence.

Improved sampling guarantees for underdamped Langevin Monte Carlo without restrictive assumptions.

Improved sampling for high-dimensional posteriors with underdamped Langevin.

New Langevin method achieves third order convergence for strongly log-concave distributions.

A new sampling method reduces computational cost for high-dimensional log-concave distributions.

Develops unbiased estimation method using underdamped Langevin dynamics.

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize t…

Unified framework for constrained diffusion models on nonconvex sets with efficient landing mechanism.

New algorithms improve sampling from constrained distributions.

Enhances LMC for log-concave sampling, reducing computational cost.

A new oscillator measures trending behavior of financial instruments.

Minimal vector fields on oscillator groups studied, with specific conditions for minimality.

Study examines boundedness of oscillating singular integrals on specific Lie groups.

Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "an…

Estimates box dimension of fractal interpolation surfaces using oscillation vectors.

Researchers classify lattices in a specific four-dimensional group.

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…

The Duffing oscillator's parameters are identified online using variational message passing.

New method linearizes nonlinear coupled oscillators on graphs.

Study on Wasserstein distance for numerical approximations of stochastic differential equations.

The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the van der Pol equation which is a deterministic approximation of…

The study derives generalization bounds for neural oscillators, improving their performance with regularization.

KIPLMC methods improve statistical inference in latent variable models.

We study the problem of sampling from a distribution $p^*(x) \propto \exp\left(-U(x)\right)$, where the function $U$ is $L$-smooth everywhere and $m$-strongly convex outside a ball of radius $R$, but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bound…

Study finds the spectrum of a cubic Dirac operator on specific oscillator group manifolds.

Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.

We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.

New method identifies physical constants from video data alone.

Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the one real parameter is vanished.

Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one…

Graph-Coupled Oscillator Networks (GraphCON) tackles graph-based learning problems.

Large learning rates cause oscillations in NN weights that improve generalization.

In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific …

Quantifies fractional isoperimetric inequality with strong control over boundary oscillation.

The paper analyzes convergence of Langevin dynamics with time-dependent metrics.

Improved KLMC for sampling under various conditions.

Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization…