arXiv research

New algorithm learns bridged diffusion processes without time-reversals.

Time reversal invariance can be summarized as follows: no difference can be measured if a sequence of events is run forward or backward in time. Because price time series are dominated by a randomness that hides possible structures and orders, the existence of time reversal invariance requires care to be investigated. …

This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.

Machine learning infers time-reversible dynamics from data.

New method bypasses time-reversal for diffusion-based generative models.

Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-rever…

We study time reversal, last passage time, and $h$-transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyze the distribution of the time left until killing after the last passage time. With these tools, we develop a…

mfBm models and forecasts volatility with different Hurst exponents and correlations.

New neural net learns time-reversible symplectic dynamics.

Generative model handles varying data dimensions using jump diffusion processes.

TRS-ODENs learn dynamics with time-reversal symmetry for more efficient learning.

DDS samples from noisy data by reversing diffusion, providing theoretical guarantees.

New method simulates diffusion bridges using score matching.

Generative models using PDMPs with explicit jump rates and kernels.

A new method predicts dynamical systems better by using two different latent spaces.

We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are linear and quadratic in past returns. A non-parametric fit on NYSE stock data sho…

We study velocity correlations induced by diffusion and dissipation in a simple dissipative dynamical system. We observe that diffusion, as a result of time reversible microscopic processes, leads to correlations with different spatial parity from those caused by dissipation, consisting of time irreversible microscopic…

We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents $p_\pm$ usually vary with the strength of the lar…

Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential distributions can be accommodated by it. The demonstration is based on a mathematical …

Ultrasound (US) imaging is based on the time-reversal principle, in which individual channel RF measurements are back-propagated and accumulated to form an image after applying specific delays. While this time reversal is usually implemented as a delay-and-sum (DAS) beamformer, the image quality quickly degrades as the…

In this paper we classify maps from a torus phase space $X$ to $\mathcal{H}_n^*$, the space of $n \times n$, non-singular hermitian operators up to equivariant homotopy. The equivariance is with respect to a time-reversal involution on $X$ and an involution on $\mathcal{H}_n^*$ defining a certain symmetry class. Furthe…

We propose a novel method to forecast the future from the present using time-reversed data.

Generalizes JT gravity to time-reversal symmetric theories with fermions and supersymmetry.

We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a Lévy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of $Z…

We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents $p_\pm$ usually vary with the strength of the large vo…

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distribu…

A new ML method predicts long-time-step molecular dynamics, preserving symplectic and time-reversible properties.

We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, test…

New model captures asymmetric rough volatility with Zumbach effect.

Efficiently trains forward processes to minimize generative trajectories curvature.

Unified framework for sampling from complex distributions, including discrete and mixed-variable systems.

The percolation model of stock market speculation allows an asymmetry (in the return distribution) leading to fast downward crashes and slow upward recovery. We see more small upturns and more intermediate downturns.

CD learning is shown to be an adversarial game for fitting models.

PDDS samples from unnormalized densities using iterative particle scheme.

In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…

Paper introduces infinite-dimensional generative models using Doob's h-transform.

Improves generative models by adding jump-diffusion noise.

New insights into 4d YM and 5d topological field theories with higher symmetries.

Deep neural network improves ultrasound imaging quality.

Paper introduces DMPMs for efficient discrete data generation with sharp convergence bounds.

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a u…

There are eight possible Pin groups that can be used to describe the transformation behaviour of fermions under parity and time reversal. We show that only two of these are compatible with general relativity, in the sense that the configuration space of fermions coupled to gravity transforms appropriately under the spa…

Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that…

This paper simplifies OPE in large state spaces using state abstractions.

Improved sampling via learned diffusions using variational losses.

IDBM solves Schrödinger bridge problems with iterative sampling.

This paper extends neural network approximation results to denoising diffusion models.

Study improves sampling efficiency of diffusion models using RL and PDEs.