arXiv research

Learn true model from metastable samples of discrete distributions.

New methods use machine learning to simulate rare transitions in molecular systems.

New method detects metastable basins in high dimensions using trajectory sampling.

The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task, due to the curse of dimensionality and the scarcity of transition data. In this paper,…

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-siz…

A new framework uses stochastic optimal control to estimate rare events more accurately.

This paper addresses metaconsistency in Bayesian inference for metastable systems.

Paper tackles sampling from non-log-concave distributions using denoising diffusion.

Proves triviality of inertia groups in high-dimensional manifolds.

Enhanced VMC methods improve neural wavefunction training.

Lipid necks, large curvature bridges, are shown to be metastable.

We introduce a machine learning approach for extracting fine-grained representations of protein evolution from molecular dynamics datasets. Metastable switching linear dynamical systems extend standard switching models with a physically-inspired stability constraint. This constraint enables the learning of nuanced repr…

Timewarp accelerates molecular dynamics by learning to simulate long timescales.

In this paper we first analyzed the inductive bias underlying the data scattered across complex free energy landscapes (FEL), and exploited it to train deep neural networks which yield reduced and clustered representation for the FEL. Our parametric method, called Information Distilling of Metastability (IDM), is end-t…

This paper is on the classical Knotting Problem: for a given manifold N and a number m describe the set of isotopy classes of embeddings $N\to S^m$. We study the specific case of knotted tori, i. e. the embeddings $S^p \times S^q \to S^m$. The classification of knotted tori up to isotopy in the metastable dimension ran…

This paper studies how to find compact state embeddings from high-dimensional Markov state trajectories, where the transition kernel has a small intrinsic rank. In the spirit of diffusion map, we propose an efficient method for learning a low-dimensional state embedding and capturing the process's dynamics. This idea a…

An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…

The paper studies how search and distillation improve reasoning in large language models.

New method clusters directed graphs using Koopman operators.

Study shows social reinforcement learning can lead to persistent but metastable polarization.

ISOKANN learns collective variables and effective dynamics for metastable transitions.

An algorithmically hard phase was described in a range of inference problems: even if the signal can be reconstructed with a small error from an information theoretic point of view, known algorithms fail unless the noise-to-signal ratio is sufficiently small. This hard phase is typically understood as a metastable bran…

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanis…

New method makes machine learning approximations unbiased and efficient.

Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.

We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to …

Study improves policy search in continuous control by using heavy-tailed distributions.

Develops methods to simulate rare transitions in molecular systems.

We study the detailed path-wise behavior of the discrete-time Langevin algorithm for non-convex Empirical Risk Minimization (ERM) through the lens of metastability, adopting some techniques from Berglund and Gentz (2003. For a particular local optimum of the empirical risk, with an arbitrary initialization, we show tha…

Jeffreys Flow improves robustness of Boltzmann generators for rare event sampling.

Study finds the number of modes in Gaussian kernel density estimators scales with sqrt(β log β).

Discovering quasipotential equations from data using machine learning.

Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embe…

Given Poincare spaces M and X, we study the possibility of compressing embeddings of M x I in X x I down to embeddings of M in X. This results in a new approach to embedding in the metastable range both in the smooth and Poincare duality categories.

The purpose of this note is to attract attention to the following conjecture (metastable $r$-fold Whitney trick) by clarifying its status as not having a complete proof, in the sense described in the paper. Assume that $D=D_1\sqcup\ldots\sqcup D_r$ is disjoint union of $r$ disks of dimension $s$, $f:D\to B^d$ a proper …

RC flow learns molecular kinetics in low dimensions.

Study shows bifurcating price dynamics in ASME with traders.

Let EMBED(k,d) be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into R^d? Known results easily imply polynomiality of EMBED(k,2) (k=1,2; the case k=1, d=2 is graph planarity) and of EMBED(k,2k) for all k>2 (even if k i…

We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection-diffusion equation to Lagrangian coordinates, in which it takes the form of a time-dependent diffusion or h…

We develop a new approach to the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. This approach involves studying of a new embedding invariant, of almost-embeddings and of smoothing, as well as explicit constructions of embeddings. Using this approach we obtain complete conc…

Efficiently simulates slow dynamics of high-dimensional stochastic systems.

This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the assumption that it can be deformed off of any proper subcollection in a homotopy c…

Algorithm learns stochastic system dynamics from data.

A clear understanding of topology of higher-dimensional objects is important in many branches of both pure and applied mathematics. In this survey we attempt to present some results of higher-dimensional topology in a way which makes clear the visual and intuitive part of the constructions and the arguments. In particu…

Stochastic defense improves natural classifiers against adversarial attacks.

Although standard economics textbooks are seldom interested in production networks, modern economies are more and more based upon suppliers/customers interactions. One can consider entire sectors of the economy as generalised supply chains. We will take this view in the present paper and study under which conditions lo…

This paper is devoted to the classification of embeddings of higher dimensional manifolds. We study the case of embeddings $S^p\times S^q\to S^m$, which we call knotted tori. The set of knotted tori in the the space of sufficiently high dimension, namely in the metastable range $m\ge p+3q/2+2$, $p\le q$, which is a nat…

A new method uses string method to explore diffusion models.