Related papers: Learning collective variables that respect permuta…

Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…

We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms (also known as collective variables) is known a priori.…

This paper proposes a general interpretable predictive system with shared information. The system is able to perform predictions in a multi-task setting where distinct tasks are not bound to have the same input/output structure. Embeddings…

A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction…

Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…

In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions.…

We present a new and efficient method for computing the transition pathways, free energy barriers, and transition rates in complex systems with relatively smooth energy landscapes. The method proceeds by evolving strings, i.e. smooth curves…

We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…

We study discrete-time dynamical systems that switch between different evolution rules based on thresholds that themselves adapt over time. Specifically, we analyze the coupled recursion $a_{n+1} = f(a_n)$ if $a_n \leq c_n$ and $a_{n+1} =…

Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…

Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in…

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…

We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the…

Language models trained on natural text learn to represent numbers using periodic features with dominant periods at $T=2, 5, 10$. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs,…

Disentangled representation learning offers useful properties such as dimension reduction and interpretability, which are essential to modern deep learning approaches. Although deep learning techniques have been widely applied to…

Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant.…

We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over…

We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…

How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional…

Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…