Related papers: The world as a neural network

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems.…

Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…

A theory of neural networks (NNs) built upon collective variables would provide scientists with the tools to better understand the learning process at every stage. In this work, we introduce two such variables, the entropy and the trace of…

Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…

The relation between neural activity and behaviorally relevant variables is at the heart of neuroscience research. When strong, this relation is termed a neural representation. There is increasing evidence, however, for partial…

The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neural network architectures. Recent works have experimentally shown that two different solutions found…

Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…

Learning relies on coordinated synaptic changes in recurrently connected populations of neurons. Therefore, understanding the collective evolution of synaptic connectivity over learning is a key challenge in neuroscience and machine…

We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein…

This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. Specifically, we develop neural networks as a composition of several vector-valued functions. Although neural networks are…

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…

Many experiments have been performed that use evolutionary algorithms for learning the topology and connection weights of a neural network that controls a robot or virtual agent. These experiments are not only performed to better understand…

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a…

Despite their great success, neural networks still remain as black-boxes due to the lack of interpretability. Here we propose a new analyzing method, namely the weight pathway analysis (WPA), to make them transparent. We consider weights in…

We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…

In certain situations, neural networks will represent environment states in their hidden activations. Our goal is to visualize what environment states the networks are representing. We experiment with a recurrent neural network (RNN)…

Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…

We consider optimizing two-layer neural networks in the mean-field regime where the learning dynamics of network weights can be approximated by the evolution in the space of probability measures over the weight parameters associated with…

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…