Related papers: Ising models of deep neural networks

We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…

In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the…

Energy-based models (EBMs) are a simple yet powerful framework for generative modeling. They are based on a trainable energy function which defines an associated Gibbs measure, and they can be trained and sampled from via well-established…

Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings,…

Deep learning uses neural networks which are parameterised by their weights. The neural networks are usually trained by tuning the weights to directly minimise a given loss function. In this paper we propose to re-parameterise the weights…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…

This article describes a gradient complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown analytically and experimentally that the strength…

Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…

Recently, there have been many works on the deep learning of statistical ensembles to determine the critical temperature of a possible phase transition. We analyze the detailed structure of an optimized deep learning machine and prove the…

We show experimentally that the accuracy of a trained neural network can be predicted surprisingly well by looking only at its weights, without evaluating it on input data. We motivate this task and introduce a formal setting for it. Even…

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…

Networked structure emerged from a wide range of fields such as biological systems, World Wide Web and technological infrastructure. A deeply insight into the topological complexity of these networks has been gained. Some works start to pay…

This paper presents an empirical study on the weights of neural networks, where we interpret each model as a point in a high-dimensional space -- the neural weight space. To explore the complex structure of this space, we sample from a…

To what extent is the success of deep visualization due to the training? Could we do deep visualization using untrained, random weight networks? To address this issue, we explore new and powerful generative models for three popular deep…

Tie strength prediction, sometimes named weight prediction, is vital in exploring the diversity of connectivity pattern emerged in networks. Due to the fundamental significance, it has drawn much attention in the field of network analysis…

Training a neural network is synonymous with learning the values of the weights. By contrast, we demonstrate that randomly weighted neural networks contain subnetworks which achieve impressive performance without ever training the weight…

The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random and external field strength. Thermal states and thermodynamic properties are obtained for all…