相关论文: Generalization in the Hopfield Model

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and…

A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…

Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…

The robust generalization of models to rare, in-distribution (ID) samples drawn from the long tail of the training distribution and to out-of-training-distribution (OOD) samples is one of the major challenges of current deep learning…

In this preregistration submission, we propose an empirical study of how networks handle changes in complexity of the data. We investigate the effect of network capacity on generalization performance in the face of increasing data…

The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…

The Hopfield network is reconstructed as an inverse Ising problem by passing messages. The applied susceptibility propagation algorithm is shown to improve significantly on other mean-field-type methods and extends well into the low…

While it has not yet been proven, empirical evidence suggests that model generalization is related to local properties of the optima which can be described via the Hessian. We connect model generalization with the local property of a…

Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of…

This paper studies how the generalization ability of neurons can be affected by mutual processing of different signals. This study is done on the basis of a feedforward artificial neural network. The mutual processing of signals can…

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence…

Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…

The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…

Message-passing graph neural networks (MPNNs) have emerged as the leading approach for machine learning on graphs, attracting significant attention in recent years. While a large set of works explored the expressivity of MPNNs, i.e., their…

There are two prominent paradigms to the modeling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the…

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Hybrid optical neural networks (HONNs) offload some electronic computation to optical preprocessors to achieve low-power and fast training and inference phases in machine learning tasks. Our contribution to the development of HONNs is a…

Using message-passing graph neural networks (MPNNs) for node and link prediction is crucial in various scientific and industrial domains, which has led to the development of diverse MPNN architectures. Besides working well in practical…

Humans have an impressive ability to reason about new concepts and experiences from just a single example. In particular, humans have an ability for one-shot generalization: an ability to encounter a new concept, understand its structure,…