Publication

Asymptotic generalization error of a single-layer graph convolutional network

2024

Abstract

While graph convolutional networks show great practical promises, the theoretical understanding of their generalization properties as a function of the number of samples is still in its infancy compared to the more broadly studied case of supervised fully connected neural networks. In this article, we predict the performances of a single-layer graph convolutional network (GCN) trained on data produced by attributed stochastic block models (SBMs) in the highdimensional limit. Previously, only ridge regression on contextual-SBM (CSBM) has been considered in [1]; we generalize the analysis to arbitrary convex loss and regularization for the CSBM and add the analysis for another data model, the neural-prior SBM. We derive the optimal parameters of the GCN. We also study the high signal-to-noise ratio limit, detail the convergence rates of the GCN and show that, while consistent, it does not reach the Bayes-optimal rate for any of the considered cases. , Asymptotic generalization error of a single-layer graph convolutional network.

Official source

https://infoscience.epfl.ch/entities/publication/568948be-75e3-4239-96c8-7ce1243d7a83

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2024

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/568948be-75e3-4239-96c8-7ce1243d7a83

About this result

Related concepts (32)

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Types of artificial neural networks

There are many types of artificial neural networks (ANN). Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research.

Recurrent neural network

A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition.

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Asymptotic generalization error of a single-layer graph convolutional network

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