Comparison of extrapolation in ReLU MLPs and GNNs. The left part of the image shows a plot of the predictions of MLPs both within and outside the training data range. The right part of the image shows a hypothetical architecture of GNNs with appropriate non-linearities in the input representation. The center of the image shows a text box with the main hypotheses and theorems supporting them.

How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks

Neural networks have been successful in a variety of tasks due to their ability to learn and generalize patterns in the input data. One common task is to learn a function that maps inputs to outputs through supervised learning. Feedforward to graph neural networks are a type of neural network that processes fixed-size inputs layer by layer, propagating information forward until they produce a final output. During training, they learn to generalize patterns in the input data to make predictions on new, unseen data.

However, the extrapolation capability of feedforward neural networks is limited to the inputs that they have seen during training. They may not be able to generalize well to inputs outside the training data distribution. This limitation motivates the development of more powerful neural network models that can extrapolate to new and unseen inputs.

Graph neural networks (GNNs) are a type of neural network that generalizes feedforward networks to process graph-structured data. Unlike feedforward networks, GNNs use message passing to aggregate information from neighboring nodes and edges in a graph. This allows them to generalize patterns to unseen graph structures, making them suitable for extrapolation tasks.

During training, GNNs learn to extract and encode features from the input graph. This allows them to make predictions for new graphs, including graphs with varying size and structure. By leveraging graph convolutions and pooling operations, GNNs can handle complex graph topologies and generalize well to unseen data.

One of the key advantages of GNNs is their ability to model relationships between nodes in a graph. For example, in a social network graph, nodes represent individuals and edges represent relationships between individuals. GNNs can capture information about the relationships between individuals to make predictions about the behavior of the network as a whole.

NNs have successfully applied to various tasks, such as node classification, link prediction, and graph classification. Researchers and engineers have also utilized them in applications such as drug discovery, recommendation systems, and social network analysis.

In conclusion, while feedforward neural networks are powerful models, they are limited in their ability to extrapolate to new and unseen inputs. GNNs provide a more powerful framework for processing graph-structured data and can generalize well to new and unseen graph structures. As such, they are becoming increasingly popular in many areas of research and industry.

how neural networks extrapolate: from feedforward to graph neural networks pdf

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