Interrelation of equivariant Gaussian processes and convolutional neural networks
This work provides a foundational link between two key areas in machine learning, potentially advancing theoretical understanding for researchers in equivariant models and Gaussian processes.
The paper establishes a theoretical connection between the many-channel limit of equivariant convolutional neural networks (CNNs) and equivariant Gaussian processes (GPs), specifically for two-dimensional Euclidean groups with vector-valued activations.
Currently there exists rather promising new trend in machine leaning (ML) based on the relationship between neural networks (NN) and Gaussian processes (GP), including many related subtopics, e.g., signal propagation in NNs, theoretical derivation of learning curve for NNs, QFT methods in ML, etc. An important feature of convolutional neural networks (CNN) is their equivariance (consistency) with respect to the symmetry transformations of the input data. In this work we establish a relationship between the many-channel limit for CNNs equivariant with respect to two-dimensional Euclidean group with vector-valued neuron activations and the corresponding independently introduced equivariant Gaussian processes (GP).