ИСТИНА

The topic within which this work was carried out is related to the establishment of relationships between various methods of machine learning (ML). The ultimate goal of establishing such interrelations is to achieve a better theoretical understanding of these methods and their improvement. In particular, a correspondence has recently been established between the appropriate asymptotics of deep neural networks (DNNs), including convolutional ones (CNNs), and the ML method based on Gaussian processes. Since Gaussian processes are mathematically equivalent to free (Euclidean) quantum field theory (QFT), one of the intriguing consequences of these relationships is the potential for using a broad range of QFT methods for analyzing DNNs. There are evidences (including experimental) that non-asymptotic (that is, implementable in practice) DNNs correspond to QFT with interactions. An important feature of convolutional networks 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 of equivariant CNNs and the corresponding equivariant Gaussian process (GP), and hence the QFT with the appropriate symmetry. The approach used provides explicit equivariance at each stage of the derivation of the relationship.