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High-Order Tensor Formulation of Convolution in Sparse CNNs

A tensor-algebra framework that formulates convolution over high-order tensors in real Hilbert spaces and builds a generic theory of regression for sparse convolutional neural networks, from which the backpropagation algorithm is re-derived in its simplest, most generic tensor-based form. The emphasis is mathematical clarity and generality rather than a new empirical model.

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High-Order Tensor Regression in Sparse Convolutional Neural Networks Roberto Dias Algarte∗

This theoretical article reformulates convolution in machine learning using high-order tensor algebra over real Hilbert spaces rather than conventional array-based notation. Working with tensors as e…