Machines of finite depth: towards a formalization of neural networks

• URL: http://arxiv.org/abs/2204.12786v1
• Date: Wed, 27 Apr 2022 09:17:15 GMT
• Title: Machines of finite depth: towards a formalization of neural networks
• Authors: Pietro Vertechi and Mattia G. Bergomi
• Abstract summary: We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. We prove this statement theoretically and practically, via a unified implementation that generalizes several classical architectures--dense, convolutional, and recurrent neural networks with a rich shortcut structure--and their respective backpropagation rules.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a precise definition, from which several properties follow naturally. Machines of finite depth are modular (they can be combined), efficiently computable and differentiable. The backward pass of a machine is again a machine and can be computed without overhead using the same procedure as the forward pass. We prove this statement theoretically and practically, via a unified implementation that generalizes several classical architectures--dense, convolutional, and recurrent neural networks with a rich shortcut structure--and their respective backpropagation rules.

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