Machines of finite depth: towards a formalization of neural networks
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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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