Parametric machines: a fresh approach to architecture search
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Using tools from category theory, we provide a framework where artificial neural networks, and their architectures, can be formally described. We first define the notion of machine in a general categorical context, and show how simple machines can be combined into more complex ones. We explore finite- and infinite-depth machines, which generalize neural networks and neural ordinary differential equations. Borrowing ideas from functional analysis and kernel methods, we build complete, normed, infinite-dimensional spaces of machines, and discuss how to find optimal architectures and parameters – within those spaces – to solve a given computational problem. In our numerical experiments, these kernel-inspired networks can outperform classical neural networks when the training dataset is small.
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