Simplicial Neural Networks:First Steps and Future Applications
It is well-known that artificial neural networks are universal approximators. The Universal Approximation Theorem proves that, given a continuous function on a compact set embedded in an $n$-dimensional space, there exists a one-hidden-layer feed-forward network that approximates the function; however, it does not provide a way of building such a network. In previous work, the authors presented a constructive approach to tackle this problem for the case of a continuous function on triangulated spaces by connecting the Simplicial Approximation Theorem, a classical result from algebraic topology, and the Universal Approximation Theorem. In this paper, we revisit such a result and propose future applications.
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