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arXiv Machine Learning By Victor Bovdi, Ambrus Pal

Proofs of strong forms of the Bovdi--Geche universality conjecture and a complex analogue

Read the original on arXiv Machine Learning →

The paper proves two universality theorems for single‑neuron neural networks. First, it establishes a strong form of the Bovdi–Geche universality conjecture for neurons over finite fields, employing a modified discrete logarithm activation function and the Weil bound on multiplicative character sums. Second, it generalises Aizenberg’s universality theorem to complex binary neurons with a weight vector independent of the target function, using an equidistribution theorem for dilates of maps into tori.

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