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Semialgebraic Neural Networks

A neural-network architecture (SANN) that exactly represents any bounded semialgebraic function by parameterizing the vector field of an ODE from a polynomial homotopy-continuation root-finding method and integrating it with a numerical ODE solver, built from polynomials and ReLU activations and capable of representing discontinuous semialgebraic functions.

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Published as a conference paper at ICLR 2025 SEMIALGEBRAIC NEURAL NETWORKS: FROM ROOTS TO

Semialgebraic Neural Networks (SANNs) are a neural-network architecture that can exactly represent any bounded semialgebraic function - a function whose graph is defined by finitely many polynomial e…