algebraic-geometry

Approximating Latent Manifolds in Neural Networks via Vanishing Ideals

May 30, 2025 · Our ICML25 paper Approximating Latent Manifolds in Neural Networks via Vanishing Ideals introduces a novel approach to understanding data representation in neural networks through vanishing ideals. To characterize the structure of latent spaces, we scale vanishing ideal algorithms to handle high-dimensional data. The resulting algebraic characterizations can be used to replace standard network layers with more compact and efficient polynomial layers, leading to significant parameter reduction and potential improvements in inference speed while maintaining competitive performance.