SAMPAT: A New Interpretable Neural Architecture for Smooth Functions

Traditional deep neural networks often lack interpretability, making it difficult for scientists to gain insights beyond quantitative predictions. A new neural architecture, SAMPAT (Smooth Approximation via Multivariate Polynomials and Analytic Transformations), addresses this by offering a provably interpretable model. SAMPAT is a three-layer network capable of learning continuous, everywhere differentiable functions that can closely approximate any smooth function. Its key innovation is expressing the learned approximation as a compact, closed-form algebraic and analytic expression, ensuring full transparency into its workings. Experiments on various datasets show SAMPAT achieves competitive performance, often with just two layers. The architecture's design allows for flexible approximation types, including polynomials, rational expressions, and Gaussians, and can even optimize the model family during learning when combined with skip connections.