All you need is SAMPAT

• URL: http://arxiv.org/abs/2607.09235v1
• Date: Fri, 10 Jul 2026 09:31:01 GMT
• Title: All you need is SAMPAT
• Abstract summary: Interpretability is crucial to gleaning insights while analyzing experimental data.<n>We present a three layer neural architecture, SAMPAT, that can provably learn a continuous, everywhere differentiable function.<n>Experiments on synthetic and benchmark datasets indicate that SAMPAT yields competitive performance with simpler representations.
• Score: 4.978871870250063
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The current state of the art in AI/ML rests on deep neural architectures, which, in general, suffer from a lack of interpretability. Interpretability is crucial to gleaning insights while analyzing experimental data, where quantitative predictions may not be adequate for a scientist. We present a three layer neural architecture, SAMPAT (Smooth Approximation via Multivariate Polynomials and Analytic Transformations), that can provably learn a continuous, everywhere differentiable function, that can approximate any smooth function arbitrarily closely. SAMPAT's approximant can be expressed as a closed and compact algebraic, analytic expression, providing complete interpretability. Experiments on synthetic and benchmark datasets indicate that SAMPAT yields competitive performance with simpler representations. For many tasks, a two layer SAMPAT suffices. By imposing restrictions on the connectivity between neurons, SAMPAT may be used to provide a range of approximants, including regular and trigonometric polynomials, rational expressions, Gaussians, mixtures of Gaussians, as well as arbitrary combinations of the same; without restrictions, it learns a suitable structure. SAMPAT may be used to factorize polynomials and model nonlinear systems. With the addition of skip connections, a 4 to 6 layer SAMPAT is adequate to represent a substantive range of methods widely used in AI/ML, allowing the choice of a model's family, not just its parameters, to also be optimized as part of the learning process.

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