SAMPAT: A New Interpretable Neural Architecture for Smooth Functions

Jayadeva, Madhur Aswani· July 13, 2026 View original

Summary

Researchers introduce SAMPAT, a three-layer neural architecture designed to learn continuous, differentiable functions and approximate any smooth function with high interpretability. It provides a closed-form algebraic expression for its approximant, offering complete transparency.

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.

Why it matters

Professionals in fields requiring transparent models can leverage SAMPAT to gain deeper insights from experimental data, moving beyond black-box predictions to understandable algebraic relationships. This is crucial for scientific discovery and regulatory compliance.

How to implement this in your domain

  1. 1Evaluate SAMPAT's performance on specific domain datasets where interpretability is paramount.
  2. 2Integrate SAMPAT into existing machine learning pipelines for tasks requiring transparent function approximation.
  3. 3Explore its ability to factorize polynomials or model nonlinear systems in engineering or scientific applications.
  4. 4Compare its computational efficiency and accuracy against current interpretable models.

Who benefits

HealthcarePharmaceuticalsScientific ResearchFinancial ServicesManufacturing

Key takeaways

  • SAMPAT is a novel neural architecture offering provable interpretability for smooth function approximation.
  • It generates closed-form algebraic expressions, providing complete transparency into its learned models.
  • The architecture demonstrates competitive performance with fewer layers and supports diverse approximation types.
  • Its interpretability is valuable for scientific insight and applications requiring transparent AI.

Original post by Jayadeva, Madhur Aswani

"arXiv:2607.09235v1 Announce Type: new 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 quantitat…"

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Originally posted by Jayadeva, Madhur Aswani on X · view source

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