Tractable Inference with Kolmogorov-Arnold Networks

Key points

• Machine-learning surrogates in computational science often require not only accurate predictions but also expectations, variances, conserved integrals, and normalization constants.1
• Conventional neural networks, including Kolmogorov--Arnold networks (KANs), generally evaluate these quantities through Monte Carlo sampling or multidimensional quadrature, making repeated inference costly, particularly in high dimensions.1
• Under factorizing input measures, expectations and higher moments then reduce algebraically to deterministic recursions over one-dimensional leaf integrals.1
• TOUCKANs also conserved Cahn--Hilliard mass to machine precision and imposed normalization and orthogonality through deterministic moments, enabling joint computation of the lowest four Schrödinger eigenpairs in two, three, and five dimensions.1

Sources (1)

• [1]Tractable Inference with Kolmogorov-Arnold Networks
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 03:49 PM

  We introduce KANs with Tractable Operators for Uncertainty and Constraints (TOUCKANs), whose finite-degree polynomial outer functions yield a decomposable sum--product representation.

  Machine-learning surrogates in computational science often require not only accurate predictions but also expectations, variances, conserved integrals, and normalization constants.

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