← 研踪 PaperTrailarXiv:2608.25807 · v2
Geometry-Constrained Kolmogorov-Arnold Networks: Learning Edge Geometry via Banach Duality
首次提交 2026-08-26 21:53
版本更新 2026-11-05 18:36
雷达观测 2026-11-06 12:09
摘要
Kolmogorov-Arnold Networks (KANs) learn univariate functions on edges, making the choice of edge response central to their design. Existing variants use basis expansions such as splines or polynomials, whose functional form is chosen before training. We introduce geometry-constrained KANs, which instead learn the shape of power-law edge responses through an exponent inspired by Banach duality maps. Banach-KAN combines this adaptive power-law response with a bounded hyperbolic tangent (tanh) component. We relate these responses to convex potentials and bound edge sensitivity on bounded input ranges. Across symbolic regression benchmarks, Banach-KAN is competitive with fixed-basis models, particularly with limited clean data. Learned power-law responses remain competitive under measurement noise, while splines are stronger with plentiful clean data. Fixed-exponent and branch-removal controls on a core subset support learning the exponent and retaining both Banach components. Learned exponents describe the shapes of the fitted edge responses.
作者备注：Accepted at NeurIPS 2026 Code: https://github.com/seshkumar/geometric-kan-neurips2026
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-05 18:36 · 最新观测版本
Geometry-Constrained Kolmogorov-Arnold Networks: Learning Edge Geometry via Banach Duality
Kolmogorov-Arnold Networks (KANs) learn univariate functions on edges, making the choice of edge response central to their design. Existing variants use basis expansions such as splines or polynomials, whose functional form is chosen before training. We introduce geometry-constrained KANs, which instead learn the shape of power-law edge responses through an exponent inspired by Banach duality maps. Banach-KAN combines this adaptive power-law response with a bounded hyperbolic tangent (tanh) component. We relate these responses to convex potentials and bound edge sensitivity on bounded input ranges. Across symbolic regression benchmarks, Banach-KAN is competitive with fixed-basis models, particularly with limited clean data. Learned power-law responses remain competitive under measurement noise, while splines are stronger with plentiful clean data. Fixed-exponent and branch-removal controls on a core subset support learning the exponent and retaining both Banach components. Learned exponents describe the shapes of the fitted edge responses.
查看此版本解读 →查看此版本原文 ↗