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New theory on spline KANs addresses approximation-stability tension

By PulseAugur Editorial · [1 sources] ·

This paper introduces a novel approach to approximating deep spline superposition networks within a strict layerwise Lipschitz budget. It defines two key quantities: factorisation stability complexity and budget-compatible approximation complexity. The research provides an exact solution for finite-depth diagonal balancing problems and a constructive spline discretisation theorem that maintains the budget with controlled slack. Additionally, it establishes minimax lower bounds for linear spline-valued operators and demonstrates that layer errors do not necessarily cancel under composition. AI

IMPACT Introduces theoretical frameworks for improving the stability and approximation capabilities of deep spline networks within computational constraints.

RANK_REASON The item is an academic paper detailing theoretical advancements in spline KANs. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New theory on spline KANs addresses approximation-stability tension

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The item is an academic paper detailing theoretical advancements in spline KANs. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Aleksander Tankman ·

    Stability-Constrained Approximation in Spline KANs: Exact Layer Balancing and Budget-Compatible Saturation

    arXiv:2609.17619v1 Announce Type: new Abstract: Deep spline superposition networks face a tension between approximation order and stability across depth. We study approximation under a hard layerwise Lipschitz budget, and organise it around two quantities: the factorisation stabi…

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