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Article Type

Research Article

Abstract

Kolmogorov-Arnold Networks (KANs) replace fixed node activations with learnable univariate edge functions, but standard KAN inference treats two equal-valued features identically even when one is accompanied by an explicit quality warning. NIT-KAN introduces a neutrosophic indeterminacy-transport mechanism for this setting. Each node carries an indeterminacy state in [0, 1]; a monotone gate g(I)=(1-I)α attenuates uncertain evidence on the predictive path, while a sensitivity-weighted transport rule carries indeterminacy through the underlying KAN computation. A terminal audit maps signed evidence to truth-support, falsity-support, and conflict-augmented indeterminacy without interpreting these quantities as class probabilities. We establish boundedness, monotone suppression, sensitivity relevance, exact reduction of the predictive path to the base KAN when input indeterminacy vanishes, and a first-order local perturbation-variance bound. The no-free-lunch principle is used only to delimit the claim: the proposed inductive bias is expected to help when feature-level indeterminacy is informative about structured corruption. Ten-seed experiments on the Wisconsin Diagnostic Breast Cancer dataset and a controlled Structured Sources benchmark support this conditional claim. Under 70% noisy-feature corruption, accuracy increased from 78.13% to 90.18% on WDBC and from 86.55% to 96.50% on Structured Sources; the corresponding Brier scores decreased from 0.1628 to 0.0846 and from 0.1062 to 0.0371. All four primary stress comparisons remained significant after Holm correction (adjusted p ≤ 0.0039). On clean WDBC, the base KAN retained a small accuracy advantage, consistent with specialization rather than universal dominance.

Keywords

Neutrosophic learning, Kolmogorov-Arnold networks, Indeterminacy transport, Uncertainty-aware learning, Structured corruption, No-free-lunch, Inductive bias, Robustness, Calibration

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