Journal Article

FZJ-2026-05277

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Kolmogorov–Arnold deep sampling networks: Data-adaptive multi-scale framework for high-fidelity brain connectivity and information transfer

Kadak, U.

2026
Elsevier Amsterdam [u.a.]

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Please use a persistent id in citations: doi:10.1016/j.bspc.2026.111271

Abstract: The estimation of functional connectivity (FC) from fMRI BOLD signals is limited by the inability of standard correlation measures to resolve weak, non-stationary inter-network dynamics, while classical sampling operators remain confined to fixed, analytically pre-specified kernels that cannot adapt to the heterogeneous temporal signatures of distinct brain regions. To close this gap, this paper introduces the Kolmogorov–Arnold deep sampling networks (KAN-DSN), the first framework to embed learnable Kolmogorov–Arnold Network (KAN) kernels within a provably convergent multilayer Durrmeyer integral-synthesis operator. The central novelty is the unification of two previously disjoint paradigms: the data-adaptive flexibility of KANs and the non-expansive convergence guarantees of sampling theory. Replacing rigid averaging windows with data-adaptive univariate splines under projected-gradient, normalization-preserving training yields a representation that suppresses noise while preserving large-scale signal structure, and the scale parameter w1 provides a tunable temporal resolution unavailable to single-scale estimators. Rigorous approximation-theoretic analysis establishes pointwise and uniform convergence, with quantitative Lp error estimates of O(w−α) for Lipschitz classes. Per-subject empirical validation on fMRI data (N=30) shows that KAN-DSN raises pairwise correlations across essentially all 231 region-of-interest (ROI) pairs, strengthening weak between-network couplings more than within-network ones (Δr=+0.103 vs. ＋0.085 at w1=0.5) and increasing suprathreshold edges (r>0.3) from 39 to 83, while preserving within-network block structure and removing the spurious negative correlations of the Pearson baseline. The recovered connections are neurobiologically specific, matching canonical resting-state network pairs from the independent literature. Analysed across w1, the operator further decomposes directed information transfer: it systematically reduces model-free Transfer Entropy (TE) while strengthening linear, lag-based Granger Causality (GC) — most consistently at w1=0.5 (25/30 subjects, p≈10−5) — and the Visual→Limbic directionality ratio peaks at w1=0.8, supporting w1 as a temporal-scale parameter for directed connectivity. Together, these results establish KAN-DSN as a principled bridge between Durrmeyer sampling theory and learnable deep architectures, extending functional connectivity analysis from a fixed-kernel, single-scale correlation measure to a trainable, convergent, multi-scale estimator.

Keyword(s): Medicine (2nd)

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