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Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks This post is a high-level explainer for my Master’s thesis, which involves designing hardware architectures for ultrafast inference and online learning using the Kolmogorov-Arnold Network (KAN) architecture. I’ll assume familiarity with standard machine learning concepts, as well as some understanding of hardware and digital circuits; read my previous post here for the latter. Please read the two papers below for more...
GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions
arXiv:2512.09084v3 Announce Type: replace Abstract: The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes. While recent implementations such as Kolmogorov-Arnold Networks (KANs) demonstrate high approximation capabilities, they suffer from significant parameter inefficiency due to the requirement of maintaining unique parameterizations for every network edge. In this...
Interpretable Graph Kolmogorov-Arnold Networks for Multi-Cancer Classification and Biomarker Identification using Multi-Omics Data
arXiv:2503.22939v4 Announce Type: replace Abstract: The integration of heterogeneous multi-omics datasets at a systems level remains a central challenge for developing analytical and computational models in precision cancer diagnostics. This paper introduces Multi-Omics Graph Kolmogorov-Arnold Network (MOGKAN), a deep learning framework that utilizes messenger-RNA, micro-RNA sequences, and DNA methylation samples together with Protein-Protein Interaction (PPI) networks for cancer...
Inferring hidden forcing in a biological oscillator using Kolmogorov-Arnold networks
arXiv:2606.08479v1 Announce Type: new Abstract: Inferring the forces that drive a dynamical system from partial observations is a fundamental challenge across physics, particularly when distinct underlying mechanisms produce similar observable dynamics. Here we show that the effective muscular forcing underlying avian respiratory dynamics can be reconstructed from measurements of air-sac pressure alone. Using an interpretable learning framework based on Kolmogorov-Arnold networks, we infer...
Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks
Announce Type: replace Abstract: We analyze the universal approximation property of Kolmogorov-Arnold Networks (KANs) in terms of their edge functions. If these functions are all affine, then universality clearly fails. How many non-affine functions are needed, in addition to affine ones, to ensure universality?
Sub-Kolmogorov Intermittency and Multifractal Dissipation in Multiphase Turbulence
arXiv:2606.05788v1 Announce Type: new Abstract: Multiphase turbulence displays stronger intermittency than its single-phase counterpart, yet the origin and geometrical organization of its most intense small-scale fluctuations remain poorly understood. Using direct numerical simulations of the incompressible Navier--Stokes equations with surface tension, we show that the local dissipative cutoff broadens strongly in the presence of interfaces, with dissipative events extending deep into the...
Kolmogorov equations for evaluating the boundary hitting of degenerate diffusion with unsteady drift
arXiv:2501.02729v5 Announce Type: replace Abstract: Jacobi diffusion is a representative diffusion process whose solution is bounded in a domain under certain drift and diffusion coefficient conditions. However, the process without such conditions has not been thoroughly investigated. We explore a Jacobi diffusion whose drift coefficient is affected by another deterministic process, causing the process to hit the boundary of a domain in finite time.
Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysis
arXiv:2603.28257v2 Announce Type: replace-cross Abstract: KAN-PCA is an autoencoder that uses a KAN as encoder and a linear map as decoder. It generalizes classical PCA by replacing linear projections with learned B-spline functions on each edge. The motivation is to capture more variance than classical PCA, which becomes inefficient during market crises when the linear assumption breaks down and correlations between assets change dramatically.
Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning
arXiv:2606.02936v1 Announce Type: new Abstract: In this manuscript, we propose and analyze hierarchical Kolmogorov--Arnold neural network architectures employing radial basis functions as activation functions for approximating deterministic functions and random field models. Specifically, we develop a hierarchical radial-basis-function Kolmogorov--Arnold network (hierarchical RBF-KAN) for multidimensional deterministic function approximation and a hierarchical radial-basis-function...
Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition
arXiv:2511.21731v2 Announce Type: replace Abstract: We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell's inequalities are significantly violated, which indicates the presence of a 'non-classical probability model' with probabilities that do not satisfy Kolmogorov's axioms. In the second test, also performed using ChatGPT and...