# Kan Published articles for Kan. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Geometry-Constrained Kolmogorov-Arnold Networks: Learning Edge Geometry via Banach Duality DevFeed: [Geometry-Constrained Kolmogorov-Arnold Networks: Learning Edge Geometry via Banach Duality]() Original publisher: [Read original article]() Author: K S Sesh Kumar Published: 2026-11-06T05:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Machine learning](), [Artificial Intelligence]() Tags: [adaptive](), [benchmarks](), [bounded](), [convex](), [cs-lg](), [duality](), [kan](), [learning](), [machine-learning](), [power](), [regression](), [stat-ml]() ### AI overview Banach-KAN learns the shape of power-law edge responses through a trainable exponent and combines them with a bounded tanh component. The authors relate these responses to convex potentials and bound edge sensitivity on bounded input ranges. In symbolic regression benchmarks, the method is competitive with fixed-basis models, especially with limited clean data; learned power-law responses remain competitive under measurement noise, while splines perform better with plentiful clean data. Controls on a core subset support learning the exponent and retaining both components. The learned exponents describe fitted edge-response shapes. ### Source excerpt arXiv:2608.25807v2 Announce Type: replace Abstract: 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. ## Kolmogorov-Arnold Networks vs. Multi-Layer Perceptrons: A Rigorous Statistical Benchmark on Clinical Tabular Data DevFeed: [Kolmogorov-Arnold Networks vs. Multi-Layer Perceptrons: A Rigorous Statistical Benchmark on Clinical Tabular Data]() Original publisher: [Read original article]() Author: Rafa{\\l} Wodzi\\'nski, Pawe{\\l} Szczerbiak Published: 2026-11-03T05:00:00Z Content type: article Language: en Sources: [arXiv: Artificial Intelligence](), [arXiv: Machine Learning]() Topics: [Predictive AI](), [Benchmark](), [Hyperparameter optimization](), [Structured-data]() Tags: [architectures](), [bayesian](), [benchmark](), [comparison](), [cross-validation](), [cs-ai](), [cs-lg](), [efficiency](), [hyperparameter-optimization](), [kan](), [latency](), [medical](), [metrics](), [mlp](), [performance](), [precision](), [random](), [tabular-data]() ### AI overview Across seven clinical tabular datasets, nine KAN variants showed no systematic pooled discrimination advantage over a tuned StandardMLP, though TabKAN and ReLUKAN achieved higher AUPRC on severely imbalanced datasets and could improve minority-class detection. The benchmark used repeated stratified cross-validation with nested Bayesian tuning, assessed AUPRC, Brier Score, and efficiency, and applied Bayesian equivalence testing. KANs had 1.20-1.48x longer per-sample inference latency and up to 12.5x more trainable parameters; StandardMLP remained an efficiency-focused baseline, while KANs may suit tasks prioritizing precision on rare positives. ### Source excerpt arXiv:2611.02856v1 Announce Type: new Abstract: Kolmogorov-Arnold Networks (KANs) have recently been proposed as a promising alternative to Multi-Layer Perceptrons (MLPs). However, empirical evaluations on structured medical datasets remain scarce, and commonly reported metrics like AUROC can yield overly optimistic performance estimates on imbalanced clinical cohorts. In this study, we present a standardized benchmark comparing eleven architectures - nine KAN variants (FastKAN, WavKAN, ReLUKAN, ChebyKAN, TaylorKAN, GramKAN, JacobiKAN, LegendreKAN, and TabKAN), a tuned StandardMLP, and a Random Forest baseline - across seven heterogeneous medical tabular datasets spanning oncology, cardiology, nephrology, neurology, endocrinology, and obstetrics. Our experimental protocol employs a 3x5 Repeated Stratified K-Fold cross-validation scheme with nested Bayesian hyperparameter optimization and evaluates discrimination via Area Under the Precision-Recall Curve (AUPRC), calibration through the Brier Score, and computational efficiency. Formal equivalence testing is conducted using the Bayesian Correlated t-Test with a Region of Practical Equivalence (ROPE) at +/- 0.01. The results indicate that on datasets with severe class imbalance, dedicated KAN architectures (particularly TabKAN and ReLUKAN) can improve minority-class detection and achieve higher AUPRC than standard MLPs. Nevertheless, across pooled datasets, KAN variants demonstrate comparable overall predictive discrimination rather than a systematic advantage, while requiring 1.20x to 1.48x longer inference latency per sample and up to 12.5x more trainable parameters. Consequently, StandardMLP remains a strong baseline on the efficiency Pareto frontier, while KAN variants provide a viable alternative when precision on rare positive cases is the primary clinical objective. The code for reproducing the results is available at https://github.com/rafalwodzinski/kan_mlp_comparison. ## Robust Pixel-wise Digital Image Correlation under Large Motions and Illumination Variations via a Global-to-Local Hybrid Neural Field DevFeed: [Robust Pixel-wise Digital Image Correlation under Large Motions and Illumination Variations via a Global-to-Local Hybrid Neural Field]() Original publisher: [Read original article]() Author: Xianglong Guo, Jianyang Li Published: 2026-11-03T05:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Image processing](), [mlp](), [Neural Network]() Tags: [correlation](), [cs-cv](), [cs-lg](), [experiments](), [global](), [hybrid](), [kan](), [kolmogorov-arnold-network](), [mlp](), [neural](), [pixel]() ### AI overview The framework aims to improve pixelwise digital image correlation when motion is large and image brightness changes. It first estimates the dominant in-plane rotation and translation using a coarse rotation search, phase correlation, and masked refinement. It then models residual displacement with a hybrid Kolmogorov-Arnold network (KAN) and multilayer perceptron (MLP), optimized using a valid-overlap structural loss. A local gray-value model accommodates multiplicative and additive intensity changes. The abstract reports accurate, stable recovery in simulated and real experiments involving noise, non-uniform deformation, large rotation, illumination variation, and degraded imaging; it provides no quantitative performance comparisons. ### Source excerpt arXiv:2611.01018v1 Announce Type: cross Abstract: Digital image correlation (DIC) is a widely used non-contact technique for full-field displacement measurement. Data-driven deep-learning DIC offers rapid inference but may generalize poorly to unseen speckle patterns, deformation modes, noise levels, and illumination conditions. Classical optimization-based DIC and recent image-constrained neural formulations avoid labeled displacement data, yet their convergence and accuracy remain vulnerable to initialization, large rigid-body motion, fine non-uniform deformation, and gray-value disturbances. This paper presents a global-to-local hybrid neural DIC framework for robust pixelwise measurement. Stage 1 estimates a dominant in-plane rigid transformation through coarse rotation search, phase correlation, and masked refinement, providing a reliable initialization under large translation and rotation. Stage 2 represents the residual displacement with a hybrid Kolmogorov-Arnold network (KAN) and multilayer perceptron (MLP), and optimizes it using a valid-overlap, illumination-robust structural loss. The local gray-value model explicitly accommodates multiplicative and additive intensity changes. Simulated and real experiments demonstrate accurate and stable displacement recovery under noise, non-uniform deformation, large rotation, illumination variation, and degraded imaging conditions. ## Building and Visualising Kolmogorov-Arnold Networks DevFeed: [Building and Visualising Kolmogorov-Arnold Networks]() Original publisher: [Read original article]() Author: Sam Everest Published: 2026-10-28T12:30:00Z Content type: article Language: en Sources: [Towards Data Science]() Topics: [Neural Network](), [Machine learning](), [Artificial Intelligence](), [Tool]() Tags: [architecture](), [building](), [data](), [data-science](), [editor-s-picks](), [explainable-ai](), [exploring](), [functions](), [kan](), [kolmogorov-arnold-network](), [machine-learning](), [networks](), [neural](), [neural-networks](), [science](), [symbolic-regression]() ### AI overview Kolmogorov-Arnold networks replace scalar connection weights with learnable univariate functions, making the transformations on edges inspectable and, with suitable functions, convertible into equations. In the author's LabLayer experiments, quadratic edge functions approximated a simple two-input target and collapsed directly to a polynomial. B-splines offered greater flexibility but produced piecewise expressions that were harder to simplify; Chebyshev polynomial edges yielded explicit global polynomials and recovered simple synthetic relationships. On Lorenz data, a single layer captured the additive first equation but could not represent the second and third equations' interaction terms. Adding depth enabled interactions, but stable training required normalization and a learning rate of 0.00001. Recovery depended strongly on sampling: fitting a trajectory could predict it without recovering its governing equations, while independently sampled state-space points and repeated runs produced some close coefficient recoveries. The experiments are preliminary and use substantial prior knowledge; prediction accuracy alone does not establish equation recovery. ### Source excerpt Exploring what happens when neural networks learn functions instead of weights. The post Building and Visualising Kolmogorov-Arnold Networks appeared first on Towards Data Science.