A review of Kolmogorov-Arnold networks for medical image analysis

Kolmogorov-Arnold Networks (KANs) replace selected scalar weights or fixed activations with learnable univariate edge functions. We conducted a controlled retrospective evidence reconstruction and update of Crossref, Europe PMC, arXiv, and OpenAlex, supplemented by local full texts and citation tracking, for studies published from January 2024 to February 2026. After report-level screening and version consolidation, 138 independent medical-imaging studies met explicitly defined medical-imaging eligibility criteria (127 direct imaging inputs; 11 image-derived representations). Studies were classified by primary KAN placement - backbone, bottleneck/token, physics-informed or implicit representation, or task-specific head - and evaluated for task, modality, comparator, reported result, and evidence of a KAN-specific contribution. None met the strictest contribution-evidence standard of a complete resource-controlled factorial comparison; 48 provided moderate, 46 weak/compound, and 44 insufficient evidence for the independent KAN contribution. Whole-model results were favorable in 68 studies, mixed or trade-off in 30, unfavorable or without incremental gain in 4, and indeterminate or not comparable in 36; these labels do not isolate the effect of KAN. External validation, calibration, repeated-run stability, and deployment metrics were inconsistently reported. The evidence supports KAN chiefly as a task-dependent module for controlled testing within established convolutional, Transformer, state-space, or physics-informed pipelines, rather than as a generally superior replacement. Priorities include matched ablations, function-stability analysis, external-center evaluation, and standardized resource reporting.