Kolmogorov–Arnold classification heads for pulmonary nodule malignancy in a multitask Swin UNETR

Lung cancer is the leading cause of cancer death worldwide, and the assessment of pulmonary nodule malignancy on computed tomography underlies early diagnosis. Nodule size is an established radiological criterion of malignancy risk, yet the LIDC-IDRI studies reviewed report AUCs above 0.93 without a size-only baseline for comparison, so this work quantifies what the classification head and its descriptor contribute beyond nodule geometry. A multitask Swin UNETR segmented each nodule and classified its malignancy from features extracted by the frozen encoder, combining multi-head attention with a Kolmogorov–Arnold network (KAN) head whose univariate activations are explicit functions that can be fitted individually (2622 nodules, patient-disjoint split). Fitting those activations to closed-form expressions motivated six comparison methods evaluated under an identical protocol (same folds, out-of-fold Matthews correlation for model selection, per-fold threshold calibration, one test pass): a size feature from the predicted mask, four geometric descriptors, radiomics, a 3D CNN trained from scratch, and a linear probe. Comparisons used a paired bootstrap over ten seeds combining test-set and seed variability. The activation contributing most to the output was a monotonically increasing, bounded function of relative nodule size (R² = 0.987). On the radiologist-consensus subset (n = 170), the model reached a macro-F1 of 0.872 ± 0.008, statistically indistinguishable from a single-variable logistic regression on size (0.870; difference 0.001, 95% CI −0.044 to 0.046) and from classical radiomics (0.887), and it exceeded only the latent-only variant (0.565 ± 0.077) and the linear probe. Study labels agreed with the confirmed diagnosis in 73% of auditable nodules (n = 67). Examining the individual activations identified this size dependence and motivated these controls; the confidence interval limits any gain over a single diameter measurement to 0.046 macro-F1, so the learned representation adds little over a criterion already in clinical use, and a size baseline is necessary before clinical value is attributed to such models.