Evidential Involution–Attention Based Networks for Medical Imaging Diagnosis

Convolution is spatially fixed and channel-specific, whereas involution is location-specific and channel-agnostic, capturing spatially varying patterns efficiently. Existing involutional networks, however, generate point-estimate kernels and expose no native measure of where the operator is uncertain, while prevailing uncertainty and calibration methods act on the network output rather than on the aggregation operator itself. We propose Evidential Involution–Attention (EvIA) networks, which recast involution as a distributional operator whose per-location neighborhood aggregation is a Dirichlet distribution. This yields, in a single forward pass and at the same parameter cost as involution, a closed-form epistemic-uncertainty (vacuity) map. The vacuity drives a parameter-free, precision-weighted gate that fuses the local involution branch with a global branch, instantiated as windowed self-attention (EvIA-W) or lightweight channel attention (EvIA-C). A lemma and three propositions establish that normalized involution is the infinite-evidence limit of the operator, that convex aggregation makes it non-expansive, that the Dirichlet strength is the precision of the aggregated feature, and that the gate is the minimum-variance unbiased fusion of the two branches. An evidential head trained with a differentiable calibration objective produces reliable confidences. Over five seeds with paired tests on brain magnetic resonance imaging, chest radiography, and dermatoscopy, the windowed variant EvIA-W is significantly stronger on brain MRI, attaining 0.803 ± 0.026 accuracy against 0.714 ± 0.019 (p = 0.006) by EvIA-C, and reducing the area under the risk–coverage curve from 0.187 to 0.092 (p = 0.001). Architecture-matched controls show that the discrimination gain on brain MRI comes from the global branch, while substituting evidential for standard involution leaves accuracy, calibration, and selective risk statistically unchanged, so the operator supplies its uncertainty machinery at no measurable cost. We further report that the spatial vacuity map does not localize input corruption, because the aggregation weights are invariant to the evidence scale and no objective term supervises it, an analysis that motivates the operator-level regularizers we define for future work.