Less is more: minimal Kolmogorov–Arnold integration enhances efficiency, transparency, and explainability of vision transformers for sedimentary facies classification

Automated petrographic image classification can accelerate sedimentary-facies analysis and support depositional interpretation and subsurface exploration. However, the multiscale textures and visual overlap of carbonate and siliciclastic facies remain challenging for conventional deep-learning models. Kolmogorov–Arnold Networks (KANs) offer adaptive edge-wise nonlinear functions, but the optimal scope of their integration within pretrained vision transformers is unclear. We introduce KAN-DeiT and compare three integration strategies: replacing only the classification head, extending KAN to the feed-forward sublayers, and further extending it to the attention projections. As a proof of concept, head-only KAN-DeiT achieved 100% accuracy on a held-out eight-class carbonate microfacies test set. On a more ambiguous four-class mudstone dataset, the head-only KAN-DeiT model achieved 91.47% accuracy and a macro F1-score of 0.9139, outperforming the accuracy of pretrained ResNet-50 (82.95%), EfficientNet-B0 (85.27%), vanilla ViT (88.37%), and MLP-DeiT (89.92%). In contrast, Hybrid and Full KAN integration achieved only 67.44–73.64% and 65.04–65.89% accuracy, respectively, with the same overall pattern observed for RBF and B-spline parameterizations. Deeper integration increased parameter counts by up to 8.8-fold and substantially raised computational cost, whereas head-only integration added less than 0.1% parameters with unchanged GFLOPs and comparable inference latency. Attention rollout, Grad-CAM, and learned edge-function analyses indicated that the head-only model preserved the pretrained spatial representation while modifying how geologically relevant textures contributed to class decisions, although occasional responses to possible image artifacts were observed. These findings indicate that targeted KAN integration at the classification head offers a more accurate and efficient strategy than extensive transformer-wide substitution for data-constrained petrographic classification.