The proposed pipeline integrates a representation-flow convolutional neural network with a dynamics- and uncertainty-aware tree-based Gaussian Process classifier. In this framework, latent motion dynamics are exploited both as discriminative representations and as a source of input uncertainty, enhancing robustness against temporal variations and abnormal motion transitions. Compared with conventional deep learning approaches, the proposed strategy requires less training data and offers improved computational efficiency. To further improve classification performance, we introduce novel semantic-aware compound kernels that effectively capture semantic, flow, and dynamic information embedded in surgical video features. In addition, uncertainty-aware kernels are developed to strengthen the robustness and practical applicability of the compound kernel framework. The proposed method is evaluated on two benchmark datasets, namely the JIGSAWS and the Cataract-LMM (Capsulorhexis) datasets. Experimental results demonstrate strong performance across both datasets, including the LOSO and LOUO evaluation protocols on JIGSAWS, including the subject-independent LOUO protocol on JIGSAWS, on which the framework attains a mean accuracy of \ph{96.9}\%; results under the within-subject LOSO protocol are reported for comparability with prior work, achieving competitive accuracy while substantially reducing computational cost. Overall, the proposed pipeline provides an efficient and accurate framework for video-based surgical skill assessment.

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