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Adversarial training (AT) enhances neural network robustness. Typically, AT updates all trainable parameters, but can lead to overfitting and increased errors on clean data. Research suggests that fine-tuning specific parameters may be more effective; however, methods for identifying these essential parameters and establishing effective optimization objectives remain inadequately addressed. We present CLAT, an innovative adversarial fine-tuning algorithm that mitigates adversarial overfitting by integrating "criticality" into the training process. Instead of tuning the entire model, CLAT identifies and fine-tunes fewer parameters in robustness-critical layers—those predominantly learning non-robust features—while keeping the rest of the model fixed. Additionally, CLAT employs a dynamic layer selection process that adapts to changes in layer criticality during training. Empirical results demonstrate that CLAT can be seamlessly integrated with existing adversarial training methods, enhancing clean accuracy and adversarial robustness by over 2% compared to baseline approaches.