Understanding how feature representations evolve across layers in large language models (LLMs) is key to improving their interpretability and robustness. While recent studies have identified critical layers linked to specific functions or behaviors, these efforts typically rely on data-dependent analyses of fine-tuned models, limiting their use to post-hoc settings. In contrast, we introduce a data-oblivious approach to identify intrinsic critical layers in pre-fine-tuned LLMs by analyzing representation dynamics via Centered Kernel Alignment (CKA). We show that layers with significant shifts in representation space are also those most affected during fine-tuning—a pattern that holds consistently across tasks for a given model. Our spectral analysis further reveals that these shifts are driven by changes in the top principal components, which encode semantic transitions from rationales to conclusions.We further apply these findings to two practical scenarios: efficient domain adaptation, where fine-tuning critical layers leads to greater loss reduction compared to non-critical layers; and backdoor defense, where freezing them reduces attack success rates by up to 40%.

ICD coding is designed to assign the disease codes to electronic health records (EHRs) upon discharge, which is crucial for billing and clinical statistics. In an attempt to improve the effectiveness and efficiency of manual coding, many methods have been proposed to automatically predict ICD codes from clinical notes. However, most previous works ignore the decisive information contained in structured medical data in EHRs, which is hard to be captured from the noisy clinical notes. In this paper, we propose a Tree-enhanced Multimodal Attention Network (TreeMAN) to fuse tabular features and textual features into multimodal representations by enhancing the text representations with tree-based features via the attention mechanism. Tree-based features are constructed according to decision trees learned from structured multimodal medical data, which capture the decisive information about ICD coding. We can apply the same multi-label classifier from previous text models to the multimodal representations to predict ICD codes. Experiments on two MIMIC datasets show that our method outperforms prior state-of-the-art ICD coding approaches. The code is available at https://github.com/liu-zichen/TreeMAN.