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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%.

Foundation models (FMs) trained on electronic health records (EHRs) have shown strong performance on a range of clinical prediction tasks. However, adapting these models to local health systems remains challenging due to limited data availability and resource constraints. In this study, we investigated what these models learn and evaluated the transferability of an FM trained on MIMIC-IV to an institutional EHR dataset at the University of Chicago Medical Center. We assessed their ability to identify outlier patients and examined representation-space patient trajectories in relation to future clinical outcomes. We also evaluated the performance of supervised fine-tuned classifiers on both source and target datasets. Our findings offer insights into the adaptability of FMs across different healthcare systems, highlight considerations for their effective implementation, and provide an empirical analysis of the underlying factors that contribute to their predictive performance.

Critical to representation learning has led to much empirical success to the accuracy of value predictions is the quality and is the core of many high-performing agents such as of state representations. In this work, we consider DQN (Mnih et al., 2013). A natural question ensues: can we the question: how does end-to-end TD-learning characterize the representation learned by such end-to-end impact the representation over time? Complementary updates? to prior work, we provide a set of analysis that sheds further light on the representation dynamics The answer to this question has been attempted by a number under TD-learning. We first show that of prior work, including the study of the convergence of endto-end when the environments are reversible, end-to-end TD-learning under the over-parameterized regimes, TD-learning strictly decreases the value approximation i.e., when the value functions are learned by very wide neural error over time. Under further assumptions networks (Cai et al., 2019; Zhang et al., 2020; Agazzi and on the environments, we can connect the Lu, 2022; Sirignano and Spiliopoulos, 2022); the study of representation dynamics with spectral decomposition TD-learning dynamics under smooth homogeneous function over the transition matrix. This latter finding approximation, e.g., with ReLU networks (Brandfonbrener establishes fitting multiple value functions from and Bruna, 2019); the study of representation dynamics under randomly generated rewards as a useful auxiliary TD-learning with restrictive assumptions on the weight task for representation learning, as we empirically parameter (Lyle et al., 2021). See Section 6 for an in-depth validate on both tabular and Atari game suites.