Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical instabilities along class-separating directions, but practical methods to detect and exploit these windows in trained models are still limited. We show that tracking the class-conditional entropy of a latent semantic variable given the noisy state provides a reliable signature of these transition regimes. By restricting the entropy to semantic partitions, the entropy can furthermore resolve semantic decisions at different levels of abstraction. We analyze this behavior in high-dimensional Gaussian mixture models and show that the entropy rate concentrates on the same logarithmic time scale as the speciation symmetry-breaking instability previously identified in variance-preserving diffusion. We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation. Finally, we use our framework to quantify how guidance redistributes semantic information over time. Together, these results connect information-theoretic and statistical physics perspectives on diffusion and provide a principled basis for time-localized control.

Time series foundation models (TSFMs) offer strong zero-shot forecasting via large-scale pre-training, yet fine-tuning remains critical for boosting performance in domains with limited public data. With the growing number of TSFMs, efficiently identifying the best model for downstream fine-tuning becomes increasingly challenging. Leveraging the natural tabular structure formed by dataset meta-features, model characteristics, and fine-tuned performance, we employ tabular foundation models to serve as in-context learners. We establish a comprehensive benchmark for transferability estimation including 10 datasets, 10 foundation models, and 3 forecasting tasks. 's estimation demonstrates strong alignment with actual fine-tuned performance for previously unseen datasets, achieving a mean rank correlation of approximately 0.6 and a 30% improvement compared to using zero-shot performance as the transferability score. The emergence of time series foundation models (TSFMs) is reshaping the paradigm of time series forecasting (Liang et al., 2025) through their strong zero-shot capabilities. Although efficient and cost-effective, zero-shot inference often underperforms in out-of-distribution scenarios, particularly in domains with limited public data, such as healthcare (Gupta et al., 2024) and finance (Fu et al., 2024). Fine-tuning helps bridge the gap by transferring generalized knowledge from large-scale pre-training to specific, resource-limited downstream tasks (Li & Zhu, 2025). However, due to the inherent diversity of time series data, no single model consistently outperforms others in all scenarios (Brigato et al., 2025).

Transformer models have revolutionized fields from natural language processing to computer vision, yet their internal computational dynamics remain poorly understood raising concerns about predictability and robustness. In this work, we introduce Entropy-Lens, a scalable, model-agnostic framework that leverages information theory to interpret frozen, off-the-shelf large-scale transformers. By quantifying the evolution of Shannon entropy within intermediate residual streams, our approach extracts computational signatures that distinguish model families, categorize task-specific prompts, and correlate with output accuracy. We further demonstrate the generality of our method by extending the analysis to vision transformers. Our results suggest that entropy-based metrics can serve as a principled tool for unveiling the inner workings of modern transformer architectures.