arXiv:2505.23354v5 Announce Type: replace-cross Abstract: The local structure of a protein strongly impacts its function and interactions with other molecules. Therefore, a concise, informative representation of a local protein environment is essential for modeling and designing proteins and biomolecular interactions. However, these environments' extensive structural and chemical variability makes them challenging to model, and such representations remain under-explored. In this work, we propose a novel representation for a local protein environment derived from the intermediate features of atomistic foundation models (AFMs). We demonstrate that this embedding effectively captures both local structure (e.g., secondary motifs), and chemical features (e.g., amino-acid identity and protonation state). We further show that the AFM-derived representation space exhibits meaningful structure, enabling the construction of data-driven priors over the distribution of biomolecular environments. Finally, in the context of biomolecular NMR spectroscopy, we demonstrate that the proposed representations enable a first-of-its-kind physics-informed chemical shift predictor that achieves state-of-the-art accuracy. Our results demonstrate the surprising effectiveness of atomistic foundation models and their emergent representations for protein modeling beyond traditional molecular simulations. We believe this will open new lines of work in constructing effective functional representations for protein environments.

arXiv:2508.06066v3 Announce Type: replace-cross Abstract: Learning from time series is fundamentally different from learning from i.i.d.\ data: temporal dependence can make long sequences effectively information-poor, yet standard evaluation protocols conflate sequence length with statistical information. We propose a dependence-aware evaluation methodology that controls for effective sample size $N_{\text{eff}}$ rather than raw length $N$, and provide end-to-end generalization guarantees for Temporal Convolutional Networks (TCNs) on $\beta$-mixing sequences. Our analysis combines a blocking/coupling reduction that extracts $B = \Theta(N/\log N)$ approximately independent anchors with an architecture-aware Rademacher bound for $\ell_{2,1}$-norm-controlled convolutional networks, yielding $O(\sqrt{D\log p / B})$ complexity scaling in depth $D$ and kernel size $p$. Empirically, we find that stronger temporal dependence can \emph{reduce} generalization gaps when comparisons control for $N_{\text{eff}}$ - a conclusion that reverses under standard fixed-$N$ evaluation, with observed rates of $N_{\text{eff}}^{-0.9}$ to $N_{\text{eff}}^{-1.2}$ substantially faster than the worst-case $O(N^{-1/2})$ mixing-based prediction. Our results suggest that dependence-aware evaluation should become standard practice in temporal deep learning benchmarks.