Energy-Adaptive Equivariant State Space Models for Noise-Robust Protein Structure Representation

Structure-informed protein representation learning is essential for effective protein function annotation and $\textit{de novo}$ design. With the rapid progress of protein structure prediction and experimental structure determination, a central challenge in the field is shifting from merely obtaining structural models to reliably leveraging predicted or measured structures for downstream learning. However, both crystal and AlphaFold-like predicted structures can contain structural uncertainty, which can bias local neighborhood construction and make robust protein representation learning challenging. To address these issues, we propose a novel equivariant Transformer-State Space Model (SSM) hybrid framework, termed $E^3$former, designed for efficient and robust protein representation. Our approach uses energy function-based receptive fields to construct proximity graphs that adaptively stabilize neighborhood selection under structural deviations, and incorporates an equivariant high-tensor-elastic selective SSM within the transformer architecture. These components allow the model to adapt to complex geometric interactions and extract structural features with a higher signal-to-noise ratio. Empirical results demonstrate that our model outperforms existing methods in structure-intensive tasks, such as inverse folding and binding site prediction, particularly when using predicted structures, owing to its enhanced tolerance to data deviation and structural uncertainty. Our approach offers a novel perspective for conducting biological function research and drug discovery using imperfect but increasingly available protein structure data. Our code is available on \url{https://anonymous.4open.science/r/E3former-207E}.