Adaptive Multi-Frame Learning for Expressive and Stable Atomic Representations

Reliable prediction of material properties from atomistic structures requires machine learning models that respect SE(3) symmetry. Frame-based methods address this challenge by constructing equivariant coordinate systems that align SE(3)-equivalent structures into unified representations. While attractive for their flexibility and efficiency, existing frame-based methods face two major limitations: a single frame type is often insufficient for heterogeneous atomic environments, and frame constructions can become unstable near highly symmetric or degenerate configurations. To address these issues, we propose the Multi-Frame Adaptive Network (MFAN), which leverages multiple frame types and introduces a local adaptive mechanism to combine them according to atomic environments, enabling different geometric references across atoms and complementary local-global information for each atom. Building on this multi-frame architecture, we further incorporate a frame-quality-aware weighting scheme that downweights unreliable frames before degeneration, thereby improving the continuity of the resulting representation. Experiments on crystal property prediction benchmarks demonstrate the leading performance of MFAN, with consistent gains from adaptive multi-frame learning. Additional force prediction experiments show improved robustness in continuity-sensitive settings.