A Resolution-Agnostic Geometric Transformer for Chromosome Modeling Using Inertial Frame

Chromosomes are the carriers of genetic information. Further understanding their 3D structure can help reveal gene-regulatory mechanisms and cellular functions. A standard pipeline for reconstructing the chromosome 3D structure first applies the single-cell Hi-C high-throughput screening method to measure pairwise interactions between DNA fragments at different resolutions; then it adopts computational methods to reconstruct the 3D structures from these contacts. These include traditional numerical methods and deep learning models, which struggle with limited model expressiveness and poor generalization across resolutions. To solve this issue, we propose InertialGenome, a novel transformer-based framework for robust and resolution-agnostic chromosome reconstruction. InertialGenome first adopts the inertial frame for the pose canonicalization. Then, based on such an invariant frame, it proposes a Transformer with geometry-aware positional encoding, leveraging Nyström estimation. To verify the effect of InertialGenome, we evaluate our model on two single-cell 3D reconstruction datasets with four resolutions, reaching superior performance over all four computational baselines. In addition to the structure metrics, we observe that InertialGenome outperforms when analyzing the function of reconstructed structures on two validation tasks. Finally, we leverage InertialGenome for cross-resolution transfer learning, yielding up to a 5\% improvement from low to high resolution.