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. However, high-resolution 3D structures are often missing due to the high cost and inherent noise of experimental screening. 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 handle 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 pose, it proposes a Transformer with geometry-aware positional encoding, leveraging Nyström estimation. To verify the effectiveness of InertialGenome, we conduct experiments on two single-cell 3D reconstruction datasets with four resolutions, reaching superior performance over all four computational baselines. Additionally, we observe that the 3D structure reconstructed by InertialGenome is more in line with the results of real experimental results on two functional verification tasks. Finally, we leverage InertialGenome for cross-resolution transfer learning, yielding up to a 5\% improvement from low to high resolution. The source code is available at https://github.com/yize1203/InertialGenome.