We provide additional qualitative comparative results on both ShapeNetandPix3DinFig8,9.

Designing novel functional proteins crucially depends on accurately modeling their fitness landscape. Given the limited availability of functional annotations from wet-lab experiments, previous methods have primarily relied on self-supervised models trained on vast, unlabeled protein sequence or structure datasets. While initial protein representation learning studies solely focused on either sequence or structural features, recent hybrid architectures have sought to merge these modalities to harness their respective strengths. However, these sequence-structure models have so far achieved only incremental improvements when compared to the leading sequence-only approaches, highlighting unresolved challenges effectively leveraging these modalities together. Moreover, the function of certain proteins is highly dependent on the granular aspects of their surface topology, which have been overlooked by prior models.To address these limitations, we introduce the Sequence-Structure-Surface Fitness ( S3F

Designing novel functional proteins crucially depends on accurately modeling their fitness landscape. Given the limited availability of functional annotations from wet-lab experiments, previous methods have primarily relied on self-supervised models trained on vast, unlabeled protein sequence or structure datasets. While initial protein representation learning studies solely focused on either sequence or structural features, recent hybrid architectures have sought to merge these modalities to harness their respective strengths. However, these sequence-structure models have so far achieved only incremental improvements when compared to the leading sequence-only approaches, highlighting unresolved challenges effectively leveraging these modalities together. Moreover, the function of certain proteins is highly dependent on the granular aspects of their surface topology, which have been overlooked by prior models.To address these limitations, we introduce the Sequence-Structure-Surface Fitness (S3F) model -- a novel multimodal representation learning framework that integrates protein features across several scales.

Statistical shape models (SSMs) are an established way to represent the anatomy of a population with various clinically relevant applications. However, they typically require domain expertise, and labor-intensive landmark annotations to construct. We address these shortcomings by proposing an unsupervised method that leverages deep geometric features and functional correspondences to simultaneously learn local and global shape structures across population anatomies. Our pipeline significantly improves unsupervised correspondence estimation for SSMs compared to baseline methods, even on highly irregular surface topologies. We demonstrate this for two different anatomical structures: the thyroid and a multi-chamber heart dataset. Furthermore, our method is robust enough to learn from noisy neural network predictions, potentially enabling scaling SSMs to larger patient populations without manual segmentation annotation.