Stabilizing proteins is a foundational step in protein engineering.

Differently, our unsupervised multi-body task requires the model's ability to handle part-level local equivariance, Figure 1: Structure of our feature extractor based on EPN. "EPNConv" is the SE(3)-equivariant convolution proposed in the vanilla EPN network. Part-level SE(3)-equivariance is desirable for motion analysis, especially rotation estimation. Song and Y ang utilized the methodology proposed by Choy et al . All other objects were considered part of the background.

The supplemental material is organized as follows. Section A provides the results of all the additional synthetic experiments and real data results for various kernel-based methods and the detailed settings. Section B describes the algorithm details we use in Section A. In Section C, we provide some useful lemmas and all the technical proofs of the theoretical results in the main text. In this section, we provide more experiment results, including KRR (Section A.1), KQR for various Section A.7. A.1 Kernel ridge regression For the squared loss, we consider the following two examples. TIRW estimator still performs significantly better. A.2 Kernel quantile regression For the check loss, we consider the following two examples.

It is often implemented with variable permutation schemes.

We begin by illustrating successful verification results in Appendix A.1, To further contextualize our TP's advantages, we juxtapose these standard HRs encompass a multitude of verified patches; for visual clarity, we've outlined the SIFT points A.2 Standard verification results: compared with SP Hence, our method suitably ranks these accurate index images highly. We further evaluate our topological verification outcomes against those of the SP method. In addition to successful verification instances, we also explore cases where our method fails. Regions (HRs) identified by our method on ROxford. Regarding false negative cases, our method fails to detect any HRs.