Clifford Group Equivariant Neural Network Layers for Protein Structure Prediction

Alberto Pepe, Sven Buchholz, Joan Lasenby

Keywords: geometric deep learning, Clifford algebra, protein structure prediction, Geometric algebra, machine learning

TL;DR: We use a geometric deep learning approach with neurons sitting in 3D Clifford algebra to predict 3D coordinates of atoms in protein chains.

Abstract: We employ Clifford Group Equivariant Neural Network (CGENN) layers to predict protein coordinates in a Protein Structure Prediction (PSP) pipeline. PSP is the estimation of the 3D structure of a protein, generally through deep learning architectures. Information about the geometry of the protein chain has been proven to be crucial for accurate predictions of 3D structures. However, this information is usually flattened as machine learning features that are not representative of the geometric nature of the problem. Leveraging recent advances in geometric deep learning, we redesign a PSP architecture with the addition of CGENN layers. CGENNs can achieve better generalization and robustness when dealing with data that show rotational or translational invariance such as protein coordinates, which are independent of the chosen reference frame. CGENNs inputs, outputs, weights and biases are objects in the Geometric Algebra of 3D Euclidean space, i.e. $\mathcal{G}_{3,0,0}$, and hence are interpretable from a geometrical perspective. We test 6 approaches to PSP and show that CGENN layers increase the prediction accuracy by up to 2.1\%, with fewer trainable parameters compared to linear layers and give a clear geometric interpretation of their outputs.

Submission Number: 11