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Equivariant Neural Operator Learning with Graphon Convolution
Nov 17, 2023
We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve SE(3)-equivariance by design. From the graph spectrum view, our method can be interpreted as convolution on graphons (dense graphs with infinitely many nodes), which we term InfGCN. By leveraging both the continuous graphon structure and the discrete graph structure of the input data, our model can effectively capture the geometric information while preserving equivariance. Through extensive experiments on large-scale electron density datasets, we observed that our model significantly outperformed the current state-of-the-art architectures. Multiple ablation studies were also carried out to demonstrate the effectiveness of the proposed architecture.
Equivariant Point Cloud Analysis via Learning Orientations for Message Passing
Mar 28, 2022
Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find the equivariant property could be obtained by introducing an orientation for each point to decouple the relative position for each point from the global pose of the entire point cloud. Therefore, we extend current message passing networks with a module that learns orientations for each point. Before aggregating information from the neighbors of a point, the networks transforms the neighbors' coordinates based on the point's learned orientations. We provide formal proofs to show the equivariance of the proposed framework. Empirically, we demonstrate that our proposed method is competitive on both point cloud analysis and physical modeling tasks. Code is available at https://github.com/luost26/Equivariant-OrientedMP .
Directed Weight Neural Networks for Protein Structure Representation Learning
Jan 28, 2022
A protein performs biological functions by folding to a particular 3D structure. To accurately model the protein structures, both the overall geometric topology and local fine-grained relations between amino acids (e.g. side-chain torsion angles and inter-amino-acid orientations) should be carefully considered. In this work, we propose the Directed Weight Neural Network for better capturing geometric relations among different amino acids. Extending a single weight from a scalar to a 3D directed vector, our new framework supports a rich set of geometric operations on both classical and SO(3)--representation features, on top of which we construct a perceptron unit for processing amino-acid information. In addition, we introduce an equivariant message passing paradigm on proteins for plugging the directed weight perceptrons into existing Graph Neural Networks, showing superior versatility in maintaining SO(3)-equivariance at the global scale. Experiments show that our network has remarkably better expressiveness in representing geometric relations in comparison to classical neural networks and the (globally) equivariant networks. It also achieves state-of-the-art performance on various computational biology applications related to protein 3D structures.
DeepVar: An End-to-End Deep Learning Approach for Genomic Variant Recognition in Biomedical Literature
Jun 05, 2020
We consider the problem of Named Entity Recognition (NER) on biomedical scientific literature, and more specifically the genomic variants recognition in this work. Significant success has been achieved for NER on canonical tasks in recent years where large data sets are generally available. However, it remains a challenging problem on many domain-specific areas, especially the domains where only small gold annotations can be obtained. In addition, genomic variant entities exhibit diverse linguistic heterogeneity, differing much from those that have been characterized in existing canonical NER tasks. The state-of-the-art machine learning approaches in such tasks heavily rely on arduous feature engineering to characterize those unique patterns. In this work, we present the first successful end-to-end deep learning approach to bridge the gap between generic NER algorithms and low-resource applications through genomic variants recognition. Our proposed model can result in promising performance without any hand-crafted features or post-processing rules. Our extensive experiments and results may shed light on other similar low-resource NER applications.