Zhiming Ma

Shengchao Liu, Weitao Du, Yanjing Li et al.

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these scientific problems, molecules serve as the fundamental building blocks, and machine learning has emerged as a highly effective and powerful tool for modeling their geometric structures. Nevertheless, due to the rapidly evolving process of the field and the knowledge gap between science (e.g., physics, chemistry, & biology) and machine learning communities, a benchmarking study on geometrical representation for such data has not been conducted. To address such an issue, in this paper, we first provide a unified view of the current symmetry-informed geometric methods, classifying them into three main categories: invariance, equivariance with spherical frame basis, and equivariance with vector frame basis. Then we propose a platform, coined Geom3D, which enables benchmarking the effectiveness of geometric strategies. Geom3D contains 16 advanced symmetry-informed geometric representation models and 14 geometric pretraining methods over 46 diverse datasets, including small molecules, proteins, and crystalline materials. We hope that Geom3D can, on the one hand, eliminate barriers for machine learning researchers interested in exploring scientific problems; and, on the other hand, provide valuable guidance for researchers in computational chemistry, structural biology, and materials science, aiding in the informed selection of representation techniques for specific applications.

Yimeng Chen, Ruibin Xiong, Zhiming Ma et al.

By inferring latent groups in the training data, recent works introduce invariant learning to the case where environment annotations are unavailable. Typically, learning group invariance under a majority/minority split is empirically shown to be effective in improving out-of-distribution generalization on many datasets. However, theoretical guarantee for these methods on learning invariant mechanisms is lacking. In this paper, we reveal the insufficiency of existing group invariant learning methods in preventing classifiers from depending on spurious correlations in the training set. Specifically, we propose two criteria on judging such sufficiency. Theoretically and empirically, we show that existing methods can violate both criteria and thus fail in generalizing to spurious correlation shifts. Motivated by this, we design a new group invariant learning method, which constructs groups with statistical independence tests, and reweights samples by group label proportion to meet the criteria. Experiments on both synthetic and real data demonstrate that the new method significantly outperforms existing group invariant learning methods in generalizing to spurious correlation shifts.

Bowen Gao, Yinjun Jia, Yuanle Mo et al.

Pocket representations play a vital role in various biomedical applications, such as druggability estimation, ligand affinity prediction, and de novo drug design. While existing geometric features and pretrained representations have demonstrated promising results, they usually treat pockets independent of ligands, neglecting the fundamental interactions between them. However, the limited pocket-ligand complex structures available in the PDB database (less than 100 thousand non-redundant pairs) hampers large-scale pretraining endeavors for interaction modeling. To address this constraint, we propose a novel pocket pretraining approach that leverages knowledge from high-resolution atomic protein structures, assisted by highly effective pretrained small molecule representations. By segmenting protein structures into drug-like fragments and their corresponding pockets, we obtain a reasonable simulation of ligand-receptor interactions, resulting in the generation of over 5 million complexes. Subsequently, the pocket encoder is trained in a contrastive manner to align with the representation of pseudo-ligand furnished by some pretrained small molecule encoders. Our method, named ProFSA, achieves state-of-the-art performance across various tasks, including pocket druggability prediction, pocket matching, and ligand binding affinity prediction. Notably, ProFSA surpasses other pretraining methods by a substantial margin. Moreover, our work opens up a new avenue for mitigating the scarcity of protein-ligand complex data through the utilization of high-quality and diverse protein structure databases.

Wen-Xuan Lang, Shaoshi Yang, Jianhua Zhang et al.

A mathematical framework for information-theoretic analysis is established, with a new viewpoint of describing transmitted messages and communication channels by the nonlinear expectation theory, beyond the framework of classical probability theory. The major motivation of this research is to emphasize the probabilistic distribution uncertainty within the ever increasingly complex communication networks, where random phenomena are often nonstationary, heterogeneous, and cannot be characterized by a single probability distribution. Based on the nonlinear expectation theory, in this paper we first explicitly define several fundamental concepts, such as nonlinear information entropy, nonlinear joint entropy, nonlinear conditional entropy and nonlinear mutual information, and establish their basic properties. Secondly, by using the strong law of large numbers under sublinear expectations, we propose a nonlinear source coding theorem, which shows that the nonlinear information entropy is the upper bound of the achievable coding rate of sources whose distributions are uncertain under the maximum error probability criterion, and determines a cluster point of the coding rate of such sources under the minimum error probability criterion. Thirdly, we propose a nonlinear channel coding theorem, which gives the explicit expression of the upper bound under the maximum error probability criterion and a cluster point under the minimum error probability criterion, respectively, for the achievable coding rate of communication channels whose distributions are uncertain. Additionally, we propose a nonlinear rate-distortion source coding theorem, proving that the rate distortion function based on the nonlinear mutual information is a cluster point of the lossy compression performance of uncertain-distribution sources under the minimum expected distortion criterion.