Greedy MAXCUT Algorithms and their Information Content

MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning, computer vision and statistical physics. Greedy algorithms to approximately solve MAXCUT rely on greedy vertex labelling or on an edge contraction strategy. These algorithms have been studied by measuring their approximation ratios in the worst case setting but very little is known to characterize their robustness to noise contaminations of the input data in the average case. Adapting the framework of Approximation Set Coding, we present a method to exactly measure the cardinality of the algorithmic approximation sets of five greedy MAXCUT algorithms. Their information contents are explored for graph instances generated by two different noise models: the edge reversal model and Gaussian edge weights model. The results provide insights into the robustness of different greedy heuristics and techniques for MAXCUT, which can be used for algorithm design of general USM problems.Comment: This is a longer version of the paper published in 2015 IEEE Information Theory Workshop (ITW

From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models

Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension, a continuous DR-submodular extension for integer submodular functions. We study central properties of this extension and formulate a new probabilistic model which is defined through integer submodular functions. Then, we introduce a block-coordinate ascent algorithm to perform approximate inference for those class of models. Finally, we demonstrate its effectiveness and viability on several real-world social connection graph datasets with integer submodular objectives

Activity Cliff Prediction: Dataset and Benchmark

Activity cliffs (ACs), which are generally defined as pairs of structurally similar molecules that are active against the same bio-target but significantly different in the binding potency, are of great importance to drug discovery. Up to date, the AC prediction problem, i.e., to predict whether a pair of molecules exhibit the AC relationship, has not yet been fully explored. In this paper, we first introduce ACNet, a large-scale dataset for AC prediction. ACNet curates over 400K Matched Molecular Pairs (MMPs) against 190 targets, including over 20K MMP-cliffs and 380K non-AC MMPs, and provides five subsets for model development and evaluation. Then, we propose a baseline framework to benchmark the predictive performance of molecular representations encoded by deep neural networks for AC prediction, and 16 models are evaluated in experiments. Our experimental results show that deep learning models can achieve good performance when the models are trained on tasks with adequate amount of data, while the imbalanced, low-data and out-of-distribution features of the ACNet dataset still make it challenging for deep neural networks to cope with. In addition, the traditional ECFP method shows a natural advantage on MMP-cliff prediction, and outperforms other deep learning models on most of the data subsets. To the best of our knowledge, our work constructs the first large-scale dataset for AC prediction, which may stimulate the study of AC prediction models and prompt further breakthroughs in AI-aided drug discovery. The codes and dataset can be accessed by https://drugai.github.io/ACNet/

SyNDock: N Rigid Protein Docking via Learnable Group Synchronization

The regulation of various cellular processes heavily relies on the protein complexes within a living cell, necessitating a comprehensive understanding of their three-dimensional structures to elucidate the underlying mechanisms. While neural docking techniques have exhibited promising outcomes in binary protein docking, the application of advanced neural architectures to multimeric protein docking remains uncertain. This study introduces SyNDock, an automated framework that swiftly assembles precise multimeric complexes within seconds, showcasing performance that can potentially surpass or be on par with recent advanced approaches. SyNDock possesses several appealing advantages not present in previous approaches. Firstly, SyNDock formulates multimeric protein docking as a problem of learning global transformations to holistically depict the placement of chain units of a complex, enabling a learning-centric solution. Secondly, SyNDock proposes a trainable two-step SE(3) algorithm, involving initial pairwise transformation and confidence estimation, followed by global transformation synchronization. This enables effective learning for assembling the complex in a globally consistent manner. Lastly, extensive experiments conducted on our proposed benchmark dataset demonstrate that SyNDock outperforms existing docking software in crucial performance metrics, including accuracy and runtime. For instance, it achieves a 4.5% improvement in performance and a remarkable millionfold acceleration in speed

Understanding and Improving Feature Learning for Out-of-Distribution Generalization

A common explanation for the failure of out-of-distribution (OOD) generalization is that the model trained with empirical risk minimization (ERM) learns spurious features instead of invariant features. However, several recent studies challenged this explanation and found that deep networks may have already learned sufficiently good features for OOD generalization. Despite the contradictions at first glance, we theoretically show that ERM essentially learns both spurious and invariant features, while ERM tends to learn spurious features faster if the spurious correlation is stronger. Moreover, when fed the ERM learned features to the OOD objectives, the invariant feature learning quality significantly affects the final OOD performance, as OOD objectives rarely learn new features. Therefore, ERM feature learning can be a bottleneck to OOD generalization. To alleviate the reliance, we propose Feature Augmented Training (FeAT), to enforce the model to learn richer features ready for OOD generalization. FeAT iteratively augments the model to learn new features while retaining the already learned features. In each round, the retention and augmentation operations are performed on different subsets of the training data that capture distinct features. Extensive experiments show that FeAT effectively learns richer features thus boosting the performance of various OOD objectives.Comment: Yongqiang Chen, Wei Huang, and Kaiwen Zhou contributed equally; NeurIPS 2023, 55 pages, 64 figure

Rethinking and Simplifying Bootstrapped Graph Latents

Graph contrastive learning (GCL) has emerged as a representative paradigm in graph self-supervised learning, where negative samples are commonly regarded as the key to preventing model collapse and producing distinguishable representations. Recent studies have shown that GCL without negative samples can achieve state-of-the-art performance as well as scalability improvement, with bootstrapped graph latent (BGRL) as a prominent step forward. However, BGRL relies on a complex architecture to maintain the ability to scatter representations, and the underlying mechanisms enabling the success remain largely unexplored. In this paper, we introduce an instance-level decorrelation perspective to tackle the aforementioned issue and leverage it as a springboard to reveal the potential unnecessary model complexity within BGRL. Based on our findings, we present SGCL, a simple yet effective GCL framework that utilizes the outputs from two consecutive iterations as positive pairs, eliminating the negative samples. SGCL only requires a single graph augmentation and a single graph encoder without additional parameters. Extensive experiments conducted on various graph benchmarks demonstrate that SGCL can achieve competitive performance with fewer parameters, lower time and space costs, and significant convergence speedup.Comment: Accepted by WSDM 202