We present CrystalDiT, a diffusion transformer for crystal structure generation that achieves state-of-the-art performance by challenging the trend of architectural complexity. Instead of intricate, multi-stream designs, CrystalDiT employs a unified transformer that imposes a powerful inductive bias: treating lattice and atomic properties as a single, interdependent system. Combined with a periodic table-based atomic representation and a balanced training strategy, our approach achieves 8.78% SUN (Stable, Unique, Novel) rate on MP-20, substantially outperforming recent methods including FlowMM (4.21%) and MatterGen (3.66%). Notably, CrystalDiT generates 63.28% unique and novel structures while maintaining comparable stability rates, demonstrating that architectural simplicity can be more effective than complexity for materials discovery. Our results suggest that in data-limited scientific domains, carefully designed simple architectures outperform sophisticated alternatives that are prone to overfitting.

Zhiyin Yu, Yuchen Mou, Juncheng Yan, Junyu Luo, Chunchun Chen, Xing Wei, Yunhui Liu, Hongru Sun, Yuxing Zhang, Jun Xu, Yatao Bian, Ming Zhang, Wei Ye, Tieke He, Jie Yang, Guanjie Zheng, Zhonghai Wu, Bo Zhang, Lei Bai, Xiao Luo. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Retrieval-augmented generation (RAG) has demonstrated its ability to enhance Large Language Models (LLMs) by integrating external knowledge sources. However, multi-hop questions, which require the identification of multiple knowledge targets to form a synthesized answer, raise new challenges for RAG systems. Under the multi-hop settings, existing methods often struggle to fully understand the questions with complex semantic structures and are susceptible to irrelevant noise during the retrieval of multiple information targets. To address these limitations, we propose a novel graph representation learning framework for multi-hop question retrieval. We first introduce a Multi-information Level Knowledge Graph (Multi-L KG) to model various information levels for a more comprehensive understanding of multi-hop questions. Based on this, we design a Question-Adaptive Graph Neural Network (Quest-GNN) for representation learning on the Multi-L KG. Quest-GNN employs intra/inter-level message passing mechanisms, and in each message passing the information aggregation is guided by the question, which not only facilitates multi-granular information aggregation but also significantly reduces the impact of noise. To enhance its ability to learn robust representations, we further propose two synthesized data generation strategies for pre-training the Quest-GNN. Extensive experimental results demonstrate the effectiveness of our framework in multi-hop scenarios, especially in high-hop questions the improvement can reach 33.8%. The code is available at: https://github.com/Jerry2398/QSGNN.

Time series forecasting is essential for planning and management across various domains. Existing models struggle to maintain long-term trends in extended predictions and overlook the interplay between time and frequency-domain dependencies. To address these challenges, we propose TFformer, a hierarchical time–frequency representation architecture with Transformer, involving two key innovations: (i) spectrum decomposition isolates long-term patterns from short-term fluctuations and (ii) sequence aggregation integrates two categories of features distinguished by different energy intensities in a hierarchical manner. Experiments on six real-world datasets show that TFformer outperforms the frequency-domain baseline (FreTS) with an average 16.54% improvement in Mean Squared Error (MSE) and surpasses the time-domain baseline (iTransformer) with an average 5.91% MSE improvement, highlighting its effectiveness in capturing both time and frequency-domain patterns.

Advancements in the text-to-image diffusion model have raised security concerns due to their potential to generate images with inappropriate themes such as societal biases and copyright infringements. Current studies have made notable progress in preventing the model from generating images containing specific high-risk visual concepts. However, these methods neglect the issue that inappropriate themes may also arise from the combination of benign visual concepts. A crucial challenge arises because the same image theme can be represented through multiple distinct visual concept combinations, and the model's ability to generate individual concepts may become distorted when processing these combinations. Consequently, effectively erasing such visual concept combinations from the diffusion model remains a formidable challenge. To tackle this problem, we formalize the problem as the Concept Combination Erasing (CCE) problem and propose a Concept Graph-based high-level Feature Decoupling framework (CoGFD) to address CCE. CoGFD identifies and decomposes visual concept combinations with a consistent image theme from an LLM-induced concept logic graph, and erases these combinations through decoupling co-occurrent high-level features. These techniques enable CoGFD to eliminate undesirable visual concept combinations while minimizing adverse effects on the generative fidelity of related individual concepts, outperforming state-of-the-art baselines. Extensive experiments across diverse visual concept combination scenarios verify the effectiveness of CoGFD.

Exploring chemical space to find novel molecules that simultaneously satisfy multiple properties is crucial in drug discovery. However, existing methods often struggle with trading off multiple properties due to the conflicting or correlated nature of chemical properties. To tackle this issue, we introduce InversionGNN framework, an effective yet sample-efficient dual-path graph neural network (GNN) for multi-objective drug discovery. In the direct prediction path of InversionGNN, we train the model for multi-property prediction to acquire knowledge of the optimal combination of functional groups. Then the learned chemical knowledge helps the inversion generation path to generate molecules with required properties. In order to decode the complex knowledge of multiple properties in the inversion path, we propose a gradient-based Pareto search method to balance conflicting properties and generate Pareto optimal molecules. Additionally, InversionGNN is able to search the full Pareto front approximately in discrete chemical space. Comprehensive experimental evaluations show that InversionGNN is both effective and sample-efficient in various discrete multi-objective settings including drug discovery.

Machine learning models must continuously self-adjust themselves for novel data distribution in the open world. As the predominant principle, entropy minimization (EM) has been proven to be a simple yet effective cornerstone in existing test-time adaption (TTA) methods. While unfortunately its fatal limitation (i.e., overconfidence) tends to result in model collapse. For this issue, we propose to \textbf{\texttt{Co}}nservatively \textbf{\texttt{M}}inimize the \textbf{\texttt{E}}ntropy (\texttt{COME}), which is a simple drop-in replacement of traditional EM to elegantly address the limitation. In essence, \texttt{COME} explicitly models the uncertainty by characterizing a Dirichlet prior distribution over model predictions during TTA. By doing so, \texttt{COME} naturally regularizes the model to favor conservative confidence on unreliable samples. Theoretically, we provide a preliminary analysis to reveal the ability of \texttt{COME} in enhancing the optimization stability by introducing a data-adaptive lower bound on the entropy. Empirically, our method achieves state-of-the-art performance on commonly used benchmarks, showing significant improvements in terms of classification accuracy and uncertainty estimation under various settings including standard, life-long and open-world TTA, i.e., up to $34.5\%$ improvement on accuracy and $15.1\%$ on false positive rate. Our code is available at: \href{https://github.com/BlueWhaleLab/COME}{https://github.com/BlueWhaleLab/COME}.

Recently, there has been a surge of interest in extending the success of large language models (LLMs) from texts to molecules. Most existing approaches adopt a graph neural network to represent a molecule as a series of node tokens for molecule-language alignment, which, however, have overlooked the inherent hierarchical structures in molecules. Notably, higher-order molecular structures contain rich semantics of functional groups, which encode crucial biochemical functionalities of the molecules. We show that neglecting the hierarchical information in tokenization will lead to subpar molecule-language alignment and severe hallucination. To address this limitation, we propose HIerarchical GrapH Tokenization (HIGHT). HIGHT employs a hierarchical graph tokenizer that encodes the hierarchy of atom, motif, and molecular levels of informative tokens to improve the molecular perception of LLMs. HIGHT also adopts an augmented instruction tuning dataset, enriched with the hierarchical graph information, to further enhance the molecule-language alignment. Extensive experiments on 14 real-world benchmarks verify the effectiveness of HIGHT in reducing hallucination by 40%, and significant improvements in various molecule-language downstream tasks. The project is available at https: //higraphllm.github.io/.

Large language models (LLMs) are widely adopted to generate synthetic datasets for various natural language processing (NLP) tasks, such as text classification and summarization. However, accurately measuring the diversity of these synthetic datasets—an aspect crucial for robust model performance—remains a significant challenge. In this paper, we introduce DCScore, a novel method for measuring synthetic dataset diversity from a classification perspective. Specifically, DCScore formulates diversity evaluation as a sample classification task, leveraging mutual relationships among samples. We further provide theoretical verification of the diversity-related axioms satisfied by DCScore, highlighting its role as a principled diversity evaluation method. Experimental results on synthetic datasets reveal that DCScore enjoys a stronger correlation with multiple diversity pseudo-truths of evaluated datasets, underscoring its effectiveness. Moreover, both empirical and theoretical evidence demonstrate that DCScore substantially reduces computational costs compared to existing methods. Code is available at: https://github.com/bluewhalelab/dcscore.

The remarkable success of Large Language Models (LLMs) across diverse tasks has driven the research community to extend their capabilities to molecular applications. However, most molecular LLMs employ adapter-based architectures that fail to equally integrate molecule and text modalities and lack explicit supervision signals for the molecular modality. To address these issues, we introduce UniMoT, a Unified Molecule-Text LLM adopting a tokenizer-based architecture that expands the vocabulary of LLMs with molecule tokens. Specifically, we introduce a Vector Quantization-driven tokenizer that incorporates a Q-Former to bridge the modality gap between molecule and text. This tokenizer transforms molecular structures into sequences of tokens exhibiting causal dependency, thereby encapsulating both high-level molecular features and textual information. Equipped with this tokenizer, UniMoT unifies molecule and text modalities under a shared token representation and an autoregressive training paradigm. This enables the model to process molecular structures as a distinct linguistic system and generate them in textual form. Through a four-stage training scheme, UniMoT functions as a multi-modal generalist capable of performing both molecule-to-text and text-to-molecule tasks. Extensive experiments demonstrate that UniMoT achieves state-of-the-art performance across a wide range of molecule comprehension and generation tasks.

Masked graph modeling (MGM) is a promising approach for molecular representation learning (MRL). However, extending the success of re-mask decoding from 2D to 3D MGM is non-trivial, primarily due to two conflicting challenges: avoiding 2D structure leakage to the decoder, while still providing sufficient 2D context for reconstructing re-masked atoms. To address these challenges, we propose 3D-GSRD: a 3D Molecular Graph Auto-Encoder with Selective Re-mask Decoding. The core innovation of 3D-GSRD lies in its Selective Re-mask Decoding (SRD), which re-masks only 3D-relevant information from encoder representations while preserving the 2D graph structures. This SRD is synergistically integrated with a 3D Relational-Transformer (3D-ReTrans) encoder alongside a structure-independent decoder. We analyze that SRD, combined with the structure-independent decoder, enhances the encoder's role in MRL. Extensive experiments show that 3D-GSRD achieves strong downstream performance, setting a new state-of-the-art on 7 out of 8 targets in the widely used MD17 molecular property prediction benchmark. The code is released at https://github.com/WuChang0124/3D-GSRD.

Meta-learning enables learning systems to adapt quickly to new tasks, similar to humans. Different meta-learning approaches all work under/with the mini-batch episodic training framework. Such framework naturally gives the information about task identity, which can serve as additional supervision for meta-training to improve generalizability. We propose to exploit task identity as additional supervision in meta-training, inspired by the alignment and discrimination ability which is is intrinsic in human's fast learning. This is achieved by contrasting what meta-learners learn, i.e., model representations. The proposed ConML is evaluating and optimizing the contrastive meta-objective under a problem- and learner-agnostic meta-training framework. We demonstrate that ConML integrates seamlessly with existing meta-learners, as well as in-context learning models, and brings significant boost in performance with small implementation cost.

Existing methods to enhance the reasoning capability of large language models predominantly rely on supervised fine-tuning (SFT) followed by reinforcement learning (RL) on reasoning-specific data. These approaches critically depend on external supervisions--such as labeled reasoning traces, verified golden answers, or pre-trained reward models. In this work, we propose Entropy Minimized Policy Optimization (EMPO), which makes an early attempt at fully unsupervised LLM reasoning incentivization. By minimizing the semantic entropy of LLMs on unlabeled questions, EMPO achieves competitive performance compared to supervised counterparts. Specifically, without any supervised signals, EMPO boosts the accuracy of Qwen2.5-Math-7B Base from 33.7\% to 51.6\% on math benchmarks and improves the accuracy of Qwen2.5-7B Base from 32.1\% to 50.1\% on MMLU-Pro. Primary analysis are also provided to interpret the effectiveness of EMPO. Code is available at https://github.com/QingyangZhang/EMPO.

Hypergraph-based modeling has gained significant attention for capturing complex higher-order interactions among vertices. While random walks serve as fundamental tools for analyzing hypergraphs, existing approaches either fail to fully leverage edge-dependent vertex weights (EDVWs) or lack sufficient expressiveness to model intricate hypergraph structures. To address these limitations, we propose a unified random walk framework that integrates hyperedge degrees and vertex weights, offering a more robust approach to hypergraph modeling. We establish equivalence conditions between hypergraph and graph random walks, leading to a novel unified random-walk-based hypergraph Laplacian that incorporates EDVWs, ensuring expressiveness and desirable spectral properties. Building on this foundation, we introduce the General Hypergraph Spectral Convolution (GHSC) framework, which extends existing Graph Convolutional Neural Networks (GCNNs) for effective hypergraph learning, supporting both edge-independent and edge-dependent vertex weights. Extensive experiments across diverse datasets, including citation networks, visual objects, and protein modeling tasks, demonstrate state-of-the-art performance, with notable improvements in protein structure modeling using EDVW-hypergraphs. This work advances the theoretical understanding of hypergraph random walks and spectral theory while providing a versatile framework for deep hypergraph learning. Code is available at GHSC_H_GNNs.

Liang Chen, Yatao Bian, Yang Deng, Deng Cai, Shuaiyi Li, Peilin Zhao, Kam-Fai Wong. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

Protein complex formation, a pivotal challenge in contemporary biology, has recently gained interest from the machine learning community, particularly concerning protein-ligand docking tasks. In this paper, we delve into the equally crucial but comparatively under-investigated domain of protein-protein docking. Specifically, we propose a geometric deep learning framework, termed EBMDock, which employs statistical potential as its energy function. This approach produces a probability distribution over docking poses, such that the identified docking pose aligns with a minimum point in the energy landscape. We employ a differential algorithm grounded in Langevin dynamics to efficiently sample from the docking pose distribution. Additionally, we incorporate energy-based training using contrastive divergence, enhancing both performance and stability. Empirical results demonstrate that our approach achieves superior performance on two benchmark datasets DIPS and DB5.5. Furthermore, the results suggest EBMDock can serve as an orthogonal enhancement to existing methods.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Interpretable graph neural networks (XGNNs ) are widely adopted in various scientific applications involving graph-structured data. Existing XGNNs predominantly adopt the attention-based mechanism to learn edge or node importance for extracting and making predictions with the interpretable subgraph. However, the representational properties and limitations of these methods remain inadequately explored. In this work, we present a theoretical framework that formulates interpretable subgraph learning with the multilinear extension of the subgraph distribution, coined as subgraph multilinear extension (SubMT). Extracting the desired interpretable subgraph requires an accurate approximation of SubMT, yet we find that the existing XGNNs can have a huge gap in fitting SubMT. Consequently, the SubMT approximation failure will lead to the degenerated interpretability of the extracted subgraphs. To mitigate the issue, we design a new XGNN architecture called Graph Multilinear neT (GMT), which is provably more powerful in approximating SubMT. We empirically validate our theoretical findings on a number of graph classification benchmarks. The results demonstrate that GMT outperforms the state-of-the-art up to 10% in terms of both interpretability and generalizability across 12 regular and geometric graph benchmarks.

Recent studies have highlighted fairness issues in Graph Neural Networks (GNNs), where they produce discriminatory predictions against specific protected groups categorized by sensitive attributes such as race and age. While various efforts to enhance GNN fairness have made significant progress, these approaches are often tailored to specific sensitive attributes. Consequently, they necessitate retraining the model from scratch to accommodate changes in the sensitive attribute requirement, resulting in high computational costs. To gain deeper insights into this issue, we approach the graph fairness problem from a causal modeling perspective, where we identify the confounding effect induced by the sensitive attribute as the underlying reason. Motivated by this observation, we formulate the fairness problem in graphs from an invariant learning perspective, which aims to learn invariant representations across environments. Accordingly, we propose a graph fairness framework based on invariant learning, namely FairINV, which enables the training of fair GNNs to accommodate various sensitive attributes within a single training session. Specifically, FairINV incorporates sensitive attribute partition and trains fair GNNs by eliminating spurious correlations between the label and various sensitive attributes. Experimental results on several real-world datasets demonstrate that FairINV significantly outperforms state-of-the-art fairness approaches, underscoring its effectiveness. Our code is available via: https://github.com/ZzoomD/FairINV/.

Out-of-distribution (OOD) detection is essential for model trustworthiness which aims to sensitively identity semantic OOD samples and robustly generalize for covariate-shifted OOD samples. However, we discover that the superior OOD detection performance of state-of-the-art methods is achieved by secretly sacrificing the OOD generalization ability. The classification accuracy frequently collapses catastrophically when even slight noise is encountered. Such a phenomenon violates the motivation of trustworthiness and significantly limits the model's deployment in the real world. What is the hidden reason behind such a limitation? In this work, we theoretically demystify the "\textit{sensitive-robust}" dilemma that lies in previous OOD detection methods. Consequently, a theory-inspired algorithm is induced to overcome such a dilemma. By decoupling the uncertainty learning objective from a Bayesian perspective, the conflict between OOD detection and OOD generalization is naturally harmonized and a dual-optimized performance could be expected. Empirical studies show that our method achieves superior performance on commonly used benchmarks. To our best knowledge, this work is the first principled OOD detection method that achieves state-of-the-art OOD detection performance without sacrificing OOD generalization ability. Our code is available at https://github.com/QingyangZhang/DUL.

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.

The emergence of Graph Convolutional Network (GCN) has greatly boosted the progress of graph learning. However, two disturbing factors, noise and redundancy in graph data, and lack of interpretation for prediction results, impede further development of GCN. One solution is to recognize a predictive yet compressed subgraph to get rid of the noise and redundancy and obtain the interpretable part of the graph. This setting of subgraph is similar to the information bottleneck (IB) principle, which is less studied on graph-structured data and GCN. Inspired by the IB principle, we propose a novel subgraph information bottleneck (SIB) framework to recognize such subgraphs, named IB-subgraph. However, the intractability of mutual information and the discrete nature of graph data makes the objective of SIB notoriously hard to optimize. To this end, we introduce a bilevel optimization scheme coupled with a mutual information estimator for irregular graphs. Moreover, we propose a continuous relaxation for subgraph selection with a connectivity loss for stabilization. We further theoretically prove the error bound of our estimation scheme for mutual information and the noise-invariant nature of IB-subgraph. Extensive experiments on graph learning and large-scale point cloud tasks demonstrate the superior property of IB-subgraph.

Multivariate Time Series Anomaly Detection (MTS-AD) is crucial for the effective management and maintenance of devices in complex systems, such as server clusters, spacecrafts, and financial systems, and so on. However, upgrade or cross-platform deployment of these devices will introduce the issue of cross-domain distribution shift, which leads to the prototypical problem of domain adaptation for MTS-AD. Compared with general domain adaptation problems, MTS-AD domain adaptation presents two peculiar challenges: (1) the dimensions of data from the source domain and the target domain are usually different, so alignment without losing any information is necessary; and (2) the association between different variates plays a vital role in the MTS-AD task, which is overlooked by traditional domain adaptation approaches. Aiming at addressing the above issues, we propose a Variate Associated Domain Adaptation Method Combined with a Graph Deviation Network (VANDA) for MTS-AD, which includes two major contributions. First, we characterize the intra-domain variate associations of the source domain by a graph deviation network (GDN), which can share parameters across domains without dimension alignment. Second, we propose a sliding similarity to measure the inter-domain variate associations and perform joint training by minimizing the optimal transport distance between source and target data for transferring variate associations across domains. VANDA achieves domain adaptation by transferring both variate associations and GDN parameters from the source domain to the target domain. We construct two pairs of MTS-AD datasets from existing MTS-AD data and combine three domain adaptation strategies with six MTS-AD backbones as the benchmark methods for experimental evaluation and comparison. Extensive experiments demonstrate the effectiveness of our approach, which outperforms the benchmark methods, and significantly improves the AD performance of the target domain by effectively utilizing the source domain knowledge.

AI-aided drug discovery (AIDD) is gaining popularity due to its potential to make the search for new pharmaceuticals faster, less expensive, and more effective. Despite its extensive use in numerous fields (e.g., ADMET prediction, virtual screening), little research has been conducted on the out-of-distribution (OOD) learning problem with noise. We present DrugOOD, a systematic OOD dataset curator and benchmark for AIDD. Particularly, we focus on the drug-target binding affinity prediction problem, which involves both macromolecule (protein target) and small-molecule (drug compound). DrugOOD offers an automated dataset curator with user-friendly customization scripts, rich domain annotations aligned with biochemistry knowledge, realistic noise level annotations, and rigorous benchmarking of SOTA OOD algorithms, as opposed to only providing fixed datasets. Since the molecular data is often modeled as irregular graphs using graph neural network (GNN) backbones, DrugOOD also serves as a valuable testbed for graph OOD learning problems. Extensive empirical studies have revealed a significant performance gap between in-distribution and out-of-distribution experiments, emphasizing the need for the development of more effective schemes that permit OOD generalization under noise for AIDD.

Graph neural networks (GNNs) have achieved state-of-the-art performance in representation learning for graphs recently. However, the effectiveness of GNNs, which capitalize on the key operation of message propagation, highly depends on the quality of the topology structure. Most of the graphs in real-world scenarios follow a long-tailed distribution on their node degrees, that is, a vast majority of the nodes in the graph are tail nodes with only a few connected edges. GNNs produce inferior node representations for tail nodes due to the lack of sufficient structural information. In the pursuit of promoting the performance of GNNs for tail nodes, we explore how the deficiency of structural information deteriorates the performance of tail nodes and propose a general structural augmentation based tailno de representation learning framework, dubbed as øurs, which can jointly learn to augment the graph structure and extract more informative representations for tail nodes. Extensive experiments on six public benchmark datasets demonstrate that øurs outperforms the state-of-the-art methods for tail node representation learning.

Large language models (LLMs) outperform information retrieval techniques for downstream knowledge-intensive tasks when being prompted to generate world knowledge.Yet, community concerns abound regarding the factuality and potential implications of using this uncensored knowledge.In light of this, we introduce CONNER, a COmpreheNsive kNowledge Evaluation fRamework, designed to systematically and automatically evaluate generated knowledge from six important perspectives -Factuality, Relevance, Coherence, Informativeness, Helpfulness and Validity.We conduct an extensive empirical analysis of the generated knowledge from three different types of LLMs on two widely-studied knowledge-intensive tasks, i.e., open-domain question answering and knowledge-grounded dialogue.Surprisingly, our study reveals that the factuality of generated knowledge, even if lower, does not significantly hinder downstream tasks.Instead, the relevance and coherence of the outputs are more important than small factual mistakes.Further, we show how to use CONNER to improve knowledge-intensive tasks by designing two strategies: Prompt Engineering and Knowledge Selection.Our evaluation code and LLMgenerated knowledge with human annotations will be released 1 to facilitate future research.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning. We then propose a new framework Graph invAriant Learning Assistant (GALA). GALA incorporates an assistant model that needs to be sensitive to graph environment changes or distribution shifts. The correctness of the proxy predictions by the assistant model hence can differentiate the variations in spurious subgraphs. We show that extracting the maximally invariant subgraph to the proxy predictions provably identifies the underlying invariant subgraph for successful OOD generalization under the established minimal assumptions. Extensive experiments on datasets including DrugOOD with various graph distribution shifts confirm the effectiveness of GALA.

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.

Large language models have demonstrated surprising ability to perform in-context learning, i.e., these models can be directly applied to solve numerous downstream tasks by conditioning on a prompt constructed by a few input-output examples. However, prior research has shown that in-context learning can suffer from high instability due to variations in training examples, example order, and prompt formats. Therefore, the construction of an appropriate prompt is essential for improving the performance of in-context learning. In this paper, we revisit this problem from the view of predictive bias. Specifically, we introduce a metric to evaluate the predictive bias of a fixed prompt against labels or a given attributes. Then we empirically show that prompts with higher bias always lead to unsatisfactory predictive quality. Based on this observation, we propose a novel search strategy based on the greedy search to identify the near-optimal prompt for improving the performance of in-context learning. We perform comprehensive experiments with state-of-the-art mainstream models such as GPT-3 on various downstream tasks. Our results indicate that our method can enhance the model's in-context learning performance in an effective and interpretable manner.

Molecular representation learning lays the foundation for drug discovery. However, existing methods suffer from poor out-of-distribution (OOD) generalization, particularly when data for training and testing originate from different environments. To address this issue, we propose a new framework for learning molecular representations that exhibit invariance and robustness against distribution shifts. Specifically, we propose a strategy called ``first-encoding-then-separation'' to identify invariant molecule features in the latent space, which deviates from conventional practices. Prior to the separation step, we introduce a residual vector quantization module that mitigates the over-fitting to training data distributions while preserving the expressivity of encoders. Furthermore, we design a task-agnostic self-supervised learning objective to encourage precise invariance identification, which enables our method widely applicable to a variety of tasks, such as regression and multi-label classification. Extensive experiments on 18 real-world molecular datasets demonstrate that our model achieves stronger generalization against state-of-the-art baselines in the presence of various distribution shifts. Our code is available at https://github.com/HICAI-ZJU/iMoLD.

Despite the success of graph neural networks (GNNs) over the Web in recent years, the typical transductive learning setting for node classification requires GNNs to be retrained frequently, making them vulnerable to poisoning attacks by corrupting the training graph. Poisoning attacks on graphs are, however, non-trivial as the attack space is potentially large, and the discrete graph structure makes the poisoning function non-differentiable. In this paper, we revisit the bi-level optimization problem in graph poisoning and propose a novel graph poisoning method, termed Curriculum Graph Poisoning (CuGPo), inspired by curriculum learning. In contrast to other poisoning attacks that use heuristics or directly optimize the graph, our method learns to generate poisoned graphs from basic adversarial knowledge first and advanced knowledge later. Specifically, for the outer optimization, we utilize the slightly perturbed graphs which represent the easy poisoning task at the beginning, and then enlarge the attack space until the final; for the inner optimization, we firstly exploit the knowledge from the clean graph and then adapt quickly to perturbed graphs to obtain the adversarial knowledge. Extensive experiments demonstrate that CuGPo achieves state-of-the-art performance in graph poisoning attacks.

Graph neural networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs, as a result of their ability to exploit node features and topological information simultaneously. However, most GNNs implicitly assume that the labels of nodes and their neighbors in a graph are the same or consistent, which does not hold in heterophilic graphs, where the labels of linked nodes are likely to differ. Moreover, when the topology is non-informative for label prediction, ordinary GNNs may work significantly worse than simply applying multi-layer perceptrons (MLPs) on each node. To tackle the above problem, we propose a new $p$-Laplacian based GNN model, termed as $^p$GNN, whose message passing mechanism is derived from a discrete regularization framework and could be theoretically explained as an approximation of a polynomial graph filter defined on the spectral domain of $p$-Laplacians. The spectral analysis shows that the new message passing mechanism works as low-high-pass filters, thus making $^p$GNNs are effective on both homophilic and heterophilic graphs. Empirical studies on real-world and synthetic datasets validate our findings and demonstrate that $^p$GNNs significantly outperform several state-of-the-art GNN architectures on heterophilic benchmarks while achieving competitive performance on homophilic benchmarks. Moreover, $^p$GNNs can adaptively learn aggregation weights and are robust to noisy edges.

Recently, the pretrain-finetuning paradigm has attracted tons of attention in graph learning community due to its power of alleviating the lack of labels problem in many real-world applications. Current studies use existing techniques, such as weight constraint, representation constraint, which are derived from images or text data, to transfer the invariant knowledge from the pre-train stage to fine-tuning stage. However, these methods failed to preserve invariances from graph structure and Graph Neural Network (GNN) style models. In this paper, we present a novel optimal transport-based fine-tuning framework called GTOT-Tuning, namely, Graph Topology induced Optimal Transport fine-Tuning, for GNN style backbones. GTOT-Tuning is required to utilize the property of graph data to enhance the preservation of representation produced by fine-tuned networks. Toward this goal, we formulate graph local knowledge transfer as an Optimal Transport (OT) problem with a structural prior and construct the GTOT regularizer to constrain the fine-tuned model behaviors. By using the adjacency relationship amongst nodes, the GTOT regularizer achieves node-level optimal transport procedures and reduces redundant transport procedures, resulting in efficient knowledge transfer from the pre-trained models. We evaluate GTOT-Tuning on eight downstream tasks with various GNN backbones and demonstrate that it achieves state-of-the-art fine-tuning performance for GNNs.

Deep graph learning (DGL) has achieved remarkable progress in both business and scientific areas ranging from finance and e-commerce, to drug and advanced material discovery. Despite the progress, how to ensure various DGL algorithms behave in a socially responsible manner and meet regulatory compliance requirements becomes an emerging problem, especially in risk-sensitive domains. Trustworthy graph learning (TwGL) aims to solve the above problems from a technical viewpoint. In contrast to conventional graph learning which mainly cares about model performance, TwGL considers various reliability and safety aspects of DGL, including but not limited to adversarial robustness, explainability, and privacy protection. Whilst several previous tutorials have been made for the introduction of DGL in KDD, seldom is there a special focus on its safety aspects, including reliability, explainability, and privacy protection capability. This tutorial mainly covers the key achievements of trustworthy graph learning in recent years. Specifically, we will discuss three essential topics, that is, the reliability of DGL against inherent noise, distribution shift and adversarial attack, explainability methods, and privacy protection for DGL. Meanwhile, we will introduce some guidelines for applying DGL to risk-sensitive applications (e.g., AI drug discovery) to ensure GNN models behave in a trustworthy way. We hope our tutorial can offer a comprehensive review of recent advances in this area and also provide some useful suggestions to guide the developers to choose appropriate techniques for their applications.

Few-shot object detection (FSOD) is to detect objects with a few examples. However, existing FSOD methods do not consider hierarchical fine-grained category structures of objects that exist widely in real life. For example, animals are taxonomically classified into orders, families, genera and species etc. In this paper, we propose and solve a new problem called hierarchical few-shot object detection (Hi-FSOD), which aims to detect objects with hierarchical categories in the FSOD paradigm. To this end, on the one hand, we build the first large-scale and high-quality Hi-FSOD benchmark dataset HiFSOD-Bird, which contains 176,350 wild-bird images falling to 1,432 categories. All the categories are organized into a 4-level taxonomy, consisting of 32 orders, 132 families, 572 genera and 1,432 species. On the other hand, we propose the first Hi-FSOD method HiCLPL, where a hierarchical contrastive learning approach is developed to constrain the feature space so that the feature distribution of objects is consistent with the hierarchical taxonomy and the model's generalization power is strengthened. Meanwhile, a probabilistic loss is designed to enable the child nodes to correct the classification errors of their parent nodes in the taxonomy. Extensive experiments on the benchmark dataset HiFSOD-Bird show that our method HiCLPL outperforms the existing FSOD methods.

Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses unique challenges to adopting the invariance principle. In particular, distribution shifts on graphs can appear in a variety of forms such as attributes and structures, making it difficult to identify the invariance. Moreover, domain or environment partitions, which are often required by OOD methods on Euclidean data, could be highly expensive to obtain for graphs. To bridge this gap, we propose a new framework, called Causality Inspired Invariant Graph LeArning (CIGA), to capture the invariance of graphs for guaranteed OOD generalization under various distribution shifts. Specifically, we characterize potential distribution shifts on graphs with causal models, concluding that OOD generalization on graphs is achievable when models focus only on subgraphs containing the most information about the causes of labels. Accordingly, we propose an information-theoretic objective to extract the desired subgraphs that maximally preserve the invariant intra-class information. Learning with these subgraphs is immune to distribution shifts. Extensive experiments on 16 synthetic or real-world datasets, including a challenging setting -- DrugOOD, from AI-aided drug discovery, validate the superior OOD performance of CIGA.

Subpopulation shift widely exists in many real-world machine learning applications, referring to the training and test distributions containing the same subpopulation groups but varying in subpopulation frequencies. Importance reweighting is a normal way to handle the subpopulation shift issue by imposing constant or adaptive sampling weights on each sample in the training dataset. However, some recent studies have recognized that most of these approaches fail to improve the performance over empirical risk minimization especially when applied to over-parameterized neural networks. In this work, we propose a simple yet practical framework, called uncertainty-aware mixup (UMIX), to mitigate the overfitting issue in over-parameterized models by reweighting the ''mixed'' samples according to the sample uncertainty. The training-trajectories-based uncertainty estimation is equipped in the proposed UMIX for each sample to flexibly characterize the subpopulation distribution. We also provide insightful theoretical analysis to verify that UMIX achieves better generalization bounds over prior works. Further, we conduct extensive empirical studies across a wide range of tasks to validate the effectiveness of our method both qualitatively and quantitatively. Code is available at https://github.com/TencentAILabHealthcare/UMIX.

Learning set functions becomes increasingly important in many applications like product recommendation and compound selection in AI-aided drug discovery. The majority of existing works study methodologies of set function learning under the function value oracle, which, however, requires expensive supervision signals. This renders it impractical for applications with only weak supervisions under the Optimal Subset (OS) oracle, the study of which is surprisingly overlooked. In this work, we present a principled yet practical maximum likelihood learning framework, termed as EquiVSet, that simultaneously meets the following desiderata of learning neural set functions under the OS oracle: i) permutation invariance of the set mass function being modeled; ii) permission of varying ground set; iii) minimum prior and iv) scalability. The main components of our framework involve: an energy-based treatment of the set mass function, DeepSet-style architectures to handle permutation invariance, mean-field variational inference, and its amortized variants. Thanks to the delicate combination of these advanced architectures, empirical studies on three real-world applications (including Amazon product recommendation, set anomaly detection, and compound selection for virtual screening) demonstrate that EquiVSet outperforms the baselines by a large margin.

Click-Through Rate (CTR) prediction, which aims to estimate the probability that a user will click an item, is an essential component of online advertising. Existing methods mainly attempt to mine user interests from users' historical behaviours, which contain users' directly interacted items. Although these methods have made great progress, they are often limited by the recommender system's direct exposure and inactive interactions, and thus fail to mine all potential user interests. To tackle these problems, we propose Neighbor-Interaction based CTR prediction (NI-CTR), which considers this task under a Heterogeneous Information Network (HIN) setting. In short, Neighbor-Interaction based CTR prediction involves the local neighborhood of the target user-item pair in the HIN to predict their linkage. In order to guide the representation learning of the local neighbourhood, we further consider different kinds of interactions among the local neighborhood nodes from both explicit and implicit perspective, and propose a novel Graph-Masked Transformer (GMT) to effectively incorporates these kinds of interactions to produce highly representative embeddings for the target user-item pair. Moreover, in order to improve model robustness against neighbour sampling, we enforce a consistency regularization loss over the neighbourhood embedding. We conduct extensive experiments on two real-world datasets with millions of instances and the experimental results show that our proposed method outperforms state-of-the-art CTR models significantly. Meanwhile, the comprehensive ablation studies verify the effectiveness of every component of our model. Furthermore, we have deployed this framework on the WeChat Official Account Platform with billions of users. The online A/B tests demonstrate an average CTR improvement of 21.9% against all online baselines.

Fake News detection has attracted much attention in recent years. Social context based detection methods attempt to model the spreading patterns of fake news by utilizing the collective wisdom from users on social media. This task is challenging for three reasons: (1) There are multiple types of entities and relations in social context, requiring methods to effectively model the heterogeneity. (2) The emergence of news in novel topics in social media causes distribution shifts, which can significantly degrade the performance of fake news detectors. (3) Existing fake news datasets usually lack of great scale, topic diversity and user social relations, impeding the development of this field. To solve these problems, we formulate social context based fake news detection as a heterogeneous graph classification problem, and propose a fake news detection model named Post-User Interaction Network (PSIN), which adopts a divide-and-conquer strategy to model the post-post, user-user and post-user interactions in social context effectively while maintaining their intrinsic characteristics. Moreover,we adopt an adversarial topic discriminator for topic-agnostic feature learning, in order to improve the generalizability of our method for new-emerging topics. Furthermore, we curate a new dataset for fake news detection, which contains over 27,155 news from 5 topics, 5 million posts, 2 million users and their induced social graph with 0.2 billion edges. It has been published on https://github.com/qwerfdsaplking/MC-Fake. Extensive experiments illustrate that our method outperforms SOTA baselines in both in-topic and out-of-topic settings.

MOTIVATION: The crux of molecular property prediction is to generate meaningful representations of the molecules. One promising route is to exploit the molecular graph structure through graph neural networks (GNNs). Both atoms and bonds significantly affect the chemical properties of a molecule, so an expressive model ought to exploit both node (atom) and edge (bond) information simultaneously. Inspired by this observation, we explore the multi-view modeling with GNN (MVGNN) to form a novel paralleled framework, which considers both atoms and bonds equally important when learning molecular representations. In specific, one view is atom-central and the other view is bond-central, then the two views are circulated via specifically designed components to enable more accurate predictions. To further enhance the expressive power of MVGNN, we propose a cross-dependent message-passing scheme to enhance information communication of different views. The overall framework is termed as CD-MVGNN. RESULTS: We theoretically justify the expressiveness of the proposed model in terms of distinguishing non-isomorphism graphs. Extensive experiments demonstrate that CD-MVGNN achieves remarkably superior performance over the state-of-the-art models on various challenging benchmarks. Meanwhile, visualization results of the node importance are consistent with prior knowledge, which confirms the interpretability power of CD-MVGNN. AVAILABILITY AND IMPLEMENTATION: The code and data underlying this work are available in GitHub at https://github.com/uta-smile/CD-MVGNN. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Recently, the teacher-student knowledge distillation framework has demonstrated its potential in training Graph Neural Networks (GNNs). However, due to the difficulty of training over-parameterized GNN models, one may not easily obtain a satisfactory teacher model for distillation. Furthermore, the inefficient training process of teacher-student knowledge distillation also impedes its applications in GNN models. In this paper, we propose the first teacher-free knowledge distillation method for GNNs, termed GNN Self-Distillation (GNN-SD), that serves as a drop-in replacement of the standard training process. The method is built upon the proposed neighborhood discrepancy rate (NDR), which quantifies the non-smoothness of the embedded graph in an efficient way. Based on this metric, we propose the adaptive discrepancy retaining (ADR) regularizer to empower the transferability of knowledge that maintains high neighborhood discrepancy across GNN layers. We also summarize a generic GNN-SD framework that could be exploited to induce other distillation strategies. Experiments further prove the effectiveness and generalization of our approach, as it brings: 1) state-of-the-art GNN distillation performance with less training cost, 2) consistent and considerable performance enhancement for various popular backbones.

Graph Convolutional Networks (GCNs) are promising deep learning approaches in learning representations for graph-structured data. Despite the proliferation of such methods, it is well known that they are vulnerable to carefully crafted adversarial attacks on the graph structure. In this paper, we first conduct an adversarial vulnerability analysis based on matrix perturbation theory. We prove that the low- frequency components of the symmetric normalized Laplacian, which is usually used as the convolutional filter in GCNs, could be more robust against structural perturbations when their eigenvalues fall into a certain robust interval. Our results indicate that not all low-frequency components are robust to adversarial attacks and provide a deeper understanding of the relationship between graph spectrum and robustness of GCNs. Motivated by the theory, we present GCN-LFR, a general robust co-training paradigm for GCN-based models, that encourages transferring the robustness of low-frequency components with an auxiliary neural network. To this end, GCN-LFR could enhance the robustness of various kinds of GCN-based models against poisoning structural attacks in a plug-and-play manner. Extensive experiments across five benchmark datasets and five GCN-based models also confirm that GCN-LFR is resistant to the adversarial attacks without compromising on performance in the benign situation.

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 this class of models and finally, we demonstrate its effectiveness and viability on several real-world social connection graph datasets with integer submodular objectives.

How to obtain informative representations of molecules is a crucial prerequisite in AI-driven drug design and discovery. Recent researches abstract molecules as graphs and employ Graph Neural Networks (GNNs) for molecular representation learning. Nevertheless, two issues impede the usage of GNNs in real scenarios: (1) insufficient labeled molecules for supervised training; (2) poor generalization capability to new-synthesized molecules. To address them both, we propose a novel framework, GROVER, which stands for Graph Representation frOm self-superVised mEssage passing tRansformer. With carefully designed self-supervised tasks in node-, edge- and graph-level, GROVER can learn rich structural and semantic information of molecules from enormous unlabelled molecular data. Rather, to encode such complex information, GROVER integrates Message Passing Networks into the Transformer-style architecture to deliver a class of more expressive encoders of molecules. The flexibility of GROVER allows it to be trained efficiently on large-scale molecular dataset without requiring any supervision, thus being immunized to the two issues mentioned above. We pre-train GROVER with 100 million parameters on 10 million unlabelled molecules---the biggest GNN and the largest training dataset in molecular representation learning. We then leverage the pre-trained GROVER for molecular property prediction followed by task-specific fine-tuning, where we observe a huge improvement (more than 6% on average) from current state-of-the-art methods on 11 challenging benchmarks. The insights we gained are that well-designed self-supervision losses and largely-expressive pre-trained models enjoy the significant potential on performance boosting.

Mean field inference for discrete graphical models is generally a highly nonconvex problem, which also holds for the class of probabilistic log-submodular models. Existing optimization methods, e.g., coordinate ascent algorithms, typically only find local optima. In this work we propose provable mean filed methods for probabilistic log-submodular models and its posterior agreement (PA) with strong approximation guarantees. The main algorithmic technique is a new Double Greedy scheme, termed DR-DoubleGreedy, for continuous DR-submodular maximization with box-constraints. It is a one-pass algorithm with linear time complexity, reaching the optimal 1/2 approximation ratio, which may be of independent interest. We validate the superior performance of our algorithms against baselines on both synthetic and real-world datasets.

The recent years have witnessed advances in parallel algorithms for large-scale optimization problems. Notwithstanding the demonstrated success, existing algorithms that parallelize over features are usually limited by divergence issues under high parallelism or require data preprocessing to alleviate these problems. In this paper, we propose a Parallel Coordinate Descent algorithm using approximate Newton steps (PCDN) that is guaranteed to converge globally without data preprocessing. The key component of the PCDN algorithm is the high-dimensional line search, which guarantees the global convergence with high parallelism. The PCDN algorithm randomly partitions the feature set into b subsets/bundles of size P, and sequentially processes each bundle by first computing the descent directions for each feature in parallel and then conducting P-dimensional line search to compute the step size. We show that: 1) the PCDN algorithm is guaranteed to converge globally despite increasing parallelism and 2) the PCDN algorithm converges to the specified accuracy ϵ within the limited iteration number of Tϵ, and Tϵdecreases with increasing parallelism. In addition, the data transfer and synchronization cost of the P-dimensional line search can be minimized by maintaining intermediate quantities. For concreteness, the proposed PCDN algorithm is applied to L1-regularized logistic regression and L1-regularized L2-loss support vector machine problems. Experimental evaluations on seven benchmark data sets show that the PCDN algorithm exploits parallelism well and outperforms the state-of-the-art methods.

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive as they potentially require fewer communication rounds to converge. However, there are significant drawbacks that impede their wide adoption, such as the computation and the communication of a large Hessian matrix. In this paper we present a new algorithm for distributed training of generalized linear models that only requires the computation of diagonal blocks of the Hessian matrix on the individual workers. To deal with this approximate information we propose an adaptive approach that - akin to trust-region methods - dynamically adapts the auxiliary model to compensate for modeling errors. We provide theoretical rates of convergence for a wide class of problems including $L_1$-regularized objectives. We also demonstrate that our approach achieves state-of-the-art results on multiple large benchmark datasets.

Decentralized machine learning is a promising emerging paradigm in view of global challenges of data ownership and privacy. We consider learning of linear classification and regression models, in the setting where the training data is decentralized over many user devices, and the learning algorithm must run on-device, on an arbitrary communication network, without a central coordinator. We propose COLA, a new decentralized training algorithm with strong theoretical guarantees and superior practical performance. Our framework overcomes many limitations of existing methods, and achieves communication efficiency, scalability, elasticity as well as resilience to changes in data and allows for unreliable and heterogeneous participating devices.

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation guarantees. Specifically, i) We introduce the weak DR property that gives a unified characterization of submodularity for all set, integer-lattice and continuous functions; ii) for maximizing monotone DR-submodular continuous functions under general down-closed convex constraints, we propose a Frank-Wolfe variant with (1-1/e) approximation guarantee, and sub-linear convergence rate; iii) for maximizing general non-monotone submodular continuous functions subject to box constraints, we propose a DoubleGreedy algorithm with 1/3 approximation guarantee. Submodular continuous functions naturally find applications in various real-world settings, including influence and revenue maximization with continuous assignments, sensor energy management, facility location, etc. Experimental results show that the proposed algorithms efficiently generate superior solutions compared to baseline algorithms.

We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $\alpha$ and the submodularity ratio $\gamma$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $\frac{1}{\alpha}(1- e^{-\gamma\alpha})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.

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.