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Existing Video Corpus Moment Retrieval (VCMR) is limited to coarse-grained understanding, which hinders precise video moment localization when given fine-grained queries. In this paper, we propose a more challenging fine-grained VCMR benchmark requiring methods to localize the best-matched moment from the corpus with other partially matched candidates. To improve the dataset construction efficiency and guarantee high-quality data annotations, we propose VERIFIED, an automatic \underline{V}id\underline{E}o-text annotation pipeline to generate captions with \underline{R}el\underline{I}able \underline{FI}n\underline{E}-grained statics and \underline{D}ynamics. Specifically, we resort to large language models (LLM) and large multimodal models (LMM) with our proposed Statics and Dynamics Enhanced Captioning modules to generate diverse fine-grained captions for each video. To filter out the inaccurate annotations caused by the LLM hallucination, we propose a Fine-Granularity Aware Noise Evaluator where we fine-tune a video foundation model with disturbed hard-negatives augmented contrastive and matching losses. With VERIFIED, we construct a more challenging fine-grained VCMR benchmark containing Charades-FIG, DiDeMo-FIG, and ActivityNet-FIG which demonstrate a high level of annotation quality. We evaluate several state-of-the-art VCMR models on the proposed dataset, revealing that there is still significant scope for fine-grained video understanding in VCMR. Code and Datasets are in \href{https://github.com/hlchen23/VERIFIED}{https://github.com/hlchen23/VERIFIED}., Comment: Accepted by 38th NeurIPS Datasets & Benchmarks Track (NeurIPS 2024)

Multi-modal generative AI has received increasing attention in both academia and industry. Particularly, two dominant families of techniques are: i) The multi-modal large language model (MLLM) such as GPT-4V, which shows impressive ability for multi-modal understanding; ii) The diffusion model such as Sora, which exhibits remarkable multi-modal powers, especially with respect to visual generation. As such, one natural question arises: Is it possible to have a unified model for both understanding and generation? To answer this question, in this paper, we first provide a detailed review of both MLLM and diffusion models, including their probabilistic modeling procedure, multi-modal architecture design, and advanced applications to image/video large language models as well as text-to-image/video generation. Then, we discuss the two important questions on the unified model: i) whether the unified model should adopt the auto-regressive or diffusion probabilistic modeling, and ii) whether the model should utilize a dense architecture or the Mixture of Experts(MoE) architectures to better support generation and understanding, two objectives. We further provide several possible strategies for building a unified model and analyze their potential advantages and disadvantages. We also summarize existing large-scale multi-modal datasets for better model pretraining in the future. To conclude the paper, we present several challenging future directions, which we believe can contribute to the ongoing advancement of multi-modal generative AI.

Video generation has witnessed great success recently, but their application in generating long videos still remains challenging due to the difficulty in maintaining the temporal consistency of generated videos and the high memory cost during generation. To tackle the problems, in this paper, we propose a brave and new idea of Multi-sentence Video Grounding for Long Video Generation, connecting the massive video moment retrieval to the video generation task for the first time, providing a new paradigm for long video generation. The method of our work can be summarized as three steps: (i) We design sequential scene text prompts as the queries for video grounding, utilizing the massive video moment retrieval to search for video moment segments that meet the text requirements in the video database. (ii) Based on the source frames of retrieved video moment segments, we adopt video editing methods to create new video content while preserving the temporal consistency of the retrieved video. Since the editing can be conducted segment by segment, and even frame by frame, it largely reduces the memory cost. (iii) We also attempt video morphing and personalized generation methods to improve the subject consistency of long video generation, providing ablation experimental results for the subtasks of long video generation. Our approach seamlessly extends the development in image/video editing, video morphing and personalized generation, and video grounding to the long video generation, offering effective solutions for generating long videos at low memory cost.

Graph Neural Architecture Search (GNAS) has achieved superior performance on various graph-structured tasks. However, existing GNAS studies overlook the applications of GNAS in resource-constraint scenarios. This paper proposes to design a joint graph data and architecture mechanism, which identifies important sub-architectures via the valuable graph data. To search for optimal lightweight Graph Neural Networks (GNNs), we propose a Lightweight Graph Neural Architecture Search with Graph SparsIfication and Network Pruning (GASSIP) method. In particular, GASSIP comprises an operation-pruned architecture search module to enable efficient lightweight GNN search. Meanwhile, we design a novel curriculum graph data sparsification module with an architecture-aware edge-removing difficulty measurement to help select optimal sub-architectures. With the aid of two differentiable masks, we iteratively optimize these two modules to efficiently search for the optimal lightweight architecture. Extensive experiments on five benchmarks demonstrate the effectiveness of GASSIP. Particularly, our method achieves on-par or even higher node classification performance with half or fewer model parameters of searched GNNs and a sparser graph., Comment: Accepted by KDD 2024. The two first authors made equal contributions

Generative models are widely utilized to model the distribution of fused images in the field of infrared and visible image fusion. However, current generative models based fusion methods often suffer from unstable training and slow inference speed. To tackle this problem, a novel fusion method based on consistency model is proposed, termed as CoMoFusion, which can generate the high-quality images and achieve fast image inference speed. In specific, the consistency model is used to construct multi-modal joint features in the latent space with the forward and reverse process. Then, the infrared and visible features extracted by the trained consistency model are fed into fusion module to generate the final fused image. In order to enhance the texture and salient information of fused images, a novel loss based on pixel value selection is also designed. Extensive experiments on public datasets illustrate that our method obtains the SOTA fusion performance compared with the existing fusion methods.

Graph NAS has emerged as a promising approach for autonomously designing GNN architectures by leveraging the correlations between graphs and architectures. Existing methods fail to generalize under distribution shifts that are ubiquitous in real-world graph scenarios, mainly because the graph-architecture correlations they exploit might be spurious and varying across distributions. We propose to handle the distribution shifts in the graph architecture search process by discovering and exploiting the causal relationship between graphs and architectures to search for the optimal architectures that can generalize under distribution shifts. The problem remains unexplored with following challenges: how to discover the causal graph-architecture relationship that has stable predictive abilities across distributions, and how to handle distribution shifts with the discovered causal graph-architecture relationship to search the generalized graph architectures. To address these challenges, we propose Causal-aware Graph Neural Architecture Search (CARNAS), which is able to capture the causal graph-architecture relationship during the architecture search process and discover the generalized graph architecture under distribution shifts. Specifically, we propose Disentangled Causal Subgraph Identification to capture the causal subgraphs that have stable prediction abilities across distributions. Then, we propose Graph Embedding Intervention to intervene on causal subgraphs within the latent space, ensuring that these subgraphs encapsulate essential features for prediction while excluding non-causal elements. Additionally, we propose Invariant Architecture Customization to reinforce the causal invariant nature of the causal subgraphs, which are utilized to tailor generalized graph architectures. Extensive experiments demonstrate that CARNAS achieves advanced out-of-distribution generalization ability.

Generating customized content in videos has received increasing attention recently. However, existing works primarily focus on customized text-to-video generation for single subject, suffering from subject-missing and attribute-binding problems when the video is expected to contain multiple subjects. Furthermore, existing models struggle to assign the desired actions to the corresponding subjects (action-binding problem), failing to achieve satisfactory multi-subject generation performance. To tackle the problems, in this paper, we propose DisenStudio, a novel framework that can generate text-guided videos for customized multiple subjects, given few images for each subject. Specifically, DisenStudio enhances a pretrained diffusion-based text-to-video model with our proposed spatial-disentangled cross-attention mechanism to associate each subject with the desired action. Then the model is customized for the multiple subjects with the proposed motion-preserved disentangled finetuning, which involves three tuning strategies: multi-subject co-occurrence tuning, masked single-subject tuning, and multi-subject motion-preserved tuning. The first two strategies guarantee the subject occurrence and preserve their visual attributes, and the third strategy helps the model maintain the temporal motion-generation ability when finetuning on static images. We conduct extensive experiments to demonstrate our proposed DisenStudio significantly outperforms existing methods in various metrics. Additionally, we show that DisenStudio can be used as a powerful tool for various controllable generation applications.

In the field of Artificial Intelligence for Information Technology Operations, causal discovery is pivotal for operation and maintenance of graph construction, facilitating downstream industrial tasks such as root cause analysis. Temporal causal discovery, as an emerging method, aims to identify temporal causal relationships between variables directly from observations by utilizing interventional data. However, existing methods mainly focus on synthetic datasets with heavy reliance on intervention targets and ignore the textual information hidden in real-world systems, failing to conduct causal discovery for real industrial scenarios. To tackle this problem, in this paper we propose to investigate temporal causal discovery in industrial scenarios, which faces two critical challenges: 1) how to discover causal relationships without the interventional targets that are costly to obtain in practice, and 2) how to discover causal relations via leveraging the textual information in systems which can be complex yet abundant in industrial contexts. To address these challenges, we propose the RealTCD framework, which is able to leverage domain knowledge to discover temporal causal relationships without interventional targets. Specifically, we first develop a score-based temporal causal discovery method capable of discovering causal relations for root cause analysis without relying on interventional targets through strategic masking and regularization. Furthermore, by employing Large Language Models (LLMs) to handle texts and integrate domain knowledge, we introduce LLM-guided meta-initialization to extract the meta-knowledge from textual information hidden in systems to boost the quality of discovery. We conduct extensive experiments on simulation and real-world datasets to show the superiority of our proposed RealTCD framework over existing baselines in discovering temporal causal structures.

Large language models (LLMs) have achieved great success in many fields, and recent works have studied exploring LLMs for graph discriminative tasks such as node classification. However, the abilities of LLMs for graph generation remain unexplored in the literature. Graph generation requires the LLM to generate graphs with given properties, which has valuable real-world applications such as drug discovery, while tends to be more challenging. In this paper, we propose LLM4GraphGen to explore the ability of LLMs for graph generation with systematical task designs and extensive experiments. Specifically, we propose several tasks tailored with comprehensive experiments to address key questions regarding LLMs' understanding of different graph structure rules, their ability to capture structural type distributions, and their utilization of domain knowledge for property-based graph generation. Our evaluations demonstrate that LLMs, particularly GPT-4, exhibit preliminary abilities in graph generation tasks, including rule-based and distribution-based generation. We also observe that popular prompting methods, such as few-shot and chain-of-thought prompting, do not consistently enhance performance. Besides, LLMs show potential in generating molecules with specific properties. These findings may serve as foundations for designing good LLMs based models for graph generation and provide valuable insights and further research.

The existing graph neural architecture search (GNAS) methods heavily rely on supervised labels during the search process, failing to handle ubiquitous scenarios where supervisions are not available. In this paper, we study the problem of unsupervised graph neural architecture search, which remains unexplored in the literature. The key problem is to discover the latent graph factors that drive the formation of graph data as well as the underlying relations between the factors and the optimal neural architectures. Handling this problem is challenging given that the latent graph factors together with architectures are highly entangled due to the nature of the graph and the complexity of the neural architecture search process. To address the challenge, we propose a novel Disentangled Self-supervised Graph Neural Architecture Search (DSGAS) model, which is able to discover the optimal architectures capturing various latent graph factors in a self-supervised fashion based on unlabeled graph data. Specifically, we first design a disentangled graph super-network capable of incorporating multiple architectures with factor-wise disentanglement, which are optimized simultaneously. Then, we estimate the performance of architectures under different factors by our proposed self-supervised training with joint architecture-graph disentanglement. Finally, we propose a contrastive search with architecture augmentations to discover architectures with factor-specific expertise. Extensive experiments on 11 real-world datasets demonstrate that the proposed model is able to achieve state-of-the-art performance against several baseline methods in an unsupervised manner., Comment: NeurIPS'23

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts., Comment: NeurIPS'23

In a scenario where multi-modal cameras are operating together, the problem of working with non-aligned images cannot be avoided. Yet, existing image fusion algorithms rely heavily on strictly registered input image pairs to produce more precise fusion results, as a way to improve the performance of downstream high-level vision tasks. In order to relax this assumption, one can attempt to register images first. However, the existing methods for registering multiple modalities have limitations, such as complex structures and reliance on significant semantic information. This paper aims to address the problem of image registration and fusion in a single framework, called BusRef. We focus on Infrared-Visible image registration and fusion task (IVRF). In this framework, the input unaligned image pairs will pass through three stages: Coarse registration, Fine registration and Fusion. It will be shown that the unified approach enables more robust IVRF. We also propose a novel training and evaluation strategy, involving the use of masks to reduce the influence of non-reconstructible regions on the loss functions, which greatly improves the accuracy and robustness of the fusion task. Last but not least, a gradient-aware fusion network is designed to preserve the complementary information. The advanced performance of this algorithm is demonstrated by

Recently, researchers have attempted to investigate the capability of LLMs in handling videos and proposed several video LLM models. However, the ability of LLMs to handle video grounding (VG), which is an important time-related video task requiring the model to precisely locate the start and end timestamps of temporal moments in videos that match the given textual queries, still remains unclear and unexplored in literature. To fill the gap, in this paper, we propose the LLM4VG benchmark, which systematically evaluates the performance of different LLMs on video grounding tasks. Based on our proposed LLM4VG, we design extensive experiments to examine two groups of video LLM models on video grounding: (i) the video LLMs trained on the text-video pairs (denoted as VidLLM), and (ii) the LLMs combined with pretrained visual description models such as the video/image captioning model. We propose prompt methods to integrate the instruction of VG and description from different kinds of generators, including caption-based generators for direct visual description and VQA-based generators for information enhancement. We also provide comprehensive comparisons of various VidLLMs and explore the influence of different choices of visual models, LLMs, prompt designs, etc, as well. Our experimental evaluations lead to two conclusions: (i) the existing VidLLMs are still far away from achieving satisfactory video grounding performance, and more time-related video tasks should be included to further fine-tune these models, and (ii) the combination of LLMs and visual models shows preliminary abilities for video grounding with considerable potential for improvement by resorting to more reliable models and further guidance of prompt instructions.

Human albumin is essential for indicating the body's overall health. Accurately predicting plasma albumin levels and determining appropriate doses are urgent clinical challenges, particularly in critically ill patients, to maintain optimal blood levels. However, human albumin prediction is non-trivial that has to leverage the dynamics of biochemical markers as well as the experience of treating patients. Moreover, the problem of distribution shift is often encountered in real clinical data, which may lead to a decline in the model prediction performance and reduce the reliability of the model's application. In this paper, we propose a framework named Out-of-Distribution Generalized Dynamic Graph Neural Network for Human Albumin Prediction (DyG-HAP), which is able to provide accurate albumin predictions for Intensity Care Unit (ICU) patients during hospitalization. We first model human albumin prediction as a dynamic graph regression problem to model the dynamics and patient relationship. Then, we propose a disentangled dynamic graph attention mechanism to capture and disentangle the patterns whose relationship to labels under distribution shifts is invariant and variant respectively. Last, we propose an invariant dynamic graph regression method to encourage the model to rely on invariant patterns to make predictions. Moreover, we propose a dataset named Albumin level testing and nutritional dosing data for Intensive Care (ANIC) for evaluation. Extensive experiments demonstrate the superiority of our method compared to several baseline methods in human albumin prediction., Comment: MedAI'23

Dynamic graph neural networks (DyGNNs) have demonstrated powerful predictive abilities by exploiting graph structural and temporal dynamics. However, the existing DyGNNs fail to handle distribution shifts, which naturally exist in dynamic graphs, mainly because the patterns exploited by DyGNNs may be variant with respect to labels under distribution shifts. In this paper, we propose Disentangled Intervention-based Dynamic graph Attention networks with Invariance Promotion (I-DIDA) to handle spatio-temporal distribution shifts in dynamic graphs by discovering and utilizing invariant patterns, i.e., structures and features whose predictive abilities are stable across distribution shifts. Specifically, we first propose a disentangled spatio-temporal attention network to capture the variant and invariant patterns. By utilizing the disentangled patterns, we design a spatio-temporal intervention mechanism to create multiple interventional distributions and an environment inference module to infer the latent spatio-temporal environments, and minimize the variance of predictions among these intervened distributions and environments, so that our model can make predictions based on invariant patterns with stable predictive abilities under distribution shifts. Extensive experiments demonstrate the superiority of our method over state-of-the-art baselines under distribution shifts. Our work is the first study of spatio-temporal distribution shifts in dynamic graphs, to the best of our knowledge.

In an era marked by the increasing adoption of Large Language Models (LLMs) for various tasks, there is a growing focus on exploring LLMs' capabilities in handling web data, particularly graph data. Dynamic graphs, which capture temporal network evolution patterns, are ubiquitous in real-world web data. Evaluating LLMs' competence in understanding spatial-temporal information on dynamic graphs is essential for their adoption in web applications, which remains unexplored in the literature. In this paper, we bridge the gap via proposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic graphs, to the best of our knowledge, for the first time. Specifically, we propose the LLM4DyG benchmark, which includes nine specially designed tasks considering the capability evaluation of LLMs from both temporal and spatial dimensions. Then, we conduct extensive experiments to analyze the impacts of different data generators, data statistics, prompting techniques, and LLMs on the model performance. Finally, we propose Disentangled Spatial-Temporal Thoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal understanding abilities. Our main observations are: 1) LLMs have preliminary spatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph tasks show increasing difficulties for LLMs as the graph size and density increase, while not sensitive to the time span and data generation mechanism, 3) the proposed DST2 prompting method can help to improve LLMs' spatial-temporal understanding abilities on dynamic graphs for most tasks. The data and codes are publicly available at Github., Comment: Accepted by ACM KDD'24

Large models have emerged as the most recent groundbreaking achievements in artificial intelligence, and particularly machine learning. However, when it comes to graphs, large models have not achieved the same level of success as in other fields, such as natural language processing and computer vision. In order to promote applying large models for graphs forward, we present a perspective paper to discuss the challenges and opportunities associated with developing large graph models. First, we discuss the desired characteristics of large graph models. Then, we present detailed discussions from three key perspectives: representation basis, graph data, and graph models. In each category, we provide a brief overview of recent advances and highlight the remaining challenges together with our visions. Finally, we discuss valuable applications of large graph models. We believe this perspective can encourage further investigations into large graph models, ultimately pushing us one step closer towards artificial general intelligence (AGI). We are the first to comprehensively study large graph models, to the best of our knowledge., Comment: Accepted by NeurIPS 2023 New Frontiers in Graph Learning Workshop. Comments are welcome

Graph neural architecture search (GraphNAS) has recently aroused considerable attention in both academia and industry. However, two key challenges seriously hinder the further research of GraphNAS. First, since there is no consensus for the experimental setting, the empirical results in different research papers are often not comparable and even not reproducible, leading to unfair comparisons. Secondly, GraphNAS often needs extensive computations, which makes it highly inefficient and inaccessible to researchers without access to large-scale computation. To solve these challenges, we propose NAS-Bench-Graph, a tailored benchmark that supports unified, reproducible, and efficient evaluations for GraphNAS. Specifically, we construct a unified, expressive yet compact search space, covering 26,206 unique graph neural network (GNN) architectures and propose a principled evaluation protocol. To avoid unnecessary repetitive training, we have trained and evaluated all of these architectures on nine representative graph datasets, recording detailed metrics including train, validation, and test performance in each epoch, the latency, the number of parameters, etc. Based on our proposed benchmark, the performance of GNN architectures can be directly obtained by a look-up table without any further computation, which enables fair, fully reproducible, and efficient comparisons. To demonstrate its usage, we make in-depth analyses of our proposed NAS-Bench-Graph, revealing several interesting findings for GraphNAS. We also showcase how the benchmark can be easily compatible with GraphNAS open libraries such as AutoGL and NNI. To the best of our knowledge, our work is the first benchmark for graph neural architecture search.

Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are independent and identically distributed. However, the existing literature fails to solve TSP instances when training and testing data have different distributions. Concretely, we find that different training and testing distribution will result in more difficult TSP instances, i.e., the solution obtained by the model has a large gap from the optimal solution. To tackle this problem, in this work, we study learning-based TSP methods when training and testing data have different distributions using adaptive-hardness, i.e., how difficult a TSP instance can be for a solver. This problem is challenging because it is non-trivial to (1) define hardness measurement quantitatively; (2) efficiently and continuously generate sufficiently hard TSP instances upon model training; (3) fully utilize instances with different levels of hardness to learn a more powerful TSP solver. To solve these challenges, we first propose a principled hardness measurement to quantify the hardness of TSP instances. Then, we propose a hardness-adaptive generator to generate instances with different hardness. We further propose a curriculum learner fully utilizing these instances to train the TSP solver. Experiments show that our hardness-adaptive generator can generate instances ten times harder than the existing methods, and our proposed method achieves significant improvement over state-of-the-art models in terms of the optimality gap., Comment: AAAI 2022

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning., Comment: 11 pages

Recent years have witnessed an upsurge in research interests and applications of machine learning on graphs. However, manually designing the optimal machine learning algorithms for different graph datasets and tasks is inflexible, labor-intensive, and requires expert knowledge, limiting its adaptivity and applicability. Automated machine learning (AutoML) on graphs, aiming to automatically design the optimal machine learning algorithm for a given graph dataset and task, has received considerable attention. However, none of the existing libraries can fully support AutoML on graphs. To fill this gap, we present Automated Graph Learning (AutoGL), the first dedicated library for automated machine learning on graphs. AutoGL is open-source, easy to use, and flexible to be extended. Specifically, we propose a three-layer architecture, consisting of backends to interface with devices, a complete automated graph learning pipeline, and supported graph applications. The automated machine learning pipeline further contains five functional modules: auto feature engineering, neural architecture search, hyper-parameter optimization, model training, and auto ensemble, covering the majority of existing AutoML methods on graphs. For each module, we provide numerous state-of-the-art methods and flexible base classes and APIs, which allow easy usage and customization. We further provide experimental results to showcase the usage of our AutoGL library. We also present AutoGL-light, a lightweight version of AutoGL to facilitate customizing pipelines and enriching applications, as well as benchmarks for graph neural architecture search. The codes of AutoGL are publicly available at https://github.com/THUMNLab/AutoGL., Comment: Extended version; initial version published at ICLR 2021 Workshop on Geometrical and Topological Representation Learning

In a given production planning horizon, the demands may only be comfirmed in part of the whole periods, and the others are uncertain. In this paper, we consider a two-stage stochastic lot-sizing problem with chance-constrained condition in the second stage. In the first stage, the demand is deterministic in each period, while in the second stage, the demands are random variables with finite distribution. We prove the optimality condition of the solutions under modified Wagner-Whitin condition and further develop a new equivalent MIP formulation which can depict the feasible region better. We also show that any subproblem fixing the selection of occurred scenarios has a complete linear description of its convex hull. A branch-and-bound algorithm is provided utilizing the character of the given subproblems.