Polynomial Width is Sufficient for Set Representation with High-dimensional Features

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension $L$, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension $L$ on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in $L$ that grows exponentially with the set size $N$ and feature dimension $D$. To investigate the minimal value of $L$ that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that $L$ being poly$(N, D)$ is sufficient for set representation using both embedding layers. We also provide a lower bound of $L$ for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction

Graph Anomaly Detection (GAD) is a technique used to identify abnormal nodes within graphs, finding applications in network security, fraud detection, social media spam detection, and various other domains. A common method for GAD is Graph Auto-Encoders (GAEs), which encode graph data into node representations and identify anomalies by assessing the reconstruction quality of the graphs based on these representations. However, existing GAE models are primarily optimized for direct link reconstruction, resulting in nodes connected in the graph being clustered in the latent space. As a result, they excel at detecting cluster-type structural anomalies but struggle with more complex structural anomalies that do not conform to clusters. To address this limitation, we propose a novel solution called GAD-NR, a new variant of GAE that incorporates neighborhood reconstruction for graph anomaly detection. GAD-NR aims to reconstruct the entire neighborhood of a node, encompassing the local structure, self-attributes, and neighbor attributes, based on the corresponding node representation. By comparing the neighborhood reconstruction loss between anomalous nodes and normal nodes, GAD-NR can effectively detect any anomalies. Extensive experimentation conducted on six real-world datasets validates the effectiveness of GAD-NR, showcasing significant improvements (by up to 30% in AUC) over state-of-the-art competitors. The source code for GAD-NR is openly available. Importantly, the comparative analysis reveals that the existing methods perform well only in detecting one or two types of anomalies out of the three types studied. In contrast, GAD-NR excels at detecting all three types of anomalies across the datasets, demonstrating its comprehensive anomaly detection capabilities.

Structural Re-weighting Improves Graph Domain Adaptation

In many real-world applications, graph-structured data used for training and testing have differences in distribution, such as in high energy physics (HEP) where simulation data used for training may not match real experiments. Graph domain adaptation (GDA) is a method used to address these differences. However, current GDA primarily works by aligning the distributions of node representations output by a single graph neural network encoder shared across the training and testing domains, which may often yield sub-optimal solutions. This work examines different impacts of distribution shifts caused by either graph structure or node attributes and identifies a new type of shift, named conditional structure shift (CSS), which current GDA approaches are provably sub-optimal to deal with. A novel approach, called structural reweighting (StruRW), is proposed to address this issue and is tested on synthetic graphs, four benchmark datasets, and a new application in HEP. StruRW has shown significant performance improvement over the baselines in the settings with large graph structure shifts, and reasonable performance improvement when node attribute shift dominates.

Hierarchical Reinforcement Learning for Modeling User Novelty-Seeking Intent in Recommender Systems

Recommending novel content, which expands user horizons by introducing them to new interests, has been shown to improve users' long-term experience on recommendation platforms \cite{chen2021values}. Users however are not constantly looking to explore novel content. It is therefore crucial to understand their novelty-seeking intent and adjust the recommendation policy accordingly. Most existing literature models a user's propensity to choose novel content or to prefer a more diverse set of recommendations at individual interactions. Hierarchical structure, on the other hand, exists in a user's novelty-seeking intent, which is manifested as a static and intrinsic user preference for seeking novelty along with a dynamic session-based propensity. To this end, we propose a novel hierarchical reinforcement learning-based method to model the hierarchical user novelty-seeking intent, and to adapt the recommendation policy accordingly based on the extracted user novelty-seeking propensity. We further incorporate diversity and novelty-related measurement in the reward function of the hierarchical RL (HRL) agent to encourage user exploration \cite{chen2021values}. We demonstrate the benefits of explicitly modeling hierarchical user novelty-seeking intent in recommendations through extensive experiments on simulated and real-world datasets. In particular, we demonstrate that the effectiveness of our proposed hierarchical RL-based method lies in its ability to capture such hierarchically-structured intent. As a result, the proposed HRL model achieves superior performance on several public datasets, compared with state-of-art baselines.

Prompt Tuning Large Language Models on Personalized Aspect Extraction for Recommendations

Existing aspect extraction methods mostly rely on explicit or ground truth aspect information, or using data mining or machine learning approaches to extract aspects from implicit user feedback such as user reviews. It however remains under-explored how the extracted aspects can help generate more meaningful recommendations to the users. Meanwhile, existing research on aspect-based recommendations often relies on separate aspect extraction models or assumes the aspects are given, without accounting for the fact the optimal set of aspects could be dependent on the recommendation task at hand. In this work, we propose to combine aspect extraction together with aspect-based recommendations in an end-to-end manner, achieving the two goals together in a single framework. For the aspect extraction component, we leverage the recent advances in large language models and design a new prompt learning mechanism to generate aspects for the end recommendation task. For the aspect-based recommendation component, the extracted aspects are concatenated with the usual user and item features used by the recommendation model. The recommendation task mediates the learning of the user embeddings and item embeddings, which are used as soft prompts to generate aspects. Therefore, the extracted aspects are personalized and contextualized by the recommendation task. We showcase the effectiveness of our proposed method through extensive experiments on three industrial datasets, where our proposed framework significantly outperforms state-of-the-art baselines in both the personalized aspect extraction and aspect-based recommendation tasks. In particular, we demonstrate that it is necessary and beneficial to combine the learning of aspect extraction and aspect-based recommendation together. We also conduct extensive ablation studies to understand the contribution of each design component in our framework.

Improving Graph Neural Networks on Multi-node Tasks with Labeling Tricks

In this paper, we provide a theory of using graph neural networks (GNNs) for \textit{multi-node representation learning}, where we are interested in learning a representation for a set of more than one node such as a link. Existing GNNs are mainly designed to learn single-node representations. When we want to learn a node-set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN. In this paper, we show a fundamental limitation of such an approach, namely the inability to capture the dependence among multiple nodes in a node set, and argue that directly aggregating individual node representations fails to produce an effective joint representation for multiple nodes. A straightforward solution is to distinguish target nodes from others. Formalizing this idea, we propose \text{labeling trick}, which first labels nodes in the graph according to their relationships with the target node set before applying a GNN and then aggregates node representations obtained in the labeled graph for multi-node representations. The labeling trick also unifies a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, ID-GNN, and NBFNet. Besides node sets in graphs, we also extend labeling tricks to posets, subsets and hypergraphs. Experiments verify that the labeling trick technique can boost GNNs on various tasks, including undirected link prediction, directed link prediction, hyperedge prediction, and subgraph prediction. Our work explains the superior performance of previous node-labeling-based methods and establishes a theoretical foundation for using GNNs for multi-node representation learning.

SUREL+: Moving from Walks to Sets for Scalable Subgraph-based Graph Representation Learning

Subgraph-based graph representation learning (SGRL) has recently emerged as a powerful tool in many prediction tasks on graphs due to its advantages in model expressiveness and generalization ability. Most previous SGRL models face computational issues associated with the high cost of extracting subgraphs for each training or testing query. Recently, SUREL has been proposed as a new framework to accelerate SGRL, which samples random walks offline and joins these walks as subgraphs online for prediction. Due to the reusability of sampled walks across different queries, SUREL achieves state-of-the-art performance in both scalability and prediction accuracy. However, SUREL still suffers from high computational overhead caused by node redundancy in sampled walks. In this work, we propose a novel framework SUREL+ that upgrades SUREL by using node sets instead of walks to represent subgraphs. This set-based representation avoids node duplication by definition, but the sizes of node sets can be irregular. To address this issue, we design a dedicated sparse data structure to efficiently store and fast index node sets, and provide a specialized operator to join them in parallel batches. SUREL+ is modularized to support multiple types of set samplers, structural features, and neural encoders to complement the loss of structural information due to the reduction from walks to sets. Extensive experiments have been performed to validate SUREL+ in the prediction tasks of links, relation types, and higher-order patterns. SUREL+ achieves 3-11$\times$ speedups of SUREL while maintaining comparable or even better prediction performance; compared to other SGRL baselines, SUREL+ achieves $\sim$20$\times$ speedups and significantly improves the prediction accuracy.

Unsupervised Learning for Combinatorial Optimization Needs Meta-Learning

A general framework of unsupervised learning for combinatorial optimization (CO) is to train a neural network (NN) whose output gives a problem solution by directly optimizing the CO objective. Albeit with some advantages over traditional solvers, the current framework optimizes an averaged performance over the distribution of historical problem instances, which misaligns with the actual goal of CO that looks for a good solution to every future encountered instance. With this observation, we propose a new objective of unsupervised learning for CO where the goal of learning is to search for good initialization for future problem instances rather than give direct solutions. We propose a meta-learning-based training pipeline for this new objective. Our method achieves good empirical performance. We observe that even just the initial solution given by our model before fine-tuning can significantly outperform the baselines under various evaluation settings including evaluation across multiple datasets, and the case with big shifts in the problem scale. The reason we conjecture is that meta-learning-based training lets the model be loosely tied to each local optima for a training instance while being more adaptive to the changes of optimization landscapes across instances.

Graph Federated Learning with Hidden Representation Sharing

Learning on Graphs (LoG) is widely used in multi-client systems when each client has insufficient local data, and multiple clients have to share their raw data to learn a model of good quality. One scenario is to recommend items to clients with limited historical data and sharing similar preferences with other clients in a social network. On the other hand, due to the increasing demands for the protection of clients' data privacy, Federated Learning (FL) has been widely adopted: FL requires models to be trained in a multi-client system and restricts sharing of raw data among clients. The underlying potential data-sharing conflict between LoG and FL is under-explored and how to benefit from both sides is a promising problem. In this work, we first formulate the Graph Federated Learning (GFL) problem that unifies LoG and FL in multi-client systems and then propose sharing hidden representation instead of the raw data of neighbors to protect data privacy as a solution. To overcome the biased gradient problem in GFL, we provide a gradient estimation method and its convergence analysis under the non-convex objective. In experiments, we evaluate our method in classification tasks on graphs. Our experiment shows a good match between our theory and the practice.