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We study the Densest Subgraph (DSG) problem under the additional constraint of differential privacy. DSG is a fundamental theoretical question which plays a central role in graph analytics, and so privacy is a natural requirement. All known private algorithms for Densest Subgraph lose constant multiplicative factors, despite the existence of non-private exact algorithms. We show that, perhaps surprisingly, this loss is not necessary: in both the classic differential privacy model and the LEDP model (local edge differential privacy, introduced recently by Dhulipala et al. [FOCS 2022]), we give $(\epsilon, \delta)$-differentially private algorithms with no multiplicative loss whatsoever. In other words, the loss is \emph{purely additive}. Moreover, our additive losses match or improve the best-known previous additive loss (in any version of differential privacy) when $1/\delta$ is polynomial in $n$, and are almost tight: in the centralized setting, our additive loss is $O(\log n /\epsilon)$ while there is a known lower bound of $\Omega(\sqrt{\log n / \epsilon})$. We also give a number of extensions. First, we show how to extend our techniques to both the node-weighted and the directed versions of the problem. Second, we give a separate algorithm with pure differential privacy (as opposed to approximate DP) but with worse approximation bounds. And third, we give a new algorithm for privately computing the optimal density which implies a separation between the structural problem of privately computing the densest subgraph and the numeric problem of privately computing the density of the densest subgraph.

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The complexity of the alignment problem stems from the fact that existing methods are considered unstable. Reinforcement Learning from Human Feedback (RLHF) addresses this issue by minimizing the KL divergence between the trained policy and the initial supervised fine-tuned policy (SFT) to avoid generating out-of-domain samples for the reward model (RM). Recently, many methods have emerged that shift from online to offline optimization, reformulating the RLHF objective and removing the reward model (DPO, IPO, KTO). Despite eliminating the reward model and the challenges it posed, these algorithms are still constrained in terms of closeness of the trained policy to the SFT one. In our paper, we argue that this implicit limitation in the offline optimization methods leads to suboptimal results. To address this issue, we propose a class of new methods called Trust Region (TR-DPO, TR-IPO, TR-KTO), which update the reference policy during training. With this straightforward update approach, we demonstrate the effectiveness of the new paradigm of language model alignment against the classical one on the Anthropic-HH and Reddit TL;DR datasets. Most notably, when automatically comparing TR methods and baselines side by side using pretrained Pythia 6.9B models on the Reddit TL;DR task, the difference in win rates reaches 8.4% for DPO, 14.3% for IPO, and 15% for KTO. Finally, by assessing model response ratings grounded on criteria such as coherence, correctness, helpfulness, and harmlessness, we demonstrate that our proposed methods significantly outperform existing techniques.

Over the past few years, Federated Learning (FL) has become a popular distributed machine learning paradigm. FL involves a group of clients with decentralized data who collaborate to learn a common model under the coordination of a centralized server, with the goal of protecting clients' privacy by ensuring that local datasets never leave the clients and that the server only performs model aggregation. However, in realistic scenarios, the server may be able to collect a small amount of data that approximately mimics the population distribution and has stronger computational ability to perform the learning process. To address this, we focus on the hybrid FL framework in this paper. While previous hybrid FL work has shown that the alternative training of clients and server can increase convergence speed, it has focused on the scenario where clients fully participate and ignores the negative effect of partial participation. In this paper, we provide theoretical analysis of hybrid FL under clients' partial participation to validate that partial participation is the key constraint on convergence speed. We then propose a new algorithm called FedCLG, which investigates the two-fold role of the server in hybrid FL. Firstly, the server needs to process the training steps using its small amount of local datasets. Secondly, the server's calculated gradient needs to guide the participated clients' training and the server's aggregation. We validate our theoretical findings through numerical experiments, which show that our proposed method FedCLG outperforms state-of-the-art methods.

Synthetic Control Methods (SCMs) have become an essential tool for comparative case studies. The fundamental idea of SCMs is to estimate the counterfactual outcomes of a treated unit using a weighted sum of the observed outcomes of untreated units. The accuracy of the synthetic control (SC) is critical for evaluating the treatment effect of a policy intervention; therefore, the estimation of SC weights has been the focus of extensive research. In this study, we first point out that existing SCMs suffer from an endogeneity problem, the correlation between the outcomes of untreated units and the error term of the synthetic control, which yields a bias in the treatment effect estimator. We then propose a novel SCM based on density matching, assuming that the density of outcomes of the treated unit can be approximated by a weighted average of the joint density of untreated units (i.e., a mixture model). Based on this assumption, we estimate SC weights by matching the moments of treated outcomes with the weighted sum of moments of untreated outcomes. Our proposed method has three advantages over existing methods: first, our estimator is asymptotically unbiased under the assumption of the mixture model; second, due to the asymptotic unbiasedness, we can reduce the mean squared error in counterfactual predictions; third, our method generates full densities of the treatment effect, not merely expected values, which broadens the applicability of SCMs. We provide experimental results to demonstrate the effectiveness of our proposed method.

Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

Text Classification is an important and classical problem in natural language processing. There have been a number of studies that applied convolutional neural networks (convolution on regular grid, e.g., sequence) to classification. However, only a limited number of studies have explored the more flexible graph convolutional neural networks (convolution on non-grid, e.g., arbitrary graph) for the task. In this work, we propose to use graph convolutional networks for text classification. We build a single text graph for a corpus based on word co-occurrence and document word relations, then learn a Text Graph Convolutional Network (Text GCN) for the corpus. Our Text GCN is initialized with one-hot representation for word and document, it then jointly learns the embeddings for both words and documents, as supervised by the known class labels for documents. Our experimental results on multiple benchmark datasets demonstrate that a vanilla Text GCN without any external word embeddings or knowledge outperforms state-of-the-art methods for text classification. On the other hand, Text GCN also learns predictive word and document embeddings. In addition, experimental results show that the improvement of Text GCN over state-of-the-art comparison methods become more prominent as we lower the percentage of training data, suggesting the robustness of Text GCN to less training data in text classification.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.

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