ABKD: Graph Neural Network Compression with Attention-Based Knowledge Distillation

Graph Neural Networks (GNNs) have proven to be quite versatile for a variety of applications, including recommendation systems, fake news detection, drug discovery, and even computer vision. Due to the expanding size of graph-structured data, GNN models have also increased in complexity, leading to substantial latency issues. This is primarily attributed to the irregular structure of graph data and its access pattern into memory. The natural solution to reduce latency is to compress large GNNs into small GNNs. One way to do this is via knowledge distillation (KD). However, most KD approaches for GNNs only consider the outputs of the last layers and do not consider the outputs of the intermediate layers of the GNNs; these layers may contain important inductive biases indicated by the graph structure. To address this shortcoming, we propose a novel KD approach to GNN compression that we call Attention-Based Knowledge Distillation (ABKD). ABKD is a KD approach that uses attention to identify important intermediate teacher-student layer pairs and focuses on aligning their outputs. ABKD enables higher compression of GNNs with a smaller accuracy dropoff compared to existing KD approaches. On average, we achieve a 1.79% increase in accuracy with a 32.3x compression ratio on OGBN-Mag, a large graph dataset, compared to state-of-the-art approaches.

On the Inherent Privacy Properties of Discrete Denoising Diffusion Models

Privacy concerns have led to a surge in the creation of synthetic datasets, with diffusion models emerging as a promising avenue. Although prior studies have performed empirical evaluations on these models, there has been a gap in providing a mathematical characterization of their privacy-preserving capabilities. To address this, we present the pioneering theoretical exploration of the privacy preservation inherent in discrete diffusion models (DDMs) for discrete dataset generation. Focusing on per-instance differential privacy (pDP), our framework elucidates the potential privacy leakage for each data point in a given training dataset, offering insights into data preprocessing to reduce privacy risks of the synthetic dataset generation via DDMs. Our bounds also show that training with $s$-sized data points leads to a surge in privacy leakage from $(\epsilon, \mathcal{O}(\frac{1}{s^2\epsilon}))$-pDP to $(\epsilon, \mathcal{O}(\frac{1}{s\epsilon}))$-pDP during the transition from the pure noise to the synthetic clean data phase, and a faster decay in diffusion coefficients amplifies the privacy guarantee. Finally, we empirically verify our theoretical findings on both synthetic and real-world datasets.

GraphMaker: Can Diffusion Models Generate Large Attributed Graphs?

Large-scale graphs with node attributes are fundamental in real-world scenarios, such as social and financial networks. The generation of synthetic graphs that emulate real-world ones is pivotal in graph machine learning, aiding network evolution understanding and data utility preservation when original data cannot be shared. Traditional models for graph generation suffer from limited model capacity. Recent developments in diffusion models have shown promise in merely graph structure generation or the generation of small molecular graphs with attributes. However, their applicability to large attributed graphs remains unaddressed due to challenges in capturing intricate patterns and scalability. This paper introduces GraphMaker, a novel diffusion model tailored for generating large attributed graphs. We study the diffusion models that either couple or decouple graph structure and node attribute generation to address their complex correlation. We also employ node-level conditioning and adopt a minibatch strategy for scalability. We further propose a new evaluation pipeline using models trained on generated synthetic graphs and tested on original graphs to evaluate the quality of synthetic data. Empirical evaluations on real-world datasets showcase GraphMaker's superiority in generating realistic and diverse large-attributed graphs beneficial for downstream tasks.

DIG-MILP: a Deep Instance Generator for Mixed-Integer Linear Programming with Feasibility Guarantee

Mixed-integer linear programming (MILP) stands as a notable NP-hard problem pivotal to numerous crucial industrial applications. The development of effective algorithms, the tuning of solvers, and the training of machine learning models for MILP resolution all hinge on access to extensive, diverse, and representative data. Yet compared to the abundant naturally occurring data in image and text realms, MILP is markedly data deficient, underscoring the vital role of synthetic MILP generation. We present DIG-MILP, a deep generative framework based on variational auto-encoder (VAE), adept at extracting deep-level structural features from highly limited MILP data and producing instances that closely mirror the target data. Notably, by leveraging the MILP duality, DIG-MILP guarantees a correct and complete generation space as well as ensures the boundedness and feasibility of the generated instances. Our empirical study highlights the novelty and quality of the instances generated by DIG-MILP through two distinct downstream tasks: (S1) Data sharing, where solver solution times correlate highly positive between original and DIG-MILP-generated instances, allowing data sharing for solver tuning without publishing the original data; (S2) Data Augmentation, wherein the DIG-MILP-generated instances bolster the generalization performance of machine learning models tasked with resolving MILP problems.

GDL-DS: A Benchmark for Geometric Deep Learning under Distribution Shifts

Geometric deep learning (GDL) has gained significant attention in various scientific fields, chiefly for its proficiency in modeling data with intricate geometric structures. Yet, very few works have delved into its capability of tackling the distribution shift problem, a prevalent challenge in many relevant applications. To bridge this gap, we propose GDL-DS, a comprehensive benchmark designed for evaluating the performance of GDL models in scenarios with distribution shifts. Our evaluation datasets cover diverse scientific domains from particle physics and materials science to biochemistry, and encapsulate a broad spectrum of distribution shifts including conditional, covariate, and concept shifts. Furthermore, we study three levels of information access from the out-of-distribution (OOD) testing data, including no OOD information, only OOD features without labels, and OOD features with a few labels. Overall, our benchmark results in 30 different experiment settings, and evaluates 3 GDL backbones and 11 learning algorithms in each setting. A thorough analysis of the evaluation results is provided, poised to illuminate insights for DGL researchers and domain practitioners who are to use DGL in their applications.

On the Stability of Expressive Positional Encodings for Graph Neural Networks

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) \emph{Non-uniqueness}: there are many different eigendecompositions of the same Laplacian, and (2) \emph{Instability}: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

Towards Poisoning Fair Representations

Fair machine learning seeks to mitigate model prediction bias against certain demographic subgroups such as elder and female. Recently, fair representation learning (FRL) trained by deep neural networks has demonstrated superior performance, whereby representations containing no demographic information are inferred from the data and then used as the input to classification or other downstream tasks. Despite the development of FRL methods, their vulnerability under data poisoning attack, a popular protocol to benchmark model robustness under adversarial scenarios, is under-explored. Data poisoning attacks have been developed for classical fair machine learning methods which incorporate fairness constraints into shallow-model classifiers. Nonetheless, these attacks fall short in FRL due to notably different fairness goals and model architectures. This work proposes the first data poisoning framework attacking FRL. We induce the model to output unfair representations that contain as much demographic information as possible by injecting carefully crafted poisoning samples into the training data. This attack entails a prohibitive bilevel optimization, wherefore an effective approximated solution is proposed. A theoretical analysis on the needed number of poisoning samples is derived and sheds light on defending against the attack. Experiments on benchmark fairness datasets and state-of-the-art fair representation learning models demonstrate the superiority of our attack.

Optimal Resource Allocation for U-Shaped Parallel Split Learning

Split learning (SL) has emerged as a promising approach for model training without revealing the raw data samples from the data owners. However, traditional SL inevitably leaks label privacy as the tail model (with the last layers) should be placed on the server. To overcome this limitation, one promising solution is to utilize U-shaped architecture to leave both early layers and last layers on the user side. In this paper, we develop a novel parallel U-shaped split learning and devise the optimal resource optimization scheme to improve the performance of edge networks. In the proposed framework, multiple users communicate with an edge server for SL. We analyze the end-to-end delay of each client during the training process and design an efficient resource allocation algorithm, called LSCRA, which finds the optimal computing resource allocation and split layers. Our experimental results show the effectiveness of LSCRA and that U-shaped PSL can achieve a similar performance with other SL baselines while preserving label privacy. Index Terms: U-shaped network, split learning, label privacy, resource allocation, 5G/6G edge networks.

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.

Differentially Private Decoupled Graph Convolutions for Multigranular Topology Protection

Graph learning methods, such as Graph Neural Networks (GNNs) based on graph convolutions, are highly successful in solving real-world learning problems involving graph-structured data. However, graph learning methods expose sensitive user information and interactions not only through their model parameters but also through their model predictions. Consequently, standard Differential Privacy (DP) techniques that merely offer model weight privacy are inadequate. This is especially the case for node predictions that leverage neighboring node attributes directly via graph convolutions that create additional risks of privacy leakage. To address this problem, we introduce Graph Differential Privacy (GDP), a new formal DP framework tailored to graph learning settings that ensures both provably private model parameters and predictions. Furthermore, since there may be different privacy requirements for the node attributes and graph structure, we introduce a novel notion of relaxed node-level data adjacency. This relaxation can be used for establishing guarantees for different degrees of graph topology privacy while maintaining node attribute privacy. Importantly, this relaxation reveals a useful trade-off between utility and topology privacy for graph learning methods. In addition, our analysis of GDP reveals that existing DP-GNNs fail to exploit this trade-off due to the complex interplay between graph topology and attribute data in standard graph convolution designs. To mitigate this problem, we introduce the Differentially Private Decoupled Graph Convolution (DPDGC) model, which benefits from decoupled graph convolution while providing GDP guarantees. Extensive experiments on seven node classification benchmarking datasets demonstrate the superior privacy-utility trade-off of DPDGC over existing DP-GNNs based on standard graph convolution design.