Unsupervised Learning for Combinatorial Optimization with Principled Objective Relaxation

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard relaxation-plus-rounding approach and adopts neural networks to parameterize the relaxed solutions so that simple back-propagation can train the model end-to-end. Our key contribution is the observation that if the relaxed objective satisfies entry-wise concavity, a low optimization loss guarantees the quality of the final integral solutions. This observation significantly broadens the applicability of the previous framework inspired by Erdos' probabilistic method. In particular, this observation can guide the design of objective models in applications where the objectives are not given explicitly while requiring being modeled in prior. We evaluate our framework by solving a synthetic graph optimization problem, and two real-world applications including resource allocation in circuit design and approximate computing. Our framework largely outperforms the baselines based on na\"{i}ve relaxation, reinforcement learning, and Gumbel-softmax tricks.

Two-Dimensional Weisfeiler-Lehman Graph Neural Networks for Link Prediction

Link prediction is one important application of graph neural networks (GNNs). Most existing GNNs for link prediction are based on one-dimensional Weisfeiler-Lehman (1-WL) test. 1-WL-GNNs first compute node representations by iteratively passing neighboring node features to the center, and then obtain link representations by aggregating the pairwise node representations. As pointed out by previous works, this two-step procedure results in low discriminating power, as 1-WL-GNNs by nature learn node-level representations instead of link-level. In this paper, we study a completely different approach which can directly obtain node pair (link) representations based on \textit{two-dimensional Weisfeiler-Lehman (2-WL) tests}. 2-WL tests directly use links (2-tuples) as message passing units instead of nodes, and thus can directly obtain link representations. We theoretically analyze the expressive power of 2-WL tests to discriminate non-isomorphic links, and prove their superior link discriminating power than 1-WL. Based on different 2-WL variants, we propose a series of novel 2-WL-GNN models for link prediction. Experiments on a wide range of real-world datasets demonstrate their competitive performance to state-of-the-art baselines and superiority over plain 1-WL-GNNs.

A Framework of Meta Functional Learning for Regularising Knowledge Transfer

Machine learning classifiers' capability is largely dependent on the scale of available training data and limited by the model overfitting in data-scarce learning tasks. To address this problem, this work proposes a novel framework of Meta Functional Learning (MFL) by meta-learning a generalisable functional model from data-rich tasks whilst simultaneously regularising knowledge transfer to data-scarce tasks. The MFL computes meta-knowledge on functional regularisation generalisable to different learning tasks by which functional training on limited labelled data promotes more discriminative functions to be learned. Based on this framework, we formulate three variants of MFL: MFL with Prototypes (MFL-P) which learns a functional by auxiliary prototypes, Composite MFL (ComMFL) that transfers knowledge from both functional space and representational space, and MFL with Iterative Updates (MFL-IU) which improves knowledge transfer regularisation from MFL by progressively learning the functional regularisation in knowledge transfer. Moreover, we generalise these variants for knowledge transfer regularisation from binary classifiers to multi-class classifiers. Extensive experiments on two few-shot learning scenarios, Few-Shot Learning (FSL) and Cross-Domain Few-Shot Learning (CD-FSL), show that meta functional learning for knowledge transfer regularisation can improve FSL classifiers.

Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks

Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task-based on sets of nodes such as link/motif prediction and so on. Many works have recently proposed to address this problem by using random node features or node distance features. However, they suffer from either slow convergence, inaccurate prediction, or high complexity. In this work, we revisit GNNs that allow using positional features of nodes given by positional encoding (PE) techniques such as Laplacian Eigenmap, Deepwalk, etc. GNNs with PE often get criticized because they are not generalizable to unseen graphs (inductive) or stable. Here, we study these issues in a principled way and propose a provable solution, a class of GNN layers termed PEG with rigorous mathematical analysis. PEG uses separate channels to update the original node features and positional features. PEG imposes permutation equivariance w.r.t. the original node features and rotation equivariance w.r.t. the positional features simultaneously. Extensive link prediction experiments over 8 real-world networks demonstrate the advantages of PEG in generalization and scalability.

Algorithm and System Co-design for Efficient Subgraph-based Graph Representation Learning

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from a scalability issue since they require extracting subgraphs for each training and testing query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over seven homogeneous, heterogeneous and higher-order graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10$\times$ speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50% prediction accuracy improvement. SUREL is also applied to the brain vessel prediction task. SUREL significantly outperforms the state-of-the-art baseline in both prediction accuracy and efficiency.

Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction

Graph neural networks (GNNs) have drawn significant research attention recently, mostly under the setting of semi-supervised learning. When task-agnostic representations are preferred or supervision is simply unavailable, the auto-encoder framework comes in handy with a natural graph reconstruction objective for unsupervised GNN training. However, existing graph auto-encoders are designed to reconstruct the direct links, so GNNs trained in this way are only optimized towards proximity-oriented graph mining tasks, and will fall short when the topological structures matter. In this work, we revisit the graph encoding process of GNNs which essentially learns to encode the neighborhood information of each node into an embedding vector, and propose a novel graph decoder to reconstruct the entire neighborhood information regarding both proximity and structure via Neighborhood Wasserstein Reconstruction (NWR). Specifically, from the GNN embedding of each node, NWR jointly predicts its node degree and neighbor feature distribution, where the distribution prediction adopts an optimal-transport loss based on the Wasserstein distance. Extensive experiments on both synthetic and real-world network datasets show that the unsupervised node representations learned with NWR have much more advantageous in structure-oriented graph mining tasks, while also achieving competitive performance in proximity-oriented ones.

Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism

Interpretable graph learning is in need as many scientific applications depend on learning models to collect insights from graph-structured data. Previous works mostly focused on using post-hoc approaches to interpret a pre-trained model (graph neural network models in particular). They argue against inherently interpretable models because good interpretation of these models is often at the cost of their prediction accuracy. And, the widely used attention mechanism for inherent interpretation often fails to provide faithful interpretation in graph learning tasks. In this work, we address both issues by proposing Graph Stochastic Attention (GSAT), an attention mechanism derived from the information bottleneck principle. GSAT leverages stochastic attention to block the information from the task-irrelevant graph components while learning stochasticity-reduced attention to select the task-relevant subgraphs for interpretation. GSAT can also apply to fine-tuning and interpreting pre-trained models via stochastic attention mechanism. Extensive experiments on eight datasets show that GSAT outperforms the state-of-the-art methods by up to 20%$\uparrow$ in interpretation AUC and 5%$\uparrow$ in prediction accuracy.

High-Level Synthesis Performance Prediction using GNNs: Benchmarking, Modeling, and Advancing

Agile hardware development requires fast and accurate circuit quality evaluation from early design stages. Existing work of high-level synthesis (HLS) performance prediction usually needs extensive feature engineering after the synthesis process. To expedite circuit evaluation from as earlier design stage as possible, we propose a rapid and accurate performance modeling, exploiting the representation power of graph neural networks (GNNs) by representing C/C++ programs as graphs. The contribution of this work is three-fold. First, we build a standard benchmark containing 40k C synthesizable programs, which includes both synthetic programs and three sets of real-world HLS benchmarks. Each program is implemented on FPGA to generate ground-truth performance metrics. Second, we formally formulate the HLS performance prediction problem on graphs, and propose multiple modeling strategies with GNNs that leverage different trade-offs between prediction timeliness (early/late prediction) and accuracy. Third, we further propose a novel hierarchical GNN that does not sacrifice timeliness but largely improves prediction accuracy, significantly outperforming HLS tools. We apply extensive evaluations for both synthetic and unseen real-case programs; our proposed predictor largely outperforms HLS by up to 40X and excels existing predictors by 2X to 5X in terms of resource usage and timing prediction.

Ranking Distance Calibration for Cross-Domain Few-Shot Learning

Recent progress in few-shot learning promotes a more realistic cross-domain setting, where the source and target datasets are from different domains. Due to the domain gap and disjoint label spaces between source and target datasets, their shared knowledge is extremely limited. This encourages us to explore more information in the target domain rather than to overly elaborate training strategies on the source domain as in many existing methods. Hence, we start from a generic representation pre-trained by a cross-entropy loss and a conventional distance-based classifier, along with an image retrieval view, to employ a re-ranking process for calibrating a target distance matrix by discovering the reciprocal k-nearest neighbours within the task. Assuming the pre-trained representation is biased towards the source, we construct a non-linear subspace to minimise task-irrelevant features therewithin while keep more transferrable discriminative information by a hyperbolic tangent transformation. The calibrated distance in this target-aware non-linear subspace is complementary to that in the pre-trained representation. To impose such distance calibration information onto the pre-trained representation, a Kullback-Leibler divergence loss is employed to gradually guide the model towards the calibrated distance-based distribution. Extensive evaluations on eight target domains show that this target ranking calibration process can improve conventional distance-based classifiers in few-shot learning.

Nested Graph Neural Networks

Graph neural network (GNN)'s success in graph classification is closely related to the Weisfeiler-Lehman (1-WL) algorithm. By iteratively aggregating neighboring node features to a center node, both 1-WL and GNN obtain a node representation that encodes a rooted subtree around the center node. These rooted subtree representations are then pooled into a single representation to represent the whole graph. However, rooted subtrees are of limited expressiveness to represent a non-tree graph. To address it, we propose Nested Graph Neural Networks (NGNNs). NGNN represents a graph with rooted subgraphs instead of rooted subtrees, so that two graphs sharing many identical subgraphs (rather than subtrees) tend to have similar representations. The key is to make each node representation encode a subgraph around it more than a subtree. To achieve this, NGNN extracts a local subgraph around each node and applies a base GNN to each subgraph to learn a subgraph representation. The whole-graph representation is then obtained by pooling these subgraph representations. We provide a rigorous theoretical analysis showing that NGNN is strictly more powerful than 1-WL. In particular, we proved that NGNN can discriminate almost all r-regular graphs, where 1-WL always fails. Moreover, unlike other more powerful GNNs, NGNN only introduces a constant-factor higher time complexity than standard GNNs. NGNN is a plug-and-play framework that can be combined with various base GNNs. We test NGNN with different base GNNs on several benchmark datasets. NGNN uniformly improves their performance and shows highly competitive performance on all datasets.