arXiv subjects

Neil Shah

Publications and source records attributed to Neil Shah.

At least 91 records · Page 5Linked to original sources

arXiv2023

Causal Modifications of Gravity and Their Observational Bounds

Since general relativity is the unique theory of massless spin 2 particles at large distances, the most reasonable way to have significant modifications is to introduce one or more light scalars that mediate a new long-range force. Most existing studies of such scalars invoke models that exhibit some kind of "screening" at short distances to hide the force from solar system tests. However, as is well known, such modifications also exhibit superluminality, which can be interpreted as a form of acausality. In this work we explore explicitly subluminal and causal scalar field models. In particular, we study a conformally coupled scalar $ϕ$, with a small coupling to matter to obey solar system bounds, and a non-canonical kinetic term $K(X)$ ($X=(\partialϕ)^2/2$) that obeys all subluminality constraints and is hyperbolic. We consider $K(X)$ that is canonical for small $X$, but beyond some nonlinear scale enters a new scaling regime of power $p$, with $1/2<p<1$ (the DBI kinetic term is the limit $p=1/2$ and a canonical scalar is $p=1$). As opposed to screening (and superluminality), this new force becomes more and more important in the regime of high densities (and subluminality). We then turn to the densest environments to put bounds on this new interaction. We compute constraints from precession in binary systems such as Hulse-Taylor, we compute corrections to neutron star hydrostatic equilibrium, and we compute power in radiation, both tensor mode corrections and the new scalar mode, which can be important during mergers.

hep-th↗

arXiv2023

Graph Data Augmentation for Graph Machine Learning: A Survey

Data augmentation has recently seen increased interest in graph machine learning given its demonstrated ability to improve model performance and generalization by added training data. Despite this recent surge, the area is still relatively under-explored, due to the challenges brought by complex, non-Euclidean structure of graph data, which limits the direct analogizing of traditional augmentation operations on other types of image, video or text data. Our work aims to give a necessary and timely overview of existing graph data augmentation methods; notably, we present a comprehensive and systematic survey of graph data augmentation approaches, summarizing the literature in a structured manner. We first introduce three different taxonomies for categorizing graph data augmentation methods from the data, task, and learning perspectives, respectively. Next, we introduce recent advances in graph data augmentation, differentiated by their methodologies and applications. We conclude by outlining currently unsolved challenges and directions for future research. Overall, our work aims to clarify the landscape of existing literature in graph data augmentation and motivates additional work in this area, providing a helpful resource for researchers and practitioners in the broader graph machine learning domain. Additionally, we provide a continuously updated reading list at https://github.com/zhao-tong/graph-data-augmentation-papers.

cs.LG↗

arXiv2022

GStarX: Explaining Graph Neural Networks with Structure-Aware Cooperative Games

Explaining machine learning models is an important and increasingly popular area of research interest. The Shapley value from game theory has been proposed as a prime approach to compute feature importance towards model predictions on images, text, tabular data, and recently graph neural networks (GNNs) on graphs. In this work, we revisit the appropriateness of the Shapley value for GNN explanation, where the task is to identify the most important subgraph and constituent nodes for GNN predictions. We claim that the Shapley value is a non-ideal choice for graph data because it is by definition not structure-aware. We propose a Graph Structure-aware eXplanation (GStarX) method to leverage the critical graph structure information to improve the explanation. Specifically, we define a scoring function based on a new structure-aware value from the cooperative game theory proposed by Hamiache and Navarro (HN). When used to score node importance, the HN value utilizes graph structures to attribute cooperation surplus between neighbor nodes, resembling message passing in GNNs, so that node importance scores reflect not only the node feature importance, but also the node structural roles. We demonstrate that GStarX produces qualitatively more intuitive explanations, and quantitatively improves explanation fidelity over strong baselines on chemical graph property prediction and text graph sentiment classification.

cs.LG↗

arXiv2022

Flashlight: Scalable Link Prediction with Effective Decoders

Link prediction (LP) has been recognized as an important task in graph learning with its broad practical applications. A typical application of LP is to retrieve the top scoring neighbors for a given source node, such as the friend recommendation. These services desire the high inference scalability to find the top scoring neighbors from many candidate nodes at low latencies. There are two popular decoders that the recent LP models mainly use to compute the edge scores from node embeddings: the HadamardMLP and Dot Product decoders. After theoretical and empirical analysis, we find that the HadamardMLP decoders are generally more effective for LP. However, HadamardMLP lacks the scalability for retrieving top scoring neighbors on large graphs, since to the best of our knowledge, there does not exist an algorithm to retrieve the top scoring neighbors for HadamardMLP decoders in sublinear complexity. To make HadamardMLP scalable, we propose the Flashlight algorithm to accelerate the top scoring neighbor retrievals for HadamardMLP: a sublinear algorithm that progressively applies approximate maximum inner product search (MIPS) techniques with adaptively adjusted query embeddings. Empirical results show that Flashlight improves the inference speed of LP by more than 100 times on the large OGBL-CITATION2 dataset without sacrificing effectiveness. Our work paves the way for large-scale LP applications with the effective HadamardMLP decoders by greatly accelerating their inference.

cs.SI↗

arXiv2022

A Practical, Progressively-Expressive GNN

Message passing neural networks (MPNNs) have become a dominant flavor of graph neural networks (GNNs) in recent years. Yet, MPNNs come with notable limitations; namely, they are at most as powerful as the 1-dimensional Weisfeiler-Leman (1-WL) test in distinguishing graphs in a graph isomorphism testing frame-work. To this end, researchers have drawn inspiration from the k-WL hierarchy to develop more expressive GNNs. However, current k-WL-equivalent GNNs are not practical for even small values of k, as k-WL becomes combinatorially more complex as k grows. At the same time, several works have found great empirical success in graph learning tasks without highly expressive models, implying that chasing expressiveness with a coarse-grained ruler of expressivity like k-WL is often unneeded in practical tasks. To truly understand the expressiveness-complexity tradeoff, one desires a more fine-grained ruler, which can more gradually increase expressiveness. Our work puts forth such a proposal: Namely, we first propose the (k, c)(<=)-SETWL hierarchy with greatly reduced complexity from k-WL, achieved by moving from k-tuples of nodes to sets with <=k nodes defined over <=c connected components in the induced original graph. We show favorable theoretical results for this model in relation to k-WL, and concretize it via (k, c)(<=)-SETGNN, which is as expressive as (k, c)(<=)-SETWL. Our model is practical and progressively-expressive, increasing in power with k and c. We demonstrate effectiveness on several benchmark datasets, achieving several state-of-the-art results with runtime and memory usage applicable to practical graphs. We open source our implementation at https://github.com/LingxiaoShawn/KCSetGNN.

cs.LG↗

arXiv2022

Imbalanced Graph Classification via Graph-of-Graph Neural Networks

Graph Neural Networks (GNNs) have achieved unprecedented success in identifying categorical labels of graphs. However, most existing graph classification problems with GNNs follow the protocol of balanced data splitting, which misaligns with many real-world scenarios in which some classes have much fewer labels than others. Directly training GNNs under this imbalanced scenario may lead to uninformative representations of graphs in minority classes, and compromise the overall classification performance, which signifies the importance of developing effective GNNs towards handling imbalanced graph classification. Existing methods are either tailored for non-graph structured data or designed specifically for imbalanced node classification while few focus on imbalanced graph classification. To this end, we introduce a novel framework, Graph-of-Graph Neural Networks (G$^2$GNN), which alleviates the graph imbalance issue by deriving extra supervision globally from neighboring graphs and locally from stochastic augmentations of graphs. Globally, we construct a graph of graphs (GoG) based on kernel similarity and perform GoG propagation to aggregate neighboring graph representations. Locally, we employ topological augmentation via masking node features or dropping edges with self-consistency regularization to generate stochastic augmentations of each graph that improve the model generalibility. Extensive graph classification experiments conducted on seven benchmark datasets demonstrate our proposed G$^2$GNN outperforms numerous baselines by roughly 5\% in both F1-macro and F1-micro scores. The implementation of G$^2$GNN is available at https://github.com/YuWVandy/G2GNN}{https://github.com/YuWVandy/G2GNN

cs.LG↗

arXiv2022

Graph Condensation for Graph Neural Networks

Given the prevalence of large-scale graphs in real-world applications, the storage and time for training neural models have raised increasing concerns. To alleviate the concerns, we propose and study the problem of graph condensation for graph neural networks (GNNs). Specifically, we aim to condense the large, original graph into a small, synthetic and highly-informative graph, such that GNNs trained on the small graph and large graph have comparable performance. We approach the condensation problem by imitating the GNN training trajectory on the original graph through the optimization of a gradient matching loss and design a strategy to condense node futures and structural information simultaneously. Extensive experiments have demonstrated the effectiveness of the proposed framework in condensing different graph datasets into informative smaller graphs. In particular, we are able to approximate the original test accuracy by 95.3% on Reddit, 99.8% on Flickr and 99.0% on Citeseer, while reducing their graph size by more than 99.9%, and the condensed graphs can be used to train various GNN architectures.Code is released at https://github.com/ChandlerBang/GCond.

cs.LG↗

arXiv2022

From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness

Message Passing Neural Networks (MPNNs) are a common type of Graph Neural Network (GNN), in which each node's representation is computed recursively by aggregating representations (messages) from its immediate neighbors akin to a star-shaped pattern. MPNNs are appealing for being efficient and scalable, how-ever their expressiveness is upper-bounded by the 1st-order Weisfeiler-Lehman isomorphism test (1-WL). In response, prior works propose highly expressive models at the cost of scalability and sometimes generalization performance. Our work stands between these two regimes: we introduce a general framework to uplift any MPNN to be more expressive, with limited scalability overhead and greatly improved practical performance. We achieve this by extending local aggregation in MPNNs from star patterns to general subgraph patterns (e.g.,k-egonets):in our framework, each node representation is computed as the encoding of a surrounding induced subgraph rather than encoding of immediate neighbors only (i.e. a star). We choose the subgraph encoder to be a GNN (mainly MPNNs, considering scalability) to design a general framework that serves as a wrapper to up-lift any GNN. We call our proposed method GNN-AK(GNN As Kernel), as the framework resembles a convolutional neural network by replacing the kernel with GNNs. Theoretically, we show that our framework is strictly more powerful than 1&2-WL, and is not less powerful than 3-WL. We also design subgraph sampling strategies which greatly reduce memory footprint and improve speed while maintaining performance. Our method sets new state-of-the-art performance by large margins for several well-known graph ML tasks; specifically, 0.08 MAE on ZINC,74.79% and 86.887% accuracy on CIFAR10 and PATTERN respectively.

cs.LG↗

arXiv2022

Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation

Graph Neural Networks (GNNs) are popular for graph machine learning and have shown great results on wide node classification tasks. Yet, they are less popular for practical deployments in the industry owing to their scalability challenges incurred by data dependency. Namely, GNN inference depends on neighbor nodes multiple hops away from the target, and fetching them burdens latency-constrained applications. Existing inference acceleration methods like pruning and quantization can speed up GNNs by reducing Multiplication-and-ACcumulation (MAC) operations, but the improvements are limited given the data dependency is not resolved. Conversely, multi-layer perceptrons (MLPs) have no graph dependency and infer much faster than GNNs, even though they are less accurate than GNNs for node classification in general. Motivated by these complementary strengths and weaknesses, we bring GNNs and MLPs together via knowledge distillation (KD). Our work shows that the performance of MLPs can be improved by large margins with GNN KD. We call the distilled MLPs Graph-less Neural Networks (GLNNs) as they have no inference graph dependency. We show that GLNNs with competitive accuracy infer faster than GNNs by 146X-273X and faster than other acceleration methods by 14X-27X. Under a production setting involving both transductive and inductive predictions across 7 datasets, GLNN accuracies improve over stand-alone MLPs by 12.36% on average and match GNNs on 6/7 datasets. Comprehensive analysis shows when and why GLNNs can achieve competitive accuracies to GNNs and suggests GLNN as a handy choice for latency-constrained applications.

cs.LG↗

arXiv2022

Automated Self-Supervised Learning for Graphs

Graph self-supervised learning has gained increasing attention due to its capacity to learn expressive node representations. Many pretext tasks, or loss functions have been designed from distinct perspectives. However, we observe that different pretext tasks affect downstream tasks differently cross datasets, which suggests that searching pretext tasks is crucial for graph self-supervised learning. Different from existing works focusing on designing single pretext tasks, this work aims to investigate how to automatically leverage multiple pretext tasks effectively. Nevertheless, evaluating representations derived from multiple pretext tasks without direct access to ground truth labels makes this problem challenging. To address this obstacle, we make use of a key principle of many real-world graphs, i.e., homophily, or the principle that "like attracts like," as the guidance to effectively search various self-supervised pretext tasks. We provide theoretical understanding and empirical evidence to justify the flexibility of homophily in this search task. Then we propose the AutoSSL framework which can automatically search over combinations of various self-supervised tasks. By evaluating the framework on 7 real-world datasets, our experimental results show that AutoSSL can significantly boost the performance on downstream tasks including node clustering and node classification compared with training under individual tasks. Code is released at https://github.com/ChandlerBang/AutoSSL.

cs.LG↗

arXiv2022

Which numbers are not the sum plus the product of three positive integers?

We investigate the number $R_3(n)$ of representations of $n$ as the sum plus the product of three positive integers. On average, $R_3(n)$ is $\frac{1}{2}\log^2 n$. We give an upper bound for $R_3(n)$ and an upper bound for the number of $n \leq N$ such that $R_3(n) = 0$. We conjecture that $R_3(n)= 0$ infinitely often.

math.NT↗

arXiv2022

Finding a Concise, Precise, and Exhaustive Set of Near Bi-Cliques in Dynamic Graphs

A variety of tasks on dynamic graphs, including anomaly detection, community detection, compression, and graph understanding, have been formulated as problems of identifying constituent (near) bi-cliques (i.e., complete bipartite graphs). Even when we restrict our attention to maximal ones, there can be exponentially many near bi-cliques, and thus finding all of them is practically impossible for large graphs. Then, two questions naturally arise: (Q1) What is a "good" set of near bi-cliques? That is, given a set of near bi-cliques in the input dynamic graph, how should we evaluate its quality? (Q2) Given a large dynamic graph, how can we rapidly identify a high-quality set of near bi-cliques in it? Regarding Q1, we measure how concisely, precisely, and exhaustively a given set of near bi-cliques describes the input dynamic graph. We combine these three perspectives systematically on the Minimum Description Length principle. Regarding Q2, we propose CutNPeel, a fast search algorithm for a high-quality set of near bi-cliques. By adaptively re-partitioning the input graph, CutNPeel reduces the search space and at the same time improves the search quality. Our experiments using six real-world dynamic graphs demonstrate that CutNPeel is (a) High-quality: providing near bi-cliques of up to 51.2% better quality than its state-of-the-art competitors, (b) Fast: up to 68.8x faster than the next-best competitor, and (c) Scalable: scaling to graphs with 134 million edges. We also show successful applications of CutNPeel to graph compression and pattern discovery.

cs.SI↗

arXiv2021

Acausality in Superfluid Dark Matter and MOND-like Theories

There has been much interest in novel models of dark matter that exhibit interesting behavior on galactic scales. A primary motivation is the observed Baryonic Tully-Fisher Relation in which the mass of galaxies increases as the quartic power of rotation speed. This scaling is not obviously accounted for by standard cold dark matter. This has prompted the development of dark matter models that exhibit some form of so-called MONDian phenomenology to account for this galactic scaling, while also recovering the success of cold dark matter on large scales. A beautiful example of this are the so-called superfluid dark matter models, in which a complex bosonic field undergoes spontaneous symmetry breaking on galactic scales, entering a superfluid phase with a 3/2 kinetic scaling in the low energy effective theory, that mediates a long-ranged MONDian force. In this work we examine the causality and locality properties of these and other related models. We show that the Lorentz invariant completions of the superfluid models exhibit high energy perturbations that violate global hyperbolicity of the equations of motion in the MOND regime and can be superluminal in other parts of phase space. We also examine a range of alternate models, finding that they also exhibit forms of non-locality.

astro-ph.CO↗

arXiv2021

A Unified View on Graph Neural Networks as Graph Signal Denoising

Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. A single GNN layer typically consists of a feature transformation and a feature aggregation operation. The former normally uses feed-forward networks to transform features, while the latter aggregates the transformed features over the graph. Numerous recent works have proposed GNN models with different designs in the aggregation operation. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models including GCN, GAT, PPNP, and APPNP can be regarded as (approximately) solving a graph denoising problem with a smoothness assumption. Such a unified view across GNNs not only provides a new perspective to understand a variety of aggregation operations but also enables us to develop a unified graph neural network framework UGNN. To demonstrate its promising potential, we instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes. Comprehensive experiments show the effectiveness of ADA-UGNN.

cs.LG↗

arXiv2021

Attributed Graph Modeling with Vertex Replacement Grammars

Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We relax this restriction and introduce the Attributed Vertex Replacement Grammar (AVRG), which can be efficiently extracted from heterogeneous (i.e., typed, colored, or attributed) graphs. Unlike current state-of-the-art methods, which train enormous models over complicated deep neural architectures, the AVRG model is unsupervised and interpretable. It is based on context-free string grammars and works by encoding graph rewriting rules into a graph grammar containing graphlets and instructions on how they fit together. We show that the AVRG can encode succinct models of input graphs yet faithfully preserve their structure and assortativity properties. Experiments on large real-world datasets show that graphs generated from the AVRG model exhibit substructures and attribute configurations that match those found in the input networks.

cs.SI↗

arXiv2021

FairOD: Fairness-aware Outlier Detection

Fairness and Outlier Detection (OD) are closely related, as it is exactly the goal of OD to spot rare, minority samples in a given population. However, when being a minority (as defined by protected variables, such as race/ethnicity/sex/age) does not reflect positive-class membership (such as criminal/fraud), OD produces unjust outcomes. Surprisingly, fairness-aware OD has been almost untouched in prior work, as fair machine learning literature mainly focuses on supervised settings. Our work aims to bridge this gap. Specifically, we develop desiderata capturing well-motivated fairness criteria for OD, and systematically formalize the fair OD problem. Further, guided by our desiderata, we propose FairOD, a fairness-aware outlier detector that has the following desirable properties: FairOD (1) exhibits treatment parity at test time, (2) aims to flag equal proportions of samples from all groups (i.e. obtain group fairness, via statistical parity), and (3) strives to flag truly high-risk samples within each group. Extensive experiments on a diverse set of synthetic and real world datasets show that FairOD produces outcomes that are fair with respect to protected variables, while performing comparable to (and in some cases, even better than) fairness-agnostic detectors in terms of detection performance.

cs.LG↗

arXiv2021

Action Sequence Augmentation for Early Graph-based Anomaly Detection

The proliferation of web platforms has created incentives for online abuse. Many graph-based anomaly detection techniques are proposed to identify the suspicious accounts and behaviors. However, most of them detect the anomalies once the users have performed many such behaviors. Their performance is substantially hindered when the users' observed data is limited at an early stage, which needs to be improved to minimize financial loss. In this work, we propose Eland, a novel framework that uses action sequence augmentation for early anomaly detection. Eland utilizes a sequence predictor to predict next actions of every user and exploits the mutual enhancement between action sequence augmentation and user-action graph anomaly detection. Experiments on three real-world datasets show that Eland improves the performance of a variety of graph-based anomaly detection methods. With Eland, anomaly detection performance at an earlier stage is better than non-augmented methods that need significantly more observed data by up to 15% on the Area under the ROC curve.

cs.LG↗

arXiv2021

Semi-Supervised Multi-aspect Detection of Misinformation using Hierarchical Joint Decomposition

Distinguishing between misinformation and real information is one of the most challenging problems in today's interconnected world. The vast majority of the state-of-the-art in detecting misinformation is fully supervised, requiring a large number of high-quality human annotations. However, the availability of such annotations cannot be taken for granted, since it is very costly, time-consuming, and challenging to do so in a way that keeps up with the proliferation of misinformation. In this work, we are interested in exploring scenarios where the number of annotations is limited. In such scenarios, we investigate how tapping on a diverse number of resources that characterize a news article, henceforth referred to as "aspects" can compensate for the lack of labels. In particular, our contributions in this paper are twofold: 1) We propose the use of three different aspects: article content, context of social sharing behaviors, and host website/domain features, and 2) We introduce a principled tensor based embedding framework that combines all those aspects effectively. We propose HiJoD a 2-level decomposition pipeline which not only outperforms state-of-the-art methods with F1-scores of 74% and 81% on Twitter and Politifact datasets respectively but also is an order of magnitude faster than similar ensemble approaches.

cs.SI↗