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Graph neural networks are prominent models for representation learning over graphs, where the idea is to iteratively compute representations of nodes of an input graph through a series of transformations in such a way that the learned graph function is isomorphism invariant on graphs, which makes the learned representations graph invariants. On the other hand, it is well-known that graph invariants learned by these class of models are incomplete: there are pairs of non-isomorphic graphs which cannot be distinguished by standard graph neural networks. This is unsurprising given the computational difficulty of graph isomorphism testing on general graphs, but the situation begs to differ for special graph classes, for which efficient graph isomorphism testing algorithms are known, such as planar graphs. The goal of this work is to design architectures for efficiently learning complete invariants of planar graphs. Inspired by the classical planar graph isomorphism algorithm of Hopcroft and Tarjan, we propose PlanE as a framework for planar representation learning. PlanE includes architectures which can learn complete invariants over planar graphs while remaining practically scalable. We empirically validate the strong performance of the resulting model architectures on well-known planar graph benchmarks, achieving multiple state-of-the-art results.

Diffusion MRI (dMRI) is a widely used imaging modality, but requires long scanning times to acquire high resolution datasets. By leveraging the unique geometry present within this domain, we present a novel approach to dMRI angular super-resolution that extends upon the parametric continuous convolution (PCConv) framework. We introduce several additions to the operation including a Fourier feature mapping, global coordinates, and domain specific context. Using this framework, we build a fully parametric continuous convolution network (PCCNN) and compare against existing models. We demonstrate the PCCNN performs competitively while using significantly less parameters. Moreover, we show that this formulation generalises well to clinically relevant downstream analyses such as fixel-based analysis, and neurite orientation dispersion and density imaging.

In this paper, we devise a scheme for kernelizing, in sublinear space and polynomial time, various problems on planar graphs. The scheme exploits planarity to ensure that the resulting algorithms run in polynomial time and use O((sqrt(n) + k) log n) bits of space, where n is the number of vertices in the input instance and k is the intended solution size. As examples, we apply the scheme to Dominating Set and Vertex Cover. For Dominating Set, we also show that a well-known kernelization algorithm due to Alber et al. (JACM 2004) can be carried out in polynomial time and space O(k log n). Along the way, we devise restricted-memory procedures for computing region decompositions and approximating the aforementioned problems, which might be of independent interest.

Smart contracts play a vital role in the Ethereum ecosystem. Due to the prevalence of kinds of security issues in smart contracts, the smart contract verification is urgently needed, which is the process of matching a smart contract's source code to its on-chain bytecode for gaining mutual trust between smart contract developers and users. Although smart contract verification services are embedded in both popular Ethereum browsers (e.g., Etherscan and Blockscout) and official platforms (i.e., Sourcify), and gain great popularity in the ecosystem, their security and trustworthiness remain unclear. To fill the void, we present the first comprehensive security analysis of smart contract verification services in the wild. By diving into the detailed workflow of existing verifiers, we have summarized the key security properties that should be met, and observed eight types of vulnerabilities that can break the verification. Further, we propose a series of detection and exploitation methods to reveal the presence of vulnerabilities in the most popular services, and uncover 19 exploitable vulnerabilities in total. All the studied smart contract verification services can be abused to help spread malicious smart contracts, and we have already observed the presence of using this kind of tricks for scamming by attackers. It is hence urgent for our community to take actions to detect and mitigate security issues related to smart contract verification, a key component of the Ethereum smart contract ecosystem.

In this paper, we explore the feasibility of finding algorithm implementations from code. Successfully matching code and algorithms can help understand unknown code, provide reference implementations, and automatically collect data for learning-based program synthesis. To achieve the goal, we designed a new language named p-language to specify the algorithms and a static analyzer for the p-language to automatically extract control flow, math, and natural language information from the algorithm descriptions. We embedded the output of p-language (p-code) and source code in a common vector space using self-supervised machine learning methods to match algorithm with code without any manual annotation. We developed a tool named Beryllium. It takes pseudo code as a query and returns a list of ranked code snippets that likely match the algorithm query. Our evaluation on Stony Brook Algorithm Repository and popular GitHub projects show that Beryllium significantly outperformed the state-of-the-art code search tools in both C and Java. Specifically, for 98.5%, 93.8%, and 66.2% queries, we found the algorithm implementations in the top 25, 10, and 1 ranked list, respectively. Given 87 algorithm queries, we found implementations for 74 algorithms in the GitHub projects where we did not know the algorithms before.

Magnitude pruning is one of the mainstream methods in lightweight architecture design whose goal is to extract subnetworks with the largest weight connections. This method is known to be successful, but under very high pruning regimes, it suffers from topological inconsistency which renders the extracted subnetworks disconnected, and this hinders their generalization ability. In this paper, we devise a novel magnitude pruning method that allows extracting subnetworks while guarantying their topological consistency. The latter ensures that only accessible and co-accessible -- impactful -- connections are kept in the resulting lightweight networks. Our solution is based on a novel reparametrization and two supervisory bi-directional networks which implement accessibility/co-accessibility and guarantee that only connected subnetworks will be selected during training. This solution allows enhancing generalization significantly, under very high pruning regimes, as corroborated through extensive experiments, involving graph convolutional networks, on the challenging task of skeleton-based action recognition.

The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total distance to the voters, given only the rankings, but not the actual distances. As a result, in the worst case, each deterministic rule picks a candidate whose total distance is at least three times larger than that of an optimal one, i.e., has distortion at least 3. A recent breakthrough result showed that achieving this bound of 3 is possible; however, the proof is non-constructive, and the voting rule itself is a complicated exhaustive search. Our main result is an extremely simple voting rule, called Plurality Veto, which achieves the same optimal distortion of 3. Each candidate starts with a score equal to his number of first-place votes. These scores are then gradually decreased via an n-round veto process in which a candidate drops out when his score reaches zero. One after the other, voters decrement the score of their bottom choice among the standing candidates, and the last standing candidate wins. We give a one-paragraph proof that this voting rule achieves distortion 3. This rule is also immensely practical, and it only makes two queries to each voter, so it has low communication overhead. We also generalize Plurality Veto into a class of randomized voting rules in the following way: Plurality veto is run only for k < n rounds; then, a candidate is chosen with probability proportional to his residual score. This general rule interpolates between Random Dictatorship (for k=0) and Plurality Veto (for k=n-1), and k controls the variance of the output. We show that for all k, this rule has distortion at most 3.

Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.

Training machine learning models in a meaningful order, from the easy samples to the hard ones, using curriculum learning can provide performance improvements over the standard training approach based on random data shuffling, without any additional computational costs. Curriculum learning strategies have been successfully employed in all areas of machine learning, in a wide range of tasks. However, the necessity of finding a way to rank the samples from easy to hard, as well as the right pacing function for introducing more difficult data can limit the usage of the curriculum approaches. In this survey, we show how these limits have been tackled in the literature, and we present different curriculum learning instantiations for various tasks in machine learning. We construct a multi-perspective taxonomy of curriculum learning approaches by hand, considering various classification criteria. We further build a hierarchical tree of curriculum learning methods using an agglomerative clustering algorithm, linking the discovered clusters with our taxonomy. At the end, we provide some interesting directions for future work.

Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at //github.com/gitgiter/Graph-Adversarial-Learning.