A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications

Geometric graph is a special kind of graph with geometric features, which is vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To tackle this issue, researchers proposed a variety of Geometric Graph Neural Networks equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of Geometric GNNs at the end of this survey.

Enhancing Multi-modal Cooperation via Fine-grained Modality Valuation

One primary topic of multi-modal learning is to jointly incorporate heterogeneous information from different modalities. However, most models often suffer from unsatisfactory multi-modal cooperation, which could not jointly utilize all modalities well. Some methods are proposed to identify and enhance the worse learnt modality, but are often hard to provide the fine-grained observation of multi-modal cooperation at sample-level with theoretical support. Hence, it is essential to reasonably observe and improve the fine-grained cooperation between modalities, especially when facing realistic scenarios where the modality discrepancy could vary across different samples. To this end, we introduce a fine-grained modality valuation metric to evaluate the contribution of each modality at sample-level. Via modality valuation, we regretfully observe that the multi-modal model tends to rely on one specific modality, resulting in other modalities being low-contributing. We further analyze this issue and improve cooperation between modalities by enhancing the discriminative ability of low-contributing modalities in a targeted manner. Overall, our methods reasonably observe the fine-grained uni-modal contribution at sample-level and achieve considerable improvement on different multi-modal models.

Identifying Ransomware Actors in the Bitcoin Network

Due to the pseudo-anonymity of the Bitcoin network, users can hide behind their bitcoin addresses that can be generated in unlimited quantity, on the fly, without any formal links between them. Thus, it is being used for payment transfer by the actors involved in ransomware and other illegal activities. The other activity we consider is related to gambling since gambling is often used for transferring illegal funds. The question addressed here is that given temporally limited graphs of Bitcoin transactions, to what extent can one identify common patterns associated with these fraudulent activities and apply them to find other ransomware actors. The problem is rather complex, given that thousands of addresses can belong to the same actor without any obvious links between them and any common pattern of behavior. The main contribution of this paper is to introduce and apply new algorithms for local clustering and supervised graph machine learning for identifying malicious actors. We show that very local subgraphs of the known such actors are sufficient to differentiate between ransomware, random and gambling actors with 85% prediction accuracy on the test data set.

LOCCNet: a machine learning framework for distributed quantum information processing

Distributed quantum information processing is essential for building quantum networks and enabling more extensive quantum computations. In this regime, several spatially separated parties share a multipartite quantum system, and the most natural set of operations are Local Operations and Classical Communication (LOCC). As a pivotal part in quantum information theory and practice, LOCC has led to many vital protocols such as quantum teleportation. However, designing practical LOCC protocols is challenging due to LOCC's intractable structure and limitations set by near-term quantum devices. Here we introduce LOCCNet, a machine learning framework facilitating protocol design and optimization for distributed quantum information processing tasks. As applications, we explore various quantum information tasks such as entanglement distillation, quantum state discrimination, and quantum channel simulation. We discover novel protocols with evident improvements, in particular, for entanglement distillation with quantum states of interest in quantum information. Our approach opens up new opportunities for exploring entanglement and its applications with machine learning, which will potentially sharpen our understanding of the power and limitations of LOCC.

Bounded Incentives in Manipulating the Probabilistic Serial Rule

The Probabilistic Serial mechanism is well-known for its desirable fairness and efficiency properties. It is one of the most prominent protocols for the random assignment problem. However, Probabilistic Serial is not incentive-compatible, thereby these desirable properties only hold for the agents' declared preferences, rather than their genuine preferences. A substantial utility gain through strategic behaviors would trigger self-interested agents to manipulate the mechanism and would subvert the very foundation of adopting the mechanism in practice. In this paper, we characterize the extent to which an individual agent can increase its utility by strategic manipulation. We show that the incentive ratio of the mechanism is $\frac{3}{2}$. That is, no agent can misreport its preferences such that its utility becomes more than 1.5 times of what it is when reports truthfully. This ratio is a worst-case guarantee by allowing an agent to have complete information about other agents' reports and to figure out the best response strategy even if it is computationally intractable in general. To complement this worst-case study, we further evaluate an agent's utility gain on average by experiments. The experiments show that an agent' incentive in manipulating the rule is very limited. These results shed some light on the robustness of Probabilistic Serial against strategic manipulation, which is one step further than knowing that it is not incentive-compatible.