The biomedical domain is a complex network of interconnected knowledge, encompassing genetics, diseases, drugs, and biological processes. While knowledge graphs (KGs) excel at organizing and linking this information, their complexity often makes them difficult for users to query. Ideally, users should be able to ask questions in natural language and receive precise answers directly from the KG, without needing specialized query expertise. However, enabling deep learning-based systems to query KGs using natural language remains a major challenge. Existing biomedical knowledge graph question answering (BioKGQA) datasets are small and limited in scope, typically containing only a few hundred question answering (QA) pairs.

We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory. To address whether a particular motif distribution is characteristic of the training task, or function of the DNN, we compare the connectivity structure of 350 DNNs trained to simulate a bio-mechanical flight control system with different randomly initialized parameters. We develop and implement algorithms for counting second- and third-order motifs and calculate their significance using their Z-score. The DNNs are trained to solve the inverse problem of the flight dynamics model in Bustamante, et al. (2022) (i.e., predict the controls necessary for controlled flight from the initial and final state-space inputs) and are sparsified through an iterative pruning and retraining algorithm Zahn, et al. (2022). We show that, despite random initialization of network parameters, enforced sparsity causes DNNs to converge to similar connectivity patterns as characterized by their motif distributions. The results suggest how neural network function can be encoded in motif distributions, suggesting a variety of experiments for informing function and control.

The reliability of controlled experiments, or "A/B tests," can often be compromised due to the phenomenon of network interference, wherein the outcome for one unit is influenced by other units. To tackle this challenge, we propose a machine learning-based method to identify and characterize heterogeneous network interference. Our approach accounts for latent complex network structures and automates the task of "exposure mapping'' determination, which addresses the two major limitations in the existing literature. We introduce "causal network motifs'' and employ transparent machine learning models to establish the most suitable exposure mapping that reflects underlying network interference patterns. Our method's efficacy has been validated through simulations on two synthetic experiments and a real-world, large-scale test involving 1-2 million Instagram users, outperforming conventional methods such as design-based cluster randomization and analysis-based neighborhood exposure mapping. Overall, our approach not only offers a comprehensive, automated solution for managing network interference and improving the precision of A/B testing results, but it also sheds light on users' mutual influence and aids in the refinement of marketing strategies.

Small subgraphs (graphlets) are important features to describe fundamental units of a large network. The calculation of the subgraph frequency distributions has a wide application in multiple domains including biology and engineering. Unfortunately due to the inherent complexity of this task, most of the existing methods are computationally intensive and inefficient. In this work, we propose GNNS, a novel representational learning framework that utilizes graph neural networks to sample subgraphs efficiently for estimating their frequency distribution. Our framework includes an inference model and a generative model that learns hierarchical embeddings of nodes, subgraphs, and graph types. With the learned model and embeddings, subgraphs are sampled in a highly scalable and parallel way and the frequency distribution estimation is then performed based on these sampled subgraphs. Eventually, our methods achieve comparable accuracy and a significant speedup by three orders of magnitude compared to existing methods.

Dear friends, Welcome to the July 4th issue of the Sunday Briefing. This week we're happy to announce the second post of "Visualization for Science" substack: Time Series State Map so check it out and don't forget to Subscribe to V4Sci so you never miss a post! You can also checkout the latest post at G4Sci: Network Motifs: Frequent patterns in Graphs where we introduce the ESU algorithm for exhaustive enumeration of all subgraphs of a given size. You should Subscribe to G4Sci to make sure you never miss a post! Over at Medium, Competing CoVID-19 Strains is the most recent post on the Epidemiology series and Mediation is the latest for the Causality series while we continue to work on the particularly long section 3.8 of the Primer.

Temporal networks serve as abstractions of many real-world dynamic systems. These networks typically evolve according to certain laws, such as the law of triadic closure, which is universal in social networks. Inductive representation learning of temporal networks should be able to capture such laws and further be applied to systems that follow the same laws but have not been unseen during the training stage. Previous works in this area depend on either network node identities or rich edge attributes and typically fail to extract these laws. Here, we propose Causal Anonymous Walks (CAWs) to inductively represent a temporal network. CAWs are extracted by temporal random walks and work as automatic retrieval of temporal network motifs to represent network dynamics while avoiding the time-consuming selection and counting of those motifs. CAWs adopt a novel anonymization strategy that replaces node identities with the hitting counts of the nodes based on a set of sampled walks to keep the method inductive, and simultaneously establish the correlation between motifs. We further propose a neural-network model CAW-N to encode CAWs, and pair it with a CAW sampling strategy with constant memory and time cost to support online training and inference. CAW-N is evaluated to predict links over 6 real temporal networks and uniformly outperforms previous SOTA methods by averaged 15% AUC gain in the inductive setting. CAW-N also outperforms previous methods in 5 out of the 6 networks in the transductive setting.

Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called "network motifs". In this article we show that network science tools can be successfully applied also to the study of artificial neural networks operating according to self-organizing (learning) principles. In particular, we study the emergence of network motifs in multi-layer perceptrons, whose initial connectivity is defined as a stack of fully-connected, bipartite graphs. Our simulations show that the final network topology is primarily shaped by learning dynamics, but can be strongly biased by choosing appropriate weight initialization schemes. Overall, our results suggest that non-trivial initialization strategies can make learning more effective by promoting the development of useful network motifs, which are often surprisingly consistent with those observed in general transduction networks.

Classical stochastic models, such as the Erd os-R enyi, Barabasi-Albert, and the stochastic block model generate graphs based on a predefined set of parameters, such as the probability of edge formation within and between communities [1]. In contrast, modern approaches to graph generation based on deep learning, including NetGAN [2], GraphGAN [3], and GraphRNN [4], are flexible enough to learn multiple different properties of an input graph simultaneously. The graphs generated by these architectures may be used for downstream learning tasks such as data augmentation [5], recommendation [6], and link prediction [7]. Many real-world networks consist of entities with complex mutual interrelations. Such networks cannot be modeled effectively as graphs with simple pairwise relations, despite the fact that pairwise relations provide a wealth of information for learning. Studying higher-order relationships in a graph is fundamental for our understanding of the network behavior and function. Higher-order relationships are usually termed hyperedges (collections of more than two nodes) [8, 9] or network motifs (recurrent node connectivity patterns that are statistically significant compared to some ground truth random graph model) [10]. These higher-order structures are the actual building blocks of complex networks, as they capture fundamental functional properties.

In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as web search, online advertising, and recommendation. In such applications, real-time performance is critical. The proposed methods do not require any explicit training data, nor do they derive an embedding from the graph data, or perform any explicit learning. Existing methods with the above desired properties are all based on closing triangles (common neighbors, Jaccard similarity, and the ilk). In this work, we investigate higher-order network motifs and develop techniques based on the notion of closing higher-order motifs that move beyond closing simple triangles. All methods described in this work are fast with a runtime that is sublinear in the number of nodes. The experimental results indicate the importance of closing higher-order motifs for ranking and link prediction applications. Finally, the proposed notion of higher-order motif closure can serve as a basis for studying and developing better ranking and link prediction methods.

This paper describes a general framework for learning Higher-Order Network Embeddings (HONE) from graph data based on network motifs. The HONE framework is highly expressive and flexible with many interchangeable components. The experimental results demonstrate the effectiveness of learning higher-order network representations. In all cases, HONE outperforms recent embedding methods that are unable to capture higher-order structures with a mean relative gain in AUC of $19\%$ (and up to $75\%$ gain) across a wide variety of networks and embedding methods.