With the adoption of deep learning models to low-power, small-memory edge devices, energy consumption and storage usage of such models have become a key concern. The problem exacerbates even further with ever-growing data and equally-matched bulkier models. This concern is particularly pronounced for graph data due to its quadratic storage, irregular (non-grid) geometry, and very large size. Typical graph data, such as road networks, infrastructure networks, and social networks, easily exceeds millions of nodes, and several gigabytes of storage is needed just to store the node embedding vectors, let alone the model parameters. In recent years, the memory issue has been addressed by moving away from memory-intensive double precision floating-point arithmetic towards single-precision or even half-precision, often by trading-off marginally small performance. Along this effort, we propose Node2Binary, which embeds graph nodes in as few as 128 binary bits, thereby reducing the memory footprint of vertex embedding vectors by several orders of magnitude. Node2Binary. leverages a fast community detection algorithm to convert the given graph into a hierarchical partition tree and then find embeddings of graph vertices in binary space by solving a combinatorial optimization (CO) task over the tree edges. CO is NP-hard, but Node2Binary uses an innovative combination of discrete gradient descent and randomization to solve this task effectively and efficiently. Extensive experiments over four real-world graphs show that Node2Binary achieves competitive performance compared to the state-of-the art graph embedding methods in both node classification and link prediction tasks.

For natural language understanding and generation, embedding concepts using an order-based representation is an essential task. Unlike traditional point vector based representation, an order-based representation imposes geometric constraints on the representation vectors for explicitly capturing various semantic relationships that may exist between a pair of concepts. In existing literature, several approaches on order-based embedding have been proposed, mostly focusing on capturing hierarchical relationships; examples include vectors in Euclidean space, complex, Hyperbolic, order, and Box Embedding. Box embedding creates region-based rich representation of concepts, but along the process it sacrifices simplicity, requiring a custom-made optimization scheme for learning the representation. Hyperbolic embedding improves embedding quality by exploiting the ever-expanding property of Hyperbolic space, but it also suffers from the same fate as box embedding as gradient descent like optimization is not simple in the Hyperbolic space. In this work, we propose Binder, a novel approach for order-based representation. Binder uses binary vectors for embedding, so the embedding vectors are compact with an order of magnitude smaller footprint than other methods. Binder uses a simple and efficient optimization scheme for learning representation vectors with a linear time complexity. Our comprehensive experimental results show that Binder is very accurate, yielding competitive results on the representation task. But Binder stands out from its competitors on the transitive closure link prediction task as it can learn concept embeddings just from the direct edges, whereas all existing order-based approaches rely on the indirect edges. In particular, Binder achieves a whopping 70% higher F1-score than the second best method (98.6% vs 29%) in our largest dataset, WordNet Nouns (743,241 edges), when using only direct edges during training.

An electronic voting (E-voting) oriented cybersecurity curriculum, proposed by Hostler et al. [4] in 2021, leverages the rich security features of E-voting systems and E-voting process to teach essential concepts of cybersecurity. Existing curricular guidelines describe topics in computer security, but do not instantiate them with examples. This is because their goals are different. In this case study, we map the e-voting curriculum into the CSEC2017 curriculum guidelines, to demonstrate how such a mapping is done. Further, this enables teachers to select the parts of the e-voting curriculum most relevant to their classes, by basing the selection on the relevant CSEC2017 learning objectives. We conclude with a brief discussion on generalizing this mapping to other curricular guidelines.