Byzantine Consensus in Abstract MAC Layer

This paper studies the design of Byzantine consensus algorithms in an asynchronous single-hop network equipped with the “abstract MAC layer” [DISC09], which captures core properties of modern wireless MAC protocols. Newport [PODC14], Newport and Robinson [DISC18], and Tseng and Zhang [PODC22] study crash-tolerant consensus in the model. In our setting, a Byzantine faulty node may behave arbitrarily, but it cannot break the guarantees provided by the underlying abstract MAC layer. To our knowledge, we are the first to study Byzantine faults in this model. We harness the power of the abstract MAC layer to develop a Byzantine approximate consensus algorithm and a Byzantine randomized binary consensus algorithm. Both of our algorithms require only the knowledge of the upper bound on the number of faulty nodes f, and do not require the knowledge of the number of nodes n. This demonstrates the “power” of the abstract MAC layer, as consensus algorithms in traditional message-passing models require the knowledge of both n and f. Additionally, we show that it is necessary to know f in order to reach consensus. Hence, from this perspective, our algorithms require the minimal knowledge. The lack of knowledge of n brings the challenge of identifying a quorum explicitly, which is a common technique in traditional message-passing algorithms. A key technical novelty of our algorithms is to identify “implicit quorums” which have the necessary information for reaching consensus. The quorums are implicit because nodes do not know the identity of the quorums – such notion is only used in the analysis

Analysis of Attention Mechanisms in Box-Embedding Systems

Large-scale Knowledge Graphs (KGs) have recently gained considerable research attention for their ability to model the inter- and intra- relationships of data. However, the huge scale of KGs has necessitated the use of querying methods to facilitate human use. Question Answering (QA) systems have shown much promise in breaking down this human-machine barrier. A recent QA model that achieved state-of-the-art performance, Query2box, modelled queries on a KG using box embeddings with an attention mechanism backend to compute the intersections of boxes for query resolution. In this paper, we introduce a new model, Query2Geom, which replaces the Query2box attention mechanism with a novel, exact geometric calculation. Our findings show that Query2Geom generally matches the performance of Query2box while having many fewer parameters. Our analysis of the two models leads us to formally describe the interaction between knowledge graph data and box embeddings with the concepts of semantic-geometric alignment and mismatch. We create the Attention Deviation Metric as a measure of how well the geometry of box embeddings captures the semantics of a knowledge graph, and apply it to explain the difference in performance between Query2box and Query2Geom. We conclude that Query2box’s attention mechanism operates using “latent intersections” that attend to the semantic properties in embeddings not expressed in box geometry, acting as a limit on model interpretability. Finally, we generalise our results and propose that semantic-geometric mismatch is a more general property of attention mechanisms, and provide future directions on how to formally model the interaction between attention and latent semantics

Cholula: Fast, Fault-tolerant, and Strongly Consistent Off-chain Object Storage

Emerging security technologies such as Blockchain are prominent to secure data. Blockchain inherits the advanced principles of cryptography and decentralization. This paper explores an appropriate design for distributed object storage systems for off-chain data. Our system Cholula has the following salient features: (i) Strong consistency; (ii) Optimal fast-path latency (1 RTT when there is no conflicting write); (iii) Tolerance of Byzantine servers; (iv) Security (preventing from an imposter attack); and (v) Censorship-resistance. We present our design and evaluation in this work. We demonstrate that Cholula has a better performance than the state-of-the-art object storage system Giza (the system behind Microsoft OneDrive) and Cassandra in the context of geo-replicated off-chain data