Local to Global: A Distributed Quantum Approximate Optimization Algorithm for Pseudo-Boolean Optimization Problems

With the rapid advancement of quantum computing, Quantum Approximate Optimization Algorithm (QAOA) is considered as a promising candidate to demonstrate quantum supremacy, which exponentially solves a class of Quadratic Unconstrained Binary Optimization (QUBO) problems. However, limited qubit availability and restricted coherence time challenge QAOA to solve large-scale pseudo-Boolean problems on currently available Near-term Intermediate Scale Quantum (NISQ) devices. In this paper, we propose a distributed QAOA which can solve a general pseudo-Boolean problem by converting it to a simplified Ising model. Different from existing distributed QAOAs' assuming that local solutions are part of a global one, which is not often the case, we introduce community detection using Louvian algorithm to partition the graph where subgraphs are further compressed by community representation and merged into a higher level subgraph. Recursively and backwards, local solutions of lower level subgraphs are updated by heuristics from solutions of higher level subgraphs. Compared with existing methods, our algorithm incorporates global heuristics into local solutions such that our algorithm is proven to achieve a higher approximation ratio and outperforms across different graph configurations. Also, ablation studies validate the effectiveness of each component in our method.Comment: 12 pages, 6 figure

Random graphs containing arbitrary distributions of subgraphs

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly non-tree-like neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a new class of random graph models that incorporates general subgraphs, allowing for non-tree-like neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.Comment: 12 pages, 6 figures, 1 tabl

Characterizing the Shape of Activation Space in Deep Neural Networks

The representations learned by deep neural networks are difficult to interpret in part due to their large parameter space and the complexities introduced by their multi-layer structure. We introduce a method for computing persistent homology over the graphical activation structure of neural networks, which provides access to the task-relevant substructures activated throughout the network for a given input. This topological perspective provides unique insights into the distributed representations encoded by neural networks in terms of the shape of their activation structures. We demonstrate the value of this approach by showing an alternative explanation for the existence of adversarial examples. By studying the topology of network activations across multiple architectures and datasets, we find that adversarial perturbations do not add activations that target the semantic structure of the adversarial class as previously hypothesized. Rather, adversarial examples are explainable as alterations to the dominant activation structures induced by the original image, suggesting the class representations learned by deep networks are problematically sparse on the input space

Dynamic load balancing for the distributed mining of molecular structures

In molecular biology, it is often desirable to find common properties in large numbers of drug candidates. One family of methods stems from the data mining community, where algorithms to find frequent graphs have received increasing attention over the past years. However, the computational complexity of the underlying problem and the large amount of data to be explored essentially render sequential algorithms useless. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. This problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely, a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiverinitiated load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening data set, where we were able to show close-to linear speedup in a network of workstations. The proposed approach also allows for dynamic resource aggregation in a non dedicated computational environment. These features make it suitable for large-scale, multi-domain, heterogeneous environments, such as computational grids

apk2vec: Semi-supervised multi-view representation learning for profiling Android applications

Building behavior profiles of Android applications (apps) with holistic, rich and multi-view information (e.g., incorporating several semantic views of an app such as API sequences, system calls, etc.) would help catering downstream analytics tasks such as app categorization, recommendation and malware analysis significantly better. Towards this goal, we design a semi-supervised Representation Learning (RL) framework named apk2vec to automatically generate a compact representation (aka profile/embedding) for a given app. More specifically, apk2vec has the three following unique characteristics which make it an excellent choice for largescale app profiling: (1) it encompasses information from multiple semantic views such as API sequences, permissions, etc., (2) being a semi-supervised embedding technique, it can make use of labels associated with apps (e.g., malware family or app category labels) to build high quality app profiles, and (3) it combines RL and feature hashing which allows it to efficiently build profiles of apps that stream over time (i.e., online learning). The resulting semi-supervised multi-view hash embeddings of apps could then be used for a wide variety of downstream tasks such as the ones mentioned above. Our extensive evaluations with more than 42,000 apps demonstrate that apk2vec's app profiles could significantly outperform state-of-the-art techniques in four app analytics tasks namely, malware detection, familial clustering, app clone detection and app recommendation.Comment: International Conference on Data Mining, 201