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Partial Differential Equations (PDEs) describe several problems relevant to many fields of applied sciences, and their discrete counterparts typically involve the solution of sparse linear systems. In this context, we focus on the analysis of the computational aspects related to the solution of large and sparse linear systems with HPC solvers, by considering the performances of direct and iterative solvers in terms of computational efficiency, scalability, and numerical accuracy. Our aim is to identify the main criteria to support application-domain specialists in the selection of the most suitable solvers, according to the application requirements and available resources. To this end, we discuss how the numerical solver is affected by the regular/irregular discretisation of the input domain, the discretisation of the input PDE with piecewise linear or polynomial basis functions, which generally result in a higher/lower sparsity of the coefficient matrix, and the choice of different initial conditions, which are associated with linear systems with multiple right-hand side terms. Finally, our analysis is independent of the characteristics of the underlying computational architectures, and provides a methodological approach that can be applied to different classes of PDEs or with approximation problems.

The detection and estimation of sinusoids is a fundamental signal processing task for many applications related to sensing and communications. While algorithms have been proposed for this setting, quantization is a critical, but often ignored modeling effect. In wireless communications, estimation with low resolution data converters is relevant for reduced power consumption in wideband receivers. Similarly, low resolution sampling in imaging and spectrum sensing allows for efficient data collection. In this work, we propose SignalNet, a neural network architecture that detects the number of sinusoids and estimates their parameters from quantized in-phase and quadrature samples. We incorporate signal reconstruction internally as domain knowledge within the network to enhance learning and surpass traditional algorithms in mean squared error and Chamfer error. We introduce a worst-case learning threshold for comparing the results of our network relative to the underlying data distributions. This threshold provides insight into why neural networks tend to outperform traditional methods and into the learned relationships between the input and output distributions. In simulation, we find that our algorithm is always able to surpass the threshold for three-bit data but often cannot exceed the threshold for one-bit data. We use the learning threshold to explain, in the one-bit case, how our estimators learn to minimize the distributional loss, rather than learn features from the data.

Embedded and Internet-of-Things (IoT) devices have seen an increase in adoption in many domains. The security of these devices is of great importance as they are often used to control critical infrastructure, medical devices, and vehicles. Existing solutions to isolate microcontroller (MCU) resources in order to increase their security face significant challenges such as specific hardware unavailability, Memory Protection Unit (MPU) limitations and a significant lack of Direct Memory Access (DMA) support. Nevertheless, DMA is fundamental for the power and performance requirements of embedded applications. In this paper, we present D-Box, a systematic approach to enable secure DMA operations for compartmentalization solutions of embedded applications using real-time operating systems (RTOS). D-Box defines a reference architecture and a workflow to protect DMA operations holistically. It provides practical methods to harden the kernel and define capability-based security policies for easy definition of DMA operations with strong security properties. We implemented a D-Box prototype for the Cortex-M3/M4 on top of the popular FreeRTOS-MPU (F-MPU). The D-Box procedures and a stricter security model enabled DMA operations, yet it exposed 41 times less ROP (return-orienting-programming) gadgets when compared with the standard F-MPU. D-Box adds only a 2% processor overhead while reducing the power consumption of peripheral operation benchmarks by 18.2%. The security properties and performance of D-Box were tested and confirmed on a real-world case study of a Programmable Logic Controller (PLC) application.

Large scale knowledge graph embedding has attracted much attention from both academia and industry in the field of Artificial Intelligence. However, most existing methods concentrate solely on fact triples contained in the given knowledge graph. Inspired by the fact that logic rules can provide a flexible and declarative language for expressing rich background knowledge, it is natural to integrate logic rules into knowledge graph embedding, to transfer human knowledge to entity and relation embedding, and strengthen the learning process. In this paper, we propose a novel logic rule-enhanced method which can be easily integrated with any translation based knowledge graph embedding model, such as TransE . We first introduce a method to automatically mine the logic rules and corresponding confidences from the triples. And then, to put both triples and mined logic rules within the same semantic space, all triples in the knowledge graph are represented as first-order logic. Finally, we define several operations on the first-order logic and minimize a global loss over both of the mined logic rules and the transformed first-order logics. We conduct extensive experiments for link prediction and triple classification on three datasets: WN18, FB166, and FB15K. Experiments show that the rule-enhanced method can significantly improve the performance of several baselines. The highlight of our model is that the filtered Hits@1, which is a pivotal evaluation in the knowledge inference task, has a significant improvement (up to 700% improvement).

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict "em what drugs are likely to target proteins involved with both diseases X and Y?" -- a query that requires reasoning about all possible proteins that {\em might} interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.

Objects are made of parts, each with distinct geometry, physics, functionality, and affordances. Developing such a distributed, physical, interpretable representation of objects will facilitate intelligent agents to better explore and interact with the world. In this paper, we study physical primitive decomposition---understanding an object through its components, each with physical and geometric attributes. As annotated data for object parts and physics are rare, we propose a novel formulation that learns physical primitives by explaining both an object's appearance and its behaviors in physical events. Our model performs well on block towers and tools in both synthetic and real scenarios; we also demonstrate that visual and physical observations often provide complementary signals. We further present ablation and behavioral studies to better understand our model and contrast it with human performance.

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we propose an architecture that represents numerical quantities as linear activations which are manipulated using primitive arithmetic operators, controlled by learned gates. We call this module a neural arithmetic logic unit (NALU), by analogy to the arithmetic logic unit in traditional processors. Experiments show that NALU-enhanced neural networks can learn to track time, perform arithmetic over images of numbers, translate numerical language into real-valued scalars, execute computer code, and count objects in images. In contrast to conventional architectures, we obtain substantially better generalization both inside and outside of the range of numerical values encountered during training, often extrapolating orders of magnitude beyond trained numerical ranges.

Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.

In recent years, person re-identification (re-id) catches great attention in both computer vision community and industry. In this paper, we propose a new framework for person re-identification with a triplet-based deep similarity learning using convolutional neural networks (CNNs). The network is trained with triplet input: two of them have the same class labels and the other one is different. It aims to learn the deep feature representation, with which the distance within the same class is decreased, while the distance between the different classes is increased as much as possible. Moreover, we trained the model jointly on six different datasets, which differs from common practice - one model is just trained on one dataset and tested also on the same one. However, the enormous number of possible triplet data among the large number of training samples makes the training impossible. To address this challenge, a double-sampling scheme is proposed to generate triplets of images as effective as possible. The proposed framework is evaluated on several benchmark datasets. The experimental results show that, our method is effective for the task of person re-identification and it is comparable or even outperforms the state-of-the-art methods.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.