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The problem of distributed optimization requires a group of networked agents to compute a parameter that minimizes the average of their local cost functions. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to "Byzantine" agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or assume certain statistical properties of the functions at the agents. In this paper, we provide two resilient, scalable, distributed optimization algorithms for multi-dimensional functions. Our schemes involve two filters, (1) a distance-based filter and (2) a min-max filter, which each remove neighborhood states that are extreme (defined precisely in our algorithms) at each iteration. We show that these algorithms can mitigate the impact of up to F (unknown) Byzantine agents in the neighborhood of each regular agent. In particular, we show that if the network topology satisfies certain conditions, all of the regular agents' states are guaranteed to converge to a bounded region that contains the minimizer of the average of the regular agents' functions.

Due to inevitable noises introduced during scanning and quantization, 3D reconstruction via RGB-D sensors suffers from errors both in geometry and texture, leading to artifacts such as camera drifting, mesh distortion, texture ghosting, and blurriness. Given an imperfect reconstructed 3D model, most previous methods have focused on the refinement of either geometry, texture, or camera pose. Or different optimization schemes and objectives for optimizing each component have been used in previous joint optimization methods, forming a complicated system. In this paper, we propose a novel optimization approach based on differentiable rendering, which integrates the optimization of camera pose, geometry, and texture into a unified framework by enforcing consistency between the rendered results and the corresponding RGB-D inputs. Based on the unified framework, we introduce a joint optimization approach to fully exploit the inter-relationships between geometry, texture, and camera pose, and describe an adaptive interleaving strategy to improve optimization stability and efficiency. Using differentiable rendering, an image-level adversarial loss is applied to further improve the 3D model, making it more photorealistic. Experiments on synthetic and real data using quantitative and qualitative evaluation demonstrated the superiority of our approach in recovering both fine-scale geometry and high-fidelity texture.Code is available at //adjointopti.github.io/adjoin.github.io/.

Query graph construction aims to construct the correct executable SPARQL on the KG to answer natural language questions. Although recent methods have achieved good results using neural network-based query graph ranking, they suffer from three new challenges when handling more complex questions: 1) complicated SPARQL syntax, 2) huge search space, and 3) locally ambiguous query graphs. In this paper, we provide a new solution. As a preparation, we extend the query graph by treating each SPARQL clause as a subgraph consisting of vertices and edges and define a unified graph grammar called AQG to describe the structure of query graphs. Based on these concepts, we propose a novel end-to-end model that performs hierarchical autoregressive decoding to generate query graphs. The high-level decoding generates an AQG as a constraint to prune the search space and reduce the locally ambiguous query graph. The bottom-level decoding accomplishes the query graph construction by selecting appropriate instances from the preprepared candidates to fill the slots in the AQG. The experimental results show that our method greatly improves the SOTA performance on complex KGQA benchmarks. Equipped with pre-trained models, the performance of our method is further improved, achieving SOTA for all three datasets used.

We present experimental results and a user study for hierarchical drawings of graphs. A detailed hierarchical graph drawing technique that is based on the Path Based Framework (PBF) is presented. Extensive edge bundling is applied to draw all edges of the graph and the height of the drawing is minimized using compaction. The drawings produced by this framework are compared to drawings produced by the well known Sugiyama framework in terms of area, number of bends, number of crossings, and execution time. The new algorithm runs very fast and produces drawings that are readable and efficient. Since there are advantages (and disadvantages) to both frameworks, we performed a user study and the results show that the drawings produced by the new framework are well received in terms of clarity, readability, and usability. Hence, the new technique offers an interesting alternative to drawing hierarchical graphs, and is especially useful in applications where user defined paths are important and need to be highlighted.

Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail unexpectedly deeming the networks non-operational, while checking whether a link is damaged is costly and possibly erroneous. After an event that has damaged an arbitrary subset of the edges, the network operator must find a spanning tree of the network using non-damaged edges by making as few checks as possible. Motivated by such questions, we study the problem of finding a spanning tree in a network, when we only have access to noisy queries of the form "Does edge e exist?". We design efficient algorithms, even when edges fail adversarially, for all possible error regimes; 2-sided error (where any answer might be erroneous), false positives (where "no" answers are always correct) and false negatives (where "yes" answers are always correct). In the first two regimes we provide efficient algorithms and give matching lower bounds for general graphs. In the False Negative case we design efficient algorithms for large interesting families of graphs (e.g. bounded treewidth, sparse). Using the previous results, we provide tight algorithms for the practically useful family of planar graphs in all error regimes.

We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical one -- for the difference of submodular (DS) optimization problem, and vice versa. We also illustrate the link between these two problems by analyzing a \textsc{Greedy} algorithm which approximately maximizes objective functions of the form $\Psi(f,g)$, where $f,g$ are two non-negative, monotone, submodular functions and $\Psi$ is a {quasiconvex} 2-variables function, which is non decreasing with respect to the first variable. For the choice $\Psi(f,g)\triangleq f/g$, we recover RS, and for the choice $\Psi(f,g)\triangleq f-g$, we recover DS. To the best of our knowledge, this greedy approach is new for DS optimization. For RS optimization, it reduces to the standard \textsc{GreedRatio} algorithm that has already been analyzed previously. However, our analysis is novel for this case.

Adhesive joints are increasingly used in industry for a wide variety of applications because of their favorable characteristics such as high strength-to-weight ratio, design flexibility, limited stress concentrations, planar force transfer, good damage tolerance and fatigue resistance. Finding the optimal process parameters for an adhesive bonding process is challenging: the optimization is inherently multi-objective (aiming to maximize break strength while minimizing cost) and constrained (the process should not result in any visual damage to the materials, and stress tests should not result in failures that are adhesion-related). Real life physical experiments in the lab are expensive to perform; traditional evolutionary approaches (such as genetic algorithms) are then ill-suited to solve the problem, due to the prohibitive amount of experiments required for evaluation. In this research, we successfully applied specific machine learning techniques (Gaussian Process Regression and Logistic Regression) to emulate the objective and constraint functions based on a \emph{limited} amount of experimental data. The techniques are embedded in a Bayesian optimization algorithm, which succeeds in detecting Pareto-optimal process settings in a highly efficient way (i.e., requiring a limited number of extra experiments).

A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a solution. This problem exists in both homogeneous and inhomogeneous variants; it is distinct from, but related to, the classical problem of factorization of differential operators. Recently, minimization has found applications in Transcendental Number Theory, more specifically in the computation of non-zero algebraic points where Siegel's $E$-functions take algebraic values. We present algorithms for these questions and discuss implementation and experiments.

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.