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We are concerned with the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed for the lattice translates of the correspondingly dilated polytope to cover the whole space. As our main result, we describe a new algorithm for this problem, which is simpler, more efficient and easier to implement than the only prior algorithm of Kannan (1992). Motivated by a variant of the famous Lonely Runner Conjecture, we use its geometric interpretation in terms of covering radii of zonotopes, and apply our algorithm to prove the first open case of three runners with individual starting points.

Interactive visual analysis interfaces are critical in nearly every data task. However, creating new interfaces is deeply challenging, as it requires the developer to understand the queries needed to express the desired analysis task, design the appropriate interface to express those queries for the task, and implement the interface using a combination of visualization, browser, server, and database technologies. Although prior work generates a set of interactive widgets that can express an input query log, this paper presents PI2, the first system to generate fully functional visual analysis interfaces from an example sequence of analysis queries. PI2 analyzes queries syntactically and represents a set of queries using a novel Difftree structure that encodes systematic variations between query abstract syntax trees. PI2 then maps each Difftree to a visualization that renders its results, the variations in each Difftree to interactions, and generates a good layout for the interface. We show that PI2 can express data-oriented interactions in existing visualization interaction taxonomies, reproduce or improve several real-world visual analysis interfaces, generate interfaces in 2-19s (median 6s), and scale linearly with the number of queries.

Consensus protocols have traditionally been studied in a setting where all participants are known to each other from the start of the protocol execution. In the parlance of the 'blockchain' literature, this is referred to as the permissioned setting. What differentiates Bitcoin from these previously studied protocols is that it operates in a permissionless setting, i.e. it is a protocol for establishing consensus over an unknown network of participants that anybody can join, with as many identities as they like in any role. The arrival of this new form of protocol brings with it many questions. Beyond Bitcoin, what can we prove about permissionless protocols in a general sense? How does recent work on permissionless protocols in the blockchain literature relate to the well-developed history of research on permissioned protocols in distributed computing? To answer these questions, we describe a formal framework for the analysis of both permissioned and permissionless systems. Our framework allows for "apples-to-apples" comparisons between different categories of protocols and, in turn, the development of theory to formally discuss their relative merits. A major benefit of the framework is that it facilitates the application of a rich history of proofs and techniques in distributed computing to problems in blockchain and the study of permissionless systems. Within our framework, we then address the questions above. We consider the Byzantine Generals Problem as a formalisation of the problem of reaching consensus, and address a programme of research that asks, "Under what adversarial conditions, and for what types of permissionless protocol, is consensus possible?" We prove a number of results for this programme, our main result being that deterministic consensus is not possible for decentralised permissionless protocols. To close, we give a list of eight open questions.

The goal of continuous control is to synthesize desired behaviors. In reinforcement learning (RL)-driven approaches, this is often accomplished through careful task reward engineering for efficient exploration and running an off-the-shelf RL algorithm. While reward maximization is at the core of RL, reward engineering is not the only -- sometimes nor the easiest -- way for specifying complex behaviors. In this paper, we introduce \braxlines, a toolkit for fast and interactive RL-driven behavior generation beyond simple reward maximization that includes Composer, a programmatic API for generating continuous control environments, and set of stable and well-tested baselines for two families of algorithms -- mutual information maximization (MiMax) and divergence minimization (DMin) -- supporting unsupervised skill learning and distribution sketching as other modes of behavior specification. In addition, we discuss how to standardize metrics for evaluating these algorithms, which can no longer rely on simple reward maximization. Our implementations build on a hardware-accelerated Brax simulator in Jax with minimal modifications, enabling behavior synthesis within minutes of training. We hope Braxlines can serve as an interactive toolkit for rapid creation and testing of environments and behaviors, empowering explosions of future benchmark designs and new modes of RL-driven behavior generation and their algorithmic research.

Graphic design is ubiquitous in people's daily lives. For graphic design, the most time-consuming task is laying out various components in the interface. Repetitive manual layout design will waste a lot of time for professional graphic designers. Existing templates are usually rudimentary and not suitable for most designs, reducing efficiency and limiting creativity. This paper implemented the Transformer model and conditional variational autoencoder (CVAE) to the graphic design layout generation task. It proposed an end-to-end graphic design layout generation model named LayoutT-CVAE. We also proposed element disentanglement and feature-based disentanglement strategies and introduce new graphic design principles and similarity metrics into the model, which significantly increased the controllability and interpretability of the deep model. Compared with the existing state-of-art models, the layout generated by ours performs better on many metrics.

Coding theory and combinatorial $t$-designs have close connections and interesting interplay. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. As we all known, some $t$-designs have been constructed with this approach by using certain linear codes in recent years. However, only a few infinite families of cyclic codes holding an infinite family of $3$-designs are reported in the literature. The objective of this paper is to study an infinite family of cyclic codes and determine their parameters. By the parameters of these codes and their dual, some infinite family of $3$-designs are presented and their parameters are also explicitly determined. In particular, the complements of the supports of the minimum weight codewords in the studied cyclic code form a Steiner system. Furthermore, we show that the infinite family of cyclic codes admit $3$-transitive automorphism groups.

Most existing work on automated fact checking is concerned with predicting the veracity of claims based on metadata, social network spread, language used in claims, and, more recently, evidence supporting or denying claims. A crucial piece of the puzzle that is still missing is to understand how to automate the most elaborate part of the process -- generating justifications for verdicts on claims. This paper provides the first study of how these explanations can be generated automatically based on available claim context, and how this task can be modelled jointly with veracity prediction. Our results indicate that optimising both objectives at the same time, rather than training them separately, improves the performance of a fact checking system. The results of a manual evaluation further suggest that the informativeness, coverage and overall quality of the generated explanations are also improved in the multi-task model.

People ask questions that are far richer, more informative, and more creative than current AI systems. We propose a neural program generation framework for modeling human question asking, which represents questions as formal programs and generates programs with an encoder-decoder based deep neural network. From extensive experiments using an information-search game, we show that our method can ask optimal questions in synthetic settings, and predict which questions humans are likely to ask in unconstrained settings. We also propose a novel grammar-based question generation framework trained with reinforcement learning, which is able to generate creative questions without supervised data.

Although recent neural conversation models have shown great potential, they often generate bland and generic responses. While various approaches have been explored to diversify the output of the conversation model, the improvement often comes at the cost of decreased relevance. In this paper, we propose a method to jointly optimize diversity and relevance that essentially fuses the latent space of a sequence-to-sequence model and that of an autoencoder model by leveraging novel regularization terms. As a result, our approach induces a latent space in which the distance and direction from the predicted response vector roughly match the relevance and diversity, respectively. This property also lends itself well to an intuitive visualization of the latent space. Both automatic and human evaluation results demonstrate that the proposed approach brings significant improvement compared to strong baselines in both diversity and relevance.

Generative Adversarial Networks (GAN) have shown great promise in tasks like synthetic image generation, image inpainting, style transfer, and anomaly detection. However, generating discrete data is a challenge. This work presents an adversarial training based correlated discrete data (CDD) generation model. It also details an approach for conditional CDD generation. The results of our approach are presented over two datasets; job-seeking candidates skill set (private dataset) and MNIST (public dataset). From quantitative and qualitative analysis of these results, we show that our model performs better as it leverages inherent correlation in the data, than an existing model that overlooks correlation.