The continued advances in artificial intelligence (AI), including those in machine learning (ML), raise concerns regarding their deployment in high-risk and safety-critical domains.Motivated by these concerns, there have been calls for the verification of systems of AI, including their explanation.Nevertheless, tools for the verification of systems of AI are complex, and so error-prone.This paper describes one initial effort towards the certification of logic-based explainability algorithms, focusing on monotonic classifiers.Concretely, the paper starts by using the proof assistant Coq to prove the correctness of recently proposed algorithms for explaining monotonic classifiers.Then, the paper proves that the algorithms devised for monotonic classifiers can be applied to the larger family of stable classifiers.Finally, confidence code, extracted from the proofs of correctness, is used for computing explanations that are guaranteed to be correct.The experimental results included in the paper show the scalability of the proposed approach for certifying explanations.

In distributed computing, multiple processes interact to solve a problem together. The main model of interaction is the message-passing model, where processes communicate by exchanging messages. Nevertheless, there are several models varying along important dimensions: degree of synchrony, kinds of faults, number of faults... This variety is compounded by the lack of a general formalism in which to abstract these models. One way to bring order is to constrain these models to communicate in rounds. This is the setting of the Heard-Of model, which captures many models through predicates on the messages sent in a round and received on time. Yet, it is not easy to define the predicate that captures a given operational model. The question is even harder for the asynchronous case, as unbounded message delay means the implementation of rounds must depend on details of the model. This paper shows that characterising asynchronous models by heard-of predicates is indeed meaningful. This characterization relies on delivered predicates, an intermediate abstraction between the informal operational model and the heard-of predicates. Our approach splits the problem into two steps: first extract the delivered model capturing the informal model, and then characterize the heard-of predicates that are generated by this delivered model. For the first part, we provide examples of delivered predicates, and an approach to derive more. It uses the intuition that complex models are a composition of simpler models. We define operations like union, succession or repetition that make it easier to derive complex delivered predicates from simple ones while retaining expressivity. For the second part, we formalize and study strategies for when to change rounds. Intuitively, the characterizing predicate of a model is the one generated by a strategy that waits for as much messages as possible, without blocking forever.

Message-passing models of distributed computing vary along numerous dimensions: degree of synchrony, kind of faults, number of faults... Unfortunately, the sheer number of models and their subtle distinctions hinder our ability to design a general theory of message-passing models. One way out of this conundrum restricts communication to proceed by round. A great variety of message-passing models can then be captured in the Heard-Of model, through predicates on the messages sent in a round and received during or before this round. Then, the issue is to find the most accurate Heard-Of predicate to capture a given model. This is straightforward in synchronous models, because waiting for the upper bound on communication delay ensures that all available messages are received, while not waiting forever. On the other hand, asynchrony allows unbounded message delays. Is there nonetheless a meaningful characterization of asynchronous models by a Heard-Of predicate? We formalize this characterization by introducing Delivered collections: the collections of all messages delivered at each round, whether late or not. Predicates on Delivered collections capture message-passing models. The question is to determine which Heard-Of predicates can be generated by a given Delivered predicate. We answer this by formalizing strategies for when to change round. Thanks to a partial order on these strategies, we also find the "best" strategy for multiple models, where "best" intuitively means it waits for as many messages as possible while not waiting forever. Finally, a strategy for changing round that never blocks a process forever implements a Heard-Of predicate. This allows us to translate the order on strategies into an order on Heard-Of predicates. The characterizing predicate for a model is then the greatest element for that order, if it exists.

In the asynchronous setting, distributed behavior is traditionally studied through computa- tions, the Happened-Before posets of events generated by the system. An equivalent perspective considers the linear extensions of the generated computations: each linear extension defines a sequence of events, called an execution. Both perspective were leveraged in the study of asyn- chronous point-to-point message orderings over computations; yet neither allows us to interpret message orderings defined over executions. Can we nevertheless make sense of such an ordering, maybe even use it to understand asynchronicity better? We provide a general answer by defining a topology on the set of executions which captures the fundamental assumptions of asynchronicity. This topology links each message ordering over executions with two sets of computations: its closure, the computations for which at least one linear extension satisfies the predicate; and its interior, the computations for which all linear ex- tensions satisfy it. These sets of computations represent respectively the uncertainty brought by asynchronicity – the computations where the predicate is satisfiable – and the certainty available despite asynchronicity – the computations where the predicate must hold. The paper demon- strates the use of this topological approach by examining closures and interiors of interesting orderings over executions.

Abstract Asynchronous communication is often viewed as a single entity, the counterpart of synchronous communication. Although the basic concept of asynchronous communication is the decoupling of send and receive events, there is actually room for a variety of additional specification of the communication, for instance in terms of ordering. Yet, these different asynchronous communications are used interchangeably and seldom distinguished. This paper is a contribution to the study of these models, their differences, and how they are related. In this paper, the variety of point-to-point asynchronous communication paradigms is considered with two approaches. In the first and theoretical one, communication models are specified as properties on the ordering of events in distributed executions. In the second and more practical approach that involves composition of peers, they are modeled with transition systems and message histories as part of a framework. The described framework enables to model peer composition and compatibility properties. Besides, an implemented tool chain based on the TLA + formalism and model checking is also proposed and illustrated. The conformance of the two approaches is highlighted. A hierarchy is established between the studied communication models. From the execution viewpoint, it completes existing work in the area by introducing more asynchronous communication models and showing their differences. The framework is shown to offer abstract implementations of the communication models. Both the correctness and the completeness of the descriptions in the framework are studied. This reveals necessary restrictions on the behavior of the peers so that the communication models are actually implementable.

Summary Numerical linear algebra libraries provide many kernels that can be composed to perform complex computations. For a given computation, there is typically a large number of functionally equivalent kernel compositions. Some of these compositions achieve better response times than others for particular data and when executed on a particular computer architecture. Previous research provides methods to enumerate (a subset of) these kernel compositions. In this work, we study the problem of determining the composition that yields the lowest response time. Our approach is based on a response time prediction for each candidate combination. While this prediction could in principle be obtained using analytical and/or empirical performance models, developing accurate such models is known to be challenging. Instead, we define a feature space that captures salient properties of kernel combinations and predict response time using supervised machine learning. We experiment with a standard set of machine learning algorithms and identify an effective algorithm for our kernel composition selection problem. Using this algorithm, our approach widely outperforms the strategy that would consist in always using the simplest kernel composition and is often close to the fastest kernel compositions among those evaluated. We quantify the potential benefit of our approach if it were to be implemented as part of an interactive computational tool. We find that although the potential benefit is substantial, a limiting factor is the kernel composition enumeration overhead. Copyright © 2014 John Wiley & Sons, Ltd.