State-of-the-art machine learning methods exhibit limited compositional generalization. At the same time, there is a lack of realistic benchmarks that comprehensively measure this ability, which makes it challenging to find and evaluate improvements. We introduce a novel method to systematically construct such benchmarks by maximizing compound divergence while guaranteeing a small atom divergence between train and test sets, and we quantitatively compare this method to other approaches for creating compositional generalization benchmarks. We present a large and realistic natural language question answering dataset that is constructed according to this method, and we use it to analyze the compositional generalization ability of three machine learning architectures. We find that they fail to generalize compositionally and that there is a surprisingly strong negative correlation between compound divergence and accuracy. We also demonstrate how our method can be used to create new compositionality benchmarks on top of the existing SCAN dataset, which confirms these findings.

We consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in $\mathcal{O}(T^{\max\{c,1-c\} })$ and $\mathcal{O}(T^{1-c/2})$, respectively, for any $c\in (0,1)$, where $T$ is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in $\mathcal{O}(\log(T))$ and $\mathcal{O}(\sqrt{T\log(T)})$. These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in $\mathcal{O}(T^{\max\{c,1-c/3 \} })$ and $\mathcal{O}(T^{1-c/2})$ for any $c\in (0,1)$. We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems.

We present MLRG Deep Curvature suite, a PyTorch-based, open-source package for analysis and visualisation of neural network curvature and loss landscape. Despite of providing rich information into properties of neural network and useful for a various designed tasks, curvature information is still not made sufficient use for various reasons, and our method aims to bridge this gap. We present a primer, including its main practical desiderata and common misconceptions, of \textit{Lanczos algorithm}, the theoretical backbone of our package, and present a series of examples based on synthetic toy examples and realistic modern neural networks tested on CIFAR datasets, and show the superiority of our package against existing competing approaches for the similar purposes.

Cyanure is an open-source C software package with a Python interface. The goal of Cyanure is to provide state-of-the-art solvers for learning linear models, based on stochastic variance-reduced stochastic optimization with acceleration mechanisms. It provides a simple Python API, which is very close to that of scikit-learn, which should be extended to other languages such as R or Matlab in a near future. Cyanure is distributed under BSD-3-Clause license. Even though this is non-legally binding, the author kindly ask users to cite the present arXiv document in their publications, as well as the publication related to the algorithm they have chosen (see Section 4 for the related publications).

In this article, we present a new data type agnostic algorithm calculating a concept lattice from heterogeneous and complex data. Our NextPriorityConcept algorithm is first introduced and proved in the binary case as an extension of Bordat's algorithm with the notion of strategies to select only some predecessors of each concept, avoiding the generation of unreasonably large lattices. The algorithm is then extended to any type of data in a generic way. It is inspired from pattern structure theory, where data are locally described by predicates independent of their types, allowing the management of heterogeneous data.

Time perception is the phenomenological experience of time by an individual. In this paper, we study how to replicate neural mechanisms involved in time perception, allowing robots to take a step towards temporal cognition. Our framework follows a twofold biologically inspired approach. The first step consists of estimating the passage of time from sensor measurements, since environmental stimuli influence the perception of time. Sensor data is modeled as Gaussian processes that represent the second-order statistics of the natural environment. The estimated elapsed time between two events is computed from the maximum likelihood estimate of the joint distribution of the data collected between them. Moreover, exactly how time is encoded in the brain remains unknown, but there is strong evidence of the involvement of dopaminergic neurons in timing mechanisms. Since their phasic activity has a similar behavior to the reward prediction error of temporal-difference learning models, the latter are used to replicate this behavior. The second step of this approach consists therefore of applying the agent's estimate of the elapsed time in a reinforcement learning problem, where a feature representation called Microstimuli is used. We validate our framework by applying it to an experiment that was originally conducted with mice, and conclude that a robot using this framework is able to reproduce the timing mechanisms of the animal's brain.

There exists a dichotomy between classical probabilistic graphical models, such as Bayesian networks (BNs), and modern tractable models, such as sum-product networks (SPNs). The former have generally intractable inference, but allow a high level of interpretability, while the latter admits a wide range of tractable inference routines, but are typically harder to interpret. Due to this dichotomy, tools to convert between BNs and SPNs are desirable. While one direction -- compiling BNs into SPNs -- is well discussed in Darwiche's seminal work on arithmetic circuit compilation, the converse direction -- decompiling SPNs into BNs -- has received surprisingly little attention. In this paper, we fill this gap by proposing SPN2BN, an algorithm that decompiles an SPN into a BN. SPN2BN has several salient features when compared to the only other two works decompiling SPNs. Most significantly, the BNs returned by SPN2BN are minimal independence-maps. Secondly, SPN2BN is more parsimonious with respect to the introduction of latent variables. Thirdly, the output BN produced by SPN2BN can be precisely characterized with respect to the compiled BN. More specifically, a certain set of directed edges will be added to the input BN, giving what we will call the moral-closure. It immediately follows that there is a set of BNs related to the input BN that will also return the same moral closure. Lastly, it is established that our compilation-decompilation process is idempotent. We confirm our results with systematic experiments on a number of synthetic BNs.

A BSTRACT Knowledge graph embedding research has overlooked the problem of probability calibration. We show popular embedding models are indeed uncalibrated. That means probability estimates associated to predicted triples are unreliable. We present a novel method to calibrate a model when ground truth negatives are not available, which is the usual case in knowledge graphs. We propose to use Platt scaling and isotonic regression alongside our method. Experiments on three datasets with ground truth negatives show our contribution leads to well calibrated models when compared to the gold standard of using negatives. We get significantly better results than the uncalibrated models from all calibration methods. We show isotonic regression offers the best the performance overall, not without tradeoffs. We also show that calibrated models reach state-of-the-art accuracy without the need to define relation-specific decision thresholds. 1 I NTRODUCTION Knowledge graph embedding models are neural architectures that learn vector representations (i.e.

This paper presents an automated tool called Morphy for datamorphic testing. It classifies software test artefacts into test entities and test morphisms, which are mappings on testing entities. In addition to datamorphisms, metamorphisms and seed test case makers, Morphy also employs a set of other test morphisms including test case metrics and filters, test set metrics and filters, test result analysers and test executers to realise test automation. In particular, basic testing activities can be automated by invoking test morphisms. Test strategies can be realised as complex combinations of test morphisms. Test processes can be automated by recording, editing and playing test scripts that invoke test morphisms and strategies. Three types of test strategies have been implemented in Morphy: datamorphism combination strategies, cluster border exploration strategies and strategies for test set optimisation via genetic algorithms. This paper focuses on the datamorphism combination strategies by giving their definitions and implementation algorithms. The paper also illustrates their uses for testing both traditional software and AI applications with three case studies.

Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge representation tool. Though existing ASP variants enjoy efficient implementations, generating an answer set remains intractable. The goal of this research is to define a new \asp-like rule language, 4SP, with tractable model generation. The language combines ideas of ASP and a paraconsistent rule language 4QL. Though 4SP shares the syntax of \asp and for each program all its answer sets are among 4SP models, the new language differs from ASP in its logical foundations, the intended methodology of its use and complexity of computing models. As we show in the paper, 4QL can be seen as a paraconsistent counterpart of ASP programs stratified with respect to default negation. Although model generation of well-supported models for 4QL programs is tractable, dropping stratification makes both 4QL and ASP intractable. To retain tractability while allowing non-stratified programs, in 4SP we introduce trial expressions interlacing programs with hypotheses as to the truth values of default negations. This allows us to develop a~model generation algorithm with deterministic polynomial time complexity. We also show relationships among 4SP, ASP and 4QL.