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Natural Language Inference is a challenging task that has received substantial attention, and state-of-the-art models now achieve impressive test set performance in the form of accuracy scores. Here, we go beyond this single evaluation metric to examine robustness to semantically-valid alterations to the input data. We identify three factors -insensitivity, polarity and unseen pairs -and compare their impact on three SNLI models under a variety of conditions. Our results demonstrate a number of strengths and weaknesses in the models' ability to generalise to new in-domain instances. In particular, while strong performance is possible on unseen hypernyms, unseen antonyms are more challenging for all the models. More generally, the models suffer from an insensitivity to certain small but semantically significant alterations, and are also often influenced by simple statistical correlations between words and training labels. Overall, we show that evaluations of NLI models can benefit from studying the influence of factors intrinsic to the models or found in the dataset used.

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We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity of G, we can find a neighborhood V of and a countable family γ of neighborhoods of in G such that W ∈γ V W −1 ⊆ U. We prove that every regular (Hausdorff) totally ω-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π-character has a regular G δ -diagonal. Keywords

Given a metric space (X,d), we deal with a classical problem in the theory of hyperspaces: how some important dynamical properties (namely, weakly mixing, transitivity and point-transitivity) between a discrete dynamical system f:(X,d)→(X,d) and its natural extension to the hyperspace are related. In this context, we consider the Zadeh’s extension f^ of f to F(X), the family of all normal fuzzy sets on X, i.e., the hyperspace F(X) of all upper semicontinuous fuzzy sets on X with compact supports and non-empty levels and we endow F(X) with different metrics: the supremum metric d∞, the Skorokhod metric d0, the sendograph metric dS and the endograph metric dE. Among other things, the following results are presented: (1) If (X,d) is a metric space, then the following conditions are equivalent: (a) (X,f) is weakly mixing, (b) ((F(X),d∞),f^) is transitive, (c) ((F(X),d0),f^) is transitive and (d) ((F(X),dS)),f^) is transitive, (2) if f:(X,d)→(X,d) is a continuous function, then the following hold: (a) if ((F(X),dS),f^) is transitive, then ((F(X),dE),f^) is transitive, (b) if ((F(X),dS),f^) is transitive, then (X,f) is transitive; and (3) if (X,d) be a complete metric space, then the following conditions are equivalent: (a) (X×X,f×f) is point-transitive and (b) ((F(X),d0) is point-transitive.