Comparatives, Quantifiers, Proportions: a Multi-Task Model for the Learning of Quantities from Vision

Proceedings of NAACL-HLT 2018, pages 419–430 New Orleans, Louisiana, June 1 - 6, 2018. c⃝2018 Association for Computational Linguistics Comparatives, Quantifiers, Proportions: A Multi-Task Model for the Learning of Quantities from Vision Sandro Pezzelle∗, Ionut-Teodor Sorodoc∗†, Raffaella Bernardi∗‡ ∗CIMeC - Center for Mind/Brain Sciences, University of Trento †Universitat Pompeu Fabra Barcelona ‡DISI - Department of Information Engineering and Computer Science, University of Trento ∗sandro.pezzelle@unitn.it, †ionutteodor.sorodoc@upf.edu ‡raffaella.bernardi@unitn.it Abstract The present work investigates whether differ- ent quantification mechanisms (set compari- son, vague quantification, and proportional es- timation) can be jointly learned from visual scenes by a multi-task computational model. The motivation is that, in humans, these processes underlie the same cognitive, non- symbolic ability, which allows an automatic estimation and comparison of set magnitudes. We show that when information about lower- complexity tasks is available, the higher-level proportional task becomes more accurate than when performed in isolation. Moreover, the multi-task model is able to generalize to un- seen combinations of target/non-target objects. Consistently with behavioral evidence show- ing the interference of absolute number in the proportional task, the multi-task model no longer works when asked to provide the num- ber of target objects in the scene. 1 Introduction Understanding and producing sentences like ‘There are more cars than parking lots’, ‘Most of the supporters wear blue t-shirts’, ‘Twenty percent of the trees have been planted last year’, or ‘Seven students passed the exam’, is a fundamental com- petence which allows speakers to communicate information about quantities. Crucially, the type of information conveyed by these expressions, as well as their underlying cognitive mechanisms, are not equivalent, as suggested by evidence from lin- guistics, language acquisition, and cognition. First, comparatives (‘more’, ‘less’), quantifiers (‘some’, ‘most’, ‘all’), and proportions (‘20%’, ‘two thirds’) express a comparison or relation be- tween sets (e.g., between the set of cars and the set of parking lots). Such relational information is rather coarse when expressed by comparatives and vague quantifiers, more precise when denoted by proportions. In contrast, numbers (‘one’, ‘six’, ‘twenty-two’) denote the exact, absolute cardinal- ity of the items belonging to one set (e.g., the set of students who passed the exam). Second, during language acquisition, these ex- pressions are neither learned at the same time nor governed by the same rules. Recent evidence showed that children can understand comparatives at around 3.3 years (Odic et al., 2013; Bryant, 2017), with quantifiers being learned a few months later, at around 3.4-3.6 years (Hurewitz et al., 2006; Minai, 2006; Halberda et al., 2008). Cru- cially, knowing the meaning of numbers, an ability that starts not before the age of 3.5 years (Le Corre and Carey, 2007), is not required to understand and use these expressions. As for proportions, they are acquired significantly later, being fully mastered only at the age of 9 or 10 (Hartnett and Gelman, 1998; Moss and Case, 1999; Sophian, 2000). Third, converging evidence from cognition and neuroscience supports the hypothesis that some important components of these expressions of quantity are grounded on a preverbal, non- …

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