Human-Model Divergence in the Handling of Vagueness (2021)

Abstract: While aggregate performance metrics can generate valuable insights at a large scale, their dominance means more complex and nuanced language phenomena, such as vagueness, may be overlooked. Focusing on vague terms (e.g. sunny, cloudy, young, etc.) we inspect the behavior of visually grounded and text-only models, finding systematic divergences from human judgments even when a model’s overall performance is high. To help explain this disparity, we identify two assumptions made by the datasets and models examined and, guided by the philosophy of vagueness, isolate cases where they do not hold.

## introduction part of the power of language as a medium for communication is rooted in having a reliable mapping between language and the world: we typically expect language to be used in a consistent fashion, i.e. the word "dog" refers to a relatively invariant group of animals, and not to a different set of items each time we use it. this view of language dovetails with the supervised learning paradigm, where we assume that an approximation of such a mapping can be learned from labeled examples-often collected via manual annotation by crowdworkers. in natural language processing (nlp), this learning typically takes place by treating tasks as classification problems which optimize for log-likelihood. while this paradigm has been extensively and successfully applied in nlp, it is not without both practical and theoretical shortcomings. guided by notions from the philosophy of language, we propose that borderline cases of vague terms, where the mapping between inputs and outputs is unclear, represent an edge case for the assumptions made by the supervised paradigm, and result in systematic divergences between human and model behavior. figure 1 : given a binary question involving a vague term (in this case, cloudy) humans hedge between "yes" and "no," following a sigmoid curve with borderline examples falling in the middle. standard error (grey band) shows that annotator agree even in borderline regions. in contrast, model predictions remain at extreme ends. to demonstrate this, we begin by identifying a set of canonically vague terms in the binary question subset of the visual question answering (vqa) and gqa datasets @xcite @xcite and isolating a subset of images, questions, and answers from these datasets centered around these terms. using this subset, we show that while the accuracy of lxmert @xcite on non-borderline cases is very high, its performance drops-sometimes dramatically-on borderline cases. we then compare the behavior of the model against that of human annotators, finding that while humans display behavior which aligns with theories of meaning for vague terms, model behavior is less predictable. we extend our analysis of visually-grounded terms to a text-only case, re-framing the catego-rization of statements into true statements and false ones as a task involving vagueness. controlling for world knowledge, we find that while probes over contextualized encoders can classify statements significantly better than random, their output distributions are strikingly similar to those observed in the visually-grounded case. when contrasted with scalar annotations collected from crowdworkers, these results support the notion that analytic truth itself admits of borderline cases and poses problems for supervised systems. in § 2, we provide a more thorough definition of terms used, the motivation for exploring vagueness, and the underlying assumptions of supervised learning that are violated by vague terms. ## motivation and background vague terms, broadly speaking, are ones that admit of borderline cases; for example: cloudy is vague because, while there are clearly cloudy and not cloudy days, there are also cases where the best response to the question "is it cloudy?" might be "somewhat" rather than a definitive "yes" or "no." given this definition, we can see that a large portion of the predicates we use in every-day speech are vague. this even encompasses predicates such as is true and is false, as we might have statements that are true or false to varying degrees. vague predicates in particular have been a focus of the philosophy of language, as they represent an interesting edge case for theories of meaning. take, for example, a canonical example of a vague predicate from philosophy: is a heap. there are things that are undeniable heaps, and others that are clearly not. in the extreme case, we can imagine starting with a heap of sand (say, n grains) and removing a single grain of sand from it. clearly, the resulting mass would still be a heap. this is, however, a dangerous precedent; we can now remove n -2 grains on sand until we have a single grain remaining, whose heap-ness is hard to justify, but which, by induction, is still a heap. this raises important questions: how is it that speakers avoid this paradox and are able to use and understand vague terms, even in borderline cases? is there a definitive point at which a heap becomes a non-heap? the answers to these questions should influence how we annotate the data from which we aim to learn meaning representations of vague terms. while the unequivocal instances of heaps fit well into the current paradigm of supervised learning with categorical labels, borderline heaps do present a problem. recall that the first assumption by supervised learning which we have pointed out is that the ideal mapping between the input (in this case, questions and images) and the the label set (answers) is largely fixed. for example, given the question "is this a dog?" we assume that the set of things in the world which we call "dog", also known as the extension of "dog", remains constant. in that case, the annotator's response to the question corresponds to whether what the image depicts could be plausibly considered as part of the extension of "dog." while we might easily be able to determine the set membership of poodles and terriers, we may have a harder time with jack london's white fang: half wolf, half dog. thus it is clear that the borderline cases of vague terms demand a more nuanced account than merely a forced choice between two extremes. the range of such accounts fall broadly into three classes: contextualist theories @xcite @xcite broadly hold that the interpretation of vague predicates depend on contextual and pragmatic information such as on the speaker's previous commitments, their perceived goals, and the psychological state of the interpreter. this view could in most cases be reconciled with the supervised learning paradigm, provided that the data upon which the interpretation of the vague predicate hinges (i.e. speaker commitments, etc.) is available as input. past work in modeling the meaning of vague terms has often focused on these accounts (c.f. § 6). epistemic accounts @xcite bite the proverbial bullet, allowing for a hard boundary between heaps and non-heaps to exist, but claiming that its location is unknowable. this is in contrast to the supervised paradigm, where the boundary is treated as known. logic-based approaches tackle the paradox induced by vagueness, either by claiming that borderline examples do not admit of truth values (supervaluationism), or by adapting logic to permit more granular classifications (many-valued logic; @xcite . the latter approach can sometimes accommodate the supervised paradigm. 1 ambiguity and under-specification it is important to distinguish vagueness from underspecification (imprecision in the input making the output difficult to recover) and ambiguity (the presence of multiple valid answers), both alternative explanations for annotator disagreement. indeed, @xcite include both in their taxonomy of vqa images-question pairs with high annotator disagreement. while they are major challenges in any language-based task, both are often defeasible in nature: we can provide additional information that would reveal the "correct" answer to an annotator, i.e. we could provide a better, sharper version of the image, or more contextual information. vagueness is non-defeasible: even if one were to know the exact number of grains of sand, the predicate "is a heap" would remain vague. ## visually grounded vagueness the interpretation of vague terms as described in § 1 typically occurs in a grounded setting; the question "is this a dog?" is only meaningful in the context of some state of affairs (or depiction thereof). we focus on binary questions about images, taking examples from vqa and gqa; this ensures that the vague term is the question's focus, excluding openended queries like "what is the old man doing?" which only implicitly involve vagueness. ## results and analysis we find that our control classifiers perform randomly, indicating our task has very low sensitivity. fig. 5 shows the test accuracies of all (non-control) models in all settings. we see that all models fall well below human performance, but well above the random baseline of 50%. among the probing methods, [cls] pooling slightly outperforms meanpooling. the bilinear method consistently underperforms the pooling methods, suggesting that the gap between human and model performance is not due to malformed prompts (e.g. incorrect articles in the definition or trigger phrase). appendix c gives some examples and model predictions. ## related work human-model divergence in similar vein to our work, @xcite observe that human annotators consistently disagree on natural language inference (nli) labels, and that the disagreement cannot be attributed to a lack of annotations. they similarly find that models do not implicitly learn to capture human uncertainty from categorical data. in contrast, our work seeks to pinpoint vagueness as a cause for some of the difference in behavior. 10 other work has looked at annotating data to accommodate the kinds of disagreements seen in pavlick and kwiatkowski. @xcite extends the easl framework @xcite for efficiently eliciting reliable scalar judgements from crowdworkers to nli, ob-taining scalar nli judgements rather than categorical labels. in a similar context, @xcite argue that for tasks involving plausibility, the use of cross-entropy loss drives model predictions to the extremes of the simplex, and demonstrate the benefits of shifting to a margin-based loss on the choice of plausible alternatives @xcite task. these results dovetail with our observations regarding various models' output distributions, especially in the text-only setting, where our task is very similar to tasks measuring plausibility. while @xcite focus on nli data, @xcite have noted that similar disagreements exist in the visual domain, specifically on the vqa data set, where they find that certain image-question pairs are less reliably answered than others. the ontology they propose to classify these images includes ambiguity and under-specification, but not vagueness. vagueness past work in vagueness has often focused on modeling it as a phenomenon, while our work is concerned with analyzing model performance on vague predicates, rather than capturing the semantics of vague predicates, which has been the focus of previous work such as @xcite and @xcite . although color terms provide a particularly rich substrate for modeling the semantics of vague terms, we have chosen to exclude them as we feel they demand a level of psychophysical analysis beyond the scope of this work. this work deals instead with gradable terms, following work such as @xcite , who present a type-theory record account of vagueness for learning the semantics of gradable adjectives, @xcite , who use vagueness to illustrate the need for context in a dialog-driven drawing task, and lassiter and goodman (2017), who introduce a bayesian pragmatic model of gradable adjective usage. these lines of previous work draw on the contextualist account of vagueness, holding that the meaning of vague predicates shifts with respect to the interests of the parties communicating, a notion that naturally expresses itself in rational pragmatic models of dialog. rather than modeling vagueness, we use it as a tool to examine model behavior, focusing on single interactions instead of a dialog. we refer the reader to @xcite for a full account of the analytic/synthetic distinction. text-only semantic probing the challenge of analyzing the semantic content of sentence en-codings precedes the contextual encoders studied herein; @xcite introduce a suite of simple classification tasks for probing the compositionality of lstm-based sentence embeddings, while @xcite present 10 linguistically-motivated probing tasks, including 3 semantic tasks, for lstm-and cnn-based sentence embeddings. @xcite create a set of artificial prompts, as done in this work, to probe the compositionality of infersent @xcite , while @xcite use nli-style prompts for the same purpose. similar probing suites have been proposed since the advent of contextual encoders; @xcite propose a set of edge-probing tasks that examine semantic content, and @xcite find that semantic information is typically encoded at higher transformer layers. presenting a suite of negative polarity item-based tasks, @xcite expand on the observation that different transformer layers account for different phenomena, noting that additionally, the manner in which a probing task is framed often makes a large impact. dictionary embeddings dictionary embeddings, as described by @xcite , use dictionary resources to learn a mapping from phrases to word vectors. dictionaries have also been used with a view to augmenting the semantic information in word embeddings, as in @xcite and @xcite . in contrast to these approaches, we use definitions to investigate the semantic content of existing mappings. ## conclusion we have identified clashes between the assumptions made under the current nlp paradigm and the realities of language use by focusing on the phenomenon of vagueness. by isolating a subset of examples from vqa and gqa involving vagueness, we were able to pinpoint some key divergences between model and human behavior which result in lower model performance. we then created an artificial text-only dataset, controlling for world knowledge, which we used to contrast multiple models building on multiple contextualized encoders, finding similar human-model contrasts. in closing, we would like to advocate for the broader use of concepts from the philosophy of language, such as vagueness, in challenging current models and providing additional insights beyond aggregate statistics and leaderboards.