Learning representations of words in a continuous space is perhaps the most fundamental task in NLP, however words interact in ways much richer than vector dot product similarity can provide. Many relationships between words can be expressed set-theoretically, for example, adjective-noun compounds (eg. “red cars”⊆“cars”) and homographs (eg. “tongue”∩“body” should be similar to “mouth”, while “tongue”∩“language” should be similar to “dialect”) have natural set-theoretic interpretations. Box embeddings are a novel region-based representation which provide the capability to perform these set-theoretic operations. In this work, we provide a fuzzy-set interpretation of box embeddings, and learn box representations of words using a set-theoretic training objective. We demonstrate improved performance on various word similarity tasks, particularly on less common words, and perform a quantitative and qualitative analysis exploring the additional unique expressivity provided by Word2Box.

Knowledge bases often consist of facts which are harvested from a variety of sources, many of which are noisy and some of which conflict, resulting in a level of uncertainty for each triple. Knowledge bases are also often incomplete, prompting the use of embedding methods to generalize from known facts, however, existing embedding methods only model triple-level uncertainty, and reasoning results lack global consistency. To address these shortcomings, we propose BEUrRE, a novel uncertain knowledge graph embedding method with calibrated probabilistic semantics. BEUrRE models each entity as a box (i.e. axis-aligned hyperrectangle) and relations between two entities as affine transforms on the head and tail entity boxes. The geometry of the boxes allows for efficient calculation of intersections and volumes, endowing the model with calibrated probabilistic semantics and facilitating the incorporation of relational constraints. Extensive experiments on two benchmark datasets show that BEUrRE consistently outperforms baselines on confidence prediction and fact ranking due to its probabilistic calibration and ability to capture high-order dependencies among facts.

A fundamental component to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with more geometric structure (eg. distributions, complex or hyperbolic vectors, or regions such as cones, disks, or boxes) have been explored for their alternative inductive biases and additional representational capacity. In this work, we introduce Box Embeddings, a Python library that enables researchers to easily apply and extend probabilistic box embeddings. Fundamental geometric operations on boxes are implemented in a numerically stable way, as are modern approaches to training boxes which mitigate gradient sparsity. The library is fully open source, and compatible with both PyTorch and TensorFlow, which allows existing neural network layers to be replaced with or transformed into boxes easily. In this work, we present the implementation details of the fundamental components of the library, and the concepts required to use box representations alongside existing neural network architectures.

Learning representations of entities and relations in structured knowledge bases is an active area of research, with much emphasis placed on choosing the appropriate geometry to capture the hierarchical structures exploited in, for example, isa or haspart relations. Box embeddings (Vilnis et al., 2018; Li et al., 2019; Dasgupta et al., 2020), which represent concepts as n-dimensional hyperrectangles, are capable of embedding hierarchies when training on a subset of the transitive closure. In Patel et al., (2020), the authors demonstrate that only the transitive reduction is required and further extend box embeddings to capture joint hierarchies by augmenting the graph with new nodes. While it is possible to represent joint hierarchies with this method, the parameters for each hierarchy are decoupled, making generalization between hierarchies infeasible. In this work, we introduce a learned box-to-box transformation that respects the structure of each hierarchy. We demonstrate that this not only improves the capability of modeling cross-hierarchy compositional edges but is also capable of generalizing from a subset of the transitive reduction.

Neural entity typing models typically represent fine-grained entity types as vectors in a high-dimensional space, but such spaces are not well-suited to modeling these types’ complex interdependencies. We study the ability of box embeddings, which embed concepts as d-dimensional hyperrectangles, to capture hierarchies of types even when these relationships are not defined explicitly in the ontology. Our model represents both types and entity mentions as boxes. Each mention and its context are fed into a BERT-based model to embed that mention in our box space; essentially, this model leverages typological clues present in the surface text to hypothesize a type representation for the mention. Box containment can then be used to derive both the posterior probability of a mention exhibiting a given type and the conditional probability relations between types themselves. We compare our approach with a vector-based typing model and observe state-of-the-art performance on several entity typing benchmarks. In addition to competitive typing performance, our box-based model shows better performance in prediction consistency (predicting a supertype and a subtype together) and confidence (i.e., calibration), demonstrating that the box-based model captures the latent type hierarchies better than the vector-based model does.

Given questions regarding some prototypical situation — such as Name something that people usually do before they leave the house for work? — a human can easily answer them via acquired experiences. There can be multiple right answers for such questions, with some more common for a situation than others. This paper introduces a new question answering dataset for training and evaluating common sense reasoning capabilities of artificial intelligence systems in such prototypical situations. The training set is gathered from an existing set of questions played in a long-running international trivia game show – Family Feud. The hidden evaluation set is created by gathering answers for each question from 100 crowd-workers. We also propose a generative evaluation task where a model has to output a ranked list of answers, ideally covering all prototypical answers for a question. After presenting multiple competitive baseline models, we find that human performance still exceeds model scores on all evaluation metrics with a meaningful gap, supporting the challenging nature of the task.

Recent work introduces the AI2 Reasoning Challenge (ARC) and the associated ARC dataset that partitions open domain, complex science questions into an Easy Set and a Challenge Set. That work includes an analysis of 100 questions with respect to the types of knowledge and reasoning required to answer them. However, it does not include clear definitions of these types, nor does it offer information about the quality of the labels or the annotation process used. In this paper, we introduce a novel interface for human annotation of science question-answer pairs with their respective knowledge and reasoning types, in order that the classification of new questions may be improved. We build on the classification schema proposed by prior work on the ARC dataset, and evaluate the effectiveness of our interface with a preliminary study involving 10 participants.

The recent work of Clark et al. (2018) introduces the AI2 Reasoning Challenge (ARC) and the associated ARC dataset that partitions open domain, complex science questions into easy and challenge sets. That paper includes an analysis of 100 questions with respect to the types of knowledge and reasoning required to answer them; however, it does not include clear definitions of these types, nor does it offer information about the quality of the labels. We propose a comprehensive set of definitions of knowledge and reasoning types necessary for answering the questions in the ARC dataset. Using ten annotators and a sophisticated annotation interface, we analyze the distribution of labels across the challenge set and statistics related to them. Additionally, we demonstrate that although naive information retrieval methods return sentences that are irrelevant to answering the query, sufficient supporting text is often present in the (ARC) corpus. Evaluating with human-selected relevant sentences improves the performance of a neural machine comprehension model by 42 points.