Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

Applying existing question answering (QA) systems to specialized domains like law and finance presents challenges that necessitate domain expertise. Although large language models (LLMs) have shown impressive language comprehension and in-context learning capabilities, their inability to handle very long inputs/contexts is well known. Tasks specific to these domains need significant background knowledge, leading to contexts that can often exceed the maximum length that existing LLMs can process. This study explores leveraging the semi-structured nature of legal and financial data to efficiently retrieve relevant context, enabling the use of LLMs for domain-specialized QA. The resulting system outperforms contemporary models and also provides useful explanations for the answers, encouraging the integration of LLMs into legal and financial NLP systems for future research.

Recent advances in prompt engineering enable large language models (LLMs) to solve multi-hop logical reasoning problems with impressive accuracy. However, there is little existing work investigating the robustness of LLMs with few-shot prompting techniques. Therefore, we introduce a systematic approach to test the robustness of LLMs in multi-hop reasoning tasks via domain-agnostic perturbations. We include perturbations at multiple levels of abstractions (e.g. lexical perturbations such as typos, and semantic perturbations such as the inclusion of intermediate reasoning steps in the questions) to conduct behavioral analysis on the LLMs. Throughout our experiments, we find that models are more sensitive to certain perturbations such as replacing words with their synonyms. We also demonstrate that increasing the proportion of perturbed exemplars in the prompts improves the robustness of few-shot prompting methods.

We introduce the Probabilistic Worldbuilding Model (PWM), a new fully symbolic Bayesian model of semantic parsing and reasoning, as a first step in a research program toward more domain- and task-general NLU and AI. Humans create internal mental models of their observations that greatly aid in their ability to understand and reason about a large variety of problems. In PWM, the meanings of sentences, acquired facts about the world, and intermediate steps in reasoning are all expressed in a human-readable formal language, with the design goal of interpretability. PWM is Bayesian, designed specifically to be able to generalize to new domains and new tasks. We derive and implement an inference algorithm that reads sentences by parsing and abducing updates to its latent world model that capture the semantics of those sentences, and evaluate it on two out-of-domain question-answering datasets: (1) ProofWriter and (2) a new dataset we call FictionalGeoQA, designed to be more representative of real language but still simple enough to focus on evaluating reasoning ability, while being robust against heuristics. Our method outperforms baselines on both, thereby demonstrating its value as a proof-of-concept.

We present a generative model of natural language sentences and demonstrate its application to semantic parsing. In the generative process, a logical form sampled from a prior, and conditioned on this logical form, a grammar probabilistically generates the output sentence. Grammar induction using MCMC is applied to learn the grammar given a set of labeled sentences with corresponding logical forms. We develop a semantic parser that finds the logical form with the highest posterior probability exactly. We obtain strong results on the GeoQuery dataset and achieve state-of-the-art F1 on Jobs.