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Levin et al. (2019) show experimentally that the interpretations of novel English noun compounds (e.g., stew skillet), while not fully compositional, are highly predictable based on whether the modifier and head refer to artifacts or natural kinds. Is the large language model GPT-3 governed by the same interpretive principles? To address this question, we first compare Levin et al.&#39;s experimental data with GPT-3 generations, finding a high degree of similarity. However, this evidence is consistent with GPT-3 reasoning only about specific lexical items rather than the more abstract conceptual categories of Levin et al.&#39;s theory. To probe more deeply, we construct prompts that require the relevant kind of conceptual reasoning. Here, we fail to find convincing evidence that GPT-3 is reasoning about more than just individual lexical items. These results highlight the importance of controlling for low-level distributional regularities when assessing whether a large language model latently encodes a deeper theory.

EMNLP 2022

Systematicity in GPT-3&#39;s Interpretation of Novel English Noun Compounds

noun compounds

prompting

gpt-3

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Levin et al. (2019) show experimentally that the interpretations of novel English noun compounds (e.g., stew skillet), while not fully compositional, are highly predictable based on whether the modifier and head refer to artifacts or natural kinds. Is the large language model GPT-3 governed by the same interpretive principles? To address this question, we first compare Levin et al.'s experimental data with GPT-3 generations, finding a high degree of similarity. However, this evidence is consistent with GPT-3 reasoning only about specific lexical items rather than the more abstract conceptual categories of Levin et al.'s theory. To probe more deeply, we construct prompts that require the relevant kind of conceptual reasoning. Here, we fail to find convincing evidence that GPT-3 is reasoning about more than just individual lexical items. These results highlight the importance of controlling for low-level distributional regularities when assessing whether a large language model latently encodes a deeper theory.

Systematicity in GPT-3's Interpretation of Novel English Noun Compounds

workshop paper

This paper examines the encoding of analogy in large-scale pretrained language models, such as BERT and GPT-2. Existing analogy datasets typically focus on a limited set of analogical relations, with a high similarity of the two domains between which the analogy holds. As a more realistic setup, we introduce the Scientific and Creative Analogy dataset (SCAN), a novel analogy dataset containing systematic mappings of multiple attributes and relational structures across dissimilar domains. Using this dataset, we test the analogical reasoning capabilities of several widely-used pretrained language models (LMs). We find that state-of-the-art LMs achieve low performance on these complex analogy tasks, highlighting the challenges still posed by analogy understanding.

Scientific and Creative Analogies in Pretrained Language Models

Humor is an inherently social phenomenon, with humorous utterances shaped by what is socially and culturally accepted. Understanding humor is an important NLP challenge, with many applications to human-computer interactions. In this work we explore humor in the context of Cards Against Humanity -- a party game where players complete fill-in-the-blank statements using cards that can be offensive or politically incorrect.

We introduce a novel dataset of 300,000 online games of Cards Against Humanity, including 785K unique jokes, analyze it and provide insights. We trained machine learning models to predict the winning joke per game, achieving performance twice as good (20%) as random, even without any user information.
On the more difficult task of judging novel cards, we see the models' ability to generalize is moderate. Interestingly, we find that our models are primarily focused on punchline card, with the context having little impact.
Analyzing feature importance, we observe that short, crude, juvenile punchlines tend to win.

Cards Against AI: Predicting Humor in a Fill-in-the-blank Party Game

How language models process complex input that requires multiple steps of inference is not well understood. Previous research has shown that information about intermediate values of these inputs can be extracted from the activations of the models, but it is unclear where that information is encoded and whether that information is indeed used during inference. We introduce a method for analyzing how a Transformer model processes these inputs by focusing on simple arithmetic problems and their intermediate values. To trace where information about intermediate values is encoded, we measure the correlation between intermediate values and the activations of the model using principal component analysis (PCA). Then, we perform a causal intervention by manipulating model weights.  This intervention shows that the weights identified via tracing are not merely correlated with intermediate values, but causally related to model predictions. Our findings show that the model has a locality to certain intermediate values, and this is useful for enhancing the interpretability of the models.

Tracing and Manipulating intermediate values in Neural Math Problem Solvers

In this paper, we revisit math word problems~(MWPs) from the cross-lingual and multilingual perspective. We construct our MWP solvers over pretrained multilingual language models using the sequence-to-sequence model with copy mechanism. We compare how the MWP solvers perform in cross-lingual and multilingual scenarios. To facilitate the comparison of cross-lingual performance, we first adapt the large-scale English dataset MathQA as a counterpart of the Chinese dataset Math23K. Then we extend several English datasets to bilingual datasets through machine translation plus human annotation. Our experiments show that the MWP solvers may not be transferred to a different language even if the target expressions share the same numerical constants and operator set. However, it can be better generalized if problem types exist on both source language and target language.

Investigating Math Word Problems using Pretrained Multilingual Language Models

The ability to extrapolate, i.e., to make predictions on sequences that are longer than those presented as training examples, is a challenging problem for current deep learning models. Recent work shows that this limitation persists in state-of-the-art Transformer-based models. Most solutions to this problem use specific architectures or training methods that do not generalize to other tasks. We demonstrate that large language models can succeed in extrapolation without modifying their architecture or training procedure. Our experimental results show that generating step-by-step rationales and introducing marker tokens are both required for effective extrapolation. First, we induce a language model to produce step-by-step rationales before outputting the answer to effectively communicate the task to the model. However, as sequences become longer, we find that current models struggle to keep track of token positions. To address this issue, we interleave output tokens with markup tokens that act as explicit positional and counting symbols. Our findings show how these two complementary approaches enable remarkable sequence extrapolation and highlight a limitation of current architectures to effectively generalize without explicit surface form guidance. Code available at https://anonymous.4open.science/r/induced-rationales-markup-tokens-0650/README.md

Induced Natural Language Rationales and Interleaved Markup Tokens Enable Extrapolation in Large Language Models

The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal representation that is computer-verifiable via interactive theorem provers. In this paper, we introduce a semantic parsing approach, based on the Universal Transformer architecture, that translates elementary mathematical proofs into an equivalent formalization in the language of the Coq interactive theorem prover. The same architecture is also trained to translate simple imperative code decorated with Hoare triples into formally verifiable proofs of correctness in Coq. Experiments on a limited domain of artificial and human-written proofs show that the models generalize well to intermediate lengths not seen during training and variations in natural language.

Towards Autoformalization of Mathematics and Code Correctness: Experiments with Elementary Proofs

Transformer-based language models are able to capture several linguistic properties such as hierarchical structures like dependency or constituency trees. Whether similar structures for mathematics are extractable from language models has not yet been explored. This work aims to probe current state-of-the-art models for the extractability of Operator Trees from their contextualized embeddings using the structure probe designed by Hewitt and Manning. We release the code and our data set for future analysis.

Extracting Operator Trees from Model Embeddings

The advances in language-based Artificial Intelligence (AI) technologies applied to build educational applications can present AI for social-good opportunities with a broader positive impact. Across many disciplines, enhancing the quality of mathematics education is crucial in building critical thinking and problem-solving skills at younger ages. Conversational AI systems have started maturing to a point where they could play a significant role in helping students learn fundamental math concepts. This work presents a task-oriented Spoken Dialogue System (SDS) built to support play-based learning of basic math concepts for early childhood education. The system has been evaluated via real-world deployments at school while the students are practicing early math concepts with multimodal interactions. We discuss our efforts to improve the SDS pipeline built for math learning, for which we explore utilizing MathBERT representations for potential enhancement to the Natural Language Understanding (NLU) module. We perform an end-to-end evaluation using real-world deployment outputs from the Automatic Speech Recognition (ASR), Intent Recognition, and Dialogue Manager (DM) components to understand how error propagation affects the overall performance in real-world scenarios.

End-to-End Evaluation of a Spoken Dialogue System for Learning Basic Mathematics

Math word problem solver requires both precise relation reasoning about quantities in the text and reliable generation for the diverse equation. Current sequence-to-tree or relation extraction methods regard this only from a fixed view, struggling to simultaneously handle complex semantics and diverse equations. However, human solving naturally involves two consistent reasoning views: top-down and bottom-up, just as math equations also can be expressed in multiple equivalent forms: pre-order and post-order. We propose a multi-view consistent contrastive learning for a more complete semantics-to-equation mapping. The entire process is decoupled into two independent but consistent views: top-down decomposition and bottom-up construction, and the two reasoning views are aligned in multi-granularity for consistency, enhancing global generation and precise reasoning. Experiments on multiple datasets across two languages show our approach significantly outperforms the existing baselines, especially on complex problems. We also show after consistent alignment, multi-view can absorb the merits of both views and generate more diverse results consistent with the mathematical laws.

Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problem

Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously. The source code and dataset will be available at https://github.com/yangzhch6/InterMWP.

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