Models Can and Should Embrace the Communicative Nature of Human-Generated Math

Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical entities but rich communicative intentions. While there are important advantages to treating math in a purely symbolic manner, we here hypothesize that there are benefits to treating math as situated linguistic communication and that language models are well suited for this goal, in ways that are not fully appreciated. We illustrate these points with two case studies. First, we ran an experiment in which we found that language models interpret the equals sign in a humanlike way -- generating systematically different word problems for the same underlying equation arranged in different ways. Second, we found that language models prefer proofs to be ordered in naturalistic ways, even though other orders would be logically equivalent. We advocate for AI systems that learn from and represent the communicative intentions latent in human-generated math.

To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning

Chain-of-thought (CoT) via prompting is the de facto method for eliciting reasoning capabilities from large language models (LLMs). But for what kinds of tasks is this extra ``thinking'' really helpful? To analyze this, we conducted a quantitative meta-analysis covering over 100 papers using CoT and ran our own evaluations of 20 datasets across 14 models. Our results show that CoT gives strong performance benefits primarily on tasks involving math or logic, with much smaller gains on other types of tasks. On MMLU, directly generating the answer without CoT leads to almost identical accuracy as CoT unless the question or model's response contains an equals sign, indicating symbolic operations and reasoning. Following this finding, we analyze the behavior of CoT on these problems by separating planning and execution and comparing against tool-augmented LLMs. Much of CoT's gain comes from improving symbolic execution, but it underperforms relative to using a symbolic solver. Our results indicate that CoT can be applied selectively, maintaining performance while saving inference costs. Furthermore, they suggest a need to move beyond prompt-based CoT to new paradigms that better leverage intermediate computation across the whole range of LLM applications.

Do they mean 'us'? Interpreting Referring Expressions in Intergroup Bias

The variations between in-group and out-group speech (intergroup bias) are subtle and could underlie many social phenomena like stereotype perpetuation and implicit bias. In this paper, we model the intergroup bias as a tagging task on English sports comments from forums dedicated to fandom for NFL teams. We curate a unique dataset of over 6 million game-time comments from opposing perspectives (the teams in the game), each comment grounded in a non-linguistic description of the events that precipitated these comments (live win probabilities for each team). Expert and crowd annotations justify modeling the bias through tagging of implicit and explicit referring expressions and reveal the rich, contextual understanding of language and the world required for this task. For large-scale analysis of intergroup variation, we use LLMs for automated tagging, and discover that some LLMs perform best when prompted with linguistic descriptions of the win probability at the time of the comment, rather than numerical probability. Further, large-scale tagging of comments using LLMs uncovers linear variations in the form of referent across win probabilities that distinguish in-group and out-group utterances. Code and data are available at https://github.com/venkatasg/intergroup-nfl .

Participle-Prepended Nominals Have Lower Entropy Than Nominals Appended After the Participle

English allows for both compounds (e.g., London-made) and phrasal paraphrases (e.g., made in London). While these constructions have roughly the same truth-conditional meaning, we hypothesize that the compound allows less freedom to express the nature of the semantic relationship between the participle and the pre-participle nominal. We thus predict that the pre-participle slot is more constrained than the equivalent position in the phrasal construction. We test this prediction in a large corpus by measuring the entropy of corresponding nominal slots, conditional on the participle used. That is, we compare the entropy of $\alpha$ in compound construction slots like $\alpha$-[V]ed to the entropy of $\alpha$ in phrasal constructions like [V]ed by $\alpha$ for a given verb V. As predicted, there is significantly lower entropy in the compound construction than in the phrasal construction. We consider how these predictions follow from more general grammatical properties and processing factors.

Language Models Learn Rare Phenomena from Less Rare Phenomena: The Case of the Missing AANNs

Language models learn rare syntactic phenomena, but it has been argued that they rely on rote memorization, as opposed to grammatical generalization. Training on a corpus of human-scale in size (100M words), we iteratively trained transformer language models on systematically manipulated corpora and then evaluated their learning of a particular rare grammatical phenomenon: the English Article+Adjective+Numeral+Noun (AANN) construction (``a beautiful five days''). We first compared how well this construction was learned on the default corpus relative to a counterfactual corpus in which the AANN sentences were removed. AANNs were still learned better than systematically perturbed variants of the construction. Using additional counterfactual corpora, we suggest that this learning occurs through generalization from related constructions (e.g., ``a few days''). An additional experiment showed that this learning is enhanced when there is more variability in the input. Taken together, our results provide an existence proof that models learn rare grammatical phenomena by generalization from less rare phenomena. Code available at https://github.com/kanishkamisra/aannalysis

Language models align with human judgments on key grammatical constructions

Do Large Language Models (LLMs) make human-like linguistic generalizations? Dentella et al. (2023; "DGL") prompt several LLMs ("Is the following sentence grammatically correct in English?") to elicit grammaticality judgments of 80 English sentences, concluding that LLMs demonstrate a "yes-response bias" and a "failure to distinguish grammatical from ungrammatical sentences". We re-evaluate LLM performance using well-established practices and find that DGL's data in fact provide evidence for just how well LLMs capture human behaviors. Models not only achieve high accuracy overall, but also capture fine-grained variation in human linguistic judgments.

Mission: Impossible Language Models

Chomsky and others have very directly claimed that large language models (LLMs) are equally capable of learning languages that are possible and impossible for humans to learn. However, there is very little published experimental evidence to support such a claim. Here, we develop a set of synthetic impossible languages of differing complexity, each designed by systematically altering English data with unnatural word orders and grammar rules. These languages lie on an impossibility continuum: at one end are languages that are inherently impossible, such as random and irreversible shuffles of English words, and on the other, languages that may not be intuitively impossible but are often considered so in linguistics, particularly those with rules based on counting word positions. We report on a wide range of evaluations to assess the capacity of GPT-2 small models to learn these uncontroversially impossible languages, and crucially, we perform these assessments at various stages throughout training to compare the learning process for each language. Our core finding is that GPT-2 struggles to learn impossible languages when compared to English as a control, challenging the core claim. More importantly, we hope our approach opens up a productive line of inquiry in which different LLM architectures are tested on a variety of impossible languages in an effort to learn more about how LLMs can be used as tools for these cognitive and typological investigations.

Experimental Contexts Can Facilitate Robust Semantic Property Inference in Language Models, but Inconsistently

Recent zero-shot evaluations have highlighted important limitations in the abilities of language models (LMs) to perform meaning extraction. However, it is now well known that LMs can demonstrate radical improvements in the presence of experimental contexts such as in-context examples and instructions. How well does this translate to previously studied meaning-sensitive tasks? We present a case-study on the extent to which experimental contexts can improve LMs' robustness in performing property inheritance -- predicting semantic properties of novel concepts, a task that they have been previously shown to fail on. Upon carefully controlling the nature of the in-context examples and the instructions, our work reveals that they can indeed lead to non-trivial property inheritance behavior in LMs. However, this ability is inconsistent: with a minimal reformulation of the task, some LMs were found to pick up on shallow, non-semantic heuristics from their inputs, suggesting that the computational principles of semantic property inference are yet to be mastered by LMs.

Are Language Models More Like Libraries or Like Librarians? Bibliotechnism, the Novel Reference Problem, and the Attitudes of LLMs

Are LLMs cultural technologies like photocopiers or printing presses, which transmit information but cannot create new content? A challenge for this idea, which we call bibliotechnism, is that LLMs often do generate entirely novel text. We begin by defending bibliotechnism against this challenge, showing how novel text may be meaningful only in a derivative sense, so that the content of this generated text depends in an important sense on the content of original human text. We go on to present a different, novel challenge for bibliotechnism, stemming from examples in which LLMs generate "novel reference", using novel names to refer to novel entities. Such examples could be smoothly explained if LLMs were not cultural technologies but possessed a limited form of agency (beliefs, desires, and intentions). According to interpretationism in the philosophy of mind, a system has beliefs, desires and intentions if and only if its behavior is well-explained by the hypothesis that it has such states. In line with this view, we argue that cases of novel reference provide evidence that LLMs do in fact have beliefs, desires, and intentions, and thus have a limited form of agency.

Revisiting the Optimality of Word Lengths

Zipf (1935) posited that wordforms are optimized to minimize utterances' communicative costs. Under the assumption that cost is given by an utterance's length, he supported this claim by showing that words' lengths are inversely correlated with their frequencies. Communicative cost, however, can be operationalized in different ways. Piantadosi et al. (2011) claim that cost should be measured as the distance between an utterance's information rate and channel capacity, which we dub the channel capacity hypothesis (CCH) here. Following this logic, they then proposed that a word's length should be proportional to the expected value of its surprisal (negative log-probability in context). In this work, we show that Piantadosi et al.'s derivation does not minimize CCH's cost, but rather a lower bound, which we term CCH-lower. We propose a novel derivation, suggesting an improved way to minimize CCH's cost. Under this method, we find that a language's word lengths should instead be proportional to the surprisal's expectation plus its variance-to-mean ratio. Experimentally, we compare these three communicative cost functions: Zipf's, CCH-lower , and CCH. Across 13 languages and several experimental settings, we find that length is better predicted by frequency than either of the other hypotheses. In fact, when surprisal's expectation, or expectation plus variance-to-mean ratio, is estimated using better language models, it leads to worse word length predictions. We take these results as evidence that Zipf's longstanding hypothesis holds.