Do Language Models Exhibit the Same Cognitive Biases in Problem Solving as Human Learners?

There is increasing interest in employing large language models (LLMs) as cognitive models. For such purposes, it is central to understand which cognitive properties are well-modeled by LLMs, and which are not. In this work, we study the biases of LLMs in relation to those known in children when solving arithmetic word problems. Surveying the learning science literature, we posit that the problem-solving process can be split into three distinct steps: text comprehension, solution planning and solution execution. We construct tests for each one in order to understand which parts of this process can be faithfully modeled by current state-of-the-art LLMs. We generate a novel set of word problems for each of these tests, using a neuro-symbolic method that enables fine-grained control over the problem features. We find evidence that LLMs, with and without instruction-tuning, exhibit human-like biases in both the text-comprehension and the solution-planning steps of the solving process, but not during the final step which relies on the problem's arithmetic expressions (solution execution).

Principled Gradient-based Markov Chain Monte Carlo for Text Generation

Recent papers have demonstrated the possibility of energy-based text generation by adapting gradient-based sampling algorithms, a paradigm of MCMC algorithms that promises fast convergence. However, as we show in this paper, previous attempts on this approach to text generation all fail to sample correctly from the target language model distributions. To address this limitation, we consider the problem of designing text samplers that are faithful, meaning that they have the target text distribution as its limiting distribution. We propose several faithful gradient-based sampling algorithms to sample from the target energy-based text distribution correctly, and study their theoretical properties. Through experiments on various forms of text generation, we demonstrate that faithful samplers are able to generate more fluent text while adhering to the control objectives better.

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.

The Ethics of Automating Legal Actors

The introduction of large public legal datasets has brought about a renaissance in legal NLP. Many of these datasets are comprised of legal judgements - the product of judges deciding cases. This fact, together with the way machine learning works, means that several legal NLP models are models of judges. While some have argued for the automation of judges, in this position piece, we argue that automating the role of the judge raises difficult ethical challenges, in particular for common law legal systems. Our argument follows from the social role of the judge in actively shaping the law, rather than merely applying it. Since current NLP models come nowhere close to having the facilities necessary for this task, they should not be used to automate judges. Furthermore, even in the case the models could achieve human-level capabilities, there would still be remaining ethical concerns inherent in the automation of the legal process.

Grammatical Gender's Influence on Distributional Semantics: A Causal Perspective

How much meaning influences gender assignment across languages is an active area of research in modern linguistics and cognitive science. We can view current approaches as aiming to determine where gender assignment falls on a spectrum, from being fully arbitrarily determined to being largely semantically determined. For the latter case, there is a formulation of the neo-Whorfian hypothesis, which claims that even inanimate noun gender influences how people conceive of and talk about objects (using the choice of adjective used to modify inanimate nouns as a proxy for meaning). We offer a novel, causal graphical model that jointly represents the interactions between a noun's grammatical gender, its meaning, and adjective choice. In accordance with past results, we find a relationship between the gender of nouns and the adjectives which modify them. However, when we control for the meaning of the noun, we find that grammatical gender has a near-zero effect on adjective choice, thereby calling the neo-Whorfian hypothesis into question.

Quantifying the redundancy between prosody and text

Prosody -- the suprasegmental component of speech, including pitch, loudness, and tempo -- carries critical aspects of meaning. However, the relationship between the information conveyed by prosody vs. by the words themselves remains poorly understood. We use large language models (LLMs) to estimate how much information is redundant between prosody and the words themselves. Using a large spoken corpus of English audiobooks, we extract prosodic features aligned to individual words and test how well they can be predicted from LLM embeddings, compared to non-contextual word embeddings. We find a high degree of redundancy between the information carried by the words and prosodic information across several prosodic features, including intensity, duration, pauses, and pitch contours. Furthermore, a word's prosodic information is redundant with both the word itself and the context preceding as well as following it. Still, we observe that prosodic features can not be fully predicted from text, suggesting that prosody carries information above and beyond the words. Along with this paper, we release a general-purpose data processing pipeline for quantifying the relationship between linguistic information and extra-linguistic features.

An Exploration of Left-Corner Transformations

The left-corner transformation (Rosenkrantz and Lewis, 1970) is used to remove left recursion from context-free grammars, which is an important step towards making the grammar parsable top-down with simple techniques. This paper generalizes prior left-corner transformations to support semiring-weighted production rules and to provide finer-grained control over which left corners may be moved. Our generalized left-corner transformation (GLCT) arose from unifying the left-corner transformation and speculation transformation (Eisner and Blatz, 2007), originally for logic programming. Our new transformation and speculation define equivalent weighted languages. Yet, their derivation trees are structurally different in an important way: GLCT replaces left recursion with right recursion, and speculation does not. We also provide several technical results regarding the formal relationships between the outputs of GLCT, speculation, and the original grammar. Lastly, we empirically investigate the efficiency of GLCT for left-recursion elimination from grammars of nine languages.

Formal Aspects of Language Modeling

Large language models have become one of the most commonly deployed NLP inventions. In the past half-decade, their integration into core natural language processing tools has dramatically increased the performance of such tools, and they have entered the public discourse surrounding artificial intelligence. Consequently, it is important for both developers and researchers alike to understand the mathematical foundations of large language models, as well as how to implement them. These notes are the accompaniment to the theoretical portion of the ETH Z\"urich course on large language models, covering what constitutes a language model from a formal, theoretical perspective.

On the Representational Capacity of Recurrent Neural Language Models

This work investigates the computational expressivity of language models (LMs) based on recurrent neural networks (RNNs). Siegelmann and Sontag (1992) famously showed that RNNs with rational weights and hidden states and unbounded computation time are Turing complete. However, LMs define weightings over strings in addition to just (unweighted) language membership and the analysis of the computational power of RNN LMs (RLMs) should reflect this. We extend the Turing completeness result to the probabilistic case, showing how a rationally weighted RLM with unbounded computation time can simulate any probabilistic Turing machine (PTM). Since, in practice, RLMs work in real-time, processing a symbol at every time step, we treat the above result as an upper bound on the expressivity of RLMs. We also provide a lower bound by showing that under the restriction to real-time computation, such models can simulate deterministic real-time rational PTMs.

Efficient Algorithms for Recognizing Weighted Tree-Adjoining Languages

The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to tree-adjoining grammars (TAG), linear indexed grammars (LIG), pushdown-adjoining automata (PAA), and embedded pushdown automata (EPDA). We define semiring-weighted versions of the above two-level formalisms, and we design new algorithms for computing their stringsums (the weight of all derivations of a string) and allsums (the weight of all derivations). From these, we also immediately obtain stringsum and allsum algorithms for TAG, LIG, PAA, and EPDA. For LIG, our algorithm is more time-efficient by a factor of $\mathcal{O}(n|\mathcal{N}|)$ (where $n$ is the string length and $|\mathcal{N}|$ is the size of the nonterminal set) and more space-efficient by a factor of $\mathcal{O}(|\Gamma|)$ (where $|\Gamma|$ is the size of the stack alphabet) than the algorithm of Vijay-Shanker and Weir (1989). For EPDA, our algorithm is both more space-efficient and time-efficient than the algorithm of Alonso et al. (2001) by factors of $\mathcal{O}(|\Gamma|^2)$ and $\mathcal{O}(|\Gamma|^3)$, respectively. Finally, we give the first PAA stringsum and allsum algorithms.