An $\mathbf{L^*}$ Algorithm for Deterministic Weighted Regular Languages

Extracting finite state automata (FSAs) from black-box models offers a powerful approach to gaining interpretable insights into complex model behaviors. To support this pursuit, we present a weighted variant of Angluin's (1987) $\mathbf{L^*}$ algorithm for learning FSAs. We stay faithful to the original algorithm, devising a way to exactly learn deterministic weighted FSAs whose weights support division. Furthermore, we formulate the learning process in a manner that highlights the connection with FSA minimization, showing how $\mathbf{L^*}$ directly learns a minimal automaton for the target language.

Surprise! Uniform Information Density Isn't the Whole Story: Predicting Surprisal Contours in Long-form Discourse

The Uniform Information Density (UID) hypothesis posits that speakers tend to distribute information evenly across linguistic units to achieve efficient communication. Of course, information rate in texts and discourses is not perfectly uniform. While these fluctuations can be viewed as theoretically uninteresting noise on top of a uniform target, another explanation is that UID is not the only functional pressure regulating information content in a language. Speakers may also seek to maintain interest, adhere to writing conventions, and build compelling arguments. In this paper, we propose one such functional pressure; namely that speakers modulate information rate based on location within a hierarchically-structured model of discourse. We term this the Structured Context Hypothesis and test it by predicting the surprisal contours of naturally occurring discourses extracted from large language models using predictors derived from discourse structure. We find that hierarchical predictors are significant predictors of a discourse's information contour and that deeply nested hierarchical predictors are more predictive than shallow ones. This work takes an initial step beyond UID to propose testable hypotheses for why the information rate fluctuates in predictable ways

Efficiently Computing Susceptibility to Context in Language Models

One strength of modern language models is their ability to incorporate information from a user-input context when answering queries. However, they are not equally sensitive to the subtle changes to that context. To quantify this, Du et al. (2024) gives an information-theoretic metric to measure such sensitivity. Their metric, susceptibility, is defined as the degree to which contexts can influence a model's response to a query at a distributional level. However, exactly computing susceptibility is difficult and, thus, Du et al. (2024) falls back on a Monte Carlo approximation. Due to the large number of samples required, the Monte Carlo approximation is inefficient in practice. As a faster alternative, we propose Fisher susceptibility, an efficient method to estimate the susceptibility based on Fisher information. Empirically, we validate that Fisher susceptibility is comparable to Monte Carlo estimated susceptibility across a diverse set of query domains despite its being $70\times$ faster. Exploiting the improved efficiency, we apply Fisher susceptibility to analyze factors affecting the susceptibility of language models. We observe that larger models are as susceptible as smaller ones.

Reverse-Engineering the Reader

Numerous previous studies have sought to determine to what extent language models, pretrained on natural language text, can serve as useful models of human cognition. In this paper, we are interested in the opposite question: whether we can directly optimize a language model to be a useful cognitive model by aligning it to human psychometric data. To achieve this, we introduce a novel alignment technique in which we fine-tune a language model to implicitly optimize the parameters of a linear regressor that directly predicts humans' reading times of in-context linguistic units, e.g., phonemes, morphemes, or words, using surprisal estimates derived from the language model. Using words as a test case, we evaluate our technique across multiple model sizes and datasets and find that it improves language models' psychometric predictive power. However, we find an inverse relationship between psychometric power and a model's performance on downstream NLP tasks as well as its perplexity on held-out test data. While this latter trend has been observed before (Oh et al., 2022; Shain et al., 2024), we are the first to induce it by manipulating a model's alignment to psychometric data.

Activation Scaling for Steering and Interpreting Language Models

Given the prompt "Rome is in", can we steer a language model to flip its prediction of an incorrect token "France" to a correct token "Italy" by only multiplying a few relevant activation vectors with scalars? We argue that successfully intervening on a model is a prerequisite for interpreting its internal workings. Concretely, we establish a three-term objective: a successful intervention should flip the correct with the wrong token and vice versa (effectiveness), and leave other tokens unaffected (faithfulness), all while being sparse (minimality). Using gradient-based optimization, this objective lets us learn (and later evaluate) a specific kind of efficient and interpretable intervention: activation scaling only modifies the signed magnitude of activation vectors to strengthen, weaken, or reverse the steering directions already encoded in the model. On synthetic tasks, this intervention performs comparably with steering vectors in terms of effectiveness and faithfulness, but is much more minimal allowing us to pinpoint interpretable model components. We evaluate activation scaling from different angles, compare performance on different datasets, and make activation scalars a learnable function of the activation vectors themselves to generalize to varying-length prompts.

Can Transformers Learn $n$-gram Language Models?

Much theoretical work has described the ability of transformers to represent formal languages. However, linking theoretical results to empirical performance is not straightforward due to the complex interplay between the architecture, the learning algorithm, and training data. To test whether theoretical lower bounds imply \emph{learnability} of formal languages, we turn to recent work relating transformers to $n$-gram language models (LMs). We study transformers' ability to learn random $n$-gram LMs of two kinds: ones with arbitrary next-symbol probabilities and ones where those are defined with shared parameters. We find that classic estimation techniques for $n$-gram LMs such as add-$\lambda$ smoothing outperform transformers on the former, while transformers perform better on the latter, outperforming methods specifically designed to learn $n$-gram LMs.

On the Proper Treatment of Tokenization in Psycholinguistics

Language models are widely used in computational psycholinguistics to test theories that relate the negative log probability (the surprisal) of a region of interest (a substring of characters) under a language model to its cognitive cost experienced by readers, as operationalized, for example, by gaze duration on the region. However, the application of modern language models to psycholinguistic studies is complicated by the practice of using tokenization as an intermediate step in training a model. Doing so results in a language model over token strings rather than one over character strings. Vexingly, regions of interest are generally misaligned with these token strings. The paper argues that token-level language models should be (approximately) marginalized into character-level language models before they are used in psycholinguistic studies to compute the surprisal of a region of interest; then, the marginalized character-level language model can be used to compute the surprisal of an arbitrary character substring, which we term a focal area, that the experimenter may wish to use as a predictor. Our proposal of marginalizing a token-level model into a character-level one solves this misalignment issue independently of the tokenization scheme. Empirically, we discover various focal areas whose surprisal is a better psychometric predictor than the surprisal of the region of interest itself.

Generalized Measures of Anticipation and Responsivity in Online Language Processing

We introduce a generalization of classic information-theoretic measures of predictive uncertainty in online language processing, based on the simulation of expected continuations of incremental linguistic contexts. Our framework provides a formal definition of anticipatory and responsive measures, and it equips experimenters with the tools to define new, more expressive measures beyond standard next-symbol entropy and surprisal. While extracting these standard quantities from language models is convenient, we demonstrate that using Monte Carlo simulation to estimate alternative responsive and anticipatory measures pays off empirically: New special cases of our generalized formula exhibit enhanced predictive power compared to surprisal for human cloze completion probability as well as ELAN, LAN, and N400 amplitudes, and greater complementarity with surprisal in predicting reading times.

On the Role of Context in Reading Time Prediction

We present a new perspective on how readers integrate context during real-time language comprehension. Our proposals build on surprisal theory, which posits that the processing effort of a linguistic unit (e.g., a word) is an affine function of its in-context information content. We first observe that surprisal is only one out of many potential ways that a contextual predictor can be derived from a language model. Another one is the pointwise mutual information (PMI) between a unit and its context, which turns out to yield the same predictive power as surprisal when controlling for unigram frequency. Moreover, both PMI and surprisal are correlated with frequency. This means that neither PMI nor surprisal contains information about context alone. In response to this, we propose a technique where we project surprisal onto the orthogonal complement of frequency, yielding a new contextual predictor that is uncorrelated with frequency. Our experiments show that the proportion of variance in reading times explained by context is a lot smaller when context is represented by the orthogonalized predictor. From an interpretability standpoint, this indicates that previous studies may have overstated the role that context has in predicting reading times.

Do Language Models Have a Critical Period for Language Acquisition?

Humans appear to have a critical period (CP) for language acquisition: Second language (L2) acquisition becomes harder after early childhood, and ceasing exposure to a first language (L1) after this period (but not before) typically does not lead to substantial loss of L1 proficiency. It is unknown whether these CP effects result from innately determined brain maturation or as a stabilization of neural connections naturally induced by experience. In this study, we use language models (LMs) to test the extent to which these phenomena are peculiar to humans, or shared by a broader class of language learners. We vary the age of exposure by training LMs on language pairs in various experimental conditions, and find that LMs, which lack any direct analog to innate maturational stages, do not show CP effects when trained sequentially on L1 and L2. Our results contradict the claim that CP effects are an inevitable result of learning in statistical learners, and they are consistent with an innate mechanism for CP effects. We show that we can reverse-engineer the CP by introducing a regularizer partway through training to simulate a maturational decrease in plasticity. All in all, our results suggest that L1 learning on its own may not be enough to induce a CP, and additional engineering is necessary to make language models more cognitively plausible.