Likelihood as a Performance Gauge for Retrieval-Augmented Generation

Recent work finds that retrieval-augmented generation with large language models is prone to be influenced by the order of retrieved documents in the context. However, the lack of in-depth analysis limits the use of this phenomenon for prompt engineering in practice. In this study, we posit that likelihoods serve as an effective gauge for language model performance. Through experiments on two question-answering datasets with a variety of state-of-the-art language models, we reveal correlations between answer accuracy and the likelihood of the question at both the corpus level and the instance level. In addition, we find that question likelihood can also indicate the position of the task-relevant information in the context. Based on these findings, we propose two methods that use question likelihood as a gauge for selecting and constructing prompts that lead to better performance. We demonstrate their effectiveness with experiments. In addition, our likelihood-based methods are efficient, as they only need to compute the likelihood of the input, requiring much fewer language model passes than heuristic prompt engineering methods that require generating responses. Our analysis deepens our understanding of how input prompts affect model performance and provides a promising direction for efficient prompt optimization.

Training Neural Networks as Recognizers of Formal Languages

Characterizing the computational power of neural network architectures in terms of formal language theory remains a crucial line of research, as it describes lower and upper bounds on the reasoning capabilities of modern AI. However, when empirically testing these bounds, existing work often leaves a discrepancy between experiments and the formal claims they are meant to support. The problem is that formal language theory pertains specifically to recognizers: machines that receive a string as input and classify whether it belongs to a language. On the other hand, it is common to instead use proxy tasks that are similar in only an informal sense, such as language modeling or sequence-to-sequence transduction. We correct this mismatch by training and evaluating neural networks directly as binary classifiers of strings, using a general method that can be applied to a wide variety of languages. As part of this, we extend an algorithm recently proposed by Sn{\ae}bjarnarson et al. (2024) to do length-controlled sampling of strings from regular languages, with much better asymptotic time complexity than previous methods. We provide results on a variety of languages across the Chomsky hierarchy for three neural architectures: a simple RNN, an LSTM, and a causally-masked transformer. We find that the RNN and LSTM often outperform the transformer, and that auxiliary training objectives such as language modeling can help, although no single objective uniformly improves performance across languages and architectures. Our contributions will facilitate theoretically sound empirical testing of language recognition claims in future work. We have released our datasets as a benchmark called FLaRe (Formal Language Recognition), along with our code.

Counterfactual Generation from Language Models

Understanding and manipulating the causal generation mechanisms in language models is essential for controlling their behavior. Previous work has primarily relied on techniques such as representation surgery -- e.g., model ablations or manipulation of linear subspaces tied to specific concepts -- to intervene on these models. To understand the impact of interventions precisely, it is useful to examine counterfactuals -- e.g., how a given sentence would have appeared had it been generated by the model following a specific intervention. We highlight that counterfactual reasoning is conceptually distinct from interventions, as articulated in Pearl's causal hierarchy. Based on this observation, we propose a framework for generating true string counterfactuals by reformulating language models as Generalized Structural-equation. Models using the Gumbel-max trick. This allows us to model the joint distribution over original strings and their counterfactuals resulting from the same instantiation of the sampling noise. We develop an algorithm based on hindsight Gumbel sampling that allows us to infer the latent noise variables and generate counterfactuals of observed strings. Our experiments demonstrate that the approach produces meaningful counterfactuals while at the same time showing that commonly used intervention techniques have considerable undesired side effects.

Controllable Context Sensitivity and the Knob Behind It

When making predictions, a language model must trade off how much it relies on its context vs. its prior knowledge. Choosing how sensitive the model is to its context is a fundamental functionality, as it enables the model to excel at tasks like retrieval-augmented generation and question-answering. In this paper, we search for a knob which controls this sensitivity, determining whether language models answer from the context or their prior knowledge. To guide this search, we design a task for controllable context sensitivity. In this task, we first feed the model a context (Paris is in England) and a question (Where is Paris?); we then instruct the model to either use its prior or contextual knowledge and evaluate whether it generates the correct answer for both intents (either France or England). When fine-tuned on this task, instruction-tuned versions of Llama-3.1, Mistral-v0.3, and Gemma-2 can solve it with high accuracy (85-95%). Analyzing these high-performing models, we narrow down which layers may be important to context sensitivity using a novel linear time algorithm. Then, in each model, we identify a 1-D subspace in a single layer that encodes whether the model follows context or prior knowledge. Interestingly, while we identify this subspace in a fine-tuned model, we find that the exact same subspace serves as an effective knob in not only that model but also non-fine-tuned instruct and base models of that model family. Finally, we show a strong correlation between a model's performance and how distinctly it separates context-agreeing from context-ignoring answers in this subspace. These results suggest a single subspace facilitates how the model chooses between context and prior knowledge, hinting at a simple fundamental mechanism that controls this behavior.

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.

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.

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.