A Geometric Notion of Causal Probing

Large language models rely on real-valued representations of text to make their predictions. These representations contain information learned from the data that the model has trained on, including knowledge of linguistic properties and forms of demographic bias, e.g., based on gender. A growing body of work has considered removing information about concepts such as these using orthogonal projections onto subspaces of the representation space. We contribute to this body of work by proposing a formal definition of $\textit{intrinsic}$ information in a subspace of a language model's representation space. We propose a counterfactual approach that avoids the failure mode of spurious correlations (Kumar et al., 2022) by treating components in the subspace and its orthogonal complement independently. We show that our counterfactual notion of information in a subspace is optimized by a $\textit{causal}$ concept subspace. Furthermore, this intervention allows us to attempt concept controlled generation by manipulating the value of the conceptual component of a representation. Empirically, we find that R-LACE (Ravfogel et al., 2022) returns a one-dimensional subspace containing roughly half of total concept information under our framework. Our causal controlled intervention shows that, for at least one model, the subspace returned by R-LACE can be used to manipulate the concept value of the generated word with precision.

Testing the Predictions of Surprisal Theory in 11 Languages

A fundamental result in psycholinguistics is that less predictable words take a longer time to process. One theoretical explanation for this finding is Surprisal Theory (Hale, 2001; Levy, 2008), which quantifies a word's predictability as its surprisal, i.e. its negative log-probability given a context. While evidence supporting the predictions of Surprisal Theory have been replicated widely, most have focused on a very narrow slice of data: native English speakers reading English texts. Indeed, no comprehensive multilingual analysis exists. We address this gap in the current literature by investigating the relationship between surprisal and reading times in eleven different languages, distributed across five language families. Deriving estimates from language models trained on monolingual and multilingual corpora, we test three predictions associated with surprisal theory: (i) whether surprisal is predictive of reading times; (ii) whether expected surprisal, i.e. contextual entropy, is predictive of reading times; (iii) and whether the linking function between surprisal and reading times is linear. We find that all three predictions are borne out crosslinguistically. By focusing on a more diverse set of languages, we argue that these results offer the most robust link to-date between information theory and incremental language processing across languages.

On the Efficacy of Sampling Adapters

Sampling is a common strategy for generating text from probabilistic models, yet standard ancestral sampling often results in text that is incoherent or ungrammatical. To alleviate this issue, various modifications to a model's sampling distribution, such as nucleus or top-k sampling, have been introduced and are now ubiquitously used in language generation systems. We propose a unified framework for understanding these techniques, which we term sampling adapters. Sampling adapters often lead to qualitatively better text, which raises the question: From a formal perspective, how are they changing the (sub)word-level distributions of language generation models? And why do these local changes lead to higher-quality text? We argue that the shift they enforce can be viewed as a trade-off between precision and recall: while the model loses its ability to produce certain strings, its precision rate on desirable text increases. While this trade-off is not reflected in standard metrics of distribution quality (such as perplexity), we find that several precision-emphasizing measures indeed indicate that sampling adapters can lead to probability distributions more aligned with the true distribution. Further, these measures correlate with higher sequence-level quality scores, specifically, Mauve.

Efficient Semiring-Weighted Earley Parsing

This paper provides a reference description, in the form of a deduction system, of Earley's (1970) context-free parsing algorithm with various speed-ups. Our presentation includes a known worst-case runtime improvement from Earley's $O (N^3|G||R|)$, which is unworkable for the large grammars that arise in natural language processing, to $O (N^3|G|)$, which matches the runtime of CKY on a binarized version of the grammar $G$. Here $N$ is the length of the sentence, $|R|$ is the number of productions in $G$, and $|G|$ is the total length of those productions. We also provide a version that achieves runtime of $O (N^3|M|)$ with $|M| \leq |G|$ when the grammar is represented compactly as a single finite-state automaton $M$ (this is partly novel). We carefully treat the generalization to semiring-weighted deduction, preprocessing the grammar like Stolcke (1995) to eliminate deduction cycles, and further generalize Stolcke's method to compute the weights of sentence prefixes. We also provide implementation details for efficient execution, ensuring that on a preprocessed grammar, the semiring-weighted versions of our methods have the same asymptotic runtime and space requirements as the unweighted methods, including sub-cubic runtime on some grammars.

Generalizing Backpropagation for Gradient-Based Interpretability

Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model's output with respect to its inputs. While these methods can indicate which input features may be important for the model's prediction, they reveal little about the inner workings of the model itself. In this paper, we observe that the gradient computation of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics about the gradient graph of a neural network, such as the highest-weighted path and entropy. We implement this generalized algorithm, evaluate it on synthetic datasets to better understand the statistics it computes, and apply it to study BERT's behavior on the subject-verb number agreement task (SVA). With this method, we (a) validate that the amount of gradient flow through a component of a model reflects its importance to a prediction and (b) for SVA, identify which pathways of the self-attention mechanism are most important.

A Formal Perspective on Byte-Pair Encoding

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a $\frac{1}{{\sigma(\boldsymbol{\mu}^\star)}}(1-e^{-{\sigma(\boldsymbol{\mu}^\star)}})$-approximation of an optimal merge sequence, where ${\sigma(\boldsymbol{\mu}^\star)}$ is the total backward curvature with respect to the optimal merge sequence $\boldsymbol{\mu}^\star$. Empirically the lower bound of the approximation is $\approx 0.37$. We provide a faster implementation of BPE which improves the runtime complexity from $\mathcal{O}\left(N M\right)$ to $\mathcal{O}\left(N \log M\right)$, where $N$ is the sequence length and $M$ is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Tokenization and the Noiseless Channel

Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to \emph{efficient} channel usage, where the channel is the means by which some input is conveyed to the model and efficiency can be quantified in information-theoretic terms as the ratio of the Shannon entropy to the maximum possible entropy of the token distribution. Yet, an optimal encoding according to Shannon entropy assigns extremely long codes to low-frequency tokens and very short codes to high-frequency tokens. Defining efficiency in terms of R\'enyi entropy, on the other hand, penalizes distributions with either very high or very low-frequency tokens. In machine translation, we find that across multiple tokenizers, the R\'enyi entropy with $\alpha = 2.5$ has a very strong correlation with \textsc{Bleu}: $0.78$ in comparison to just $-0.32$ for compressed length.

LEACE: Perfect linear concept erasure in closed form

Concept erasure aims to remove specified features from a representation. It can improve fairness (e.g. preventing a classifier from using gender or race) and interpretability (e.g. removing a concept to observe changes in model behavior). We introduce LEAst-squares Concept Erasure (LEACE), a closed-form method which provably prevents all linear classifiers from detecting a concept while changing the representation as little as possible, as measured by a broad class of norms. We apply LEACE to large language models with a novel procedure called "concept scrubbing," which erases target concept information from every layer in the network. We demonstrate our method on two tasks: measuring the reliance of language models on part-of-speech information, and reducing gender bias in BERT embeddings. Code is available at https://github.com/EleutherAI/concept-erasure.

Hexatagging: Projective Dependency Parsing as Tagging

We introduce a novel dependency parser, the hexatagger, that constructs dependency trees by tagging the words in a sentence with elements from a finite set of possible tags. In contrast to many approaches to dependency parsing, our approach is fully parallelizable at training time, i.e., the structure-building actions needed to build a dependency parse can be predicted in parallel to each other. Additionally, exact decoding is linear in time and space complexity. Furthermore, we derive a probabilistic dependency parser that predicts hexatags using no more than a linear model with features from a pretrained language model, i.e., we forsake a bespoke architecture explicitly designed for the task. Despite the generality and simplicity of our approach, we achieve state-of-the-art performance of 96.4 LAS and 97.4 UAS on the Penn Treebank test set. Additionally, our parser's linear time complexity and parallelism significantly improve computational efficiency, with a roughly 10-times speed-up over previous state-of-the-art models during decoding.

A Cross-Linguistic Pressure for Uniform Information Density in Word Order

While natural languages differ widely in both canonical word order and word order flexibility, their word orders still follow shared cross-linguistic statistical patterns, often attributed to functional pressures. In the effort to identify these pressures, prior work has compared real and counterfactual word orders. Yet one functional pressure has been overlooked in such investigations: the uniform information density (UID) hypothesis, which holds that information should be spread evenly throughout an utterance. Here, we ask whether a pressure for UID may have influenced word order patterns cross-linguistically. To this end, we use computational models to test whether real orders lead to greater information uniformity than counterfactual orders. In our empirical study of 10 typologically diverse languages, we find that: (i) among SVO languages, real word orders consistently have greater uniformity than reverse word orders, and (ii) only linguistically implausible counterfactual orders consistently exceed the uniformity of real orders. These findings are compatible with a pressure for information uniformity in the development and usage of natural languages.