Higher-order Derivatives of Weighted Finite-state Machines

Weighted finite-state machines are a fundamental building block of NLP systems. They have withstood the test of time -- from their early use in noisy channel models in the 1990s up to modern-day neurally parameterized conditional random fields. This work examines the computation of higher-order derivatives with respect to the normalization constant for weighted finite-state machines. We provide a general algorithm for evaluating derivatives of all orders, which has not been previously described in the literature. In the case of second-order derivatives, our scheme runs in the optimal $\mathcal{O}(A^2 N^4)$ time where $A$ is the alphabet size and $N$ is the number of states. Our algorithm is significantly faster than prior algorithms. Additionally, our approach leads to a significantly faster algorithm for computing second-order expectations, such as covariance matrices and gradients of first-order expectations.

Language Model Evaluation Beyond Perplexity

We propose an alternate approach to quantifying how well language models learn natural language: we ask how well they match the statistical tendencies of natural language. To answer this question, we analyze whether text generated from language models exhibits the statistical tendencies present in the human-generated text on which they were trained. We provide a framework--paired with significance tests--for evaluating the fit of language models to certain statistical tendencies of natural language. We find that neural language models appear to learn only a subset of the statistical tendencies considered, but align much more closely with empirical trends than theoretical laws (when present). Further, the fit to different distributions is dependent on both model architecture and generation strategy. As concrete examples, text generated under the nucleus sampling scheme adheres more closely to the type--token relationship of natural language than text produced using standard ancestral sampling; text from LSTMs reflects the natural language distributions over length, stopwords, and symbols suprisingly well.

A Non-Linear Structural Probe

Probes are models devised to investigate the encoding of knowledge -- e.g. syntactic structure -- in contextual representations. Probes are often designed for simplicity, which has led to restrictions on probe design that may not allow for the full exploitation of the structure of encoded information; one such restriction is linearity. We examine the case of a structural probe (Hewitt and Manning, 2019), which aims to investigate the encoding of syntactic structure in contextual representations through learning only linear transformations. By observing that the structural probe learns a metric, we are able to kernelize it and develop a novel non-linear variant with an identical number of parameters. We test on 6 languages and find that the radial-basis function (RBF) kernel, in conjunction with regularization, achieves a statistically significant improvement over the baseline in all languages -- implying that at least part of the syntactic knowledge is encoded non-linearly. We conclude by discussing how the RBF kernel resembles BERT's self-attention layers and speculate that this resemblance leads to the RBF-based probe's stronger performance.

A Cognitive Regularizer for Language Modeling

The uniform information density (UID) hypothesis, which posits that speakers prefer utterances that distribute information uniformly across the signal, has gained substantial traction in psycholinguistics as an explanation for certain syntactic, morphological, and prosodic choices. Could we operationalize uniform information density as an inductive bias for statistical language modeling? In this paper, we augment the canonical MLE objective for training language models by encoding UID as regularization. In experiments on ten languages spanning five language families, we find that using UID regularization consistently improves perplexity in language models, having a larger effect when training data is limited. Moreover, via analysis of generated sequences, we find that UID-regularized language models are higher-entropy and produce text that is longer and more lexically diverse. Our results not only suggest that UID is a reasonable inductive bias for language modeling, but also provide an alternative validation of the UID hypothesis using modern-day NLP tools.

How (Non-)Optimal is the Lexicon?

The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary, local constraints on sequences of symbols, and various other factors all shape the lexicons of the world's languages. Despite their importance in shaping lexical structure, the relative contributions of these factors have not been fully quantified. Taking a coding-theoretic view of the lexicon and making use of a novel generative statistical model, we define upper bounds for the compressibility of the lexicon under various constraints. Examining corpora from 7 typologically diverse languages, we use those upper bounds to quantify the lexicon's optimality and to explore the relative costs of major constraints on natural codes. We find that (compositional) morphology and graphotactics can sufficiently account for most of the complexity of natural codes -- as measured by code length.

Finding Concept-specific Biases in Form--Meaning Associations

This work presents an information-theoretic operationalisation of cross-linguistic non-arbitrariness. It is not a new idea that there are small, cross-linguistic associations between the forms and meanings of words. For instance, it has been claimed (Blasi et al., 2016) that the word for "tongue" is more likely than chance to contain the phone [l]. By controlling for the influence of language family and geographic proximity within a very large concept-aligned, cross-lingual lexicon, we extend methods previously used to detect within language non-arbitrariness (Pimentel et al., 2019) to measure cross-linguistic associations. We find that there is a significant effect of non-arbitrariness, but it is unsurprisingly small (less than 0.5% on average according to our information-theoretic estimate). We also provide a concept-level analysis which shows that a quarter of the concepts considered in our work exhibit a significant level of cross-linguistic non-arbitrariness. In sum, the paper provides new methods to detect cross-linguistic associations at scale, and confirms their effects are minor.

Quantifying Gender Bias Towards Politicians in Cross-Lingual Language Models

While the prevalence of large pre-trained language models has led to significant improvements in the performance of NLP systems, recent research has demonstrated that these models inherit societal biases extant in natural language. In this paper, we explore a simple method to probe pre-trained language models for gender bias, which we use to effect a multi-lingual study of gender bias towards politicians. We construct a dataset of 250k politicians from most countries in the world and quantify adjective and verb usage around those politicians' names as a function of their gender. We conduct our study in 7 languages across 6 different language modeling architectures. Our results demonstrate that stance towards politicians in pre-trained language models is highly dependent on the language used. Finally, contrary to previous findings, our study suggests that larger language models do not tend to be significantly more gender-biased than smaller ones.

Searching for Search Errors in Neural Morphological Inflection

Neural sequence-to-sequence models are currently the predominant choice for language generation tasks. Yet, on word-level tasks, exact inference of these models reveals the empty string is often the global optimum. Prior works have speculated this phenomenon is a result of the inadequacy of neural models for language generation. However, in the case of morphological inflection, we find that the empty string is almost never the most probable solution under the model. Further, greedy search often finds the global optimum. These observations suggest that the poor calibration of many neural models may stem from characteristics of a specific subset of tasks rather than general ill-suitedness of such models for language generation.