# Spelling convention sensitivity in neural language models

Elizabeth Nielsen† Christo Kirov∘ Brian Roark∘
†School of Informatics, University of Edinburgh, UK ∘Google
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We examine whether large neural language models, trained on very large
collections of varied English text, learn the potentially long-distance
dependency of British versus American spelling conventions, i.e., whether
spelling is consistently one or the other within model-generated strings. In
contrast to long-distance dependencies in non-surface underlying structure
(e.g., syntax), spelling consistency is easier to measure both in LMs and the
text corpora used to train them, which can provide additional insight into
certain observed model behaviors. Using a set of probe words unique to either
British or American English, we first establish that training corpora exhibit
substantial (though not total) consistency. A large T5 language model does
appear to internalize this consistency, though only with respect to observed
lexical items (not nonce words with British/American spelling patterns). We
further experiment with correcting for biases in the training data by fine-
tuning T5 on synthetic data that has been debiased, and find that finetuned T5
remains only somewhat sensitive to spelling consistency. Further experiments
show GPT2 to be similarly limited.

##  1 Introduction

The probabilities that neural language models (LMs) assign to strings can be
used to assess how effectively they capture linguistic dependencies found in
their training data. Much as in psycholinguistic experiments on human language
speakers, we can present LMs with strings both with and without agreement in
key dependencies and measure the assigned probabilities to determine whether
the model has learned these linguistic generalizations or not (see e.g.,
Futrell et al. 2018). For example, sentences both with and without
subject/verb number agreement (but otherwise identical) can be used to assess
whether the model accounts for that particular dependency, even over long
distances. Various long-distance dependencies have been investigated in this
manner, from purely linguistic phenomena such as syntactic dependencies (e.g.,
Gulordava et al. 2018) to extra-linguistic phenomena such as socio-cultural
biases (e.g., Rudinger et al. 2018).

In this paper, we examine dependencies based on orthographic cues to language
variety. Many LMs are trained on large corpora scraped from the web, and data
from different language varieties are often combined. For example, LMs trained
on web-scraped English (e.g., the WebText Corpus of Radford et al. 2019)
encounter British English, North American English, and multiple World
Englishes. Likewise, Spanish web corpora may include several distinct
varieties of Latin American Spanish, as well as Iberian Spanish (e.g.,
Kilgarriff and Renau 2013). Here we use differences between British and
American English spelling conventions to ask whether LMs trained on large and
diverse collections of English learn to apply these conventions consistently
within the same span of text. For example, if the British spelling of the word
labour appears in a sentence prefix, will the LM assign higher probabilities
to continuations that maintain British spelling conventions (e.g.,
organisation) over those that have American-spelled forms (organization)? To
the extent that such models are used within response generation systems or for
next word prediction in virtual keyboards, maintaining such consistency would
be strongly desirable so users receive results appropriate for their locale.

Of course, as with any such dependencies, models can only learn
generalizations that are present in the data, so we also look at the degree to
which corpora used to train the large LMs (LLMs) that we investigate (as well
as a few others) demonstrate spelling convention consistency. Assessing
whether syntactic or semantic generalizations are learned by models trained on
noisy, errorful and inconsistent data is complicated by the difficulty in
quantifying the actual degree of consistency of the dependency in the data
itself. In contrast to structural linguistic generalizations or other implicit
information, the explicitness of spelling conventions permits straightforward
corpus analysis in addition to model probing, providing another avenue for
explaining model performance.

The results of our data analysis are presented in §4. We find that relevant
web-scraped English text used to train LLMs unsurprisingly does not provide
perfect consistency — and further that it is heavily skewed towards American
spelling conventions — but that it provides as much or more consistency than
some curated corpora such as the British National Corpus BNC Consortium
(2007). We then present methods, in §5, to measure the degree to which two
neural LLMs – T5 Raffel et al. (2020) (both with and without additional
finetuning) and GPT2 – exhibit spelling variation consistency. We find that T5
without finetuning demonstrates a general preference for consistency, but that
this preference is weaker for British than American English and does not
extend robustly to nonce words. Finetuning T5 on a synthetically modified
portion of the British National Corpus reduces the preference for American
English. We then modify our conditional probability calculations to allow
demonstration of similar patterns of model behavior for GPT2, a very
differently architectured and trained LLM Radford et al. (2019). Lastly, in
§6, we take a slightly deeper dive into the kinds of (and reasons for)
spelling convention inconsistencies in some corpora analyzed in §4.

Overall, we demonstrate that, while T5 and GPT2 display some sensitivity to
spelling convention differences, this cannot be relied on to produce
consistent generated output. If reliable spelling consistency is an
application requirement, additional post-processing may need to be applied to
LLM output.

This paper makes several key contributions. First, we provide methods for
straightforwardly assessing the ability of LLMs to capture certain well-
attested long-distance dependencies in English, and demonstrate the strengths
and shortcomings of two well-known models in doing so. This opens up the
possibility of exploratory studies in languages where such conventions are
less well documented. In contrast to the most heavily investigated types of
long-distance dependencies (e.g., syntactic), the (previously unexplored)
dependency of spelling convention consistency is directly observable in the
surface string and hence is relatively easy to assess in both models and data.
As a result, it can be seen as a useful task for assessing LM learning in
general. We also document the degree to which web-scraped corpora exhibit
spelling consistency, making clear that the models have plenty of room for
improvement. However, American English is shown to be far more heavily
represented in the training corpora than British English, to the point that
performance for British English is demonstrably far worse than for American
English, something that language generation or word prediction systems must
address for equitable performance.

##  2 Background

###  2.1 Dependencies and LMs

Much of the work investigating whether large language models capture long-
distance linguistic generalizations has focused on non-surface dependencies,
such as co-reference. In order to correctly identify that two expressions
refer to the same entity, models often need to identify complex syntactic
relationships (e.g., c-command), or build a model of entities over an entire
discourse (e.g., Clark and Manning 2016). Despite this complexity, LLMs have
shown some promise as general-purpose co-reference resolvers Joshi et al.
(2019). This suggests that they can learn to model complex long-distance
dependencies.

Other research has shown more directly that LLMs model syntactic dependencies.
A common methodology is to compare an LM’s surprisal directly to
psycholinguistic data Futrell et al. (2018). If the LM still performs like a
human on examples that require modeling hierarchical relationships between
tokens, this suggests that the LM has learned some part of the more complex
syntactic structure of the language. Work such as Futrell et al. (2018) has
shown that a recurrent neural network language model achieves surprisal rates
that mimic human processing, including in these syntactically complex
situations. This suggests that an RNN LM can be sensitive to complex syntactic
relationships as well. Similar methods have been used to show LMs learning
syntactic dependencies in Linzen et al. (2016), Frank et al. (2016), and
Brennan et al. (2020).

Another class of methods for assessing whether LMs learn complex syntactic
dependencies involves probing the models themselves to evaluate whether
syntax-like relationships between tokens can be discovered. Details of their
methods vary widely, but Clark et al. (2019), Hewitt and Manning (2019), and
Lin et al. (2019) all suggest that many LMs learn complex syntactic
dependencies.

In contrast, the topic of the current paper – spelling convention dependencies
– is a relatively surface-level dependency. A model does not need to capture
the syntactic or semantic relationship between two words in order to evaluate
spelling consistency, rather simply their co-occurrence. Given prior results
showing that LMs can and do learn complex semantic and syntactic relationships
between words, one might expect that a relatively simple dependency like
spelling convention should be easy for an LM to learn.

###  2.2 Spelling variation

As discussed by Berg and Aronoff (2017), the orthography of English has never
been regulated by an official body, but has rather emerged dynamically over
time. Dictionaries played a key role in settling spelling conventions, with
Samuel Johnson’s Johnson (1755) dictionary being the key source of
contemporary British spelling conventions and Webster’s Webster (1828)
dictionary the key source of contemporary American spelling. The latter
included spelling reforms such as using the suffix -or instead of -our for
certain words, e.g., labor instead of labour. These reforms were adopted in
American spelling but not in British spelling conventions.

This history makes English an interesting case study for spelling variation in
particular. Languages that have historically had centralized regulatory
institutions, such as the French or Royal Spanish Academies, have much less
purely orthographic variation. For example, despite many lexical differences,
there are few spelling differences between Iberian and Latin American Spanish.
On the other hand, there are many language situations that have considerably
more spelling variation. For example, speakers of South Asian languages that
are traditionally written with Brahmic or Arabic scripts often write using the
Latin alphabet in contexts like SMS messages and social media Roark et al.
(2020). This kind of informally romanized text presents many spelling
variations due to these languages’ lack of orthography in the Latin script.
The well-documented nature of English spelling variation and its close ties to
standardized regional varieties make it a good initial case study for whether
LLMs learn systematic variation in the data. If so, such models may be useful
in more exploratory studies, such as the above-mentioned scenario where no
official orthography exists.

As far as we are aware, the issue of spelling convention consistency in
language models has not been investigated. Nguyen and Grieve (2020) looked at
whether word embeddings are robust to spelling variation, not whether
generative language models capture spelling consistency. That paper focused
mainly on the kinds of variation that arise in informal social media text, but
they also examined British versus American spelling. Unsurprisingly, they
found that cosine similarity between British and American spelled variants are
high relative to other patterns of informal spelling variability.

###  2.3 Prompting LMs

In the present work, we construct prompts to measure the probability assigned
to various tokens by LLMs. In constructing these prompts, we take into account
the findings of recent work on prompting LMs. Our work is different from the
sort of prompting described by these papers, which generally includes features
such as task-specific prefixes containing instructions (e.g., Raffel et al.
2020), verbalized class labels (e.g., Schick and Schütze 2021), or in-context
learning (e.g., Brown et al. 2020), none of which are present in our approach.
However, work such as Webson and Pavlick (2022) has shown large effects due to
small variations in the wording of prompts, even if the reasons for these
effects are not apparent. Therefore, we choose to present the model with
several different prompts and average the probabilities over all prompts, in
order to account for possible variation.

##  3 Data and models

To assess the spelling convention consistency of data and models, we use a
list of British and American English spelling differences that is part of the
open-source American British English
Translator.111https://github.com/hyperreality/American-British-English-
Translator We used the 1706 word pairs in the data/american_spellings.json
file at that site. This list includes American and British spelling variants
for words with common differences such as -or/-our (e.g., vapor/vapour),
-ize/-ise (realize/realise), consonant doubling (modeling/modelling), -er/-re
(liter/litre), along with some number of term-specific spelling differences
(aluminum/aluminium). We use this list to create prompts for probing the
language models and to establish the consistency of usage within corpora,
i.e., whether strings found in this list consistently follow one convention or
the other when they co-occur.

For model probing, we examine T5 Raffel et al. (2020), a general purpose
encoder-decoder model. We use the t5-large architecture variant on the T5X
codebase,222https://github.com/google-
research/t5x/blob/main/docs/models.md#t5-checkpoints which has approximately
770M parameters. For English, T5 is (pre-)trained using a span corruption
objective on the Colossal Clean Crawled Corpus (C4), an English language
collection derived from Common Crawl Raffel et al.
(2020).333http://commoncrawl.org/

We also examine GPT2, for which we use the open-source HuggingFace
implementation Radford et al. (2019). Unlike T5, GPT2 is a purely
autoregressive language model rather than an encoder-decoder sequence-to-
sequence model. It is trained to perform next-word prediction rather than fill
in corrupted spans of text. GPT2 is built on OpenAI’s WebText corpus Radford
et al. (2019), of which there is an open-source variant
available.444https://skylion007.github.io/OpenWebTextCorpus/

We examine C4 and OpenAI’s WebText corpus for spelling convention consistency,
along with several other corpora: English Wikipedia (downloaded 06-21-2020);
the Billion Word Benchmark Chelba et al. (2013), which is a collection of
newswire text; and the British National Corpus BNC Consortium
(2007),555http://www.natcorp.ox.ac.uk/ which is a balanced corpus of both
written and spoken material.666Code for querying corpora and generating
prompts, as well as other relevant data and code, can be found at
https://github.com/google-research/google-
research/tree/master/spelling_convention_nlm.

##  4 Training corpora consistency

To examine spelling consistency in training data, we made use of the list of
spelling variants and the five corpora mentioned in Section 3: C4, the
OpenWebText Corpus (OWT), English Wikipedia (EngWiki), the Billion Word
Benchmark (BWB), and the British National Corpus (BNC). We convert all strings
in each corpus to lowercase, and treat all characters outside of the a–z range
as whitespace for tokenization. We look for exact matches of list items in the
resulting whitespace-delimited tokens.

Let $V_{\mathrm{US}}$ be the US spelling variants777For convenience, we use US
as shorthand for American and UK as shorthand for British. of the words in the
list and $V_{\mathrm{UK}}$ the UK spelling variants. For each corpus $C$, let
$s^{k}=w_{1}\ldots w_{|s^{k}|}$ represent the $k$th string in the corpus,
consisting of $|s^{k}|$ words. We extract all pairs of words $(w_{i},w_{j})$
from $s^{k}$ such that $i<j$ and $w_{i},w_{j}\in V_{\mathrm{US}}\bigcup
V_{\mathrm{UK}}$. Each extracted pair $(w_{i},w_{j})$ is placed into one of
three classes: the pair is (1) US-matched if $w_{i},w_{j}\in V_{\mathrm{US}}$;
(2) UK-matched if $w_{i},w_{j}\in V_{\mathrm{UK}}$; and (3) mismatched
otherwise. We then aggregate the counts for pairs in these three bins across
all strings in the corpus.

| total # of | X-matched %
---|---|---
Corpus | word pairs | US | UK | mis
C4 | 542,755,756 | 74.6 | 14.7 | 10.8
OWT | 42,255,261 | 79.7 | 11.5 |  8.8
EngWiki | 1,527,529 | 58.0 | 26.5 | 15.4
BWB | 442,733 | 67.5 | 23.6 |  8.9
BNC | 74,072 | 14.5 | 64.8 | 20.8
Table 1: Study of word pairs found in the same string from either UK or US
spelling list over corpora of different sizes and characteristics, with
percent of US-matched, UK-matched and mismatched US/UK pairs.

Table 1 presents the number of pairs extracted from each corpus and the
percentage of those within each class. Several things jump out from these
results. First, all of the corpora, other than the British National Corpus,
have significantly more US-matched pairs than UK-matched pairs, with OWT and
C4 being the most skewed towards US-matched pairs. This likely indicates a
heavy overall skew towards US spelling variants, leading to a high prior
probability of US spelling variants in LLMs. Second, the percentage of
extracted pairs that are mismatched are non-negligible, however there is a lot
of consistency. For example, in the C4 corpus, if a word from
$V_{\mathrm{UK}}$ is the first word of a pair, the probability that the next
word will also be from $V_{\mathrm{UK}}$ is nearly three times the probability
that it is from $V_{\mathrm{US}}$.888Mismatched pairs in all corpora are
roughly equally split between having $V_{\mathrm{US}}$ or $V_{\mathrm{UK}}$
words first. Hence, for C4, 5.4% of pairs are $V_{\mathrm{UK}}$ followed by
$V_{\mathrm{US}}$ words (half of the mismatched probability), while 14.7% are
$V_{\mathrm{UK}}$ followed by $V_{\mathrm{UK}}$. Finally, both English
Wikipedia and the British National Corpus have somewhat elevated levels of
mismatch compared to the other corpora, something we look at more closely in
Section 6.

Having established that the level of mismatch in the C4 corpus used to train
T5 is at the lower end observed in the data we examined,999We note again the
benefit of these explicit surface-level dependencies – we can easily assess
the prevalence/consistency of the training data, in contrast to structural
dependencies. we now move on to examine whether the trained models pick up on
these dependencies.

##  5 Language model consistency

From the dictionary presented in Section 3, we kept only the words that can be
described by a small number of rules, e.g., the variation between -ize and
-ise, etc, leaving us with 1266 options. For efficiency, we sample
$\approx$16k prompt-target pairs (16028) from all possible $1266^{2}$
combinations.

To eliminate all sources of variation besides the pair of words being tested,
we created several template sentences into which we can insert pairs of words.
The full set of templates is presented in Table 9 in Appendix A. Several
considerations informed how we formulated the templates so that they work for
all the tokens we wanted to test.

First and most obviously, we need to ensure that all tokens in a template are
variety-neutral. This ensures that the probability of any of our test words
being British or American will not be swayed by any regional bias in the
template. While neutrality is difficult to enforce perfectly within a single
frame, we hope that by using multiple different templates, we can mitigate
unknown sources of bias via averaging.

Second, we need templates that will be syntactically and semantically
acceptable, regardless of the inserted tokens. LLMs may assign low probability
to tokens that result in grammatically unacceptable or semantically unlikely
sentences, and we want to avoid introducing this source of variation. This is
challenging, since the tokens we are testing include different parts of speech
and come from very different semantic domains, hence there are few contexts
where all tokens would be acceptable.

|  | T5 | T5+FT | C4
---|---|---|---|---
Condition | Word 1 | Word 2 | Word 2 | Word 2
|  | US | UK | US | UK | US | UK
Adjacent | US | 0.86 | 0.14 | 0.66 | 0.34 | 0.91 | 0.09
| UK | 0.39 | 0.61 | 0.44 | 0.56 | 0.38 | 0.62
Non-adjacent | US | 0.83 | 0.17 | 0.69 | 0.31 | 0.93 | 0.07
| UK | 0.48 | 0.52 | 0.43 | 0.57 | 0.27 | 0.73
Table 2: Conditional probability of Word 2, given a template with Word 1,
given by T5 (no finetuning) and T5+FT (finetuned on synthetic balanced BNC
data). For each instance, the probability has been normalized over each
condition (corresponding to each row for the model). We also present the
conditional probabilities from pairs found in the training corpus C4.

Fortunately, this problem has an analogue in linguistics: linguists interested
in detailed phonetic description often elicit tokens in set contexts to
eliminate extraneous sources of acoustic variation Bowern (2015). The approach
these linguists often take is to use a template that mentions the tokens in
question rather than using them. We follow this approach, and use templates
similar to 2, which contain a list of word mentions.

. My preferred words are …, …, and tree.

We then substitute pairs of words from our dictionary into the spaces marked
with ellipses, both with consistent and inconsistent spelling conventions. In
other words, given the pair of dictionary entries realize/realise and
center/centre, we use the template above to generate the four test sentences:

. . US/US: My preferred words are
realize, center, and tree. .̱ US/UK: My preferred words are
realize, centre, and tree. .̧ UK/US: My preferred words are
realise, center, and tree. .̣ UK/UK: My preferred words are
realise, centre, and tree.

We use T5 to score the probability of generating the second bolded word, as
shown in Example 2, given the first.

In the above template, the two words are adjacent in the string. We also
include a non-adjacent condition, which augments the templates by adding ten
variety-neutral tokens between the bold-face words. For the above sample, the
non-adjacent variant would be:

. My preferred words are …, flower, interesting, jump, ponderous, sky,
skipping, desk, small, ladder, lovely, …, and tree.

Since T5 is a seq2seq model trained on a span-corruption objective, we present
a prompt that includes a priming word and a blank span token representing the
second word: . My preferred words are flavour,
<blank-span-1>, and tree

The decoder then scores an output string that replaces the blank, but
represents the known inputs with span markers instead:

. <input-span-1> harbour <input=span-2>

Thus we are effectively computing the probability that the blank span will be filled with a particular word (with a US or UK spelling), given the visible input sentence (which contains a US or UK primer) — P(“harbour” | “My preferred words are flavour, …, and tree.”).

We report a few different measures to give a picture of how strongly each
model prefers spelling consistency: mean conditional probabilities, prediction
accuracy and mutual information. We then examine behavior with nonce words.

###  5.1 Measure 1: conditional probability tables

The first measure we use to show the preferences of each model is a 2x2 table
of the conditional probability of the second probe word, given the first. For
ease of interpretation, we normalize the conditional probabilities for each
conditioning word as though the two alternative second words (US and UK) are
the only possibilities, i.e., the two conditional probabilities are made to
sum to 1. That is, $P(UK|US)+P(US|US)=1$ and $P(US|UK)+P(UK|UK)=1$ for each
example. These conditional probabilities are then averaged over the whole test
corpus (16028 word pairs replicated across 29 template sentences101010For
information on the variance across prompts, see Appendix A. for a total of
464812 samples) for both the adjacent and non-adjacent conditions. Table 2
presents these mean conditional probabilities for base T5 and T5 finetuned
(TF+FT) on a synthetic balanced corpus derived from the BNC (see §5.2),
alongside conditional probabilities calculated from the pairs extracted for
the analysis in Table 1 from their training corpus (C4), under the same
adjacent and non-adjacent conditions.111111The conditional probabilities from
C4 are simply the probability that Word 2 is from the UK or US class given the
class of Word 1, with extracted pairs split by whether the words were adjacent
or not in the string. Adjacent pairs account for roughly 1% of all pairs in
the corpus.

As can be seen from these results, T5 shows a preference for spelling
consistency in both the adjacent and non-adjacent conditions — probabilities
for both the consistent US and consistent UK conditions are higher than the
probabilities for the respective inconsistent conditions. The differences are
notably larger in the adjacent conditions than the non-adjacent conditions,
indicating that the preference for spelling consistency attenuates somewhat
over longer strings. The model also shows a preference for US forms overall,
assigning a higher probability to a US form after a UK form than to a UK form
after a US form. This is likely due to US forms being over-represented in the
training data, leading to high prior probability.

Comparing the model and corpus columns in Table 2, the degree of consistency
preference displayed by T5 in the adjacent condition is actually very similar
to the consistency levels in the C4 training corpus (similarly replicating the
bias for US forms). However, C4 is much more consistent in the non-adjacent
condition than T5, indicating that the model is failing to capture some long-
distance dependencies.

###  5.2 Finetuning on synthetic data

Finding naturally occurring English text using perfectly consistent spelling
conventions of sufficient size to help improve a model’s consistency may be
difficult, given the results presented in Table 1. It would be useful,
however, to determine if T5 could be finetuned with some resource to exhibit
better spelling consistency. To that end, we created a synthetic version of
the BNC, which was changed to exhibit perfect consistency of British and
American spelling conventions for the words in our lexicon.

This synthetic BNC corpus was produced as follows. Using our list of spelling
variants, we identified strings in the corpus that contained an instance of
either the American or British spelling. We then produced a synthetic
consistent American spelling version of these strings by using the American
spelling of all of the words, along with a synthetic consistent British
spelling version of these strings by using the British spelling of all of the
words. The resulting corpus is thus balanced between American and British
spelling for these 1706 words, and every sentence is consistent in using one
convention or the other. In total, the synthetic corpus contains 954238
sentences,121212In our testing, this was not enough data to reliably train a
T5-large LLM from scratch. equally split between US and UK spelling
conventions. A small random subset of 2560 sentences was reserved for
validation, and T5 was finetuned on the rest. Finetuning used the same span-
filling masked LM task used for pretraining, with dropout set to 0.1, and the
loss normalizing factor set to 233472 as suggested in the T5 documentation.
Fine-tuning started at the default T5-large checkpoint, which represents
1000700 steps, and proceeded another 99300 steps at a batch size of 128.

As seen in Table 2, finetuning on this synthetic corpus does not appear to
improve overall spelling consistency – quite the opposite. However, it does
have at least two interesting effects. First, as might be expected, the
overwhelming preference for US English shown by base T5 is reduced.
Furthermore, the finetuned model is better able to retain long-distance
information — there is no dropoff in consistency between the adjacent and non-
adjacent conditions as seen for T5 without finetuning.

###  5.3 Measure 2: prediction accuracy

While the conditional probabilities in Table 2 show the overall preferences of
the models over the test set, we also want a measure that captures how often
the LLMs assign consistent pairs a higher probability than inconsistent pairs.
In Table 3 we show the percentage of the test set examples for which each
model predicted consistency over inconsistency. The results show a similar
pattern as the conditional probability measures in Table 2. Again, finetuning
lowers overall consistency, but results in less drop-off in non-adjacent vs.
adjacent conditions.

| Word 1 = US | Word 1 = UK
---|---|---
Condition | T5 | T5+FT | T5 | T5+FT
Adjacent | 92.2 | 71.1 | 65.1 | 63.4
Non-adjacent | 88.7 | 77.7 | 54.3 | 63.2
Table 3: Percent of test set examples for which each model prefers consistent
over inconsistent spelling.

###  5.4 Measure 3: mutual information

We also calculated the average mutual information (MI) across all
prompt/target pairs in order to measure the strength of association between
spelling conventions in both words. For each pair, we calculate four joint
probabilities — P(US,US), P(US,UK), P(UK,US), p(UK,UK). We assume these four
probabilities make up the entire universe with respect to a particular
prompt/target pair, and normalize them so they sum to 1. This also allows us
to easily calculate marginal probabilities simply by adding the appropriate
joint probabilities – e.g., P(US prompt) = P(US,US) + P(US,UK). To calculate
MI, we use a formula based on the log-likelihood ratio calculation in Moore
(2004), but equivalent to the standard formulation for mutual information,
where $x,y$ are the two probe words:

$\sum_{x\in\\{\textsc{uk},\textsc{us}\\},y\in\\{\textsc{uk},\textsc{us}\\}}{p(x,y)\log\frac{p(x,y)}{p(x)p(y)}}$

Since T5 is trained on masked token prediction, to measure the joint
probability $p(x,y)$ of each pair of probe words $x,y$ we can simply mask both
probing tokens and measure the probability of generating both of them. That
is, we present T5 with 5.4 and measure the probability of 5.4:

. . My preferred words are <blank-
span-1>, <blank-span-2>, and tree. .̱ <input-span-1> flavour <input-
span-2> harbour <input-span-3>

Condition | T5 | T5+FT
---|---|---
Adjacent | 0.0048 | 0.0017
Non-adjacent | 0.0044 | 0.0015
Table 4: Average mutual information in the adjacent and non-adjacent
conditions.

Table 4 presents these mutual information values. There doesn’t seem to be a
significant difference between adjacent and non-adjacent conditions for either
T5 variant, though finetuning does seem to cause an overall drop in MI, in
line with the overall drop in consistency seen in the measures above.

###  5.5 Nonce forms

We want to determine if T5 assigns the probabilities reported above on the
basis of dependencies between specific lexical items, or if it is learning
sub-word generalizations. In other words, does the model learn that specific
words like flavour and realise are more likely to co-occur than flavour and
realize? Or does it learn that words containing -our are more likely to co-
occur with words containing -ise? Since the model is trained using
SentencePiece tokenization Kudo and Richardson (2018), it is possible that it
exploits sub-word features.

One way of testing if a model can use sub-word features is to create nonce
words that contain British- or American-specific sub-words. If the model
treats these as being British or American, this is an indication that the
model is able to pick up on sub-word features.

We created a list of ten nonce forms by changing, adding, or removing one to
three letters in existing words in our dictionary of American and British
forms. These forms are shown in Table 5.

British | American | British | American
---|---|---|---
glavour | glavor | reptalise | reptalize
mentre | menter | amolirise | amolirize
unulise | unulize | sphectre | sphecter
malvour | malvor | imminise | imminize
larbour | larbor | voitre | voiter
Table 5: Nonce forms created by making one to three changes to words in the
American-British dictionary.

We use the same probing template and method as described above. For each
probe, we use a real American or British word for the first probe word, and
one of the nonce forms shown in Table 5 for the second. For this experiment we
queried the base T5 model in the adjacent condition. The resulting conditional
probability table is shown in Table 6.

|  | Word 2
---|---|---
|  | US | UK
Word 1 | US | 0.68 | 0.32
UK | 0.56 | 0.44
Table 6: Conditional probability table for nonce forms given by T5. The table
shows the conditional probability of Word 2 (which is a nonce form), given
Word 1. For each instance, the probability has been normalized over each
condition (i.e., each row in the table).

Table 6 shows that the patterns shown in Section 5.1 above do not generalize
very strongly to nonce forms. The probabilities assigned to US forms following
UK forms are on average higher than UK forms following UK forms. However, the
difference between these alternatives is attenuated compared to when Word 1 is
a US form, indicating that (a) there is a heavy skew towards US spelling
conditions in the training data; but (b) some sensitivity to the UK context,
if not enough to counteract the high US form priors. This suggests that the
results in Table 2 are to a large extent driven by lexical dependencies rather
than any lower-level spelling patterns encoded by wordpieces.

###  5.6 Autoregressive LLMs

|  | GPT2 (tgt only) | GPT2 (to EOS) | OWT
---|---|---|---|---
Condition | Word 1 | Word 2 | Word 2 | Word 2
|  | US | UK | US | UK | US | UK
Adjacent | US | 0.87 | 0.13 | 0.69 | 0.31 | 0.95 | 0.05
| UK | 0.36 | 0.64 | 0.51 | 0.49 | 0.34 | 0.66
Non-adjacent | US | 0.83 | 0.17 | 0.66 | 0.33 | 0.95 | 0.05
| UK | 0.49 | 0.51 | 0.54 | 0.46 | 0.28 | 0.72
Table 7: Conditional probability of Word 2, given a template with Word 1, given by GPT2 scored until the end of the target word only (tgt only) and scored until the end of the sentence (to EOS). We also present the conditional probabilities from pairs found in the training corpus, OWT. | Word 1 = US | Word 1 = UK
---|---|---
Condition | GPT2 | GPT2 | GPT2 | GPT2
| target | EOS | target | EOS
Adjacent | 94.2 | 70.1 | 70.8 | 49.4
Non-adjacent | 92.5 | 67.5 | 54.6 | 45.1
Table 8: Percent of test set examples for which each GTP2 scoring variant
prefers consistent over inconsistent spelling.

Many commonly-used LLMs (including T5) are trained to predict words in the
input that have been masked out. Another common class of LLMs, however, are
trained to perform next-word prediction instead. To examine how such
autoregressive architectures handle spelling consistency, we experiment with
OpenAI’s GPT2 Radford et al. (2019), which has a readily available open-source
implementation through HuggingFace.131313https://huggingface.co/gpt2

As GPT2 is purely autoregressive, we cannot compute the probability that a
particular probe word will fill a masked sentence span as easily as we could
with T5. We can only efficiently compute the probability of a suffix given a
prefix. Given this caveat, we have at least two options for assigning
conditional probability scores, neither of which should be treated as exactly
comparable to the T5 scores above. First, we can count only the logits
corresponding to the target word:

P(“harbour” | “My preferred words are flavour,”).

This local score ignores any words in the template occurring after the target word. Second, we can compute from the start of the target to the end of the sentence: P(“harbour, and tree” | “My preferred words are flavour,”), which accounts for the post-target suffix of the sentence.

Tables 7 and 8 show results for both of these methods for calculating the
conditional probability, compiled in the same way as the T5 results in Tables
2 and 3. Table 7 also includes the conditional probabilities from GPT2’s
training corpus, OWT. We see that GPT2 shows a similar preference for
consistency as T5, but only very locally. There is a large drop-off in
preference for consistency when moving from adjacent to non-adjacent
conditions, or when including the completion of the sentence in the
calculation. For UK English in particular, any preference for consistency
completely disappears beyond the immediate vicinity of the priming word, and
the model returns to chance performance on the task.

##  6 Further analysis of corpora

We now return to a slightly more detailed examination of two of the corpora
presented in Table 1, English Wikipedia and the British National Corpus, both
of which had relatively high levels of mismatch compared to the other corpora.

Wikipedia is an interesting case, since the documents are collectively edited
by potentially a large number of contributors, which may lead to higher
expected mismatch than in other corpora. For example, one version of the
article on air lock used both US-spelling of the word vapor and the UK-
spelling (vapour). This is explained via three versions of the introductory
sentence to the page, shown in Table 11 in Appendix B, where the two spellings
are added to the sentence at different times, years apart.

The amount of mismatch in the British National Corpus is perhaps more
surprising, given the provenance of the materials and intent of the
collection. However the diversity of sources, which include things such as
journal articles and edited volumes, likely leads to similar issues to those
found in Wikipedia, along with simple human error and/or inconsistency. Table
12 in Appendix B presents a few examples of sentences with words from both
spelling conventions, with American -ize spellings mixed with British -ise or
-our versions.

##  7 Conclusion and Future Work

We have presented results showing that T5 does tend towards consistency in
spelling, but not to the degree that could be relied upon should such
consistency be desired in generated text. We show that this general preference
for consistency reflects the data that the model is trained on, which also is
mostly consistent, but with a significant proportion of exceptions. The
model’s behavior is also shown to be affected by the relative frequency of
language varieties in the training data. We took advantage of the explicit and
surface-accessible nature of these dependencies to attribute some model
performance to the training data, while also demonstrating that modeling
improvements should be possible, since the training data itself is
substantially more consistent than the models.

These results suggest several possible avenues for future work. First, methods
for addressing bias in training data should yield improvements for British
spelling consistency in these models. We also intend to extend these results
to languages other than English and investigate how spelling variation in
other language situations is learned by LLMs. Some of the methods we used here
rely on the fact that English spelling variation is quite thoroughly
catalogued. Extending this work to less-documented cases of language variation
will require us to either (1) collect data about spelling variation from
language informants or data, or (2) develop methods that require less prior
knowledge. In the interest of finding methods that are extensible to the
greatest number of cases, we intend to pursue path (2), working on methods to
mine information about language variation from large corpora and LLMs that
have been trained on them.

## Acknowledgements

Thanks to Alexander Gutkin, Shankar Kumar, Arya McCarthy and Richard Sproat
for useful discussion and comments, and to the anonymous reviewers for helpful
suggestions.

## Limitations

Our work is focused on just a single case study of spelling variation. As
detailed in Section 2, English is a good candidate for a case study for
several reasons, but it would be beneficial to extend this work to other
language situations.

Another limitation was our choice to focus on already existing pre-trained
models, rather than directly controlling the training data that is input to
each model. This means some of the conclusions about the connection between
training data and outcome are tentative, pending experimental confirmation.

## Ethics Statement

This work does not propose a new model or dataset, but rather probes the
behavior of existing models. Thus novel ethical considerations about model
behavior and dataset contents are not directly raised by this work. While not
explicitly focused on ethical considerations, this paper’s methods hopefully
contribute to better understanding model behavior, and could be used to
understand the ways in which large language models treat underrepresented and
marginalized language varieties.

## References

  * Berg and Aronoff (2017) Kristian Berg and Mark Aronoff. 2017.  Self-organization in the spelling of English suffixes: The emergence of culture out of anarchy.  _Language_ , 93(1):37–64.
  * BNC Consortium (2007) BNC Consortium. 2007.  The British National Corpus, XML edition.  Oxford Text Archive, http://www.natcorp.ox.ac.uk.
  * Bowern (2015) Claire Bowern. 2015.  _Linguistic fieldwork : a practical guide_ , 2nd edition. edition.  Palgave Macmillian, Basingstoke, Hampshire.
  * Brennan et al. (2020) Jonathan R. Brennan, Chris Dyer, Adhiguna Kuncoro, and John T. Hale. 2020.  Localizing syntactic predictions using recurrent neural network grammars.  _Neuropsychologia_ , 146:107479.
  * Brown et al. (2020) Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. 2020.  Language models are few-shot learners.  In _Advances in Neural Information Processing Systems_ , volume 33, pages 1877–1901. Curran Associates, Inc.
  * Chelba et al. (2013) Ciprian Chelba, Tomas Mikolov, Mike Schuster, Qi Ge, Thorsten Brants, Phillipp Koehn, and Tony Robinson. 2013.  One billion word benchmark for measuring progress in statistical language modeling.  _arXiv preprint arXiv:1312.3005_.
  * Clark et al. (2019) Kevin Clark, Urvashi Khandelwal, Omer Levy, and Christopher D. Manning. 2019.  What does BERT look at? An analysis of BERT’s attention.  In _Proceedings of the 2019 ACL Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP_ , pages 276–286, Florence, Italy. Association for Computational Linguistics.
  * Clark and Manning (2016) Kevin Clark and Christopher D. Manning. 2016.  Deep reinforcement learning for mention-ranking coreference models.  In _Empirical Methods on Natural Language Processing_.
  * Frank et al. (2016) Stefan L. Frank, Thijs Trompenaars, and Shravan Vasishth. 2016.  Cross-linguistic differences in processing double-embedded relative clauses: Working-memory constraints or language statistics? _Cognitive Science_ , 40(3):554–578.
  * Futrell et al. (2018) Richard Futrell, Ethan Wilcox, Takashi Morita, and Roger Levy. 2018.  RNNs as psycholinguistic subjects: Syntactic state and grammatical dependency.  _arXiv preprint arXiv:1809.01329_.
  * Gulordava et al. (2018) Kristina Gulordava, Piotr Bojanowski, Edouard Grave, Tal Linzen, and Marco Baroni. 2018.  Colorless green recurrent networks dream hierarchically.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)_ , pages 1195–1205, New Orleans, Louisiana. Association for Computational Linguistics.
  * Hewitt and Manning (2019) John Hewitt and Christopher D. Manning. 2019.  A structural probe for finding syntax in word representations.  In _Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)_ , pages 4129–4138, Minneapolis, Minnesota. Association for Computational Linguistics.
  * Johnson (1755) Samuel Johnson. 1755.  _A Dictionary of the English Language_.  J. & P. Knapton, London.
  * Joshi et al. (2019) Mandar Joshi, Omer Levy, Luke Zettlemoyer, and Daniel Weld. 2019.  BERT for coreference resolution: Baselines and analysis.  In _Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)_ , pages 5803–5808, Hong Kong, China. Association for Computational Linguistics.
  * Kilgarriff and Renau (2013) Adam Kilgarriff and Irene Renau. 2013.  esTenTen, a vast web corpus of Peninsular and American Spanish.  _Procedia - Social and Behavioral Sciences_ , 95:12–19.  Corpus Resources for Descriptive and Applied Studies. Current Challenges and Future Directions: Selected Papers from the 5th International Conference on Corpus Linguistics (CILC2013).
  * Kudo and Richardson (2018) Taku Kudo and John Richardson. 2018.  SentencePiece: A simple and language independent subword tokenizer and detokenizer for neural text processing.  In _Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing: System Demonstrations_ , pages 66–71, Brussels, Belgium. Association for Computational Linguistics.
  * Lin et al. (2019) Yongjie Lin, Yi Chern Tan, and Robert Frank. 2019.  Open sesame: Getting inside BERT’s linguistic knowledge.  In _Proceedings of the 2019 ACL Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP_ , pages 241–253, Florence, Italy. Association for Computational Linguistics.
  * Linzen et al. (2016) Tal Linzen, Emmanuel Dupoux, and Yoav Goldberg. 2016.  Assessing the ability of LSTMs to learn syntax-sensitive dependencies.  _Transactions of the Association for Computational Linguistics_ , 4:521–535.
  * Moore (2004) Robert C. Moore. 2004.  On log-likelihood-ratios and the significance of rare events.  In _Proceedings of the 2004 Conference on Empirical Methods in Natural Language Processing_ , pages 333–340, Barcelona, Spain. Association for Computational Linguistics.
  * Nguyen and Grieve (2020) Dong Nguyen and Jack Grieve. 2020.  Do word embeddings capture spelling variation? In _Proceedings of the 28th International Conference on Computational Linguistics_ , pages 870–881, Barcelona, Spain (Online). International Committee on Computational Linguistics.
  * Radford et al. (2019) Alec Radford, Jeff Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. 2019.  Language models are unsupervised multitask learners.  _OpenAI blog_ , 1(8):9.
  * Raffel et al. (2020) Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020.  Exploring the limits of transfer learning with a unified text-to-text transformer.  _Journal of Machine Learning Research_ , 21(140):1–67.
  * Roark et al. (2020) Brian Roark, Lawrence Wolf-Sonkin, Christo Kirov, Sabrina J. Mielke, Cibu Johny, Isin Demirsahin, and Keith Hall. 2020.  Processing South Asian languages written in the Latin script: the Dakshina dataset.  In _Proceedings of the 12th Language Resources and Evaluation Conference_ , pages 2413–2423, Marseille, France. European Language Resources Association.
  * Rudinger et al. (2018) Rachel Rudinger, Jason Naradowsky, Brian Leonard, and Benjamin Van Durme. 2018.  Gender bias in coreference resolution.  In _Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers)_ , pages 8–14, New Orleans, Louisiana. Association for Computational Linguistics.
  * Schick and Schütze (2021) Timo Schick and Hinrich Schütze. 2021.  Exploiting cloze-questions for few-shot text classification and natural language inference.  In _Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume_ , pages 255–269, Online. Association for Computational Linguistics.
  * Webson and Pavlick (2022) Albert Webson and Ellie Pavlick. 2022.  Do prompt-based models really understand the meaning of their prompts? In _Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 2300–2344, Seattle, United States. Association for Computational Linguistics.
  * Webster (1828) Noah Webster. 1828.  _An American Dictionary of the English Language_.  S. Converse, New York.

##  Appendix A Prompts

Table 9 presents the 29 prompt templates that were used in this study. Table
10 gives macro-averaged conditional probabilities for T5 runs across the
different prompts, along with standard deviations to indicate how much
performance varies due to the choice of prompt.

My preferred words are <CUE> and <FILLER>.
---
My preferred words are <CUE>, <FILLER>, and tree.
She wrote the words <CUE> and <FILLER>.
She wrote the words <CUE> and <FILLER> in her notebook.
She wrote the words <CUE>, <FILLER>, and cabbage.
I wrote the words <CUE> and <FILLER>.
I wrote the words <CUE> and <FILLER> in my notebook.
I wrote the words <CUE>, <FILLER>, and cabbage.
He wrote the words <CUE> and <FILLER>.
He wrote the words <CUE> and <FILLER> in his notebook.
He wrote the words <CUE>, <FILLER>, and cabbage.
We wrote the words <CUE> and <FILLER>.
We wrote the words <CUE> and <FILLER> in our notebook.
We wrote the words <CUE>, <FILLER>, and cabbage.
Mary wrote the words <CUE> and <FILLER>.
Mary wrote the words <CUE> and <FILLER> in her notebook.
Mary wrote the words <CUE>, <FILLER>, and cabbage.
Please spell <CUE> and <FILLER>.
Please spell <CUE>, <FILLER>, and panther.
Please spell <CUE> and <FILLER> correctly.
Say <CUE> and <FILLER>.
Say <CUE>, <FILLER>, and tapestry.
Say <CUE> and <FILLER> again.
The first words on the list were <CUE> and <FILLER>.
The first words on the list were <CUE>, <FILLER>, and oligarchy.
The easiest words on the list were <CUE> and <FILLER>.
The easiest words on the list were <CUE>, <FILLER>, and oligarchy.
The hardest words on the list were <CUE> and <FILLER>.
The hardest words on the list were <CUE>, <FILLER>, and oligarchy.
Table 9: Prompts used for model evaluation. Non-adjacent versions of each prompt were created by inserting the sequence “, flower, interesting, jump, ponderous, sky, skipping, desk, small, ladder, lovely,” between the <CUE> and <FILLER> word slots. |  | T5 | T5+FT
---|---|---|---
Condition | Word 1 | Word 2 | Word 2
|  | US | UK | US | UK
Adjacent | US | 0.86 (0.01) | 0.14 (0.01) | 0.66 (0.03) | 0.34 (0.03)
| UK | 0.39 (0.06) | 0.61 (0.06) | 0.44 (0.03) | 0.56 (0.03)
Non-adjacent | US | 0.83 (0.02) | 0.17 (0.02) | 0.69 (0.02) | 0.31 (0.02)
| UK | 0.48 (0.05) | 0.52 (0.05) | 0.43 (0.04) | 0.57 (0.04)
Table 10: Conditional probability of Word 2, given a template with Word 1,
given by base T5 and T5 with additional finetuning. Each cell includes a
macro-average and standard deviation across 29 prompts.

##  Appendix B Examples of corpus mismatch

Tables 11 and 12 present examples illustrating the mixture of American and
British spelling in Wikipedia and the British National Corpus, respectively,
as discussed in Section 6.

version date |  sentence version
---|---
4 Aug. 2017 (neither vapor$\mathrm{~{}nor}$ vapour) |  An air lock is a restriction of, or complete stoppage of liquid flow caused by gas trapped in a high point of a liquid-filled pipe system.
6 Sept. 2017 (vapour replaces gas) |  An air lock is a restriction of, or complete stoppage of liquid flow caused by vapour trapped in a high point of a liquid-filled pipe system.
15 Feb. 2020 (vapor added) |  An air lock (or vapor lock) is a restriction of, or complete stoppage of liquid flow caused by vapour trapped in a high point of a liquid-filled pipe system.
Table 11: Three versions of a Wikipedia page: (1) no use of vapor or vapour in the sentence; (2) the term vapour replaces gas; and (3) the alternative name for the phenomenon "vapor lock" is introduced. Doc ID |  sentence
---|---
CPD |  ‘What this guy will do is get a demoralized sales organisation revitalised…’ said John Jones, analyst at Salomon Brothers.
CLW |  They conceptualize these differences in terms of ‘separate local labour market cultures’ (ibid., p. 104).
CBH |  It is a metaphor which attempts to create a reality of organization whereby cooperation is mobilised for fight with the outside world.
Table 12: Examples of spelling convention mismatches in the British National
Corpus, sampled from varied books and periodicals.