# Why Does Surprisal From Larger Transformer-Based Language Models Provide a
Poorer Fit to Human Reading Times?

Byung-Doh Oh
Department of Linguistics
The Ohio State University
<EMAIL_ADDRESS>
William Schuler
Department of Linguistics
The Ohio State University
<EMAIL_ADDRESS>

###### Abstract

This work presents a detailed linguistic analysis into why larger Transformer-
based pre-trained language models with more parameters and lower perplexity
nonetheless yield surprisal estimates that are less predictive of human
reading times. First, regression analyses show a strictly monotonic, positive
log-linear relationship between perplexity and fit to reading times for the
more recently released five GPT-Neo variants and eight OPT variants on two
separate datasets, replicating earlier results limited to just GPT-2 (Oh et
al., 2022). Subsequently, analysis of residual errors reveals a systematic
deviation of the larger variants, such as underpredicting reading times of
named entities and making compensatory overpredictions for reading times of
function words such as modals and conjunctions. These results suggest that the
propensity of larger Transformer-based models to ‘memorize’ sequences during
training makes their surprisal estimates diverge from humanlike expectations,
which warrants caution in using pre-trained language models to study human
language processing.

##  1 Introduction

Expectation-based theories of sentence processing (Hale, 2001; Levy, 2008)
postulate that processing difficulty is largely driven by how predictable
upcoming linguistic material is given its context. In cognitive modeling,
predictability operationalized by information-theoretic surprisal (Shannon,
1948) has been shown to be a strong predictor of behavioral and neural
measures of processing difficulty (Demberg and Keller, 2008; Smith and Levy,
2013; Hale et al., 2018; Shain et al., 2020), providing empirical support for
this position. As language models (LMs) directly define a conditional
probability distribution of a word given its context required for surprisal
calculation, they have long been evaluated as surprisal-based cognitive models
of sentence processing.

Recently, it was observed that surprisal from larger variants of the pre-
trained GPT-2 LM (Radford et al., 2019) that have more parameters and achieve
lower perplexity is less predictive of self-paced reading times and eye-gaze
durations collected during naturalistic reading (Oh et al., 2022). As the
different variants of the pre-trained GPT-2 model share the primary
architecture and training data, this offers an especially strong
counterexample to previous work that showed a negative relationship between LM
perplexity and predictive power of surprisal estimates (Goodkind and Bicknell,
2018; Hao et al., 2020; Wilcox et al., 2020). More broadly, this observation
also contradicts the recent ‘larger is better’ trend of the NLP community,
leaving open the question of why larger LMs perform worse. However, the Oh et
al. (2022) results were part of a follow-up analysis in support of a separate
claim about parser surprisal that only examined four model variants, so the
results were not tested for statistical significance or extensively explored.

The current work fills that gap by conducting a detailed linguistic analysis
of the positive relationship between LM perplexity and predictive power of
surprisal estimates. First, the robustness of the trend observed in Oh et al.
(2022) was examined by reproducing their results and additionally evaluating
surprisal estimates from different families of Transformer-based LMs (GPT-Neo,
OPT; Black et al., 2021, 2022; Wang and Komatsuzaki, 2021; Zhang et al., 2022)
on their ability to predict human reading times. Results from regression
analyses show a strictly monotonic, positive log-linear relationship between
LM perplexity and fit to reading times for the five GPT-Neo variants and eight
OPT variants on two separate datasets, which provides firm empirical support
for this trend. Subsequently, to provide an explanation for this positive
relationship, residual errors from the regression models were analyzed with a
focus on identifying linguistic phenomena that surprisal from larger variants
accounts for less accurately compared to their smaller counterparts. The
results show that regression models with surprisal predictors from GPT-2, GPT-
Neo, and OPT models generally underpredict reading times at nouns and
adjectives, and that the degree of underprediction increases along with model
size. This indicates that the poorer fit to human reading times achieved by
surprisal estimates from larger Transformer-based LMs is primarily driven by
their characteristic of assigning lower surprisal values to open-class words,
which may be accurately predicted by extensive domain knowledge gleaned from
large sets of training examples that are not available to humans. This
suggests that as Transformer-based LMs get larger, they may be problematic for
cognitive modeling because they are trained with non-human learning objectives
and different inductive biases on vast quantities of Internet text.111All code
used in this work is available at: https://github.com/byungdoh/llm_surprisal.

##  2 Related Work

In previous studies, surprisal estimates from several well-established types
of LMs, including $n$-gram models, Simple Recurrent Networks (Elman, 1991),
Gated Recurrent Unit networks (GRU; Cho et al., 2014), and Long Short-Term
Memory networks (LSTM; Hochreiter and Schmidhuber, 1997), have been compared
against behavioral measures of processing difficulty (e.g. Smith and Levy,
2013; Goodkind and Bicknell, 2018; Aurnhammer and Frank, 2019). Recently, as
Transformer-based (Vaswani et al., 2017) models have dominated many NLP tasks,
both large pre-trained and smaller ‘trained-from-scratch’ Transformer-based
LMs have also been evaluated as models of processing difficulty (Wilcox et
al., 2020; Hao et al., 2020; Merkx and Frank, 2021; Schrimpf et al., 2021).

A consistent finding that emerged out of these studies is that better LMs are
also more predictive models of comprehension difficulty, or in other words,
there is a negative correlation between LM perplexity and fit to human reading
times. Goodkind and Bicknell (2018) compared surprisal estimates from a set of
$n$-gram and LSTM LMs and observed a negative linear relationship between
perplexity and regression model fit. Wilcox et al. (2020) evaluated $n$-gram,
LSTM, Transformer, and RNNG (Dyer et al., 2016) models and replicated the
negative relationship, although they note a more exponential relationship at
certain intervals. Merkx and Frank (2021) provided further support for this
trend using GRU and Transformer models with different numbers of
layers.222Although counterexamples to this trend have been noted, they were
based on comparisons of LMs and incremental parsers that were trained on
different data (Oh et al., 2021) or evaluation on Japanese, which has a
different syntactic head-directionality than English (Kuribayashi et al.,
2021).

However, Oh et al. (2022) observed a directly contradictory relationship to
this using surprisal estimates from pre-trained GPT-2 models (Radford et al.,
2019). Using self-paced reading times from the Natural Stories Corpus (Futrell
et al., 2021) and go-past durations from the Dundee corpus (Kennedy et al.,
2003), the authors calculated the increase in log-likelihood ($\Delta$LL) to a
baseline linear-mixed effects (LME) model due to including a surprisal
predictor. Their results showed that surprisal from the largest XL variant
made the smallest contribution to regression model fit, followed by the
smaller Large, Medium, and Small variants in that order, revealing a robust
positive correlation between LM perplexity and predictive power of surprisal
estimates. The same trend was replicated when unigram surprisal was included
in the baseline, as well as when spillover effects were controlled for through
the use of continuous-time deconvolutional regression (CDR; Shain and Schuler,
2021).

Moreover, recent work has shown that surprisal from neural LMs generally tends
to underpredict human reading times of both targeted constructions and
naturalistic text. For instance, van Schijndel and Linzen (2021) and Arehalli
et al. (2022) observed that surprisal from neural LMs severely underpredicts
the magnitude of garden-path effects demonstrated by human subjects.
Additionally, Hahn et al. (2022) showed that surprisal from the pre-trained
GPT-2 model fails to accurately predict the increase in reading times at the
main verb of deeply embedded sentences. Kuribayashi et al. (2022) also
demonstrated that neural LMs yield surprisal estimates that underpredict
naturalistic reading times of English and Japanese text compared to those from
neural LMs that have a recency bias implemented as limited access to the
previous context.

##  3 Main Experiment: Predictive Power of Language Model Surprisal Estimates

In order to examine whether the positive correlation observed by Oh et al.
(2022) and others generalizes to larger Transformer-based models, surprisal
predictors from different variants of the GPT-2, GPT-Neo, and OPT LMs were
evaluated on self-paced reading times from the Natural Stories Corpus (Futrell
et al., 2021) and go-past eye-gaze durations from the Dundee Corpus (Kennedy
et al., 2003).

###  3.1 Response Data

The Natural Stories Corpus contains data from 181 subjects that read 10
naturalistic English stories that consist of a total of 10,245 tokens. The
reading times were filtered to remove observations for sentence-initial and
sentence-final words, observations from subjects who answered three or fewer
comprehension questions correctly, and observations shorter than 100 ms or
longer than 3000 ms, which resulted in a total of 770,102 observations. The
Dundee Corpus contains data from 10 subjects that read 67 newspaper editorials
that consist a total of 51,501 tokens. The durations were filtered to remove
observations for unfixated words, words following saccades longer than four
words, and words at sentence-, screen-, document-, and line-starts and ends.
This resulted in a total of 195,507 observations.

Both datasets were subsequently partitioned into an exploratory set and a
held-out set of roughly equivalent sizes.333This partitioning was conducted
based on the sum of subject ID and sentence ID, resulting in each subject-by-
sentence combination remaining intact in one partition. This partitioning
allows regression model selection (e.g. making decisions about random effects
structure) and exploratory analyses to be conducted on the exploratory set and
a single statistical significance test to be conducted on the held-out set,
thereby obviating the need for multiple trials correction. This resulted in an
exploratory set of 384,905 observations and a held-out set of 385,197
observations for the Natural Stories Corpus and an exploratory set of 98,115
observations and a held-out set of 97,392 observations for the Dundee Corpus.
All observations were log-transformed prior to model fitting.

###  3.2 Predictors

Surprisal estimates calculated from four different variants of GPT-2 models
(Radford et al., 2019) were used in Oh et al. (2022). In addition to GPT-2
surprisal, this experiment also evaluates surprisal estimates from five
variants of GPT-Neo models (Black et al., 2021, 2022; Wang and Komatsuzaki,
2021)444Technically, the two largest variants are GPT-J and GPT-NeoX models
respectively, both of which have minor architectural differences from the GPT-
Neo models. However, given that they share the same training data, they were
considered to belong to the same family as the GPT-Neo models. and eight
variants of OPT models (Zhang et al., 2022).555The largest variant of the OPT
model, which has about 175 billion parameters, was not used in this work due
to constraints in computational resources. All of these LMs are decoder-only
autoregressive Transformer-based models whose variants mainly differ in their
capacity. The model capacities of the three LM families are summarized in
Table 1.

Model | #L | #H | $d_{model}$ | Parameters
---|---|---|---|---
GPT-2 Small | 12 | 12 | 768 |  $\sim$124M
GPT-2 Medium | 24 | 16 | 1024 |  $\sim$355M
GPT-2 Large | 36 | 20 | 1280 |  $\sim$774M
GPT-2 XL | 48 | 25 | 1600 |  $\sim$1558M
GPT-Neo 125M | 12 | 12 | 768 |  $\sim$125M
GPT-Neo 1300M | 24 | 16 | 2048 |  $\sim$1300M
GPT-Neo 2700M | 32 | 20 | 2560 |  $\sim$2700M
GPT-J 6B | 28 | 16 | 4096 |  $\sim$6000M
GPT-NeoX 20B | 44 | 64 | 6144 |  $\sim$20000M
OPT 125M | 12 | 12 | 768 |  $\sim$125M
OPT 350M | 24 | 16 | 1024 |  $\sim$350M
OPT 1.3B | 24 | 32 | 2048 |  $\sim$1300M
OPT 2.7B | 32 | 32 | 2560 |  $\sim$2700M
OPT 6.7B | 32 | 32 | 4096 |  $\sim$6700M
OPT 13B | 40 | 40 | 5120 |  $\sim$13000M
OPT 30B | 48 | 56 | 7168 |  $\sim$30000M
OPT 66B | 64 | 72 | 9216 |  $\sim$66000M
Table 1: Model capacities of LM families whose surprisal estimates were
examined in this work. #L, #H, and $d_{model}$ refers to number of layers,
number of attention heads, and embedding size respectively.

Each story of the Natural Stories Corpus and each article of the Dundee Corpus
was tokenized according to the three models’ respective byte-pair encoding
(BPE; Sennrich et al., 2016) tokenizer and was provided to each model variant
to calculate surprisal estimates. In cases where each story or article did not
fit into a single context window for the LMs, the second half of the previous
context window served as the first half of a new context window to calculate
surprisal estimates for the remaining tokens. In practice, most stories and
articles fit completely within two context windows for the GPT-2 models that
have a context size of 1,024 tokens, and within one context window for the
GPT-Neo and OPT models that have a context size of 2,048 tokens. Additionally,
when a single word $w_{t}$ was tokenized into multiple subword tokens,
negative log probabilities of subword tokens corresponding to $w_{t}$ were
added together to calculate $\mathsf{S}(w_{t})=-\log\mathsf{P}(w_{t}\mid
w_{1..t-1})$.

###  3.3 Regression Modeling

Subsequently, following the methods of Oh et al. (2022), a ‘baseline’ LME
model that contains baseline predictors capturing low-level cognitive
processing and seventeen ‘full’ LME models that contain the baseline
predictors and each LM surprisal predictor were fit to the exploratory set of
self-paced reading times and go-past durations using lme4 (Bates et al.,
2015). The baseline predictors include word length measured in characters and
index of word position within each sentence (both self-paced reading and eye-
tracking), as well as saccade length and whether or not the previous word was
fixated (eye-tracking only).

All predictors were centered and scaled prior to model fitting, and the LME
models included by-subject random slopes for all fixed effects as well as
random intercepts for each subject and each word type. Additionally, for self-
paced reading times collected from 181 subjects, a random intercept for each
subject-sentence interaction was included. For eye-gaze durations collected
from a much smaller number of 10 subjects, a random intercept for each
sentence was included.

After the regression models were fit, the $\Delta$LL values were first
calculated for each regression model by subtracting the log-likelihood of the
baseline model from that of a full regression model. Moreover, to examine the
trend between LM perplexity and predictive power of surprisal estimates, the
perplexity of each LM variant was calcuated on the two corpora.

Figure 1: Perplexity measures from each LM variant, and improvements in
regression model log-likelihood from including each surprisal estimate on the
exploratory set of Natural Stories (top) and Dundee data (bottom). Dotted
lines indicate the least-squares regression line for each LM family.

###  3.4 Results

The results in Figure 1 show that surprisal from the smallest variant (i.e.
GPT-2 Small, GPT-Neo 125M, and OPT 125M) made the biggest contribution to
regression model fit on both self-paced reading times and eye-gaze durations
for the three LM families. More notably, surprisal estimates from larger LM
variants within each family yielded strictly poorer fits to reading times,
robustly replicating the trend observed by Oh et al. (2022). Interestingly,
the three LM families also seem to demonstrate a strong log-linear
relationship between perplexity and $\Delta$LL, as can be seen by the least-
squares regression lines. All regression lines had a slope significantly
greater than 0 at $p<0.05$ level according to a one-tailed $t$-test, with the
exception of the regression line for GPT-2 on Natural Stories ($p=0.07$). This
trend is highly significant overall by a binomial test (five results with
$p<0.05$ out of six trials), and directly contradicts the findings of recent
studies that report a negative correlation between LM perplexity and
predictive power of surprisal estimates.

Additionally, comparison of the GPT-2 models and OPT models of similar model
capacities (i.e. Small-125M, Medium-350M) shows that the OPT models generally
both achieve lower perplexity and yield surprisal estimates that are more
predictive of human reading times. Given the high similarity in model
architecture between the two LMs, this trend seems to be due to the difference
in the training data that were used. The most notable difference between the
two training datasets is in their size, with the training set for GPT-2
estimated to be about 15B tokens and that for OPT estimated to be about 180B
tokens (Thompson, 2022). However, the GPT-Neo models trained on about 247B
tokens show no improvement over the OPT models, yielding a mixed picture.
These results suggest that beyond a certain level, the quantity of training
data may play a secondary role to the number of model parameters in capturing
humanlike expectations.

##  4 Post-hoc Analysis: Linguistic Phenomena Underlying the Trend

In order to provide an explanation for the trend observed in Section 3, the
residual errors from the regression models were analyzed to identify data
points that surprisal from larger LM variants accounted for less accurately
compared to their smaller counterparts. For this analysis, a special emphasis
was placed on identifying subsets of data points where surprisal from larger
LM variants deviated more drastically from humanlike processing difficulty.

###  4.1 Calculation of Residual Errors

The seventeen LME models that contain each of the LM surprisal predictors
described in Section 3.3 were used to generate predictions for all data points
in the exploratory set of both self-paced reading times and go-past
durations.666The post-hoc analysis focused on the exploratory set, as the
held-out set is reserved for statistical significance testing. Subsequently,
the predictions were subtracted from the target values to calculate the
residual errors for each of the seventeen regression models.

Figure 2: Perplexity measures from each LM variant, and mean squared errors of
regression models that include each surprisal estimate on the exploratory set
of Natural Stories (top) and Dundee data (bottom). Note that the larger values
of MSE correspond to smaller values of log-likelihood in Figure 1.

However, a preliminary analysis of the LME models fitted to the Dundee Corpus
revealed a discrepancy between model likelihood and mean squared error (MSE),
where the regression models with higher likelihoods achieved similar MSEs to
those with lower likelihoods. This is because the lme4 package (Bates et al.,
2015) minimizes the penalized residual sum-of-squares, which includes a
Euclidean norm penalty on the spherical component of the random effects
variables. In other words, an LME model can achieve higher likelihood than
another if it can achieve similar MSE using less expressive random effects
variables that have lower variance.

An inspection of the fitted random effects variables revealed that the by-word
intercept was mostly responsible for the discrepancy between likelihood and
MSE for the LME models fitted to the Dundee Corpus. More specifically, the LME
models with surprisal estimates from larger LM variants had systematically
higher variance for the by-word intercept, which allowed them to achieve
similar MSEs at the cost of an increased penalty for the random effects
variables. In order to control for this confound and bring model likelihood
and MSE closer together, the seventeen LME models were fitted again to both
corpora with the by-word random intercepts removed. Since the goal of this
analysis was to identify data points that are responsible for the positive
correlation between LM perplexity and fit to human reading times, it was
thought that removing the by-word random intercepts would also yield a clearer
picture with regard to words on which the surprisal estimates from larger LMs
fall especially short.

The MSEs plotted in Figure 2, which generally replicate the inverse trend of
$\Delta$LLs in Figure 1, show that the removal of by-word random intercepts
brought model likelihoods and MSEs closer. The residual errors from these
newly fitted regression models were subsequently analyzed.

###  4.2 Annotation of Data Points

In order to guide the identification of linguistic phenomena underlying the
trend observed in Section 3.4, each data point in both corpora was associated
with various word- and sentence-level properties that are thought to influence
real-time processing. These properties were derived from the manually
annotated syntactic tree structures of both corpora from Shain et al. (2018).

Word-level properties reflect characteristics of the word that generally hold
regardless of the surrounding context:

  * •

Part-of-speech: the syntactic category of each word from a generalized
categorial grammar annotation scheme (Nguyen et al., 2012; Shain et al.,
2018). As these categories are defined in terms of primitive types (e.g. verbs
and nouns) and type-combining operators (e.g. unsatisfied preceding and
succeeding arguments), they make more fine-grained distinctions in terms of
linguistic subcategorization.

  * •

Named entities: a binary variable for whether or not the word is part of a
proper name. Since words at the beginning of sentences were excluded from
regression modeling, capitalization reliably identified such named
entities.777Words like the pronoun I and names of fictional characters that
appeared in the Natural Stories Corpus were manually excluded afterwards.

Sentence-level properties capture the syntactic structure of sentences, either
in terms of dependencies or hierarchical phrases:

  * •

Dependency Locality Theory (DLT; Gibson, 2000) cost: DLT posits that the
construction of backward-looking dependencies between words (e.g. between a
verb and its subject) incurs an ‘integration’ cost driven by memory retrieval
operations. This cost is thought to be proportional to the length of the
dependency in terms of the number of intervening discourse referents, which
are operationalized as any noun or finite verb in this work.

  * •

Left-corner parsing (Johnson-Laird, 1983): A left-corner parser incrementally
derives phrasal structures from a series of lexical match and grammatical
match decisions at every word.888See e.g. Oh et al. (2022) for a more detailed
definition of left-corner parsing models. These two decisions allow center-
embedded constituents to be distinguished from non-embedded constituents.
Additionally, the grammatical decision results in expectations about the
upcoming syntactic category, which allows words before complete constituents
(e.g. words before sentential clauses) to be identified.

This annotation allowed the data points in each corpus to be subsetted, which
subsequently helped identify where surprisal from the larger LM variants
deviated further from humanlike processing.

###  4.3 Iterative Slope-Based Analysis of Residual Errors

Subsequently, based on the properties annotated in Section 4.2, subsets of
data points that strongly drive the trend in Figure 2 were identified. To this
end, the linear relationship between log perplexity and MSEs was used; subsets
of data points that drive the general trend should show larger differences in
MSE between regression models, or in other words, have negative slopes that
are steeper than the corpus-level slope.

Based on this idea, for every corpus-LM combination (i.e. {Natural Stories,
Dundee} $\times$ {GPT-2, GPT-Neo, OPT}), a least-squares regression line was
fitted between corpus-level log perplexity and MSEs of each subset defined by
the properties outlined in Section 4.2. Subsequently, the subset with the
steepest negative slope was identified. After excluding the identified subset,
the above procedure was repeated to identify a new subset that showed the next
strongest effect. For this analysis, only subsets that contained more than 1%
of the data points in each corpus were considered at each iteration.999This
criterion amounts to $>$3,849 data points for Natural Stories and $>$981 data
points for Dundee at the first iteration. Although this may seem like a
lenient criterion, this was necessary to examine phenomena that lie at the
long tail of the Zipfian distribution of word frequencies.

Figure 3: Corpus-level perplexity measures from each GPT-2, GPT-Neo, and OPT
model variant (top, middle, and bottom rows respectively), and mean squared
errors of regression models that include each surprisal estimate on the top
five subsets (columns ordered from left to right) of Natural Stories self-
paced reading data (top panel) and Dundee eye-tracking data (bottom panel).
The ordered labels represent LM variants of different sizes, with ‘1’
representing the smallest variant. ADJ: adjective, N: noun, NP: noun phrase,
REL: relativizer, S: sentential clause.

Figure 4: Average surprisal from each GPT-2, GPT-Neo, and OPT model variant,
and sum of squared errors of regression models that include each surprisal
estimate on the top five subsets of Natural Stories self-paced reading data
and Dundee eye-tracking data. The top and bottom subplots of each row
represent values from underpredicted and overpredicted data points
respectively.

Additionally, once the subsets of interest were identified, the data points in
each subset were further separated according to whether the regression model
underpredicted or overpredicted the target reading times. In order to identify
whether the trend of MSEs is driven primarily by systematic underprediction or
overprediction of reading times, the average surprisal from each LM variant
and the sum of squared errors (SSE) were calculated for each subset. SSEs
instead of MSEs were analyzed because different regression models had
different numbers of underpredicted vs. overpredicted data points, and because
points close to 0 can distort the MSEs and obscure the overall trend of
mispredictions.

###  4.4 Results

The results in Figure 3 show that on each corpus, similar subsets were
identified as driving the trend of MSEs across different LM families. On the
Natural Stories Corpus, these subsets were primarily determined by the word’s
syntactic category, such as named entity nouns, nouns before relativizers,
attributive and predicative adjectives, and modals. The top subsets of the
Dundee Corpus were similarly determined by syntactic category, such as named
entity nouns, predicative and passivized adjectives, and single-word noun
phrases (e.g. pronouns). Subsets defined by the syntactic structure of
sentences were less commonly identified from the Natural Stories Corpus, with
ends of center-embedded constituents spanning four or more words and words
with high DLT costs emerging. From the Dundee Corpus, ends of center-embedded
constituents, ends of first conjunct constituents (both overall and noun
phrases specifically), and beginnings of adjectival noun phrases (e.g. family
in a family size pack) were identified. Additionally, words preceding a
sentential clause were identified, which corresponded to conjunctions and ends
of adjuncts. On most of these subsets, the MSEs of each regression model were
higher than those on the entire corpus, which indicates that the misprediction
of reading times that pre-trained LM surprisal already has difficulty modeling
is exacerbated as the models get larger. Subsets such as modals of Natural
Stories and first conjunct NP endings of Dundee are counterexamples to this
general trend.

The average surprisal values101010Since perplexity is equivalent to
exponentiated average surprisal, the average surprisal values for each subset
are roughly comparable to LM perplexity of e.g. Figure 2. However, caution is
warranted as these values are calculated over data points of reading times
instead of tokens. and SSEs from underpredicted and overpredicted data points
in Figure 4 shed more light on the direction and magnitude of mispredictions
from each regression model. For example, on the subset of named entities,
which emerged as the top two subsets across all corpus-by-LM combinations, the
larger LM variants show systematically higher SSEs due to underprediction.
This strong discrepancy highlights a mismatch between human sentence
processing and language modeling; named entity terms (e.g. Elvis Presley) have
been shown to incur increased processing times compared to their common noun
counterparts (e.g. a singer) due to various semantic associations that are
retrieved (Proverbio et al., 2001; Wang et al., 2013). In contrast, for
language models, named entity terms that typically consist of multiple tokens
have high mutual information, making it easy for them to accurately predict
subsequent tokens given the first (e.g. Presley given Elvis), resulting in
especially lower surprisal estimates for larger LM variants.

Similarly, across the two corpora and three LM families, the trend of MSEs for
other nouns as well as adjectives appears to be consistently driven by more
severe underpredictions from regression models containing surprisal estimates
from larger LM variants. On these subsets, the difference in average surprisal
values between the smallest and largest LM variants was typically above 2
bits, which is larger than the difference in log perplexity (i.e. corpus-level
average surprisal, Figure 2) between these variants. This indicates that these
subsets represent words that the larger LM variants predict especially
accurately, which results in low surprisal estimates that deviate from human
reading times.

In contrast, the subset of modals on the Natural Stories Corpus identified for
the GPT-2 and GPT-Neo models shows a completely opposite trend in which more
severe overpredictions drive the overall trend of MSEs. This seems to be more
due to the difference in the estimated regression coefficients rather than the
difference in the LM surprisal estimates themselves. The average surprisal
values on this subset show that their difference between the smallest and
largest variants is less than 1 bit, which indicates that the LM variants are
making more similar predictions about modals. However, since surprisal
predictors from larger LM variants are generally smaller in magnitude, the
regression models assign them higher coefficients in order to predict reading
times, resulting in a systematic overprediction given surprisal predictors of
similar values. This also explains the trend observed for words preceding a
sentential clause on the Dundee Corpus, which mainly consisted of
conjunctions.

Finally, while they were less common, subsets based on syntactic complexity
were also identified as driving the differential fit to reading times. On the
Natural Stories Corpus, a systematic underprediction of regression models with
OPT surprisal was observed on words with a DLT cost of greater than or equal
to three. These words mainly consist of nouns and finite verbs that complete
long-distance dependencies. While finite verbs in general were not identified
as subsets that showed a strong effect, it is likely that the increased
reading times caused by the construction of long-distance dependencies made
the underpredictions more salient. Ends of center-embedded constituents of
length greater than or equal to four were also identified, which typically
corresponded to nouns and adjectives. On the Natural Stories Corpus, the trend
of more severe underpredictions driving the effect is consistent with other
noun and adjective subsets. However, on the Dundee Corpus, overpredictions
seem to be responsible for the overall trend in this subset, which may hint at
subtle differences in how syntactic complexity is manifested in self-paced
reading times and eye-gaze durations.

Taken together, these results indicate that the poorer fit to human reading
times achieved by surprisal estimates from larger Transformer-based language
models is primarily driven by their characteristic of assigning lower
surprisal values to open-class words like nouns and adjectives, which may be
accurately predicted by extensive domain knowledge gleaned from large sets of
training examples that are not available to humans. In other words, the extra
parameters of the larger LM variants may be improving predictions of such
words in a way that is beyond human ability.

##  5 Discussion and Conclusion

This work presents results using multiple large pre-trained LMs showing that
larger variants with more parameters and better next-word prediction
performance (i.e. lower perplexity) nonetheless yield surprisal estimates that
are less predictive of human reading times (i.e. smaller contribution to
regression model fit), corroborating and expanding upon earlier results based
on the GPT-2 LM (Oh et al., 2022).

First, in order to examine the generalizability of this trend, surprisal
estimates from five variants of the GPT-Neo LM and eight variants of the OPT
LM were evaluated in terms of their ability to predict self-paced reading
times and eye-gaze durations. The regression analysis revealed a strictly
monotonic, positive log-linear relationship between perplexity and fit to
reading times for five GPT-Neo variants and eight OPT variants, providing
robust empirical support for this trend. Additionally, the different data used
to train each LM family seem to influence the quality of surprisal estimates,
although more pre-training data did not necessarily result in surprisal
estimates that are more predictive of reading times.

Subsequently, to identify the data points that are responsible for the
positive relationship, a post-hoc analysis of the residual errors from each
regression model was conducted. The results showed that the difference in MSEs
between regression models containing surprisal predictors from different LM
variants was especially large on nouns and adjectives, such as named entity
terms and predicative adjectives. A further inspection of their predictions
showed that the trend of MSEs on these words was driven mainly by
underpredictions of reading time delays, which were exacerbated as the larger
LM variants predicted the words more accurately and assigned lower surprisal
values. This tendency also led to higher regression coefficients for surprisal
estimates from larger LM variants, which resulted in a systematic
overprediction at function words like conjunctions and modals that had similar
surprisal estimates across LM variants.

The ‘more and more superhuman’ predictions of larger LM variants observed in
this work are consistent with findings from recent analyses of Transformer-
based LMs. For example, a mathematical analysis of Transformers (Elhage et
al., 2021) showed that a layer of self-attention essentially functions as a
lookup table that keeps track of bigram statistics of the input data. Given
this observation, it may be the case that the larger LM variants with more
attention heads at their disposal have the capability to learn stronger local
associations between tokens. This possibility was empirically supported from
the perspective of memorization by Carlini et al. (2022), who found that
larger variants of the GPT-Neo model returned more sequences verbatim from the
pre-training data during greedy decoding. This behavior may explain why nouns
and adjectives showed the strongest effect in the post-hoc analysis; since
adjectives and nouns typically have higher type-frequency than verbs or
function words, it may be the case that nouns and adjectives that are rarely
seen during training are predicted much more faithfully by the larger LM
variants with higher model capacity. Additionally, this also suggests that as
these pre-trained LMs continue to get bigger, they will continue to degrade as
models of humanlike language comprehension.

The ‘trained-from-scratch’ LMs studied in earlier psycholinguistic modeling
work (e.g. Goodkind and Bicknell, 2018; Wilcox et al., 2020) observe a
negative relationship between perplexity and fit to reading times. However,
based on regression results following the same protocols as Section 3,
surprisal estimates from LMs trained in Wilcox et al. (2020) generally seem to
be less predictive of human reading times than those from pre-trained LMs
examined in this work. Given the especially large discrepancy in model size
between newly-trained LMs and pre-trained LMs, it may be the case that they
capture two distinct regimes in terms of the relationship between LM
performance and predictive power of surprisal estimates. While the results of
the current study clearly show that surprisal estimates from smaller pre-
trained LM variants are more predictive of reading times, it remains to be
seen how much smaller LMs can become before the predictive power of surprisal
estimates starts to decrease. With recently increasing effort in developing
efficient NLP models, future work could explore the extent to which e.g.
knowledge distillation techniques (Sanh et al., 2019) can result in LMs that
are more predictive of humanlike processing difficulty.

Additionally, the importance of being ‘adequately surprised’ at nouns like
named entity terms that was identified in the current study may also explain
similar recent counterexamples to the trend observed between model perplexity
and fit to reading times (Oh et al., 2021; Kuribayashi et al., 2021). Oh et
al. (2021) showed that incorporating a character model to estimate word
generation probabilities within an incremental left-corner parser resulted in
more predictive surprisal estimates compared to those from a baseline parser
that treats words as symbols, although at a cost of higher test perplexity.
The character model may be effectively assigning higher surprisal values to
these rare words, thereby achieving better fit to human reading times. The
reading times of Japanese text studied in Kuribayashi et al. (2021) were
measured in larger units (i.e. bunsetsu; roughly equivalent to phrases) than
typical English words. Therefore, the Japanese LMs analyzed in that study are
likely to have been trained on and have made predictions on text that has been
tokenized into ‘sub-bunsetsu’ tokens, which may have made a different picture
emerge from results based on purely word-based LMs of earlier work.

In general, the tendency of pre-trained LM surprisal to underpredict reading
times observed in this work is consistent with recent empirical shortcomings
of neural LM surprisal. For example, van Schijndel and Linzen (2021) and
Arehalli et al. (2022) found that surprisal from neural LMs severely
underpredicts the magnitude of garden-path effects demonstrated by human
subjects. Similarly, Hahn et al. (2022) showed that surprisal from GPT-2 fails
to accurately predict the increase in reading times at the main verb of deeply
embedded sentences. Kuribayashi et al. (2022) also demonstrated that
implementing a recency bias by deterministically truncating the context window
of neural LMs leads to surprisal estimates that alleviate the underpredictions
of full neural LM surprisal on naturalistic reading times of English and
Japanese text. Taken together, these results suggest that neural LMs do not
make abstract, linguistic generalizations like people do.

Moreover, there are also efforts to evaluate other memory- and attention-based
predictors calculated from Transformer-based LM representations on their
ability to predict human behavior. For instance, Ryu and Lewis (2021) drew
connections between the self-attention mechanism of Transformers and cue-based
retrieval models of sentence comprehension (e.g. Lewis et al., 2006). Their
proposed attention entropy, which quantifies the diffuseness of attention
weights over previous tokens, was found to show profiles that are consistent
with similarity-based interference observed during the processing of subject-
verb agreement. Oh and Schuler (2022) expanded upon this idea and showed that
the entropy of attention weights at a given timestep as well as the shift in
attention weights across consecutive timesteps are robust predictors of
naturalistic reading times over GPT-2 surprisal. Hollenstein and Beinborn
(2021) calculated the norm of the gradient of each input token on two eye-
tracking corpora using BERT (Devlin et al., 2019) as a metric of saliency,
which showed higher correlations to fixation durations compared to raw
attention weights.

Finally, it is becoming more common in psycholinguistic modeling to use
surprisal from pre-trained LMs as a baseline predictor to study various
effects in naturalistic sentence processing (e.g. Ryu and Lewis, 2022; Clark
and Schuler, 2022). The broader implication of the current study is that
researchers should not select the largest pre-trained LM available based on
the widely-held ‘larger is better’ assumption of the NLP community. As a
general practice, surprisal estimates from smaller pre-trained LM variants
should be incorporated to form a more rigorous baseline, which will guard
against drawing unwarranted scientific conclusions.

## Acknowledgments

We thank TACL action editor Marco Baroni and the reviewers for their helpful
comments. This work was supported by the National Science Foundation grant
#1816891. All views expressed are those of the authors and do not necessarily
reflect the views of the National Science Foundation.

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