txt/2204.03592.txt

Testing the limits of natural language models for
predicting human language judgments
Tal Golan1,2∗†, Matthew Siegelman3∗,
Nikolaus Kriegeskorte1,3,4,5, Christopher Baldassano3
1Zuckerman Mind Brain Behavior Institute, Columbia University, New York, NY , USA
2Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Be’er-Sheva, Israel
3Department of Psychology, Columbia University, New York, NY , USA
4Department of Neuroscience, Columbia University, New York, NY , USA
5Department of Electrical Engineering, Columbia University, New York, NY , USA
∗The first two authors contributed equally to this work.
†To whom correspondence should be addressed; E-mail: [email protected]
Neural network language models appear to be increasingly aligned with how hu-
mans process and generate language, but identifying their weaknesses through ad-
versarial examples is challenging due to the discrete nature of language and the
complexity of human language perception. We bypass these limitations by turning
the models against each other. We generate controversial sentence pairs for which
two language models disagree about which sentence is more likely to occur. Con-
sidering nine language models (including n-gram, recurrent neural networks, and
transformers), we created hundreds of controversial sentence pairs through syn-
thetic optimization or by selecting sentences from a corpus. Controversial sentence
pairs proved highly effective at revealing model failures and identifying models that
aligned most closely with human judgments of which sentence is more likely. The
most human-consistent model tested was GPT-2, although experiments also revealed
significant shortcomings of its alignment with human perception.
Keywords— Language Models, Human Acceptability Judgments, Controversial Stimuli, Adversarial Attacks
in NLP
1 Introduction
Neural network language models are not only key tools in natural language processing (NLP) but are also draw-
ing an increasing scientific interest as potential models of human language-processing. Ranging from recurrent
neural networks [1, 2] to transformers [3–7], each of these language models (explicitly or implicitly) defines
a probability distribution over strings of words, predicting which sequences are likely to occur in natural lan-
guage. There is substantial evidence from measures such as reading times [8], functional MRI [9], scalp EEG
1arXiv:2204.03592v3  [cs.CL]  12 Sep 2023[10], and intracranial ECoG [11] that humans are sensitive to the relative probabilities of words and sentences as
captured by language models, even among sentences that are grammatically correct and semantically meaning-
ful. Furthermore, model-derived sentence probabilities can also predict human graded acceptability judgments
[12, 13]. These successes, however, have not yet addressed two central questions of interest: (1) Which of the
models is best-aligned with human language processing? (2) How close is the best-aligned model to the goal
of fully capturing human judgments?
A predominant approach for evaluating language models is to use a set of standardized benchmarks such
as those in the General Language Understanding Evaluation (GLUE) [14], or its successor, SuperGLUE [15].
Though instrumental in evaluating the utility of language models for downstream NLP tasks, these benchmarks
prove insufficient for comparing such models as candidate explanations of human language-processing. Many
components of these benchmarks do not aim to measure human alignment but rather the usefulness of the mod-
els’ language representation when tuned to a specific downstream task. Some benchmarks challenge language
models more directly by comparing the probabilities they assign to grammatical and ungrammatical sentences
(e.g., BLiMP [16]). However, since such benchmarks are driven by theoretical linguistic considerations, they
might fail to detect novel, unexpected ways in which language models may diverge from human language un-
derstanding. Lastly, an additional practical concern is that the rapid pace of NLP research has led to quick
saturation of these kinds of static benchmarks, making it difficult to distinguish between models [17].
One proposed solution to these issues is the use of dynamic human-in-the-loop benchmarks in which peo-
ple actively stress-test models with an evolving set of tests. However, this approach faces the major obstacle
that “finding interesting examples is rapidly becoming a less trivial task” [17]. We propose to complement
human-curated benchmarks with model-driven evaluation. Guided by model predictions rather than experi-
menter intuitions, we would like to identify particularly informative test sentences, where different models
make divergent predictions. This approach of running experiments mathematically optimized to “put in jeop-
ardy” particular models belongs to a long-standing scientific philosophy of design optimization [18]. We can
find these critical sentences in large corpora of natural language or synthesize novel test sentences that reveal
how different models generalize beyond their training distributions.
We propose here a systematic, model-driven approach for comparing language models in terms of their
consistency with human judgments. We generate controversial sentence pairs : pairs of sentences designed
such that two language models strongly disagree about which sentence is more likely to occur. In each of these
sentence pairs, one model assigns a higher probability to the first sentence than the second sentence, while the
other model prefers the second sentence to the first. We then collect human judgments of which sentence in
each pair is more probable to settle this dispute between the two models.
This approach builds on previous work on controversial images for models of visual classification [19].
That work relied on absolute judgments of a single stimulus, which are appropriate for classification responses.
However, asking the participants to rate each sentence’s probability on an absolute scale is complicated by
between-trial context effects common in magnitude estimation tasks [20–22], which have been shown to impact
judgments like acceptability [23]. A binary forced-choice behavioral task presenting the participants with a
choice between two sentences in each trial, the approach we used here, minimizes the role of between-trial
context effects by setting an explicit local context within each trial. Such an approach has been previously
used for measuring sentence acceptability [24] and provides substantially more statistical power compared to
designs in which acceptability ratings are provided for single sentences [25].
Our experiments demonstrate that (1) it is possible to procedurally generate controversial sentence pairs for
all common classes of language models, either by selecting pairs of sentences from a corpus or by iteratively
modifying natural sentences to yield controversial predictions; (2) the resulting controversial sentence pairs
enable efficient model comparison between models that otherwise are seemingly equivalent in their human
2consistency; and (3) all current NLP model classes incorrectly assign high probability to some non-natural
sentences (one can modify a natural sentence such that its model probability does not decrease but human
observers reject the sentence as unnatural). This framework for model comparison and model testing can give
us new insight into the classes of models that best align with human language perception and suggest directions
for future model development.
2 Results
We acquired judgments from 100 native English speakers tested online. In each experimental trial, the partic-
ipants were asked to judge which of two sentences they would be “more likely to encounter in the world, as
either speech or written text”, and provided a rating of their confidence in their answer on a 3-point scale (see
Extended Data Fig. 1 for a trial example). The experiment was designed to compare nine different language
models (Supplementary Section 6.1): probability models based on corpus frequencies of 2-word and 3-word
sequences (2-grams and 3-grams) and a range of neural network models comprising a recurrent neural network
(RNN), a long short-term memory network (LSTM), and five transformer models (BERT, RoBERTa, XLM,
ELECTRA, and GPT-2).
2.1 Efficient model comparison using natural controversial pairs
As a baseline, we randomly sampled and paired 8-word sentences from a corpus of Reddit comments. How-
ever, as shown in Fig. 1a, these sentences fail to uncover meaningful differences between the models. For
each sentence pair, all models tend to prefer the same sentence (Extended Data Fig. 2), and therefore perform
similarly in predicting human preference ratings (see Supplementary Section 7.1).
Instead, we can use an optimization procedure (Supplementary Section 6.2) to search for controversial
sentence pairs, in which one language model assigns a high probability (above the median probability for
natural sentences) only to sentence 1 and a second language model assigns a high probability only to sentence
2; see examples in Table 1. Measuring each model’s accuracy in predicting human choices for sentence pairs
in which it was one of the two targeted models indicated many significant differences in terms of model-
human alignment (Fig. 1b), with GPT-2 and RoBERTa showing the best human consistency and 2-gram the
worst. We can also compare each model pair separately (using only the stimuli targeting that model pair),
yielding a similar pattern of pairwise dominance (Extended Data Fig. 3a). All models except GPT-2, RoBERTa,
and ELECTRA performed significantly below our lower bound on the noise ceiling (the accuracy obtained
by predicting each participant’s responses from the other participants’ responses), indicating a misalignment
between these models’ predictions and human judgments which was only revealed when using controversial
sentence pairs.
30 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
0 50 100
GPT-2
p(sentence) percentile020406080100RoBERTa
p(sentence) percentile
0 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
0 50 100
GPT-2
p(sentence) percentile020406080100RoBERTa
p(sentence) percentile
aRandomly sampled natural-sentence pairs
bControversial natural-sentence pairsFigure 1: Model comparison using natural sentences. (a) (Left) Percentile-transformed sentence probabili-
ties for GPT-2 and RoBERTa (defined relative to all sentences used in the experiment) for randomly-sampled
pairs of natural sentences. Each pair of connected dots depicts one sentence pair. The two models are highly
congruent in their rankings of sentences within a pair (lines have upward slope). (Right) Accuracy of model
predictions of human choices, measured as the proportion of trials in which the same sentence was preferred
by both the model and the human participant. Each dot depicts the prediction accuracy of one candidate model
averaged across a group of 10 participants presented with a unique set of trials. The colored bars depict grand-
averages across all 100 participants. The gray bar is the noise ceiling whose left and right edges are lower
and upper bounds on the grand-average performance an ideal model would achieve (based on the consistency
across human subjects). There were no significant differences in model performance on the randomly sam-
pled natural sentences. (b)(Left) Controversial natural-sentence pairs were selected such that the models’
sentence probability ranks were incongruent (lines have downward slope). (Right) Controversial sentence pairs
enable efficient model comparison, revealing that BERT, XLM, LSTM, RNN and the n-gram models perform
significantly below the noise ceiling (asterisks indicate significance—two-sided Wilcoxon signed-rank test,
controlling the false discovery rate for nine comparisons at q<.05). On the right of the plot, each closed circle
indicates a model significantly dominating alternative models indicated by open circles (two-sided Wilcoxon
signed-rank test, controlling the false discovery rate for all 36 model pairs at q<.05). GPT-2 outperforms all
models except RoBERTA at predicting human judgments.
4sentence log probability (model 1) log probability (model 2) # human choices
n1: Rust is generally caused by salt and sand. logp(n1|GPT-2 ) =−50.72 log p(n1|ELECTRA ) =−38.54 10
n2: Where is Vernon Roche when you need him. logp(n2|GPT-2 ) =−32.26 logp(n2|ELECTRA ) =−58.26 0
n1: Excellent draw and an overall great smoking experience. logp(n1|RoBERTa ) =−67.78 log p(n1|GPT-2 ) =−36.76 10
n2: I should be higher and tied to inflation. logp(n2|RoBERTa ) =−54.61 logp(n2|GPT-2 ) =−50.31 0
n1: You may try and ask on their forum. logp(n1|ELECTRA ) =−51.44 log p(n1|LSTM ) =−44.24 10
n2: I love how they look like octopus tentacles. logp(n2|ELECTRA ) =−35.51 logp(n2|LSTM ) =−66.66 0
n1: Grow up and quit whining about minor inconveniences. logp(n1|BERT ) =−82.74 log p(n1|GPT-2 ) =−35.66 10
n2: The extra a is the correct Sanskrit pronunciation. logp(n2|BERT ) =−51.06 logp(n2|GPT-2 ) =−51.10 0
n1: I like my password manager for this reason. logp(n1|XLM ) =−68.93 log p(n1|RoBERTa ) =−49.61 10
n2: Kind of like clan of the cave bear. logp(n2|XLM ) =−44.24 logp(n2|RoBERTa ) =−67.00 0
n1: We have raised a Generation of Computer geeks. logp(n1|LSTM ) =−66.41 log p(n1|ELECTRA ) =−36.57 10
n2: I mean when the refs are being sketchy. logp(n2|LSTM ) =−42.04 logp(n2|ELECTRA ) =−52.28 0
n1: This is getting ridiculous and ruining the hobby. logp(n1|RNN) =−100.65 log p(n1|LSTM ) =−43.50 10
n2: I think the boys and invincible are better. logp(n2|RNN) =−45.16 logp(n2|LSTM ) =−59.00 0
n1: Then attach them with the supplied wood screws. logp(n1|3-gram ) =−119.09 log p(n1|GPT-2 ) =−34.84 10
n2: Sounds like you were used both a dog. logp(n2|3-gram ) =−92.07 logp(n2|GPT-2 ) =−52.84 0
n1: Cream cheese with ham and onions on crackers. logp(n1|2-gram ) =−131.99 log p(n1|RoBERTa ) =−54.62 10
n2: I may have to parallel process that drinking. logp(n2|2-gram ) =−109.46 logp(n2|RoBERTa ) =−70.69 0
Table 1: Examples of controversial natural-sentence pairs that maximally contributed to each model’s
prediction error. For each model (double row, “model 1”), the table shows results for two sentences on which
the model failed severely. In each case, the failing model 1 prefers sentence n2(higher log probability bolded),
while the model it was pitted against (“model 2”) and all 10 human subjects presented with that sentence pair
prefer sentence n1. (When more than one sentence pair induced an equal maximal error in a model, the example
included in the table was chosen at random.)
2.2 Greater model disentanglement with synthetic sentence pairs
Selecting controversial natural-sentence pairs may provide greater power than randomly sampling natural-
sentence pairs, but this search procedure considers a very limited part of the space of possible sentence pairs.
Instead, we can iteratively replace words in a natural sentence to drive different models to make opposing
predictions, forming synthetic controversial sentences that may lay outside any natural language corpora, as il-
lustrated in Fig. 2 (see Methods, “Generating synthetic controversial sentence pairs” for full details). Examples
of controversial synthetic-sentence pairs that maximally contributed to the models’ prediction error appear in
Table 2.
We evaluated how well each model predicted the human sentence choices in all of the controversial synthetic-
sentence pairs in which the model was one of the two models targeted (Fig. 3a). This evaluation of model-
human alignment resulted in an even greater separation between the models’ prediction accuracies than was
obtained when using controversial natural-sentence pairs, pushing the weaker models (RNN, 3-gram, and 2-
gram) far below the 50% chance accuracy level. GPT-2, RoBERTa, and ELECTRA were found to be signifi-
cantly more accurate than the alternative models (BERT, XLM, LSTM, RNN, 3-gram, and 2-gram) in predicting
the human responses to these trials (with similar results when comparing model pair separately, see Extended
Data Fig. 3b). All of the models except for GPT-2 were found to be significantly below the lower bound on the
noise ceiling, demonstrating misalignment with human judgments.
50 20 40 60 80 100
GPT-2
p(sentence) percentile020406080100ELECTRA
p(sentence) percentileNothing has
a world of
excitement
and joys.
Diddy has a wealth of experience
with grappling.Luke has a ton of experience
with winning.
a
0 20 40 60 80 100
RoBERTa
p(sentence) percentile0204060801003-gram
p(sentence) percentileYou have to realize
is that noise again.
I wait to see how
it shakes out.I need to see how
this played out.
bFigure 2: Synthesizing controversial sentence pairs. The small open dots denote 500 randomly sampled
natural sentences. The big open dot denotes the natural sentence used for initializing the controversial sentence
optimization, and the closed dots are the resulting synthetic sentences. (a)In this example, we start with the
randomly sampled natural sentence “Luke has a ton of experience with winning”. If we adjust this sentence to
minimize its probability according to GPT-2 (while keeping the sentence at least as likely as the natural sentence
according to ELECTRA), we obtain the synthetic sentence “Nothing has a world of excitement and joys”. By
repeating this procedure while switching the roles of the models, we generate the synthetic sentence “Diddy
has a wealth of experience with grappling”, which decreases ELECTRA’s probability while slightly increasing
GPT-2’s. (b)In this example, we start with the randomly sampled natural sentence “I need to see how this
played out”. If we adjust this sentence to minimize its probability according to RoBERTa (while keeping the
sentence at least as likely as the natural sentence according to 3-gram), we obtain the synthetic sentence “You
have to realize is that noise again”. If we instead decrease only 3-gram’s probability, we generate the synthetic
sentence “I wait to see how it shakes out”.
2.3 Pairs of natural and synthetic sentences uncover blindspots
Last, we considered trials in which the participants were asked to choose between a natural sentence and one of
the synthetic sentences which was generated from that natural sentence. If the language model is fully aligned
with human judgments, we would expect humans to agree with the model, and select the synthetic sentence
at least as much as the natural sentence. In reality, human participants showed a systematic preference for the
natural sentences over their synthetic counterparts (Fig. 3b), even when the synthetic sentences were formed
such that the stronger models (i.e., GPT-2, RoBERTA, or ELECTRA) favored them over the natural sentences;
see Extended Data Table 1 for examples. Evaluating natural sentence preference separately for each model-
pairing (Extended Data Fig. 4), we find that these imperfections can be uncovered even when pairing a strong
model with a relatively weak model (such that the strong model “accepts” the synthetic sentence and the weak
model rejects it).
60 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
0 50 100
GPT-2
p(sentence) percentile020406080100RoBERTa
p(sentence) percentile
0 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
0 50 100
GPT-2
p(sentence) percentile020406080100RoBERTa
p(sentence) percentile
aSynthetic controversial sentence pairs
bSynthetic vs. natural sentences
natural sentence synthetic sentenceFigure 3: Model comparison using synthetic sentences. (a) (Left) Percentile-transformed sentence probabil-
ities for GPT-2 and RoBERTa for controversial synthetic-sentence pairs. Each pair of connected dots depict
one sentence pair. (Right) Model prediction accuracy, measured as the proportion of trials in which the same
sentence was preferred by both the model and the human participant. GPT-2, RoBERTa and ELECTRA sig-
nificantly outperformed the other models (two-sided Wilcoxon signed-rank test, controlling the false discovery
rate for all 36 model comparisons at q<.05). All of the models except for GPT-2 were found to perform below
the noise ceiling (gray) of predicting each participant’s choices from the majority votes of the other participants
(asterisks indicate significance—two-sided Wilcoxon signed-rank test, controlling the false discovery rate for
nine comparisons at q<.05). (b)(Left) Each connected triplet of dots depicts a natural sentence and its derived
synthetic sentences, optimized to decrease the probability only under GPT-2 (left dots in a triplet) or only under
RoBERTa (bottom dots in a triplet). (Right) Each model was evaluated across all of the synthetic-natural sen-
tence pairs for which it was targeted to keep the synthetic sentence at least as probable as the natural sentence
(see Extended Data Fig. 6 for the complementary data binning). This evaluation yielded a below-chance pre-
diction accuracy for all of the models, which was also significantly below the lower bound on the noise ceiling.
This indicates that, although the models assessed that these synthetic sentences were at least as probable as the
original natural sentence, humans disagreed and showed a systematic preference for the natural sentence. See
Fig. 1’s caption for details on the visualization conventions used in this figure.
7sentence log probability (model 1) log probability (model 2) # human choices
s1: You can reach his stories on an instant. logp(s1|GPT-2 ) =−64.92 log p(s1|RoBERTa ) =−59.98 10
s2: Anybody can behead a rattles an an antelope. logp(s2|GPT-2 ) =−40.45 logp(s2|RoBERTa ) =−90.87 0
s1: However they will still compare you to others. logp(s1|RoBERTa ) =−53.40 log p(s1|GPT-2 ) =−31.59 10
s2: Why people who only give themselves to others. logp(s2|RoBERTa ) =−48.66 logp(s2|GPT-2 ) =−47.13 0
s1: He healed faster than any professional sports player. logp(s1|ELECTRA ) =−48.77 log p(s1|BERT ) =−50.21 10
s2: One gets less than a single soccer team. logp(s2|ELECTRA ) =−38.25 logp(s2|BERT ) =−59.09 0
s1: That is the narrative we have been sold. logp(s1|BERT ) =−56.14 log p(s1|GPT-2 ) =−26.31 10
s2: This is the week you have been dying. logp(s2|BERT ) =−50.66 logp(s2|GPT-2 ) =−39.50 0
s1: The resilience is made stronger by early adversity. logp(s1|XLM ) =−62.95 log p(s1|RoBERTa ) =−54.34 10
s2: Every thing is made alive by infinite Ness. logp(s2|XLM ) =−42.95 logp(s2|RoBERTa ) =−75.72 0
s1: President Trump threatens to storm the White House. logp(s1|LSTM ) =−58.78 log p(s1|RoBERTa ) =−41.67 10
s2: West Surrey refused to form the White House. logp(s2|LSTM ) =−40.35 logp(s2|RoBERTa ) =−67.32 0
s1: Las beans taste best with a mustard sauce. logp(s1|RNN) =−131.62 log p(s1|RoBERTa ) =−60.58 10
s2: Roughly lanes being alive in a statement ratings. logp(s2|RNN) =−49.31 logp(s2|RoBERTa ) =−99.90 0
s1: You are constantly seeing people play the multi. logp(s1|3-gram ) =−107.16 log p(s1|ELECTRA ) =−44.79 10
s2: This will probably the happiest contradicts the hypocrite. logp(s2|3-gram ) =−91.59 logp(s2|ELECTRA ) =−75.83 0
s1: A buyer can own a genuine product also. logp(s1|2-gram ) =−127.35 log p(s1|ELECTRA ) =−40.21 10
s2: One versed in circumference of highschool I rambled. logp(s2|2-gram ) =−113.73 logp(s2|ELECTRA ) =−92.61 0
Table 2: Examples of controversial synthetic-sentence pairs that maximally contributed to each model’s
prediction error. For each model (double row, “model 1”), the table shows results for two sentences on which
the model failed severely. In each case, the failing model 1 prefers sentence s2(higher log probability bolded),
while the model it was pitted against (“model 2”) and all 10 human subjects presented with that sentence pair
prefer sentence s1. (When more than one sentence pair induced an equal maximal error in a model, the example
included in the table was chosen at random.)
81.0
 0.5
 0.0 0.5 1.0
ordinal correlation between human ratings and models'
sentence pair probability log-ratio (signed-rank cosine similarity)GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
Figure 4: Ordinal correlation of the models’ sentence probability log-ratios and human Likert ratings.
For each sentence pair, model prediction was quantified by logp(s1|m)
p(s2|m). This log-ratio was correlated with the
Likert ratings of each particular participant, using signed-rank cosine similarity (see Methods). This analysis,
taking all trials and human confidence level into account, indicates that GPT-2 performed best in predicting
human sentence probability judgments. However, its predictions are still significantly misaligned with the
human choices. See Fig. 1’s caption for details on the visualization convention.
2.4 Evaluating the entire dataset reveals a hierarchy of models
Rather than evaluating each model’s prediction accuracy with respect to the particular sentence pairs that were
formed to compare this model to alternative models, we can maximize our statistical power by computing the
average prediction accuracy for each model with respect to all of the experimental trials we collected. Fur-
thermore, rather than binarizing the human and model judgments, here we measure the ordinal correspondence
between the graded human choices (taking confidence into account) and the log ratio of the sentence proba-
bilities assigned by each candidate model. Using this more sensitive benchmark (Fig. 4), we found GPT-2 to
be the most human-aligned, followed by RoBERTa; then ELECTRA; BERT; XLM and LSTM; and the RNN,
3-gram, and 2-gram models. However, all of the models (including GPT-2) were found to be significantly less
accurate than the lower bound on the noise ceiling.
One possible reason for the poorer performance of the bidirectional transformers (RoBERTa, ELECTRA,
BERT, and XLM) compared to the unidirectional transformer (GPT-2) is that computing sentence probabilities
in these models is complex, and the probability estimator we developed (see Methods, “Evaluating sentence
probabilities in transformer models”) could be non-optimal; Indeed, the popular pseudo-log-likelihood (PLL)
approach yields slightly higher accuracy for randomly sampled natural-sentence pairs (Extended Data Fig. 5a).
And yet, when we directly compared our estimator to PLL by means of generating and administrating new
synthetic controversial sentences, our estimator was found to be markedly better aligned to human judgments
(Extended Data Fig. 5b and Extended Data Table 2).
Finally, a control analysis employing probability measures normalized by token count revealed that such
normalization had minimal influence on the observed differences among models (Supplementary Section 7.2
and Supplementary Fig. S1).
93 Discussion
In this study, we probed the ability of language models to predict human relative sentence probability judgments
using controversial sentence pairs, selected or synthesized so that two models disagreed about which sentence
was more probable. We found that (1) GPT-2 (a unidirectional transformer model trained on predicting up-
coming tokens) and RoBERTa (a bidirectional transformer trained on a held-out token prediction task) were the
most predictive of human judgments on controversial natural-sentence pairs (Fig. 1b); (2) GPT-2, RoBERTa,
and ELECTRA (a bidirectional transformer trained on detecting corrupted tokens) were the most predictive of
human judgments on pairs of sentences synthesized to maximize controversiality (Fig. 3a); and (3) GPT-2 was
the most human-consistent model when considering the entire behavioral dataset we collected (Fig. 4). And yet,
all of the models, including GPT-2, exhibited behavior inconsistent with human judgments; using an alternative
model as a counterforce, we could corrupt natural sentences such that their probability under a model did not
decrease, but humans tended to reject the corrupted sentence as unlikely (Fig. 3b).
3.1 Implications for computational psycholinguistic modeling
Unlike convolutional neural networks, whose architectural design principles are roughly inspired by biological
vision [26], the design of current neural network language models is largely uninformed by psycholinguistics
and neuroscience. And yet, there is an ongoing effort to adopt and adapt neural network language models
to serve as computational hypotheses of how humans process language, making use of a variety of different
architectures, training corpora, and training tasks [11, 27–35]. We found that recurrent neural networks make
markedly human-inconsistent predictions once pitted against transformer-based neural networks. This find-
ing coincides with recent evidence that transformers also outperform recurrent networks for predicting neural
responses as measured by ECoG or fMRI [11, 32], as well as with evidence from model-based prediction
of human reading speed [33, 36] and N400 amplitude [36, 37]. Among the transformers, GPT-2, RoBERTa,
and ELECTRA showed the best performance. These models are trained to optimize only word-level pre-
diction tasks, as opposed to BERT and XLM which are additionally trained on next-sentence prediction and
cross-lingual tasks, respectively (and have the same architecture as RoBERTa). This suggests that local word
prediction provides better alignment with human language comprehension.
Despite the agreement between our results and previous work in terms of model ranking, the significant
failure of GPT-2 in predicting the human responses to natural versus synthetic controversial pairs (Fig. 3b)
demonstrates that GPT-2 does not fully emulate the computations employed in human processing of even short
sentences. This outcome is in some ways unsurprising, given that GPT-2 (like all of the other models we con-
sidered) is an off-the-shelf machine learning model that was not designed with human psycholinguistic and
physiological details in mind. And yet, the considerable human inconsistency we observed seems to stand in
stark contrast with the recent report of GPT-2 explaining about 100 percent of the explainable variance in fMRI
and ECoG responses to natural sentences [32]. Part of this discrepancy could be explained by the fact that
Schrimpf and colleagues [32] mapped GPT-2 hidden-layer activations to brain data by means of regularized
linear regression, which can identify a subspace within GPT-2’s language representation that is well-aligned
with brain responses even if GPT-2’s overall sentence probabilities are not human-like. More importantly,
when language models are evaluated with natural language, strong statistical models might capitalize on fea-
tures in the data that are distinct from, but highly correlated with, features that are meaningful to humans.
Therefore, a model that performs well on typical sentences might employ computational mechanisms that are
very distinct from the brain’s, which will only be revealed by testing the model in a more challenging domain.
Note that even the simplest model we considered—a 2-gram frequency table—actually performed quite well
10on predicting human judgments for randomly-sampled natural sentences, and its deficiencies only became ob-
vious when challenged by controversial sentence pairs. We predict that there will be substantial discrepancies
between neural representations and current language models when using stimuli that intentionally stress-test
this relationship, using our proposed sentence-level controversiality approach or complementary ideas such as
maximizing controversial transition probabilities between consecutive words [38].
Using controversial sentences can be seen as a generalization test of language models: can models predict
what kinds of changes to a natural sentence will lead to humans rejecting the sentence as improbable? Humans
are sometimes capable of comprehending language with atypical constructions (e.g. in cases when pragmatic
judgments can be made about a speaker’s intentions from environmental and linguistic context [39]), but none of
the models we tested were fully able to predict which syntactic or semantic perturbations would be accepted or
rejected by humans. One possibility is that stronger next-word prediction models, using different architectures,
learning rules, or training data, might close the gap between models and humans. Alternatively, it might be
that optimizing for other linguistic tasks, or even non-linguistic task demands (in particular, representing the
external world, the self, and other agents) will turn out to be critical for achieving human-like natural language
processing [40].
3.2 Controversial sentence pairs as adversarial attacks
Machine vision models are highly susceptible to adversarial examples [41, 42]. Such adversarial examples are
typically generated by choosing a correctly classified natural image and then searching for a minuscule (and
therefore human-imperceptible) image perturbation that would change the targeted model’s classification. The
prospect that similar covert model failure modes may exist also for language models has motivated proposed
generalizations of adversarial methods to textual inputs [43]. However, imperceptible perturbations cannot be
applied to written text: any modified word or character is humanly perceptible. Prior work on adversarial
examples for language models have instead relied on heuristic constraints aiming to limit the change in the
meaning of the text, such as flipping a character [44, 45], changing number or gender [46], or replacing words
with synonyms [47–49]. However, since these heuristics are only rough approximations of human language
processing, many of these methods fail to preserve semantic meaning [50]. Interactive (“human-in-the-loop”)
adversarial approaches allow human subjects to repeatedly alter model inputs such that it confuses target models
but not secondary participants [17, 51], but these approaches are inherently slow and costly and are limited by
mental models the human subjects form about the evaluated language models.
By contrast, testing language models on controversial sentence pairs does not require approximating or
querying a human ground truth during optimization—the objective of controversiality is independent of cor-
rectness. Instead, by designing inputs to elicit conflicting predictions among the models and assessing human
responses to these inputs only once the optimization loop has terminated, we capitalize on the simple fact that
if two models disagree with respect to an input, at least one of the models must be making an incorrect predic-
tion. Pitting language models against other language models also can be conducted by other approaches such
as “red-teaming”, where an alternative language model is used as a generator of potential adversarial examples
for a targeted model and a classifier is used to filter the generated examples such that the output they induce
in the targeted model is indeed incorrect [52]. Our approach shares the underlying principle that an alternative
language model can drive a more powerful test than handcrafted heuristics, but here the models have symmetric
roles (there are no “attacking” and “attacked” models) and we can optimize stimuli directly without relying on
filtering.
113.3 Limitations and future directions
While our results demonstrate that using controversial stimuli can identify subtle differences in language mod-
els’ alignment with human judgments, our study was limited in a number of ways. Our stimuli were all 8-word
English sentences, limiting our ability to make cognitively meaningful claims that apply to language use glob-
ally. 8-word sentences are long enough to include common syntactic constructions and convey meaningful
ideas but may not effectively probe long-distance syntactic dependencies [53]. Future work may introduce
additional sentence lengths and languages, as well as (potentially adaptive) controversial sentence optimization
procedures that consider large sets of candidate models, allowing for greater model coverage than our sim-
pler pairwise approach. Future work may also complement the model-comparative experimental design with
procedures designed to identify potential failure modes common to all models.
A more substantial limitation of the current study is that, like any comparison of pre-trained neural networks
as potential models of human cognition, there could be multiple reasons (i.e., training data, architecture, training
tasks, learning rules) why particular models are better aligned with human judgments. For example, as we
did not systematically control the training corpora used for training the models, it is possible that some of
the observed differences are due to differences in the training sets rather than model architecture. Therefore,
while our results expose failed model predictions, they do not readily answer why these failed predictions arise.
Future experiments could compare custom-trained or systematically manipulated models, which reflect specific
hypotheses about human language processing. In Extended Data Fig. 5, we demonstrate the power of using
synthetic controversial stimuli to conduct sensitive comparisons between models with subtle differences in how
sentence probabilities are calculated.
It is important to note that our analyses considered human relative probability judgments as reflecting
a scalar measure of acceptability. We made this assumption in order to bring the language models (which
assign a probability measure to each sentence) and the human participants onto a common footing. However,
it is possible that different types of sentence pairs engage different human cognitive processes. For pairs of
synthetic sentences, both sentences may be unacceptable in different ways (e.g. exhibit different kinds of
grammatical violations), requiring a judgment that weighs the relative importance of multiple dimensions [54]
and could therefore produce inconsistent rankings across participants or across trials [55]. By contrast, asking
participants to compare a natural and a synthetic sentence (Fig. 3b, Extended Data Table 1) may be more
analogous to previous work measuring human acceptability judgments for sentence pairs [24]. Nonetheless, it
is worth noting that for allof the controversial conditions, the noise ceiling was significantly above the models’
prediction accuracy, indicating non-random human preferences unexplained by current models that should be
accounted for by future models, which may have to be more complex and capture multiple processes.
Finally, the use of synthetic controversial sentences can be extended beyond probability judgments. A
sufficiently strong language model may enable constraining the experimental design search-space to particular
sentence distributions (e.g., movie reviews or medical questions). Given such a constrained space, we may
be able to search for well-formed sentences that elicit contradictory predictions in alternative domain-specific
models (e.g., sentiment classifiers or question-answering models). However, as indicated by our results, the
task of capturing distributions of well-formed sentences is less trivial than it seems.
124 Methods
4.1 Language models
We tested nine models from three distinct classes: n-gram models, recurrent neural networks, and transformers.
The n-gram models were trained with open source code from the Natural Language Toolkit [56], the recurrent
neural networks were trained with architectures and optimization procedures available in PyTorch [57], and
the transformers were implemented with the open-source repository HuggingFace [58]. For full details see
Supplementary Section 6.1.
4.2 Evaluating sentence probabilities in transformer models
We then sought to compute the probability of arbitrary sentences under each of the models described above.
The term “sentence” is used in this context in its broadest sense—a sequence of English words, not necessarily
restricted to grammatical English sentences. Unlike some classification tasks in which valid model predictions
may be expected only for grammatical sentences (e.g., sentiment analysis), the sentence probability comparison
task is defined over the entire domain of eight-word sequences.
For the set of unidirectional models, evaluating sentence probabilities was performed simply by summing
the log probabilities of each successive token in the sentence from left to right, given all the previous tokens.
For bidirectional models, this process was not as straightforward. One challenge is that transformer model
probabilities do not necessarily reflect a coherent joint probability; the summed log sentence probability result-
ing from adding words in one order (e.g. left to right) does not necessarily equal the probability resulting from a
different order (e.g. right to left). Here we developed a novel formulation of bidirectional sentence probabilities
in which we considered all permutations of serial word positions as possible construction orders (analogous to
the random word visitation order used to sample serial reproduction chains, [59]). In practice, we observed that
the distribution of log probabilities resulting from different permutations tends to center tightly around a mean
value (for example, for RoBERTa evaluated with natural sentences, the average coefficient of variation was
approximately 0.059). Therefore in order to efficiently calculate bidirectional sentence probability, we evaluate
100 different random permutations and define the overall sentence log probability as the mean log probability
calculated from each permutation. Specifically, we initialized an eight-word sentence with all tokens replaced
with the “mask” token used in place of to-be-predicted words during model training. We selected a random
permutation Pof positions 1 through 8, and started by computing the probability of the word at first of these
positions P1given the other seven “mask” tokens. We then replaced the “mask” at position P1with the actual
word at this position and computed the probability of the word at P2given the other six “mask” tokens and the
word at P1. This process was repeated until all “mask” tokens had been filled by the corresponding word.
A secondary challenge in evaluating sentence probabilities in bidirectional transformer models stems from
the fact that these models use word-piece tokenizers (as opposed to whole words), and that these tokenizers are
different for different models. For example, one tokenizer might include the word “beehive” as a single token,
while others strive for a smaller library of unique tokens by evaluating “beehive” as the two tokens “bee” and
“hive”. The model probability of a multi-token word—similar to the probability of a multi-word sentence—
may depend on the order in which the chain rule is applied. Therefore, all unique permutations of token order
for each multi-token word were also evaluated within their respective “masks”. For example, the probability of
the word “beehive” would be evaluated as follows:
13logp(w=beehive ) =0.5
logp(w1=bee|w2=MASK ) + log p(w2=hive|w1=bee)

+0.5
logp(w2=hive|w1=MASK ) + log p(w1=bee|w2=hive)
 (1)
This procedure aimed to yield a more fair estimate of the conditional probabilities of word-piece tokens
and therefore the overall probabilities of multi-token words by 1) ensuring that the word-piece tokens were
evaluated within the same context of surrounding words and masks, and 2) eliminating the bias of evaluating
the word-piece tokens in any one particular order in models which were trained to predict bidirectionally.
One more procedure was applied in order to ensure that all models were computing a probability distribution
over sentences with exactly 8 words. When evaluating the conditional probability of a masked word in models
with word-piece tokenizers, we normalized the model probabilities to ensure that only single words were being
considered, rather than splitting the masked tokens into multiple words. At each evaluation step, each token was
restricted to come from one of four normalized distributions: i) single-mask words were restricted to be tokens
with appended white space, ii) masks at the beginning of a word were restricted to be tokens with preceding
white space (in models with preceding white space, e.g. BERT), iii) masks at the end of words were restricted
to be tokens with trailing white space (in models with trailing white space, e.g. XLM), and iv) masks in the
middle of words were restricted to tokens with no appended white space.
4.3 Assessing potential token count effects on sentence probabilities
Note that, because tokenization schemes varied across models, the number of tokens in a sentence could dif-
fer for different models. These alternative tokenizations can be conceived of as different factorizations of the
modeled language distribution, changing how a sentence’s log probability is additively partitioned across the
conditional probability chain (but not affecting its overall probability) [60]. Had we attempted to normalize
across models by dividing the log probability by the number of tokens, as is often done when aligning model
predictions to human acceptability ratings [12, 13], our probabilities would have become strongly tokenization-
dependent [60]. To empirically confirm that tokenization differences were not driving our results, we sta-
tistically compared the token counts of each model’s preferred synthetic sentences with the token counts of
their non-preferred counterparts. While we found significant differences for some of the models, there was
no systematic association between token count and model sentence preferences (Supplementary Table S1). In
particular, lower sentence probabilities were not systematically confounded by higher token counts.
4.4 Defining a shared vocabulary
To facilitate the sampling, selection, and synthesis of sentences that could be evaluated by all of the candidate
models, we defined a shared vocabulary of 29,157unique words. Defining this vocabulary was necessary in
order to unify the space of possible sentences between the transformer models (which can evaluate any input
due to their word-piece tokenizers) and the neural network and n-gram models (which include whole words as
tokens), and to ensure we only included words that were sufficiently prevalent in the training corpora for all
models. The vocabulary consisted of the words in the subtlex database [61], after removing words that occurred
fewer than 300 times in the 300M word corpus (see Supplementary Section 6.1) used to train the n-gram and
recurrent neural network models (i.e., with frequencies lower than one in a million).
144.5 Sampling of natural sentences
Natural sentences were sampled from the same four text sources used to construct the training corpus for the
n-gram and recurrent neural network models, while ensuring that there was no overlap between training and
testing sentences. Sentences were filtered to include only those with eight distinct words and no punctuation
aside from periods, exclamation points, or question marks at the end of a sentence. Then, all eight-word
sentences were further filtered to include only the words included in the shared vocabulary and to exclude those
included in a predetermined list of inappropriate words and phrases. To identify controversial pairs of natural
sentences, we used integer linear programming to search for sentences that had above-median probability in
one model and minimum probability rank in another model (see Supplementary Section 6.2).
4.6 Generating synthetic controversial sentence pairs
For each pair of models, we synthesized 100 sentence triplets. Each triplet was initialized with a natural
sentence n(sampled from Reddit). The words in sentence nwere iteratively modified to generate a synthetic
sentence with reduced probability according to the first model but not according to the second model. This
process was repeated to generate another synthetic sentence from n, in which the roles of the two models
were reversed. Conceptually, this approach resembles Maximum Differentiation (MAD) competition [62],
introduced to compare models of image quality assessment. Each synthetic sentence was generated as a solution
for a constrained minimization problem:
s∗= argmin
slogp(s|mreject )
subject to logp(s|maccept )≥logp(n|maccept )(2)
mreject denotes the model targeted to assign reduced sentence probability to the synthetic sentence compared
to the natural sentence, and maccept denotes the model targeted to maintain a synthetic sentence probability
greater or equal to that of the natural sentence. For one synthetic sentence, one model served as maccept and
the other model served as mreject , and for the other synthetic sentence the model roles were flipped.
At each optimization iteration, we selected one of the eight words pseudorandomly (so that all eight posi-
tions would be sampled Ntimes before any position would be sampled N+ 1times) and searched the shared
vocabulary for the replacement word that would minimize the logp(s|mreject )under the constraint. We ex-
cluded potential replacement words that already appeared in the sentence, except for a list of 42 determiners and
prepositions such as “the”, “a”, or “with”, which were allowed to repeat. The sentence optimization procedure
was concluded once eight replacement attempts (i.e., words for which no loss-reducing replacement has been
found) have failed in a row.
4.7 Word-level search for bidirectional models
For models for which the evaluation of logp(s|m)is computationally cheap (2-gram, 3-gram, LSTM, and
the RNN), we directly evaluated the log-probability of the 29,157sentences resulting from each of the 29,157
possible word replacements. When such probability vectors were available for both models, we simply chose
the replacement minimizing the loss. For GPT-2, whose evaluation is slower, we evaluated sentence probabil-
ities only for word replacements for which the new word had a conditional log-probability (given the previous
words in the sentence) of no less than −10; in rare cases when this threshold yielded fewer than 10 candidate
words, we reduced the threshold in steps of 5until there were at least 10 words above the threshold. For the
15bi-directional models (BERT, RoBERTa, XLM, and ELECTRA), for which the evaluation of logp(s|m)is
costly even for a single sentence, we used a heuristic to prioritize which replacements to evaluate.
Since bi-directional models are trained as masked language models, they readily provide word-level com-
pletion probabilities. These word-level log-probabilities typically have positive but imperfect correlation with
the log-probabilities of the sentences resulting from each potential completion. We hence formed a simple
linear regression-based estimate of logp(s{i} ← w|m), the log-probability of the sentence swith word w
assigned at position i, predicting it from logp(s{i}=w|m, s{i} ←mask ), the completion log-probability
of word wat position i, given the sentence with the i-th word masked:
log ˆp(s{i} ←w|m) =β1logp(s{i}=w|m, s{i} ←mask ) +β0 (3)
This regression model was estimated from scratch for each word-level search. When a word was first
selected for being replaced, the log-probability of two sentences was evaluated: the sentence resulting from
substituting the existing word with the word with the highest completion probability and the sentence resulting
from substituting the existing word with the word with the lowest completion probability. These two word-
sentence log-probability pairs, as well as the word-sentence log-probability pair pertaining to the current word,
were used to fit the regression line. The regression prediction, together with the sentence probability for the
other model (either the exact probability, or approximate probability if the other model was also bi-directional)
was used to predict logp(s|mreject )for each of the 29,157potential replacements. We then evaluated the
true (non-approximate) sentence probabilities of the replacement word with the minimal predicted probability.
If this word indeed reduced the sentence probability, it was chosen to serve as the replacement and the word-
level search was terminated (i.e., proceeding to search a replacement for another word in the sentence). If it
did not reduce the probability, the regression model (Eq. 3) was updated with the new observation, and the
next replacement expected to minimize the sentence probability was evaluated. This word-level search was
terminated after five sentence evaluations that did not reduce the loss.
4.8 Selecting the best triplets from the optimized sentences
Since the discrete hill-climbing procedure described above is highly local, the degree to which this succeeded in
producing highly-controversial pairs varied depending on the starting sentence n. We found that typically, nat-
ural sentences with lower than average log-probability gave rise to synthetic sentences with greater controver-
siality. To better represent the distribution of natural sentences while still choosing the best (most controversial)
triplets for human testing, we used stratified selection.
First, we quantified the controversiality of each triplet as
cm1,m2(n, s1, s2) = logp(n|m1)
p(s1|m1)+ logp(n|m2)
p(s2|m2), (4)
where s1is the sentence generated to reduce the probability in model m1ands2is the sentence generated to
reduce the probability in model m2.
We employed integer programming to choose the 10 most controversial triplets from the 100 triplets opti-
mized for each model pair (maximizing the total controversiality across the selected triplets), while ensuring
that for each model, there was exactly one natural sentence in each decile of the natural sentences probability
distribution. The selected 10 synthetic triplets were then used to form 30 unique experimental trials per model
pair, comparing the natural sentence with one synthetic sentence, comparing the natural sentence with the other
synthetic sentence, and comparing the two synthetic sentences.
164.9 Design of the human experiment
Our experimental procedures were approved by the Columbia University Institutional Review Board (protocol
number IRB-AAAS0252) and were performed in accordance with the approved protocol. All participants
provided informed consent prior. We presented the controversial sentence pairs selected and synthesized by
the language models to 100 native English-speaking, US-based participants (55 male) recruited from Prolific
(www.prolific .co), and paid each participant $5.95. The average participant age was 34.08 ± 12.32. The
subjects were divided into 10 groups, and each ten-subject group was presented with a unique set of stimuli.
Each stimulus set contained exactly one sentence pair from every possible combination of model pairs and
the four main experimental conditions: selected controversial sentence pairs; natural vs. synthetic pair, where
one model served as maccept and the other as mreject ; a natural vs. synthetic pair with the reverse model
role assignments; and directly pairing the two synthetic sentences. These model-pair-condition combinations
accounted for 144 (36 ×4) trials of the task. In addition to these trials, each stimulus set also included nine trials
consisting of sentence pairs randomly sampled from the database of eight-word sentences (and not already
included in any of the other conditions). All subjects also viewed 12 control trials consisting of a randomly
selected natural sentence and the same natural sentence with the words scrambled in a random order. The order
of trials within each stimulus set as well as the left-right screen position of sentences in each sentence pair
were randomized for all participants. While each sentence triplet produced by the optimization procedure (see
subsection “Generating synthetic controversial sentence pairs”) gave rise to three trials, these were allocated
such that no subject viewed the same sentence twice.
On each trial of the task, participants were asked to make a binary decision about which of the two sentences
they considered more probable (for the full set of instructions given to participants, see Supplementary Fig. S2).
In addition, they were asked to indicate one of three levels of confidence in their decision: somewhat confident,
confident, or very confident. The trials were not timed, but a 90-minute time limit was enforced for the whole
experiment. A progress bar at the bottom of the screen indicated to participants how many trials they had
completed and had remaining to complete.
We rejected the data of 21 participants who failed to choose the original, unshuffled sentence in at least
11 of the 12 control trials, and acquired data from 21 alternative participants instead, all of whom passed this
data-quality threshold. In general, we observed high agreement in sentence preferences among our participants,
though the level of agreement varied across conditions. There was complete or near-complete agreement (at
least 9/10 participants with the same binary sentence preference) in 52.2% of trials for randomly-sampled
natural-sentence pairs, 36.6% of trials for controversial natural-sentence pairs, 67.6% of trials for natural-
synthetic pairs, and 60.0% of trials for synthetic-synthetic pairs (versus a chance rate of 1.1%, assuming a
binomial distribution with p= 0.5).
4.10 Evaluation of model-human consistency
To measure the alignment on each trial between model judgments and human judgments, we binarized both
measures; we determined which of the two sentences was assigned with a higher probability by the model,
regardless of the magnitude of the probability difference, and which of the two sentences was favored by the
subject, regardless of the reported confidence level. When both the subject and the model chose the same
sentence, the trial was considered as correctly predicted by that model. This correctness measure was averaged
across sentence pairs and across the 10 participants who viewed the same set of trials. For the lower bound on
the noise ceiling, we predicted each subject’s choices from a majority vote of the nine other subjects who were
presented with the same trials. For the upper bound (i.e., the highest possible accuracy attainable on this data
17sample), we included the subject themselves in this majority vote-based prediction.
Since each of the 10 participant groups viewed a unique trial set, these groups provided 10 independent
replications of the experiment. Models were compared to each other and to the lower bound of the noise
ceiling by a Wilcoxon signed-rank test using these 10 independent accuracy outcomes as paired samples. For
each analysis, the false discovery rate across multiple comparisons was controlled by the Benjamini-Hochberg
procedure [63].
In Fig. 4, we instead measure model-human consistency in a more continuous way, comparing the sentence
probability ratio in a model to the graded Likert ratings provided by humans; see Supplementary Section 6.3
for full details.
4.11 Selecting trials for model evaluation
All of the randomly sampled natural-sentence pairs (Fig. 1a) were evaluated for each of the candidate models.
Controversial sentence pairs (either natural, Fig. 1b or synthetic, Fig. 3) were included in a model’s evaluation
set only if they were formed to target that model specifically. The overall summary analysis (Fig. 4) evaluated
all models on all available sentence pairs.
4.12 Comparison to pseudo-log-likelihood acceptability measures
Wang & Cho [64] proposed an alternative approach for computing sentence probabilities in bidirectional
(BERT-like) models, using a pseudo-log-likelihood measure that simply sums the log-probability of each token
conditioned on all of the other tokens in the sentence. While this measure does not reflect a true probability
distribution [65], it is positively correlated with human acceptability judgments for several bidirectional models
[13, 66]. To directly compare this existing approach to our novel method for computing probabilities, we again
used the method of controversial sentence pairs to identify the approach most aligned with human judgments.
For each bidirectional model (BERT, RoBERTa, and ELECTRA), we created two copies of the model, each us-
ing a different approach for computing sentence probabilities. We synthesized 40 sentence pairs to maximally
differentiate between the two copies of each model, with each copy assigning a higher probability to a different
sentence in the pair. Subsequently, we tested 30 human participants, presenting each participant with all 120
sentence pairs. Model-human consistency was quantified as in the main experiment.
4.13 Data and code availability
The experimental stimuli, detailed behavioral testing results, sentence optimization code, and code for repro-
ducing all analyses and figures are available at github.com/dpmlab/contstimlang [67].
Acknowledgments
This material is based upon work partially supported by the National Science Foundation under Grant No.
1948004 to NK. This publication was made possible with the support of the Charles H. Revson Foundation to
TG. The statements made and views expressed, however, are solely the responsibility of the authors.
18Author Contributions
T.G., M.S., N.K., and C.B. designed the study. M.S. implemented the computational models and T.G. imple-
mented the sentence pair optimization procedures. M.S. conducted the behavioral experiments. T.G. and M.S.
analyzed the experiments’ results. T.G., M.S., N.K., and C.B. wrote the paper.
Competing Interests
The authors declare no competing interests.
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5 Extended Data
24Extended Data Figure 1: An example of one experimental trial, as presented to the participants . The participant must
choose one sentence while providing their confidence rating on a 3-point scale.
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodel 2
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodel 10.93 0.88 0.86 0.83 0.87 0.76 0.82 0.78
0.93 0.90 0.83 0.88 0.89 0.80 0.84 0.82
0.88 0.90 0.87 0.84 0.90 0.83 0.90 0.86
0.86 0.83 0.87 0.84 0.83 0.77 0.83 0.77
0.83 0.88 0.84 0.84 0.86 0.81 0.79 0.77
0.87 0.89 0.90 0.83 0.86 0.87 0.91 0.84
0.76 0.80 0.83 0.77 0.81 0.87 0.84 0.89
0.82 0.84 0.90 0.83 0.79 0.91 0.84 0.91
0.78 0.82 0.86 0.77 0.77 0.84 0.89 0.91
0.00 0.25 0.50 0.75 1.00
between model agreement rate
(proportion of sentence pairs)
Extended Data Figure 2: Between-model agreement rate
on the probability ranking of the 90 randomly sampled
and paired natural sentence pairs evaluated in the exper-
iment . Each cell represents the proportion of sentence pairs
for which two models make congruent probability ranking
(i.e., both models assign a higher probability to sentence 1,
or both models assign a higher probability to sentence 2).
25GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodel 2
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodel 10.51 0.53 0.78 0.83 0.66 0.84 0.79 0.88
0.49 0.60 0.65 0.78 0.60 0.80 0.76 0.86
0.47 0.40 0.63 0.75 0.57 0.79 0.64 0.59
0.22 0.35 0.37 0.58 0.30 0.44 0.60 0.54
0.17 0.22 0.25 0.42 0.47 0.49 0.42 0.55
0.34 0.40 0.43 0.70 0.53 0.84 0.62 0.70
0.16 0.20 0.21 0.56 0.51 0.16 0.49 0.62
0.21 0.24 0.36 0.40 0.58 0.38 0.51 0.63
0.12 0.14 0.41 0.46 0.45 0.30 0.38 0.37
0.00 0.25 0.50 0.75 1.00
human choice aligned with model 1
(proportion of trials)
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodel 2
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodel 10.55 0.61 0.79 0.84 0.85 0.86 0.76 0.92
0.45 0.36 0.60 0.89 0.81 0.96 0.94 0.95
0.39 0.64 0.49 0.88 0.89 0.95 0.98 0.95
0.21 0.40 0.51 0.71 0.73 0.86 0.78 0.90
0.16 0.11 0.12 0.29 0.51 0.70 0.72 0.91
0.15 0.19 0.11 0.27 0.49 0.79 0.65 0.71
0.14 0.04 0.05 0.14 0.30 0.21 0.32 0.55
0.24 0.06 0.02 0.22 0.28 0.35 0.68 0.67
0.08 0.05 0.05 0.10 0.09 0.29 0.45 0.33
0.00 0.25 0.50 0.75 1.00
human choice aligned with model 1
(proportion of trials)aNatural controversial sentences bSynthetic controversial sentencesExtended Data Figure 3: Pairwise model comparison of model-human consistency. For each pair of models (represented
as one cell in the matrices above), the only trials considered were those in which the stimuli were either selected (a) or
synthesized (b) to contrast the predictions of the two models. For these trials, the two models always made controversial
predictions (i.e., one sentence is preferred by the first model and the other sentence is preferred by the second model). The
matrices above depict the proportion of trials in which the binarized human judgments aligned with the row model (“model
1”). For example, GPT-2 (top-row) was always more aligned (green hues) with the human choices than its rival models. In
contrast, 2-gram (bottom-row) was always less aligned (purple hues) with the human choices than its rival models.
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodels assigned as mreject
GPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-grammodels assigned as maccept0.21 0.24 0.43 0.23 0.29 0.36 0.17 0.22
0.21 0.16 0.29 0.51 0.29 0.23 0.18 0.39
0.17 0.20 0.27 0.34 0.27 0.40 0.27 0.20
0.14 0.18 0.27 0.44 0.23 0.25 0.33 0.20
0.07 0.07 0.11 0.16 0.17 0.13 0.08 0.22
0.03 0.01 0.07 0.04 0.17 0.06 0.16 0.04
0.05 0.03 0.05 0.03 0.03 0.01 0.04 0.06
0.04 0.03 0.02 0.08 0.05 0.04 0.06 0.04
0.01 0.02 0.01 0.02 0.04 0.01 0.07 0.04
0.00 0.25 0.50 0.75 1.00
humans choice aligned with maccept
(proportion of trials)
Extended Data Figure 4: Pairwise model analysis of human re-
sponse for natural vs. synthetic sentence pairs. In each optimiza-
tion condition, a synthetic sentence swas formed by modifying a nat-
ural sentence nso the synthetic sentence would be “rejected” by one
model ( mreject , columns), minimizing p(s|mreject ), and would be
“accepted” by another model ( maccept , rows), satisfying the constraint
p(s|maccept )≥p(n|maccept ). Each cell above summarizes model-
human agreement in trials resulting from one such optimization condi-
tion. The color of each cell denotes the proportion of trials in which
humans judged a synthetic sentence to be more likely than its natural
counterpart and hence aligned with maccept . For example, the top-right
cell depicts human judgments for sentence pairs formed to minimize
the probability assigned to the synthetic sentence by the simple 2-gram
model while ensuring that GPT-2 would judge the synthetic sentence
to be at least as likely as the natural sentence; humans favored the syn-
thetic sentence in only 22 out the 100 sentence pairs in this condition.
261.0
0.5
0.0 0.5 1.0
ordinal correlation between human ratings and models'
sentence pair probability log-ratio (signed-rank cosine similarity)RoBERTa
RoBERTa (PLL)
ELECTRA
ELECTRA (PLL)
BERT
BERT (PLL)
aRandomly sampled natural-sentence pairs
1.0
0.5
0.0 0.5 1.0
ordinal correlation between human ratings and models'
sentence pair probability log-ratio (signed-rank cosine similarity)RoBERTa
RoBERTa (PLL)
ELECTRA
ELECTRA (PLL)
BERT
BERT (PLL)
bSynthetic controversial sentence pairsExtended Data Figure 5: Human consistency of bidirectional transformers: approximate log-likelihood versus pseudo-
log-likelihood (PLL). Each dot in the plots above depicts the ordinal correlation between the judgments of one participant
and the predictions of one model. (a)The performance of BERT, RoBERTa, and ELECTRA in predicting the human judg-
ments of randomly sampled natural sentence pairs in the main experiment, using two different likelihood measures: our novel
approximate likelihood method (i.e., averaging multiple conditional probability chains, see Methods) and pseudo-likelihood
(PLL, summating the probability of each word given all of the other words [64]). For each model, we statistically com-
pared the two likelihood measures to each other and to the noise ceiling using a two-sided Wilcoxon signed-rank test across
the participants. False discovery rate was controlled at q <0.05for the 9 comparisons. When predicting human pref-
erences of natural sentences, the pseudo-log-likelihood measure is at least as accurate as our proposed approximate
log-likelihood measure. (b) Results from a follow-up experiment, in which we synthesized synthetic sentence pairs for each
of the model pairs, pitting the two alternative likelihood measures against each other. Statistical testing was conducted in the
same fashion as in panel a. These results indicate that for each of the three bidirectional language models, the approximate
log-likelihood measure is considerably and significantly ( q <0.05) more human-consistent than the pseudo-likelihood mea-
sure. Synthetic controversial sentence pairs uncover a dramatic failure mode of the pseudo-log-likelihood measure,
which remains covert when the evaluation is limited to randomly-sampled natural sentences. See Extended Data Table
2 for synthetic sentence pair examples.
270 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
Extended Data Figure 6: Model prediction accuracy for pairs of
natural and synthetic sentences, evaluating each model across
all of the sentence pairs in which it was targeted to rate the syn-
thetic sentence to be less probable than the natural sentence.
The data binning applied here is complementary to the one used in
Fig. 3b, where each model was evaluated across all of the sentence
pairs in which it was targeted to rate the synthetic sentence to be
at least as probable as the natural sentence. Unlike Fig. 3b, where
all of the models performed poorly, here no models were found to
be significantly below the lower bound on the noise ceiling; typ-
ically, when a sentence was optimized to decrease its probability
under any model (despite the sentence probability not decreasing
under a second model), humans agreed that the sentence became
less probable.
sentence log probability (model 1) log probability (model 2) # human choices
n: I always cover for him and make excuses. logp(n|GPT-2 ) =−36.46 log p(n|2-gram ) =−106.95 10
s: We either wish for it or ourselves do. logp(s|GPT-2 ) =−36.15 logp(s|2-gram ) =−122.28 0
n: This is why I will never understand boys. logp(n|RoBERTa ) =−46.88 log p(n|2-gram ) =−103.11 10
s: This is why I will never kiss boys. logp(s|RoBERTa ) =−46.75 logp(s|2-gram ) =−107.91 0
n: One of the ones I did required it. logp(n|ELECTRA ) =−35.97 log p(n|LSTM ) =−40.89 10
s: Many of the years I did done so. logp(s|ELECTRA ) =−35.77 logp(s|LSTM ) =−46.25 0
n: There were no guns in the Bronze Age. logp(n|BERT ) =−48.48 log p(n|ELECTRA ) =−30.40 10
s: There is rich finds from the Bronze Age. logp(s|BERT ) =−48.46 logp(s|ELECTRA ) =−44.34 0
n: You did a great job on cleaning them. logp(n|XLM ) =−40.38 log p(n|RNN) =−43.47 10
s: She did a great job at do me. logp(s|XLM ) =−39.89 logp(s|RNN) =−61.03 0
n: This logic has always seemed flawed to me. logp(n|LSTM ) =−39.77 log p(n|RNN) =−45.92 10
s: His cell has always seemed instinctively to me. logp(s|LSTM ) =−38.89 logp(s|RNN) =−62.81 0
s: Stand near the cafe and sip your coffee. logp(s|RNN) =−65.55 log p(s|ELECTRA ) =−34.46 10
n: Sit at the front and break your neck. logp(n|RNN) =−44.18 logp(n|ELECTRA ) =−34.65 0
n: Most of my jobs have been like this. logp(n|3-gram ) =−80.72 log p(n|LSTM ) =−35.07 10
s: One of my boyfriend have been like this. logp(s|3-gram ) =−80.63 logp(s|LSTM ) =−41.44 0
n: They even mentioned that I offer white flowers. logp(n|2-gram ) =−113.38 log p(n|BERT ) =−62.81 10
s: But even fancied that would logically contradictory philosophies. logp(s|2-gram ) =−113.24 logp(s|BERT ) =−117.98 0
Extended Data Table 1: Examples of pairs of synthetic and natural sentences that maximally contributed to each
model’s prediction error. For each model (double row, “model 1”), the table shows results for two sentences on which the
model failed severely. In each case, the failing model 1 prefers synthetic sentence s(higher log probability bolded), while the
model it was pitted against (“model 2”) and all 10 human subjects presented with that sentence pair prefer natural sentence
n. (When more than one sentence pair induced an equal maximal error in a model, the example included in the table was
chosen at random.)
28sentence pseudo-log-likelihood (PLL) approximate log probability # human choices
s1: I found so many in things and called. logp(s1|BERT (PLL) ) =−55.14 log p(s1|BERT ) =−55.89 30
s2: Khrushchev schizophrenic so far
disproportionately goldfish fished alone. logp(s2|BERT (PLL) ) =−22.84 logp(s2|BERT ) =−162.31 0
s1: Figures out if you are on the lead. logp(s1|BERT (PLL) ) =−38.11 log p(s1|BERT ) =−51.27 30
s2: Neighbours unsatisfactory indistinguishable
misinterpreting schizophrenic on homecoming
cheerleading. logp(s2|BERT (PLL) ) =−16.43 logp(s2|BERT ) =−258.91 0
s1: I just say this and not the point. logp(s1|ELECTRA (PLL) ) =−34.41 log p(s1|ELECTRA ) =−33.80 30
s2: Glastonbury reliably mobilize disenfranchised
homosexuals underestimate unhealthy skeptics. logp(s2|ELECTRA (PLL) ) =−11.81 logp(s2|ELECTRA ) =−162.62 0
s1: And diplomacy is more people to the place. logp(s1|ELECTRA (PLL) ) =−62.81 log p(s1|ELECTRA ) =−47.33 30
s2: Brezhnev ingenuity disembarking Acapulco
methamphetamine arthropods unaccompanied
Khrushchev. logp(s2|ELECTRA (PLL) ) =−34.00 logp(s2|ELECTRA ) =−230.97 0
s1: Sometimes what looks and feels real to you. logp(s1|RoBERTa (PLL) ) =−36.58 log p(s1|RoBERTa ) =−51.61 30
s2: Buying something breathes or crawls
aesthetically to decorate. logp(s2|RoBERTa (PLL) ) =−9.78 logp(s2|RoBERTa ) =−110.27 0
s1: In most other high priority packages were affected. logp(s1|RoBERTa (PLL) ) =−71.13 log p(s1|RoBERTa ) =−61.60 30
s2: Stravinsky cupboard nanny contented burglar
babysitting unsupervised bathtub. logp(s2|RoBERTa (PLL) ) =−21.86 logp(s2|RoBERTa ) =−164.70 0
Extended Data Table 2: Examples of controversial synthetic-sentence pairs that maximally contributed to the pre-
diction error of bidirectional transformers using pseudo-log-likelihood (PLL). For each bidirectional model, the table
displays two sentence pairs on which the model failed severely when its prediction was based on pseudo-log-likelihood
(PLL) estimates [64]. In each of these sentence pairs, the PLL estimate favors sentence s2(higher PLL bolded), while the
approximate log-likelihood estimate and most of the human subjects presented with that sentence pair preferred sentence
s1. (When more than one sentence pair induced an equal maximal error in a model, the example included in the table was
chosen at random.) Sentences with long, multi-token words (e.g., “methamphetamine”) have high PLL estimates since
each of their tokens is well predicted by the others tokens. And yet, the entire sentence is improbable according to
human judgments and approximate log-probability estimates based on proper conditional probability chains.
296 Supplementary Methods
6.1 Language models
N-gram models. N-gram models [68], the simplest language model class, are trained by counting the
number of occurrences of all unique phrases of length N words in large text corpora. N-gram models make
predictions about upcoming words by using empirical conditional probabilities in the training corpus. We
tested both 2-gram and 3-gram variants. In 2-gram models, all unique two-word phrases are counted, and
each upcoming word probability (probability of w2conditioned on previous word w1) is determined by
dividing the count of 2-gram w1, w2by the count of unigram (word) w1. In 3-gram models, all unique three-
word phrases are counted, and upcoming word probabilities (probability of w3conditioned on previous
words w1andw2) are determined by dividing the count of 3-gram w1, w2, w3by the count of 2-gram
w1, w2. In both such models, sentence probabilities can be computed as the product of all unidirectional
word transition probabilities in a given sentence. We trained both the 2-gram and 3-gram models on a large
corpus composed of text from four sources: 1. public comments from the social media website Reddit
(reddit .com) acquired using the public API at pushshift .io, 2. articles from Wikipedia, 3. English
books and poetry available for free at Project Gutenberg ( gutenberg .org), and 4. articles compiled in
the American Local News Corpus [69]. The n-gram probability estimates were regularized by means of
Kneser-Ney smoothing [70].
Recurrent neural network models. We also tested two recurrent neural network models, including a
simple recurrent neural network (RNN) [1] and a more complex long short-term memory recurrent neural
network (LSTM) [2]. We trained both of these models on a next word prediction task using the same corpus
used to train the n-gram models. Both the RNN and LSTM had a 256-feature embedding size and a 512-
feature hidden state size, and were trained over 100 independent batches of text for 50 epochs with a learning
rate of .002. Both models’ training sets were tokenized into individual words and consisted of a vocabulary
of94,607unique tokens.
Transformer models. Similar to RNNs, transformers are designed to make predictions about sequential
inputs. However, transformers do not use a recurrent architecture, and have a number of more complex
architectural features. For example, unlike the fixed token embeddings in classic RNNs, transformers utilize
context-dependent embeddings that vary depending on a token’s position. Most transformers also contain
multiple attention heads in each layer of the model, which can help direct the model to relevant tokens in
complex ways. We tested five models with varying architectures and training procedures, including BERT
[3], RoBERTa [4], XLM [5], ELECTRA [6], and GPT-2 [7].
• We used the large version of BERT (bi-directonal encoder representations from transformers), con-
taining 24 encoding layers, 1024 hidden units in the feedforward network element of the model, and
16 attention heads. BERT is a bi-directional model trained to perform two different tasks: 1. a masked
language modeling (MLM) task, in which 15 percent of tokens are replaced with a special [MASK]
token and BERT must predict the masked word, and 2. next sentence prediction (NSP), in which
BERT aims to predict the upcoming sentence in the training corpus given the current sentence.
• RoBERTa is also a bi-directional model that uses the same architecture as BERT. However, RoBERTa
was trained on exclusively the masked word prediction task (and not next sentence prediction), and
used a different optimization procedure (including longer training on a larger dataset). This makes
empirical comparisons between BERT and RoBERTa particularly interesting, because they differ only
in training procedure and not architecture.
30• XLM is a cross-lingual bi-directional model which, too, shares BERT’s original architecture. XLM is
trained on three different tasks: 1. the same MLM task used in both BERT and RoBERTa, 2. a causal
language modeling task where upcoming words are predicted from left to right, and 3. a translation
modeling task. On this task, each training example consists of the same text in two languages, and the
model performs a masked language modeling task using context from one language to predict tokens
of another. Such a task can help the XLM model become robust to idiosyncrasies of one particular
language that may not convey much linguistic information.
• The ELECTRA model uses a training approach that involves two transformer models: a generator
and a discriminator. While the generator performs a masked language modeling task similar to other
transformers, the discriminator simultaneously tries to figure out which masked tokens were replaced
by the generator. This task may be more efficient than pure masked token prediction, because it uses
information from all input tokens rather than only the masked subset.
• GPT-2, the second iteration of GPT OpenAI’s GPT model, is the only unidirectional transformer
model that we tested. We used the pretrained GPT-2-xl version, with 48 encoding layers and 25
attention heads in each layer. Because GPT-2 is unidirectional it was trained only on the causal
language modeling task, in which tokens are predicted from left to right.
6.2 Selection of controversial natural-sentence pairs
We evaluated 231,725eight-word sentences sampled from Reddit. Reddit comments were scraped from
across the entire website and all unique eight-word sentences were saved. These sentences were subse-
quently filtered to exclude blatant spelling errors, inappropriate language, and individual words that were
not included in the corpus used to train the n-gram and recurrent neural network models in our experiment.
We estimated logp(s|m)for each natural sentence sand each model mas described above. We
then rank-transformed the sentence probabilities separately for each model, assigning the fractional rank
r(s|m) = 0 to the least probable sentence according to model mandr(s|m) = 1 to the most probable
one. This step eliminated differences between models in terms of probability calibration.
Next, we aimed to filter this corpus for controversial sentences. To prune the candidate sentences, we
eliminated any sentence sfor which no pair of models m1,m2held(r(s|m1)<0.5)and(r(s|m2)≥0.5),
where r(s|m1)is the fractional rank assigned for sentence sby model m. This step ensured that all of the
remaining sentences had a below-median probability according to one model and above-median probability
according to another, for at least one pair of models. We also excluded sentences in which any word (except
for prepositions) appeared more than once. After this pruning, 85,749candidate sentences remained, from
which85749
2

≈3.67×109possible sentence pairs can be formed.
We aimed to select 360 controversial sentence pairs, devoting 10 sentence pairs to each of the 36
models pairs. First, we defined two 360-long integer vectors m1andm2, specifying for each of the
360 yet unselected sentence pairs which model pair they contrast. We then selected 360 sentence pairs
s1
1, s2
1

,
s1
2, s2
2

...,
s1
360, s2
360

by solving the following minimization problem:
{(s1
j∗, s2
j∗)|j= 1,2, ..360}= argmin
s1,s2X
j
r(s1
j|m1
j) +r(s2
j|m2
j)

(5)
subject to ∀jr(s1
j|m2
j)≥0.5 (5a)
∀jr(s2
j|m1
j)≥0.5 (5b)
All 720 sentences are unique. (5c)
31To achieve this, we used integer linear programming (ILP) as implemented by Gurobi [71]. We repre-
sented sentence allocation as a sparse binary tensor Sof dimensions 85,749 ×360×2 (sentences, trials,
pair members) and the fractional sentence probabilities ranks as a matrix Rof dimensions 85,749 ×9 (sen-
tences, models). This enabled us to express and solve the selection problem in Eq. 5 as a standard ILP
problem:
S∗= argmin
SX
i,jSi,j,1Ri,m1
j+Si,j,2Ri,m2
j(6)
subject to Si,j,1Ri,m2
j≥0.5 (6a)
Si,j,2Ri,m1
j≥0.5 (6b)
∀iX
j,kSi,j,k≤1(each sentence iis used only once in the experiment) (6c)
∀jP
iSi,j,1= 1
∀jP
iSi,j,2= 1)
(each trial jis allocated exactly one sentence pair) (6d)
Sis binary (6e)
6.3 Evaluation of model-human consistency: Correlating model log-probability
ratios to human Likert ratings
For every model mand experimental trial i, we evaluated the log probability ratio for the trial’s two sen-
tences:
LR(s1
i, s2
i|m) = logp(s2
i|m)
p(s1
i|m)(7)
The human Likert ratings were recoded to be symmetrical around zero, mapping the six ratings appear-
ing in Extended Data Fig. 1 to (−2.5,−1.5,−0.5,+0.5,+1.5,+2.5). We then sought to correlate the model
log-ratios and with the zero-centered human Likert ratings, quantifying how well the model log-ratios were
associated with human sentence-likeliness judgments. To allow for an ordinal (not necessarily linear) asso-
ciation between the log-ratios and Likert ratings, we rank-transformed both measures (ranking within each
model or each human) while retaining the sign of the values.
For each participant h:
r(s1
i, s2
i|h) = sign( y0(s1
i, s2
i|h))·Ry0(s1
i, s2
i|h)

, (8)
where y0(s1
i, s2
i|h))is the zero-centered Likert rating provided by subject hfor trial iandR(·)is rank
transform using random tie-breaking.
For each model m:
r(s1
i, s2
i|m) = sign( LR(s1
i, s2
i|m))·RLR(s1
i, s2
i|m)

, (9)
A valid correlation measure of the model ranks and human ranks must be invariant to whether one
sentence was presented on the left ( s1) and the other on the right ( s2), or vice versa. Changing the sentence
order within a trial would flip the signs of both the log-ratio and the zero-centered Likert rating. Therefore,
the required correlation measure must be invariant to such coordinated sign flips, but not to flipping the sign
of just one of the measures. Since cosine similarity maintains such invariance, we introduced signed-rank
32cosine similarity , an ordinal analog of cosine similarity, substituting the raw data points for signed ranks (as
defined in Eq. 8-9):
SCSR=P
ir(s1
i, s2
i|m)r(s1
i, s2
i|h)qP
ir(s1
i, s2
i|m)2qP
ir(s1
i, s2
i|h)2. (10)
To eliminate the noise contributed by random tie-breaking, we used a closed-form expression of the
expected value of Eq. 10 over different random tie-breaking draws:
E(SCSR) =P
iE
r(s1
i, s2
i|m)

E
r(s1
i, s2
i|h)

pPn
k=1k2pPn
k=1k2=P
i¯r(s1
i, s2
i|m)¯r(s1
i, s2
i|h)Pn
k=1k2, (11)
where ¯r(·)denotes signed rank with average-rank assigned to ties instead of random tie-breaking, and n
denotes the number of evaluated sentence pairs. The expected value of the product in the numerator is
equal to the product of expected values of the factors since the random tie-breaking within each factor is
independent. The vector norms (the factors in the denominator) are constant since given no zero ratings,
each signed-rank rating vector always includes one of each rank 1ton(where nis the number of sentence
pairs considered), and the signs are eliminated by squaring. This derivation follows a classical result for
Spearman’s ρ[72] (see [73], appendix C, for a modern treatment). We empirically confirmed that averaging
SCSR as defined in Eq. 10 across a large number of random tie-breaking draws converges to E(SCSR)as
defined in Eq. 11. This latter expression (whose computation requires no actual random tie-breaking) was
used to quantify the correlation between each participant and model.
For each participant, the lower bound on the noise ceiling was calculated by replacing the model-derived
predictions with an across-participants average of the nine other participants’ signed-rank rating vectors. The
lower bound plotted in main text Fig. 4 is an across-subject average of this estimate. An upper bound on the
noise ceiling was calculated as a dot product between the participant’s expected signed-rank rating vector
(¯ r/pPk2) and a normalized, across-participants average of the expected signed-rank rating vectors of all
10 participants.
Inference was conducted in the same fashion as that employed for the binarized judgments (Wilcoxon
signed-rank tests across the 10 subject groups, controlling for false discovery rate).
7 Supplementary Results
7.1 Randomly sampled natural-sentence pairs fail to adjudicate among mod-
els
As a baseline, we created 90 pairs of natural sentence pairs by randomly sampling from a corpus of 8-word
sentences appearing on Reddit. Evaluating the sentence probabilities assigned to the sentences by the dif-
ferent models, we found that models tended to agree on which of the two sentences was more probable
(Extended Data Fig. 2). The between-model agreement rate ranged from 75.6% of the sentence pairs for
GPT-2 vs. RNN to 93.3% for GPT-2 vs. RoBERTa, with an average agreement between models of 84.5%.
Main text Fig. 1a (left-hand panel) provides a detailed graphical depiction of the relationship between sen-
tence probability ranks for one model pair (GPT-2 and RoBERTa).
We divided these 90 pairs into 10 sets of nine sentences and presented each set to a separate group of 10
subjects. To evaluate model-human alignment, we computed the proportion of trials where the model and the
participant agreed on which sentence was more probable. All of the nine language models performed above
33chance (50% accuracy) in predicting the human choices for the randomly sampled natural sentence pairs
(main text Fig. 1a, right-hand panel). Since we presented each group of 10 participants with a unique set of
sentence pairs, we could statistically test between-model differences while accounting for both participants
and sentence pairs as random factors by means of a simple two-sided Wilcoxon signed-rank test conducted
across the 10 participant groups. For the set of randomly sampled natural-sentence pairs, this test yielded
no significant prediction accuracy differences between the candidate models (controlling for false discovery
rate for all 36 model pairs at q<.05). This result is unsurprising considering the high level of between-
model agreement on the sentence probability ranking within each of these sentence pairs.
To obtain an estimate of the noise ceiling [74] (i.e., the best possible prediction accuracy for this dataset),
we predicted each participant’s choices by the majority vote of the nine other participants who were pre-
sented with the same trials. This measurement provided a lower bound on the noise ceiling. Including the
participant’s own choice in the prediction yields an upper bound, since no set of predictions can be more
human-aligned on average given the between-subject variability. For the randomly sampled natural sen-
tences, none of the models were found to be significantly less accurate than the lower bound on the noise
ceiling (controlling the false discovery rate for all nine models at q<.05). In other words, the 900 trials
of randomly sampled and paired natural sentences provided no statistical evidence that any of the language
models are human-inconsistent.
7.2 Comparing the accuracy of unnormalized and normalized sentence prob-
ability estimates
Previous studies (e.g., [13]) have found that normalizing language model sentence probability estimates by
the sentences’ token counts can result in greater alignment with human acceptability judgments. While we
deliberately used unnormalized sentence log probability when designing the experiment, we evaluated the
prediction accuracy of each model under such normalizations through a control analysis.
Rather than predicting human judgments based only on the relative log probabilities of the two sen-
tences, we instead used cross-validated logistic regression to predict human judgments using a combination
of unnormalized log probability differences (“LP”) and two measures from Lau and colleagues [13] that
incorporate information about the token counts in each sentence. The “MeanLP” measure normalized each
sentence’s log probability by its token count T, whereas the “PenLP” measure divided each sentence’s log
probability by a dampened version of its token count,
(5 +T)/(5 + 1)
0.8. For models trained on whole
words (LSTM, RNN, 3-gram, and 2-gram), we used character count instead of token count.
For each language model m, we fitted a separate logistic regression to predict the individual binarized
sentence choices across the entire main experiment dataset by weighing the three predictors “LP,” “MeanLP,”
and “PenLP.” We did not include an intercept due to the symmetry of the prediction task (the presentation
of sentences as sentence 1 or 2 was randomized). We cross-validated the logistic regression’s accuracy by
leaving out one sentence pair at a time, using data from all conditions of the experiment.
Taking token count into consideration led to minor improvements in the prediction accuracy of most
models (an average improvement of 0.95%), but this adjustment did not change the hierarchy of the models
in terms of their human consistency (Supplementary Fig. S1). We hypothesize that the greater disparities
between unnormalized and normalized probability measures, as observed by Lau and colleagues [13] com-
pared to those found in our study, may be attributed to their experiment involving sentences of markedly
different lengths.
347.3 Models differ in their sensitivity to low-level linguistic features
While the controversial sentences presented in this study were synthesized without consideration for partic-
ular linguistic features, we performed a post hoc analysis to explore the contribution of different features
to model and human preferences (Supplementary Fig. S3). For each controversial synthetic sentence pair,
we computed the average log-transformed word frequency for each sentence (extracted from the publicly
available subtlex database [61]). We also computed the average pairwise correlation between semantic
GloVe vector representations [75] of all eight words, based on neuroimaging research showing that there
are specific neural signatures evoked by dissimilarity in semantic vectors [10, 76]. We performed paired
sample t-tests across sentence pairs between the linguistic feature preferences for models vs. humans, and
found that GPT-2, LSTM, RNN, 3-gram, and 2-gram models were significantly more likely (vs. humans)
to prefer sentences with low GloVe correlations, while ELECTRA was significantly more likely to prefer
high GloVe correlations (controlling the false discovery rate for all nine models at q<.05). For word fre-
quency, the RNN, 3-gram, and 2-gram models were significantly biased (vs. humans) to prefer sentences
with low-frequency words, while ELECTRA and XLM showed a significant bias for high-frequency words.
These results indicate that even strong models like GPT-2 and ELECTRA can exhibit subtle misalignments
with humans in their response to simple linguistic features, when evaluated on sentences synthesized to be
controversial.
358 Supplementary Figures
0 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
a
0 25% 50% 75% 100%
human-choice prediction accuracyGPT-2
RoBERTa
ELECTRA
BERT
XLM
LSTM
RNN
3-gram
2-gram
bUnnormalized sentence probability estimates
Normalized sentence probability estimates
Supplementary Fig. S1: The predictivity of normalized and unnormalized log-probability measures.
(a)Predicting human judgments from all conditions using only unnormalized log probability differences
(equivalent to Fig. 4 in the main text, except using binarized accuracy as a dependent measure). (b)Binarized
accuracy of the logistic regression optimally combining LP, MeanLP, and PenLP for each language model.
Relative model performance is nearly identical in these two analyses, indicating that tokenization differences
across models did not play a large confounding role in our main results.
36Supplementary Fig. S2: The task instructions provided to the participants at the beginning of the experimen-
tal session.
37abSupplementary Fig. S3: Linguistic feature values for synthetic sentence pairs. (a) GloVe correlation
values of the preferred and rejected sentence for each synthetic sentence pair. Each panel depicts preferences
for both humans (red) and a specific model (black), for sentence pairs that this model was involved in
synthesizing. Black sub-panel outlines indicate significant differences between the preferences of models
and humans on that particular set of sentence pairs, according to a paired sample t-test (controlling for false
discovery rate across all nine models at q<.05). (b)Same as (a), but for average log-transformed word
frequency.
389 Supplementary Tables
modelaccepted sentence
has more tokensequal
token-countsrejected sentence
has more tokens p-value
GPT-2 24 13 3 <0.0001
RoBERTa 6 18 16 0.0656
ELECTRA 12 21 7 0.3593
BERT 4 8 28 <0.0001
XLM 2 16 22 <0.0001
Supplementary Table S1: Token count control analysis. For each transformer model, we considered syn-
thetic controversial sentence pairs where the other targeted model was also a transformer (a total of 40
sentence pairs per model). For each such pair, we evaluated the token count of the synthetic sentence to
which the model assigned a higher probability (“accepted sentence”) and the token count of the synthetic
sentence to which the model assigned a lower probability (“rejected sentence”). For each model, this table
presents the number of sentence pairs in which the accepted sentence had a higher token count, both sen-
tences had an equal number of tokens, and the rejected sentence had a higher token count. We compared the
prevalence of higher token counts in accepted and rejected sentences using a binomial test ( H0:p= 0.5)
controlled for False Discovery Rate across five comparisons.
GPT-2 assigned significantly more tokens to accepted sentences, whereas BERT and XLM assigned sig-
nificantly more tokens to rejected sentences. For RoBeRTa and ELECTRA, no significant difference was
found. Note that since the controversial sentences are driven by relative model response properties, a sig-
nificant difference for a particular model does not necessarily indicate that token count biases the model’s
sentence probability estimates. For example, GPT-2’s apparent preference for sentences with a greater token
count might reflect biases of the alternative models pitted against GPT-2. These models might prefer shorter
sentences that exhibit undetected grammatical or semantic violations over longer but felicitous sentences.
Overall, these results indicate that while certain models’ probability estimates might be biased by to-
kenization, lower sentence probabilities were not systematically confounded by higher token counts.
39