Language Models Are Better Than Humans at Next-token Prediction
Authors: Buck Shlegeris
Fabien Roger
Lawrence Chan
Euan McLean
Venue: Accepted by TMLR ()

Abstract: Current language models are considered to have sub-human capabilities at natural language tasks like question-answering or writing code. However, causal language models are not trained to perform well at these tasks; they are trained to accurately predict the next token given previous tokens in tokenized text. It is not clear whether language models are better or worse than humans at next-token prediction. To try to answer this question, we performed two distinct experiments to directly compare humans and language models on this front: one measuring top-1 accuracy and the other measuring perplexity on OpenWebText. In both experiments, we find humans to be consistently \emph{worse} than relatively small language models like GPT-Neo-1.3B or GPT-2-large at next-token prediction.

Published in Transactions on Machine Learning Research (07/2024)
Language Models Are Better Than Humans at Next-token Prediction
Buck Shlegeris' Redwood Research
buck@ndurs.com
Fabien Roger* Redwood Research
fabien. r.gger Ggmaill com
Lawrence Chan
lawwence.chan@liiveco
METR
Euan McLean PAR AI
emc031 @ com
Reviewed on OpenReview: https: // openreview. net/ forum? id- RNsnSLdmV7
Abstract
Currett language models are considered to have sub-human capabilities at natural language tasks like question-anse answering or writing code. However, causal language models are not trained to perform well at these tasks; they are trained to accurately predict the next token given previous tokens in tokenized text. not clear whether language models are better or worse than humans at next-token prediction. To try answer this question, we performed two distinct experiments to directly compare humans and language models on this front: measuring top-1 accuracy and the other measuring perplexity OpenWebText. In both experiments, we find humans to be consistently worse than relatively small language models like GPT-Neo-1.3B or GPT-2-large at next-token prediction
1 Introduction
Recent language models (LMs) have demonstrated impressive capabilities natural language tasks, like writing convincing human-like text, coding, answering general knowledge questions. However, LMs are not considered to have yet surpassed human performance at these tasks. But performance at such tasks is not fair way of comparing LMs and humans. LMs are not explicitly trained to perform well at natural language tasks. Their loss function is simply next-token prediction: accurately predicting the next token given previous tokens in tokenized lext.
How good are modern LMs compared to humans at next-token prediction? While one can construct tasks which humans make next-token predictions better than any language model, there have been no "apples-to- apples" comparisons on non- non-handerdfted datasets. To answer this question, we performed two experiments that directly compare humans to language models next-token prediction, using the OpenWebText dataset
Gokaslan & Cohen 2019).
Two natural ways of measuring the quality of next-token prediction are top-1 accuracy and perplexity, Top-1 accuracy is the fraction of times, over many predictions, that the predictor assigns the highest probability to the correct next token. This is relatively easy to measure, but does not capture information about the rest of the probability distribution that the predictor assigns over possible next tokens. A more all- all-ennoopassing
"Equal contribution
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Published in Transactions on Machine Learning Research (07 (07/2024)
but harder to measure variable is perplexity: defined by 2 where the loss L is the cross-entropy of the predictor's 8 distribution and the true distribution over possible next tokens.
Contrary to some previous claims, we found humans to be consistently worse at next-token prediction than even small models like GPT-Neo-1.3B or GPT-2-large, in terms of both top-1 accuracy and perplexity. That is, even small LMs are superhuman at next-token prediction.
We structure this paper as follows. We first review claims made date about the comparison between human and language model next-token prediction in Section 2 In sections g and we detail two small experiments we ran to measure human top-1 accuracy and perplexity respectively, along with their results. In section we discuss the implications of these results and conclude.
2 Related work
One commonly cited source on the topic of human vs LM next-token prediction is presentation by Omo- hundro (2020). This presentation contains the claim that humans have perplexity around 12, compared to the 20.5 GPT-3 [Brown et al. 2020).
This comparison is problematic for two reasons, one small and one fatal. The smaller problem is a mismatch of text corpora: the language model statistics word-level perplexities computed on Penn Tree Bank (PTB) (Marcus et al. 1993), while the human word-level perplexity estimated
the Billion Words (LBW) benchmark (Chelba et al., 2014). This is small problem in practice, as while GPT-3 was not evaluated on 1BW, GPT-2 performs slightly worse on 1BW than PTB. The bigger issuc is the methodology used to estimate human perplexity. The value for human perplexity is quoted from [Shen et al. (011)). in which, humans were asked to rate sentences on a 0-3 scale, where means "clearly inhuman" and means "clearly human". Then they computed a "human judgment score": the ratio sentences rated 3 over those rated They then fit degree-3 polynomial regression to the LMs they had (of which the best was a small LSTM), which they extrapolated significantly out of distribution to acquire the "human" perplexity (sce Figure 1 from Shen et al. (2017)) Due to this far extrapolation among other problems, we don't agree with the claim that humans have perplexity 12.
Another claim is from OpenAl regarding the LAMBADA dataset Radford et al. 2019a), where they give a perplexity around 1-2 for humans (compared to 3 for 0-shot GPT-3). However, the authors don't cite a source. The authors likely made an educated guess based on how the LAMBADA dataset was constructed.
human performance
GPT-Neo 125M
GPT-Neo 1.38
(1758)
GPT-J (6B)
Number of human players
3
10
20
30
40
50
60
Tap-1 accuracy (%)
Figure 1: The distribution of human top-1 accuracy (how often a human guesses the correct next token given previous tokens) found in our study, with GPT-Neo-125M,, GPT-Noo-1.3BB GPT-J (6B) and GPT-3 (175B) for comparison.
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In addition, LAMBADA is much restricted dataset, which consists of guessing single words requiring broad context. So this comparison isn't very informative to the question of how good language models are at the task they're trained on next-token prediction on typical internet text.
The most closely analogons study to ours is that of Goldstein et al. (2022). This found that an ensemble of humans have a top-1 accuracy of 28% vs 36% for GPT-2, which similar to what we saw for humans on webtext. However, they used a different, smaller dataset (the transcript from a podcast), which is not particularly representative of randomly-sampl
English internet text.
Owens et al. 1997) pitted 8 humans against n-gram model for missing word prediction. Humans achieved a top-1 accuracy of 26%. This is related but not the same as top-1 accuracy for next-token prediction, since the prediction was on word-level rather than token level, and the predictions were conditioned on words appearing after the target word.
There are number of more narrow datasets on which we know both human and LM performance, where some humans still oulperform LMs. The MATH dataset (Hendrycks et al. 2021 is an example. But, to our knowledge, there next-token prediction.
apples-to-apples comparison between humans and modern LMs for webtext
3 Measuring human top-1 accuracy
The main difficulty for comparing human and LM performance that, unlike with language models, is infeasible for humans to give their entire probability distribution for the next token in sequence, since GPT-2 has a vocabulary size around 50,000.
One way to get around this is to simply measure top-1 accuracy by asking humans what token is most likely to come next. We can't derive human perplexity from this, but top-1 accuracy might still give us a reasonable measure of how well humans do at next-token prediction. According to this mcasure, humans are worse than all language models we tried, even humans who have practiced for more than an hour.
3.1 Method
The human participants were either staff advisors of our lab, or members of the Bountied Rationality Facebook group. They were paid 330/hour. There were 60 participants overall.
The language models we evaluated were GPT-Neo-125M GPT-Neo-1.3B (Black et al. 2021 GPT-J-6B
(Wang& & Komatsuzaki 2021 and GPT-3 [Brown et al. 2020
We set up a top-1 token prediction game website 2 sense what next-token prediction is like.
We recommend playing the game you want to get a
In this game, the player makes their way through random segment. from the validation set of OpenWeb Text Gokaslan & Cohen 2019). At each token, they are asked to guess the single token they thought most likely to come next. The correct next token is revealed to them, and they are once again asked to predict the most likely token to follow the revealed one. A total of 18530 guesses were made across participants.
Our website did not have any way for participants to guess "visually empty" tokens, such as newlines and half-Unicode characters (displayed as <?> on the website). We excluded cases where the correct guess was impossible from our analysis. They represent 6.3% of questions asked to participants.
3.2 Results
The mean accuracy of the participants' answers this top-1 lask was 29%. Of these players, 38 gave at least 50 answers, with an accuracy of 30%. This accuracy is low compared to the accuracy of LMs: when measured on the same dataset, GPT-3 achioved an accuracy of 56%. Even GPT-Neo-125M, achieved
2 Available http::/tr-1nmee/ee gane. wegaaeeeeaaae herokuapp.com/
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Model
Split
Perplexity (per token)
Top-1 Accuracy
EPT-Nco-125M
Validation
29.26 + 11.22
0.483 + 0.009
EPT-Neo-125M
Train
22.76 + 1.62
0.481 + 0.009
GPT-Neo-1.31
Validation
17.84 + 7.79
0.547 + 0.009
GPT--Ne-1133
Train
12.89 + 0.91
0.545 + 0.009
GPT-J-6B
Validation
12.49 + 4.42
0.580 = 0.009
GPT-J-6B
Train
9.57 0.64
0.579 + 0.009
Table 1: Model accuracy and perplexity on the train and validation datasets of the Pile, We show 2-sigma standard deviations (over sequences) divided by / /Neequences uncertainties.
accuracy above all players in our dataset. Figure shows the distribution of top-1 accuracies across participants, along with the accuracy of some language models.
We found that humans don't quickly get much higher performance with practice. There were players who guessed over 500 tokens (taking roughly hours), and achieved accuracics around the average of human performance (between 0.26 and 0.32).
3.3 Additional analysis
We study the ellect of two possible confounders: the ellect of overfitting the comparison models and the effect of weird tokens on human performance.
GPT-Nco and GPT-J models used to compute the model accuracy. We study this effect by measuring the top-1 accuracy of GPT-Neo and GPT-J models on the first 256 tokens of 1024 randomly selected passages of the Pile (Gao et al. 2020) (train and validation set). We find that overfitting is very unlikely to be significant, as the top-1 accuracy on the train and val set the pile are very close, as shown in Table [
trained the pile, which may contain some of the OpenWebText data
Human participants did not extensively study the tokenization scheme of GPT-2. They were helped by the website that prevented them from providing incorrect tokens, but tokenization difficulties may still have hindered their performance. To study the impact of this effect, we report in Figure 2 the top-1 accuracy of models and human participants for tokens that correspond to words: we keep tokens that start with a space, that otherwise have only alphabetical characters in them, and followed by token starting with
human performance
TPT-Neo 125M
GPT-Neo 1.38
Number of human players
GPT:) 68
5- 4-
10
20
30
40
50
Top-1 accuracy (%)
Figure 2: The distribution of human top-1 accuracy on a filtered dataset made out of single-word tokens, with GPT-Neo and GPT-J models of varying sizes for comparison.

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space, which represent 62% of tokens from the dataset. We find that this reduces the gap between human participants and models considerably. It is unclear to what extent this is due to tokenization difficulties or to another bias introduced by filtering. For example, these mumbers may reflect bias humans may have towards single-word tokens, or LLMs' wide knowledge (relative to humans) about the frequency of rare proper nouns which are often excluded by our filter.
4 Measuring human perplexity
Language models aren't trained to guess the single most likely next token, so the previous task isn't directly assessing language models on the task they're trained on. They are trained to give a full distribution over next lokens, airiing to minimize their perplexity. Therefore, measuring top-1 accuracy may underestimate how good language models are relative to humans. In this section, therefore try to compare human and language models' perplexity.
It is easy to measure models' perplexily, because language models produce a probability distribution for every next token. Unfortunately, humans aren't able to quickly provide a probability distribution over the 50,000 possible tokens. So human perplexity must be estimated indirectly.
4.1 Method
To gather the relevant data, we set up a second language modeling game website. 54 humans participated. They were again either staff of our lab or members the Bountied Rationality Facebook group, paid $15 for answering set of 120 rounds (taking roughly 30 minutes overall per participant). 19 participants answered all 40 questions of the first set, and 11 participants answered all 80 questions of the second set, answering total of 1640 comparisons.
On each round, a prompt e from the validation dataset of OpenWebTeet (Gokaslan & Cohen 2019 is shown (with a maximum length of 120 tokens). The participant is then asked to guess the likelihood of one candidate token æ being correct, given that one the two candidates z,y are correct. From this the ratio of probabilities of æ and y can be determined, which we call r(z,ylc).
From the responses build dataset of many values of r(z, v/c) for many x, y pairs. This data can be used to estimate human perplexity. We make the following assumption: for given prompt all humans have the same probability distribution over next tokens h(ylc). In this case, the responses from participants can A(alc)
be written as r(x, ylc) A(vic)
In the following sections we detail how we translated the dataset into an estimate human perplexity Pr-
We used importance sampling generate the candidate tokens (see Section 4.1.1). This way of sampling introduce bias to the data, so modified the game slightly correct for this bias (Section 4.1.2. In Section 4.1.3 we describe how estimate an uncertainty for the results.
4.1.1 Estimating perplexity from a few relative probabilities with importance sampling
Let T' be the true distribution of tokens y after a context Human perplexity Ph. is defined as
P. = 24h, In Dog
(1)
Ln is referred to as the human loss function. We can't directly ask human for the probability of the true token k(lcc without spoiling them on the answer, and it would be cumbersome to ask for their whole probability distribution. We can do better by asking for relative likelihoods. For a given context e and true token y, hylcc) can be rewritten as
Σ M(olo) ZEB h(yle)
)
-
-(x
Σ r(z, ulc) Leen
h(vlc)-
(2)
3 Available httpt::////// htttts://rrrtttt http//rrrlnnmeee game. www.meeerouuappccomm

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where Q is the full vocabulary. That's better, but that would still cost around 50,000 questions (the number of tokens) for each value of h(rlc). To lower this number use importance sampling. The bulk of Σx r(x, u/c) is where the most likely tokens are, so it's not worth asking for every one of them. We condition a reference language model G on our context e from which we can sample the most likely tokens. We can then estimate hyle)) with the following approximation:
r(X, x(((c) [
1 E
r(z, rac,yle) ((xccc
h(ylc) Bx
Σ x~
(3)
where is the number of tokens generated by G, which can be much smaller than 50,000. g(rcc) is the probability of a given outputted by G. Ex- is the sum over the set of tokens that the model G conditioned on e generates in practice when queried n times. So in each round of the language model game, one candidate token x is the true next token, while the other, y, generated by G(c).
To decrease the variance of this estimator for h(ylc), we instead estimate
Mylc) = ExxG. g(ule) g(yle)
[9(x(c) (x, (x. ~
1 Σ z>Glle
gylc) g(x|e)
r(, ulc)
(4)
The variance is lower because, if h and are close, most lerms in the sum will be close to (whereas r(z, vlc)/g(zlc) can get very large or small on some samples).
With access to h(yle)/gyycc) we can compute LA - LG (where LG is the loss of the reference language model G defined by equation with h replaced with g). Using N samples from the true target corpus, from we find
equations and 4
(VC)) h(YIC)
1 Σ g(vce) g(rlc) (z, ule)
La LG
LG = EICYNT
log
2
Σ
log
(5)
N
(c.y)>>
ING.
We can then add the known value for LG find Ln, and from that, Ph. practice, we use GPT-2-small (117M parameters) as our generator language model G.
4.1.2 Controlling for sample bias in importance sampling
Due to the fact that one of the two candidate Lokens sampled from a language model G, the participants no longer have an incentive to submit their actual guess at r(z, ylc), since they have extra information about how and y samplod.
Naively, we would find ulc, h(zrlc)/hylcc) by making the human guess if the prompt e is followed by I or y, and then the human should answer that e is followed by I with probability ((zle)/(h(zlc)) + (yycc)). This would be true if one token was sampled from the true distribution and the other one was selected uniformly among all other tokens. However, this isn't true here because the other token is sampled from Ge.
A rational agent that perfectly knows T and G would answer that e is followed by with probability
P(x ~ P(z)T((c) Ay G(c)) T(enT(e) G(e)))~~((e)--- +(xe)))(+(x+++0)) G(c) T(c))
t(xlc)s(vlc) + t(z)e)g(vlc)*
(6)
where x G(c) refers to the event "r was sampled from the distribution G(c)", t(xlc) is the true distribution T. In the second line, we used the independence of T' & G. A human could use their knowledge of G as extra information that can help guess the right answer. For example, a human who believes T(c) to be indistinguishable from G(c) will answer 0.5 to every question, making it impossible to extract hxllc)/(((lb c).
The solution is incentivize the human give something other than their best guess. We ask the human for the probability p that is followed by x, and we reward them with weighted binary cross-entropy reward
R(p) = g(xlc) log(p) + s(vlc) log(1 p
(7)
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where 2 is the correct answer. The expected value of this reward, according to human believing that the generative model follows a distribution G, is
[[R(p)] g( log( (og(()(((())))(Geee) + ((yle) log(1 -
(8)
This is at its maximum when dE(R(p))/dp 0,
0, therefore, the optimal play satisfies
((le))(VlcMM((l (( = h(zlc) + h(vlc)
h((lee)
(9)
If we assume that humans play optimally (which is a questionable assumption), then the human's response, p": represents the human's true belief for (hxlc) + h(ycc),, no matter what their beliefs about the gencrative model are.
In practice, we use slightly different reward, R(p) 1000 (()((()))))lo(())- [og(::o(())))(((000))========== ((oe) log(0.5)) for which the optimal play is the same, but is more understandable for human. Participants get a reward of 0 for saying
0.5, and the scaling makes their score more readable.
On rounds where y, the participant isn't asked to compare their relative likelihoods. Instead, the website automatically answers that both are as likely.
4.1.3 Estimating uncertainty in our measurement of perplexity
If we assume humans play rationally in the game described above, there remain three sources of uncertainty in our measurement of human perplexity:
1. Uncortainty in the sum over (c,3) ~ T. We collected data on only 120 different (c, v) pairs, which is small considering that the per-token loss has a large variance. This causes non-negligible uncertainty over the measured perplexity, even if we had perfect estimates of each value of hCylc)/g(lc)) for each (c, y) pair. We compute the empirical standard deviation a on La over (c, y) pairs. This gives us a lower bound exp(L,, 20) and an upper bound exp(L, + 22) on the perplexity Ph = cxp(Ln..
2. Uncertainty in the sum over G(c). We now consider the uncertainty in each Myle)//(VV) sample estimated by equation A natural way to estimate this is to use the empirical standard deviation over the sum in equation 4 and propagating this uncertainty to La. But the sum in equation 4 is teavy.tailed. This means that, since we only have a small amount of samples (~ 10) for every prompt, we underestimate the perplexity of any predictor using this technique. The degree of underestimation cannot be easily quantified, as the weight the heavy-tail examples depends on the distance between human predictions and the reference LM prediction, as can be seen in Figure ! To test this effect, we estimated the loss of 14M- MaM-maraeeter LM and a B45M-parameter LM, using the 117M -arammete LM a generator. We find the underestination to be at most 0.5 bits away from the ground truth when & 40, for models that are very dissimilar (like 14M-parameter model LM, for which the difference in true loss is 1.3 bits). The results are shown in Figure 3 This is a large difference, but this is still good enough for the purpose of comparing humans to language models because we find differences between humans and LMs much larger than ~ 0.5 bits. Hence we do not allempt to estimate this error, and accept as limitation of our study.
(17M-parameter
We only include 1. in final uncertainties (shown as error bars in Figure 4 Measuring uncertainty by bootstrapping (rejecting random halves of users) yields similar results (sce Appendix B
4.1.4 Estimating perplexity for language models
To ensure a true apples-to-apples comparison, we estimated the perplexity of the language models in the same way as described for humans above, on the same datasct. We used GPT-2 models GPT-2 medium (345M parameters) and small (117M parameters) (Radford et al. (201b).. We also used a 2-layer 14M-parameter model trained ourselves the train set of OpenWebText as example of a minimal model.
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-0.25
Estimated (In bits)
-0.75
-1.00
-1.25
-1.50
error in 1 14M-parameter loss estimation
error 345M-parameter loss estimation
-1.75
109
10a
Samples given prompt (n)
Figure 3:
Difference between the loss estimated by equation and the ground truth loss for two LMs, for varying n (number of samples per prompt), for N = 1000 prompts.
As our human participants could only enter one of the 11 ratios in our interface (99%, 90%, 80%, 70%, 60% 50%, 40%, 30,, 20%, 10%, 1%), also report the "rounded" performance of our LMs that is, the performance of our LMs if they choose the checkbox that is the closest to their probability ralio. (Note that we can't access the true perplexity of rounded models, only ratios are rounded and not the probability of the correct token.). As shown in Appendix C more extreme rounding leads to much worse performance, and humans would need to produce calibrated and extreme probabilities to get low performance.
4.2 Results and limitations
Our estimates of perplexity for humans and LMs, along with the uncertainty estimate, are shown in Figure Since we used the same method for estimating perplexity for humans and LMs, this direct comparison between human and LM performance. As explained in Section 1.1.3] all losses obtained by this method are underestimations of the true loss. GPT-2-small is used the generator, which is why its measured perplexity using the estimator is perfect.
This method could also overestimate human perplexity: there could be other setups in which it would be easier for players to give calibrated probabilities. In fact, some players found the scoring system hard to understand, and led them to not express their true probability ratios, we might have underestimated
GPT-2 medium
true perplexity on the samples
GPT-2 small
measured perplexity on the samples using estimator
4M-aaaameteer model
medium rounded:
GPT-2 small rounded:
our 14M-parameter model rounded
human
20
40
80
100
160
per token perplexity
Figure 4: Our estimated perplexities for a number language models and humans. The human perplexity was obtained from our study described Section 4.1] GPT-2 small has no estimated value, since this was used as the reference generator model. Error bars are determined according uncertainty source (i)
described in Section 4.1.3
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human performance. In general, this method is very sensitive to failures at giving calibrated probability estimates: the high perplexity obtained here is probably partially due to humans being bad at giving cali- brated probabilities, rather than humans just being bad at language modeling. In addition, as humans are restricted to one of 11 ratios, our setup could also underestimate performance by artificially reducing the resolution of our human participants.
Finally, this evaluation also shares the weaknesses of our Top-1 accuracy measurements: humans could struggle with tokenization in way that would be solved by more training, and our reference language models may be overfitted to the evaluation dataset. We can't reproduce the analysis done with GPT--eeo models since the training set of GPT-2 models is unknown, but given that the perplexity values reported in Figure | are close to the validation perplexity of Table | (and are measured on similar datasets using the same tokenizer), it unlikely that our LLM perplexity measurements are far from their true value. We also find that excluding non-word tokens from our analysis does not change qualitative takcaways of our experiments (sce Appendix D).
Thus, while we don't have good way to precisely measure human perplexity, these results give reasonable evidence that it is high. In particular, humans are worse than GPT-2-small at giving calibrated estimates of token vs token probabilities.
5 Discussion
The results here suggest that humans are worse than even small language models the size of GPT-2-small (117M parameters) at next-token prediction, even on the top-1 prediction task. This is true even when the humans have practiced for 1-2 hours. Some humans may beat mediun-sized language models (GPT-2-small, GPT-Neo-1.3B) with enough practice, but seems very unlikely that even the best humans could beat substantially larger models.
These results may be surprising because humans are better at writing coherent text than GPT-2 and therefore one might expect humans to be better at next-token prediction. But actually, these tasks are very different - if you train an autoregressive model to imitate human text, the model has to dedicate capacity to all the different features that might be informative for guessing the next token (including features that don't affect human judgments of coherence). Language models are trained to guess what are all plausible lokens that could follow, while being coherent only requires finding one reasonable completion. Additionally, predicting the next token on OpenWebTess Text sometimes requires very broad knowledge that may require an amount of memory that may exceed human limits.
These findings are important for language model interpretability work, because it means you should expect language model to have more knowledge of the text than you have. It has been argued in Hurbinger (2019) that models may become more interpretable as they get to human level, and then become less interpretable again as they become superhuman. The fact that existing LMs are already superhuman (at the task they're 're trained on) is worth bearing in mind here.
6 Conclusion
In this paper, we compared the capabilities of humans and language models (LMs) in next-loken prediction tasks, using top-1 accuracy and perplexity as our metrics. We find that even relatively small language models outperform humans at next-token prodiction.
Acknowledgements and contributions
We thank varicty of people for comments and assistance (especially Paul Christiano, Nostalgebraist, and Rafe Kennedy), and to various people for playing the game. The lop-1 prediction web app was mostly written by Buck Shlegeris, Fabien Roger designed and ran the perplexity experiment and performed most of the analysis, Lawrence Chan performed the rescarch on previous measurements, and Euan McLean adapted the Alignment Forum post into a paper. Thanks to Paul Christiano for suggesting the rough approach for our human perplexity experiment, and to Paul and Adam Scherlis for helping with some of the details.
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Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Xiaodong Song. and Jacob Steinhardt. Mcasuring mathematical problem solving with the math datasct. ArXiv, abss22103.08874 2021.
E Hurbinger. Chris olah's views on agi safety, 2019. URL g2s0000aagFFyyggg///rrrrroraeeee
Mitchell Marcus, Mary Ann Marcinkiewicz, and Beatrice Santorini. Building large annotated corpus of english: The penn treebank. Compul. Lingwist., 19(2):313 330, jun 1993. ISSN 0891-2017.
Steve Omohundro. Openai's gpt-3 language model, 2020. URL https://www.slieeesttt openais-gpt- 1-p----aangaggemmodeee www.oooo-gggssttttteeeeeeree omohundro
net nes//nmenta/
M. Owens, P. O'Boyle, J. McMahon, J. Ming, and F. J. Smith. A comparison of human and statistical
language model performance using missing-word tests. Language and Speech, 40(4):377-389, 1997. doi:
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Alec Radford, Jeffrey Wu, Dario Amodei, Daniela Amodei, Jack Clark, Miles Brundage, and 1lya Sutskever. Better language models and their implications, 2019a. URL https://openai: com/blogl letter--anguage-rodaell
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAT 7 blog, 188):9, 2019b.
Xiaoyu Shen, Youssef Oualil, Clayton Greenberg, Mittul Singh, and Dietrich Klakow, Estimation of gap between current language models and human performance. In INTERSPEECH, 2017.
Ben Wang and Aran Komatsuzaki, GPT-J-6B: A Billion Parameter Autoregressive Language Model. attps://git thub. http:////iooooooo///eeeeeeeeeeee transformer---rrrrr jax, May 2021.
10

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Published in Transactions on Machine Learning Research (07 (07/2024)
A
Data collection interface
Figure and show the interfaces participants used.
Language modelling game!
Read instructions and notes here Your name:
janon
Your score: 1 / 33%
You're currently predicting document number 5885
Remember that if you want to predict a token that starts with space (which you usually do), you need to type that space explicitly. See the instructions you're confused by how the tokenization works.
Get new document
Get *th bbiggest
*Aston
Martin
latestt
*news
valid token? yes
Figure 5: Interface for the experiment described in Section
3
The interface available
https:
//rr 1m game.... hwrokuapp..com com
A new language modeling game!
Read instructions and notes here To get compared to the right token. (Don't overthink this: you should play as if you were choosing between the true next token and another chosen uniformly random between all other tokens, don't hesitate to put high probability token if you think the other highly unlikely. For more details, please check out the notes.)
high possible, simply put how likely the left token in this context
Your name: anon
Show score details
+ Show models score
Your current score: 0 (0)
You are currently in training mode. Please train bit to understand how the scoring system works, then
Start the true
launch the true game.
Read the following prompt. Token A or token B is token that appeared next in the original text. The other one was generated language model. How confident are you that token the that appeared in the original text?
Training progress: (comparison number: 20000)
Buy Photo The lookng north-on on-h--on-a clolseed section of the Blue Ridge Parkway around Milepost 375 on Dec. (Photo: Angeli-Wrightee Wiigh//awighh@eittzen times.ccmm.... ttweeetttieeeeeiouuuaoooeo Photo (ntooonn/MMnnnn MAGGIA - Rice has flying squirrels and free-branched on the brain. InVnThe The marketing director for the
Token A Token
...aa
P.rrrrl
A is likely be correct
99%
90%
80%
70%
60%
50%
40%
30%
20%
10%
1%
B is likely
be correct
Submit guess
Next completion
Figure 6: Interface for the experiment described in Section //rr Im-game. hww.kkuap..co///hccchheeeeeee
The interface is available at https:
11

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Published in Transactions on Machine Learning Research (07 (07/2024)
B Uncertainty estimation using bootstrapping
Figure 7 shows perplexity when estimating uncertainties with bootstrapping: we compute perplexity 100 times, and ignore the entries of random half of users each iteration. We report the 0.05 and 0.95 quantiles as uncertainty estimates. We find that this reduces the estimate of perplexity for both humans and language models, which is not surprising given that our estimate of perplexity underestimates the true perplexity more when the number of samples is smaller (as shown in Figure 3). Human perplexity remains above language models', which shows that our conclusion does not depend on the poor performance few users.
GPT-2 medium
true perplexity on samples
GPT-2 small
measured perplexity on the samples using
our 1/M-parameter model
GPT-2 rounded:
GPT-2 small rounded:
our 14M parameter model rounded
human
20
40 per taken perplexity
80
100
Figure 7: Our estimated perplexities for number of language models and humans when using bootstrapping to estimate uncertainty. Error bars show the median estimate, well as 0.05 and 0.95 quantiles.
C Influence of Rounding on Perplexity
Figure shows the perplexity when more rounding applied. We find that applying more rounding sig- nificantly increases language model perplexity without increasing human perplexity much, which shows the importance of using the relatively fine-grained rounding we usod.
GPT-2
exily samples
mcasured perplexity on the samples
GPT-2 small
using the est mator
our 14M parameter model
GPT-2 medium rounded
GPT-2 rounded
14M parameter model rounded
human
GPT-2 medium rounded more round
small rounded more round
1'M-parameter model rounded round
human more round
GPT-2 medium rounded even more round
GPT-2 small rounded even more round
1-M-parameter rounded even human round
10
20
40
80 100 per perpl perplexity
160
Our estimated perplexities for a number of language models and humans with more extreme rounding. 'rounded" corresponds to the level rounding the interface, "more round" corresponds to rounding to the nearest of [0.1, 0.2, 0.5, 0.8, 0.9] (human answers are rounded post-hoc) and "even more round" corresponds rounding to the nearest of [0.2, 0.5, 0.8].
Figure 8:
12

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Published in Transactions on Machine Learning Research (07/2024)
D Perplexity Estimation on Word-tokens
Figure 9 shows perplexity estimates when only keeping the 84/120 choices where the correct token is word (a token that starts with a space and otherwise only contains alphabetical characters). This does not change the conclusions drawn from the main experiments.
GPT-2 medium
true perp exity on the samples
GPT-2 small
mcasured perplexity on the samples using the estimator
14M-paramster model
GPT-2 medium rounded:
GPT-2 small rounded:
2/M-parameter rounded
human
taken perplexity
Figure 9: Our estimated perplexitics for number of language models and humans when only using questions about word tokens.
13


Reviews:
[{"review_id": "ryJnxHKpJO", "reviewer": "Reviewer_UNix", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\n\n- The authors are trying to measure and understand an important question regarding a similar target of understanding language: \nhow the method learned by causal LMs may not be the best approach for humans' ability. \n\n- The questions defined to measure human perplexity is interesting. \n\n### Weaknesses\n\n- In equation (6), one question would be `y~G` or `y|G`, either human is sample the output token or use the context to predict the token. \n\n- The word puzzle pool presented in the paper is sometimes very knowledge-heavy (e.g., `Tunisia s eIslamist *Ennahda party on athe is Isis the`) as shown in the image link: https://ibb.co/ZWtrBKm. I don't think humans would have a large enough memory to retrieve that information as the token listed in equation (6).\n\n- Some of low perplexity behaviors have actually studied by the NLP community. The authors may have another look on Ref-3. \n\nRef-3. Lower Perplexity is Not Always Human-Like, ACL 2021\n\n- The authors only select causal LM and test on `en-X` question-answer pair. I think a generic title would need to be re-considered.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work investigates how humans perform in the classical language modeling task of next token prediction. In general, it is a very interesting attempt to understand how good humans are and how to measure their ability against the loss target used to train large language models. The title should be limited to a more specific scenario (i.e., a type of English token game) used in this paper.\n\nOn the technical side, the authors define a measurement method for human error in next token predictions in two ways: uncertainty over token selection that either mitigates bias or handles the long-tail challenges. Some of the connections are missing in the studies of non-causal based language models [1,2], which need to be carefully revised.\n\n***\nReferences\n\nRef-1. Lin, C. C., Jaech, A., Li, X., Gormley, M. R., & Eisner, J. (2021, June). Limitations of Autoregressive Models and Their Alternatives. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (pp. 5147-5173).\n\nRef-2. Kaddour, Jean, et al. \"Challenges and applications of large language models.\" arXiv preprint arXiv:2307.10169 (2023).\n\n\n***\n\n#### Note\n\nI have spent some time using the evaluation platform (`https://rr-lm-game.herokuapp.com/`) to understand the behavior, but I think some of the settings are not fair for interpreting that the human cognition system is worse than the causal language model in this case.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- The authors need to reconsider their title. Firstly, only causal LMs have been evaluated in this work. There are also arguments questioning whether this specific kind of word puzzle is the best case to claim this outperforming behavior.\n\n- The authors may narrow their claims or focus on the insights (e.g., rounds or types of errors humans or machines made) to provide insight for a TMLR-based audience. In short, the current title is too broad and not aligned with the results.\n\n- When discussing the equations, the authors need to reference each equation for a more journal-level submission.", "broader_impact_concerns": "1. I think the authors would do well to add a Broader Impact section, since the topic here could be referred or summarized by the non-ML community, where the results and conclusions are actually more specific.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "mt9PPMPMAN", "reviewer": "Reviewer_qLJT", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n- The paper investigates how humans perform at the same task that large language models are tasked to perform. This is an interesting and timely question considering the general interest on LLMs and how other authors have considered the same question.\n- The paper proposes a thorough and well-reasoned method for estimating the perplexity of humans at next-token prediction.\n\nWeaknesses\n- There appears to be no consideration in the paper about training data contamination concerns, since the corpora used are from OpenWebText which is likely to have been included in the training data of the LMs under study. It would have been better to use corpora with no risk of this.\n- The studies used in the paper use a convenience sample for the participants so it's hard to make conclusion about \"humans\" in general from the results. In particular, results on \"expert\" humans (e.g. people who routinely write articles similar to those used for the study) could be a better reference for comparison, similar to how comparisons against humans for benchmarks such as MMLU also compare against experts.\n- The tokenizer used by GPT-3 doesn't align exactly with humans' typical notions of tokens/words. While the paper mentions that whitespace tokens were excluded, more analysis of other cases such as tokens that don't make up entire words and unprintable tokens (e.g. fragments of UTF-8 byte sequences which don't decode to UTF-8) would have been useful.\n- Similarly, the format of the data used requires the human participants to know about how web pages are converted to plain text as used for training LLMs, which is alien to their usual experience with consuming text. An example can be seen in Figure 5 in the appendix, where \"Buy Photo\" appears twice in odd positions.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper considers the question of language models' and humans' performance at predicting the next token when given contexts from random segments of the OpenWebText corpus. First, the authors set up a game for human research participants to iteratively predict the next token to come given the context so far; after making a prediction, the correct token is revealed, and the human player is tasked with predicting the token after that.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "## Changes to improve the work\nSmall mistakes:\n- Typo in Section 4.1.3: list items 2 and 3 have \"Equation equation 4\"\n- Section 3.1: \"top-1 token prediction game website\" is a hyperlink but the formatting does not make this obvious.\n\nRegarding the description of LMs:\n- The paper claims in several places that GPT-3 Ada has 350 million parameters. It should be made more explicit that this estimate of the number of parameters comes from Gao (2021), because the size of the GPT-3 models provided via the API has not been officially published 9as far as I know).\n- Section 4 of the paper discusses LM size in terms of the number of layers, whereas earlier parts of the paper discusses the number of parameters. I think it would be better to unify this discussion to use the number of parameters everywhere.\n\n## Changes for acceptance\n- Perform a study about training data contamination, by inspecting how the perplexity/accuracy of the LLMs change when exposed to contexts that were surely not part of their training data.\n- Perform more analysis on the impacts of tokenization on the results, e.g. what happens to humans' accuracies when all \"strange\" tokens (such as those which don't entirely consist of English letters and make up an entire word) are excluded from the accuracy calculations", "broader_impact_concerns": "No particular concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ajSWc3tait", "reviewer": "Reviewer_cN5g", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths: \n   - The study is interesting. Finding that llms are better at next-token prediction while less good for most popular language tasks, can be insightful \n   - The methodology proposed to estimate token distributions of humans looks well sounded and smart. \n   - The paper is rather well written \n\nWeakness:\n   - Not fully convinced by some assumptions and choices\n   - Not enough experiments to assess the relevance of the estimations\n   - Related work should be further detailed", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper \"Language Models Are Better Than Humans at Next-token Prediction\" proposes to assess the ability of humans at the task llms are trained one, ie next token prediction , and gives a methodology to extracts insights indicating that llms have superhuman performances for this task.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Some papers have shown that llms can be contaminated by test data, that they saw at train time. Are authors sure that this is not the case for their data ? \n\n- Next token suggestion looks very hard for humans, as we do not necessarily cut words in same tokens as llms. In other words, considering the tokenizer of the llm can induce bias in defavor of humans. Wouldn't it be better to ask humans to emit next word, and then apply the tokenizer afterwards to check if the prediction starts with the correct token ? at least for accuracy experiments it looks better. \n\n- For the model game suggested for perplexity estimation giving tokens as suggestions may look somehow unfair, as for any pair of suggestion, humans may prefer full words. Wouldn't it better to suggest two full words to humans, and go back to tokens after the selection is made ? \n\n- I feel that the assumption that humans follow a similar distribution over next token is strong. Do authors assess the level of agreement ? Wouldn't it be useful to remove outliers ? disagreement does not necessarily mean incertitude, right ?\n\n- I feel the paper lacks some review of literature about the estimation of distributions of human beliefs and their use in human in the loop models, which may have many connexions with the methodology proposed to debias given knowledge of users.\n\n- Below eq (6), authors argue that a human who believes  G is similar to T would answer 0.5 to each question is not fully detailed. I feel authors should connect the discussion more strongly with  the sampling of y. Probably an example with a G distribution that always sample the same token would be more insightful : the user quickly understand G and thus always give 1 to the true token. \n\n- I feel the paper should contain an expe that shows that the proposed perplexity estimation is more insightful  than accuracy regarding the relative performance of models would be useful. It should be possible to do this at least on a toy dataset. Or give a toy scenario that further justify the need for perplexity estimation. \n\n- To assess that the methodology proposed for debiasing estimation, I feel that authors could propose the training of a RL agent that is rewarded by 1 when it find the good token, 0 elsewhere, for a given G (maybe pathologic). The agent may finally mimic the behavior of a human that leverages his knowledge about G. This could be compared to the estimation made from choices done by an RL agent learned with the proposed reward function, highlighting the benefits. \n\n- Authors argue in section 4.1.3 that eq (4) underestimate the perplexity. Please detail further why this is the case. \n\n- In section 4.1.3 I have difficulties to really see the difference between uncertainty sources 2 and 3.  \n\n- Authors argue in section 5 that the reason why humans are better for many language tasks but not for next-token prediction is that they do not struggle at considering all possible futures for any text, as LLMs do. I am not fully convinced by this assertion. I cannot see what allows us to say that as humans we do not do exactly the same for any language task. At any new word to emit, we implicitly choose among our own vocabulary, sampling terms that look best for the current context...  I do agree that contrary to llms, we can plan objectives for our discourse, while classical llms have to embed everything in their next-tokens distribution, but it is not really the same to me. \n\n- Authors suggest other tasks than next-token prediction in the end of section 5. I cannot figure out what they have in mind, as any task can be casted in such a training setting: for instance QA can be formulated as a next token prediction task (but with a prompt that has not to be decoded). Or is the discussion more about the training setting : overcome the auto-regressive way of decoding language, enabling planification and global assessment using diffusion or RL ?  \n\n- Please give more details in the related work section to be more self-contained. Particularly, it would be useful to further develop the approach followed in Shen et Al. 2017.", "broader_impact_concerns": ".", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "FpiqWnFXvp", "reviewer": "Reviewer_5BEm", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n-  This work is investigating an interesting topic of comparing human and model performance in next token prediction. The experimental results show that language models are superior to human measured by the accuracies in next token prediction and perplexities. The findings sound natural in that it is hard to train a human to write texts in diverse areas covered in OpenWebText dataset, though, this work might have an impact in the future studies on how to fairly evaluate language model performance in the future.\n- This work proposed two methods to measure the human performance on next token prediction by accuracies and perplexities. The accuracy of top-1 prediction is trivial, though, it is very challenging to measure perplexities given that a human has to assign probabilities to all candidates. This work introduce an approximation by asking a human to assign a probability for a token given the choice of two, and fix the biases by importance sampling. It is carefully designed and apt for the probability estimation given that it is impossible to assign probabilities to all candidates.\n\nWeaknesses\n- It is not clear whether a human can assign probability to a word even for the choice of two with 11 levels. It would be good to report variances of assigning probabilities among human evaluators. Also, it is probably informative to report the results with the reduced number of levels, e.g., 3 such as hight, low or even probabilities, if the variance is high in assigning probabilities.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work compares language models with human in the next token prediction task by directly asking human to predict the next word and to assign probability to the next word given a choice of two. Experimental results show that human is inferior to language models even with a small capacity.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "As noted in the weakness, it would be informative to investigate whether human evaluators can actually assign probabilities even for the choice of two after training. Also, probably it might be interesting to compare the performance with n-gram language models to see if humans are close to the classic models or not.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper presents a novel study comparing the next-token prediction capabilities of language models and humans and is overall well-written.

Reviewers raised valid concerns about training data contamination, the impact of tokenization, and the need for further analysis regarding the variance in human probability assignments. The authors have addressed these concerns by conducting additional experiments and analyses, strengthening the paper's claims. One minor concern remains regarding the generalizability of the results due to the convenience sample used for human participants. However, the authors acknowledge this limitation and suggest future work to address it.

Given the overall quality of the paper and its relevance to TMLR's audience, and the overall positive reviews, I believe that this paper would be a valuable contribution to TMLR.
Decision: Accept (poster)