Contextual and unigram surprisal are standard predictors of reading time in computational psycholinguistics. While contextual surprisal is typically derived from neural language models, unigram surprisal is usually obtained from independent corpus counts. Although both quantities are deterministic functionals of a single underlying distribution---capturing conditional and marginal structure respectively---this practice breaks their probabilistic link and may introduce estimation error from the mismatch. We propose three principles for estimating unigram surprisal in psycholinguistic research, including the requirement that both quantities be derived from the same language model. We operationalize this principle by introducing a Monte Carlo estimator of unigram surprisal from a language model, along with a marginalized variant that has lower variance empirically. When unigram surprisal is re-estimated under this unified framework, we find evidence that predictors change in their predictive contribution to reading time. We also confirm prior findings that frequency can be a stronger predictor of processing effort than contextual surprisal under this unified framework.
Figures & tables
Figure 2: Principles for estimating unigram surprisal.
Figure 3: Comparison of {{\color[rgb]{0,0,0}\Delta_{\text{LL}}}} for various GAMMs of orthographic word gaze duration fit with unigram surprisals obtained with the wordfreq package ( Speer, 2022 ) or with one of our estimators using samples from mGPT. Values are averaged across languages. Dashed lines represent the {{\color[rgb]{0,0,0}\Delta_{\text{LL}}}} of adding contextual surprisal relative to each facet’s baseline for reference. Significance tests compare estimated unigram surprisal against the corpus-estimated values via paired permutation test on item-level {{\color[rgb]{0,0,0}\Delta_{\text{LL}}}} differences, with stars marking corrected significance at an α level of 0.05. Error bars represent 95% confidence intervals.
J
MMC variance
NMC variance
Ratio
100
1.685e-08
1.736e-07
10.30
200
8.508e-09
9.689e-08
11.39
300
5.648e-09
6.769e-08
11.98
400
4.044e-09
5.448e-08
13.47
500
3.307e-09
4.281e-08
12.94
Table 1: Mean bootstrap variance of the Marginalized (MMC) and Naive (NMC) Monte Carlo unigram frequency estimators across subsample sizes J . Ratio = NMC / MMC.
Appendix figures & tables16 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4
Boundary
Location
Condition (satisfied when)
Left
first token of {{{\color[rgb]{0,0,0}w}}}
it carries a leading ␣ (word-initial marker Ġ ), or it begins the sequence
Right
token following the last token of {{{\color[rgb]{0,0,0}w}}}
it carries a leading ␣ (marker Ġ ), or it is eos
Appendix
Table 5
Figure 4: Visualization of the bootstrapped variance estimates of our marginalized and naive Monte Carlo estimators of unigram frequency. Each line represents a single unigram from the English MECO data. The “Mean” lines refer to the average variance across all unigrams.
Figure 5: Proportion of types and tokens in the MECO corpus for which estimates can be obtained from our Naive Monte Carlo estimator at a range of sample sizes. Samples are obtained from mGPT with the maximum length hyperparameter set to 50 tokens. Estimates cannot be obtained when the target type/token never appears in the N sampled strings.
Tokens
NMC (s)
MMC (s)
1
3.788 (0.003)
86.269 (0.101)
2
3.788 (0.003)
166.344 (0.161)
3
3.787 (0.002)
247.479 (0.105)
4
3.783 (0.008)
329.654 (0.153)
Appendix
Table 2: Mean (SD) wall-clock time per estimate for the Naive (NMC) and Marginalized (MMC) Monte Carlo estimators, broken down by the number of subword tokens in the target unigram ( N=500 samples, batch size 128).
Language
Participants
Word Types
Observations
Train Size
Test Size
Dutch
45
662
31680
28512
3168
English
46
930
55120
49608
5512
Finnish
49
306
14853
13368
1485
German
45
753
43942
39548
4394
Greek
45
945
39972
35975
3997
Hebrew
47
1303
49430
44487
4943
Appendix
Table 3: Per-language counts for the NMC estimator: observations entering the gaze-duration model are per participant. Train/test split refer to the size of the folds used to fit and test each of the GAMMs.
Language
Participants
Word Types
Observations
Train Size
Test Size
Dutch
45
996
44816
40334
4482
English
46
945
55792
50213
5579
Finnish
49
1042
49783
44805
4978
German
45
1037
58171
52354
5817
Greek
45
845
35558
32002
3556
Hebrew
47
954
36248
32623
3625
Appendix
Table 4: Per-language counts for the MMC estimator: observations entering the gaze-duration model are per participant. Train/test split refer to the size of the folds used to fit and test each of the GAMMs.
Language
Participants
Word Types
Observations
Train Size
Test Size
Dutch
45
1009
45314
40783
4531
English
46
980
57883
52095
5788
Finnish
49
1076
51962
46766
5196
German
45
1047
58861
52975
5886
Greek
45
975
41229
37106
4123
Hebrew
47
1319
50126
45113
5013
Appendix
Table 5: Per-language counts for the MMC (Approx.) estimator: observations entering the gaze-duration model are per participant. Train/test split refer to the size of the folds used to fit and test each of the GAMMs.
Language
Participants
Word Types
Observations
Train Size
Test Size
Dutch
45
907
41247
37122
4125
English
46
965
56924
51232
5692
Finnish
49
823
39298
35368
3930
German
45
950
53534
48181
5353
Greek
45
957
40455
36409
4046
Hebrew
47
1303
49454
44509
4945
Appendix
Table 6: Per-language counts for the Priority MMC estimator: observations entering the gaze-duration model are per participant. Train/test split refer to the size of the folds used to fit and test each of the GAMMs.
Language
Participants
Word Types
Observations
Train Size
Test Size
Dutch
45
1009
45314
40783
4531
English
46
980
57883
52095
5788
Finnish
49
1076
51962
46766
5196
German
45
1044
58707
52836
5871
Greek
45
975
41229
37106
4123
Hebrew
47
1319
50126
45113
5013
Appendix
Table 7: Per-language counts for the Priority MMC (Approx.) estimator: observations entering the gaze-duration model are per participant. Train/test split refer to the size of the folds used to fit and test each of the GAMMs.
Unigram Surprisal Metric
Model
Macro Averages
SD Across Languages
NMC Estimate
Uni. Surp.
0.0265
0.0114
PMI
0.0071
0.0062
PMI & Uni. Surp.
0.0286
0.0121
Con. Surp.
0.0118
0.0049
Con. Surp. & Uni. Surp.
0.0283
0.0119
Corpus Estimate
Uni. Surp.
0.0282
0.0126
Appendix
Table 8: Word-level Δ LL for GAMMs of gaze duration, macro-averaged across languages. Values correspond to the NMC estimator versus the Corpus baseline (fit on NMC’s support).
Unigram Surprisal Metric
Model
Macro Averages
SD Across Languages
MMC Estimate
Uni. Surp.
0.0383
0.0195
PMI
0.0122
0.0085
PMI & Uni. Surp.
0.0415
0.0205
Con. Surp.
0.0211
0.0100
Con. Surp. & Uni. Surp.
0.0413
0.0204
Corpus Estimate
Uni. Surp.
0.0396
0.0211
Appendix
Table 9: Word-level Δ LL for GAMMs of gaze duration, macro-averaged across languages. Values correspond to the MMC estimator versus the Corpus baseline (fit on MMC’s support).
Unigram Surprisal Metric
Model
Macro Averages
SD Across Languages
MMC (Approx.) Estimate
Uni. Surp.
0.0391
0.0178
PMI
0.0130
0.0085
PMI & Uni. Surp.
0.0424
0.0191
Con. Surp.
0.0214
0.0105
Con. Surp. & Uni. Surp.
0.0421
0.0191
Corpus Estimate
Uni. Surp.
0.0396
0.0211
Appendix
Table 10: Word-level Δ LL for GAMMs of gaze duration, macro-averaged across languages. Values correspond to the MMC (Approx.) estimator versus the Corpus baseline (fit on MMC (Approx.)’s support).
Unigram Surprisal Metric
Model
Macro Averages
SD Across Languages
Priority MMC Estimate
Uni. Surp.
0.0392
0.0175
PMI
0.0111
0.0078
PMI & Uni. Surp.
0.0421
0.0184
Con. Surp.
0.0211
0.0104
Con. Surp. & Uni. Surp.
0.0416
0.0184
Corpus Estimate
Uni. Surp.
0.0387
0.0198
Appendix
Table 11: Word-level Δ LL for GAMMs of gaze duration, macro-averaged across languages. Values correspond to the Priority MMC estimator versus the Corpus baseline (fit on Priority MMC’s support).
Unigram Surprisal Metric
Model
Macro Averages
SD Across Languages
Priority MMC (Approx.) Estimate
Uni. Surp.
0.0412
0.0201
PMI
0.0110
0.0087
PMI & Uni. Surp.
0.0436
0.0208
Con. Surp.
0.0214
0.0105
Con. Surp. & Uni. Surp.
0.0433
0.0207
Corpus Estimate
Uni. Surp.
0.0397
0.0211
Appendix
Table 12: Word-level Δ LL for GAMMs of gaze duration, macro-averaged across languages: Values correspond to the Priority MMC (Approx.) estimator versus the Corpus baseline (fit on Priority MMC (Approx.)’s support).
Approx.
Full
Samples {{{\color[rgb]{0,0,0}N}}}
4×107
Maximum length
50
Strata
21
Per-unit budget k
8192
Stratum floor
64
Home share
4096
2048
Appendix
Table 13: Settings of the priority-sampled variants (Priority MMC Approx. and Priority MMC). Each variant draws its own pool of samples. The full variant’s pool additionally stores the model’s own sampled tokenizations for H . Approximate-variant single-token units need no sampling, since their numerator is the exact column sum plus the exact empty-prefix term. The full estimator’s closing mass depends on the unit, so its single-token units are sampled like any other.
Although language is predominantly spoken, empirical tests of surprisal theory rely almost entirely on written text. In practice, surprisal is estimated using language models (LMs) trained on text and applied to transcriptions, creating a text bottleneck that limits evaluation of the theory in the spoken modality. We remove this bottleneck by estimating surprisal directly from the speech signal using a speech LM. This raises a key question: should surprisal be defined over realization-specific acoustic inputs or over abstract linguistic units? Since a single unit can have many distinct acoustic realizations, each assigned a different probability by the model, defining surprisal over abstract units is difficult. To address this, we introduce an importance sampling estimator that approximates the probability of an abstract unit by marginalizing over realizations generated by a text-to-speech model. Using pupillometry data from a listening study, we evaluate surprisal theory in this text-free setting at multiple levels of granularity. Obtaining surprisal from several speech LMs, we consistently find that surprisal estimated via importance sampling better predicts pupil dilation than realization-specific surprisal for words. We also find that surprisal values for sub-lexical units are predictive of pupil dilation. While we find that surprisal can be estimated without recourse to text, and that marginalizing over distinct realizations of words is more predictive of lexical processing effort, surprisal as a whole is not a strong predictor of change in pupil size, regardless of its source.
Zachary Hopton, Samuel Kiegeland, Francesco Ignazio Re +4
This study analyzes the predictive power of LM-derived, token-level surprisal on Mandarin Chinese reading times. We first propose the Shortest Matching Sequence (SMS), an alignment scheme that maps between the word segmentation assumed by eye-tracking corpora and the LMs' subword tokenization, as the two tokenizations often disagree in the context of Mandarin Chinese. Then, using a suite of Chinese-Pythia models (14M-1.4B) trained on scratch with 30B tokens, we examine how well surprisal predicts first fixation duration, gaze duration, and total reading time in three paragraph-level eye-tracking corpora of Mandarin Chinese (GECO-CN, HKP, and MECO). Contrary to previous null findings, our results show that surprisal is predictive of Chinese reading times. However, whether predictive power scales with model size and the amount of training is corpus-specific: bigger models predict better in GECO-CN, whereas inverse scaling emerges in HKP and, at the largest sizes, in MECO. Subsequently, we tested one possible explanation for the inverse scaling in HKP and found that checkpoints whose surprisal remains closer to n-gram statistics are better predictors of reading. All in all, the predictive power of surprisal on Chinese reading time measurements is corpus-specific, which cautions against drawing scaling conclusions from a single corpus.
Hongao Zhu, Muxiaoqiao Xu, Yikang Liu +4
Department of Linguistics, UC San Diego · School of Foreign Languages, Shanghai Jiao Tong University · School of Computer Science, Shanghai Jiao Tong University +3
Surprisal, the negative log-probability a language model assigns to a word given its preceding context, reliably predicts adult reading times. Does it contribute as much to explaining when children acquire individual words? Frequency reflects a learner's cumulative exposure to a word, whereas surprisal reflects how predictable a single occurrence is given its context. We investigate this question across two corpus-based studies of Spanish. In Study 1, we modeled age of acquisition (AoA) for 225 Spanish nouns using lexical frequency and contextual diversity from child-directed speech, plus surprisal from three language models differing in architecture and training language (BETO, BERTIN, mGPT). Frequency strongly predicted AoA (r=-.597, p<.001); surprisal added little beyond frequency and word length, including in a naturalistic-context analysis. In Study 2, we modeled adult fixation durations in the Chilean Spanish subsample of the Multilingual Eye-movement Corpus (MECO Wave 2), using mGPT surprisal alongside two independent frequency measures. Surprisal robustly predicted longer fixation durations after controlling for frequency and word length, consistent across both frequency sources. A matched word-type-level comparison showed the surprisal-behavior association was stronger in reading than in acquisition (z=3.63, p<.001). The findings suggest cumulative lexical exposure and contextual predictability play different roles across the language trajectory: frequency is particularly informative about when early lexical representations are acquired, whereas surprisal captures moment-to-moment processing difficulty in an already-established linguistic system. We discuss this pattern in relation to usage-based and entrenchment-based accounts of lexical development and to the evaluation of language models as models of human language behavior.