Stochastic Surprise Signatures in Human EEG: A Reproducible Benchmark of Prediction-Error Models Using the ERP CORE Oddball Dataset

Stochastic Surprise Signatures in Human EEG: A Reproducible Benchmark of Prediction-Error Models Using the ERP CORE Oddball Dataset | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Stochastic Surprise Signatures in Human EEG: A Reproducible Benchmark of Prediction-Error Models Using the ERP CORE Oddball Dataset Brhanu Fentaw Znabu, Zohaib Atif, Pradeep devkota This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9283955/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The brain continuously generates predictions about incoming sensory input and produces characteristic neural responses when those predictions are violated. In EEG oddball paradigms, these prediction-error responses manifest as the mismatch negativity (MMN) and P3b components. However, “surprise” can be formalized in multiple ways, and no prior study has systematically compared these formulations on the same dataset using single-trial methods. Here, we implemented four hierarchical surprise estimators and applied them to the ERP CORE dataset (N = 39 subjects, auditory MMN and visual P3 paradigms). Using linear mixed-effects encoding models, we found that Bayesian surprise, quantifying the magnitude of belief revision, showed the strongest association with single-trial MMN amplitude among all models tested (uncorrected p = 0.015), though this did not survive Holm–Bonferroni correction for multiple comparisons (p_corrected = 0.062). High multicollinearity among Shannon-based and change-point regressors (VIF > 70) limited the interpretability of direct model comparisons. In a cross-subject decoding analysis, contextual surprise features did not improve classification of stimulus class beyond ERP amplitude features alone (ΔAUC = − 0.093). We conclude that Bayesian surprise shows the strongest trend among competing models, but that stationary oddball paradigms may lack sufficient power to definitively distinguish surprise formulations. All data, code, and analysis pipelines are publicly available. Computational Neuroscience prediction error surprise mismatch negativity P3b Bayesian inference EEG Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction The brain has been characterized as a prediction machine that continuously generates expectations about incoming sensory input and updates internal models when those expectations are violated (Rao & Ballard, 1999; Friston, 2005). This predictive processing framework provides a unifying account of perception, attention, and learning, where neural activity tracks the mismatch between expected and actual input. Oddball paradigms offer a direct window into neural prediction-error processing. Rare deviant stimuli appear among frequent standards, producing reliable electrophysiological responses to the deviants. The mismatch negativity (MMN) is an early fronto-central ERP component (100–250 ms post-stimulus) reflecting automatic detection of auditory deviance (Näätänen et al., 2007). The P3b is a later parietal component (250–500 ms) linked to context updating and surprise evaluation (Polich, 2007). While these ERP components are known, “surprise” can be defined in several ways. Shannon surprise (S = − log p(x)) quantifies event rarity. Bayesian surprise, defined as the KL divergence between successive posterior beliefs (Itti & Baldi, 2009), measures how much beliefs change. Change-point models (Adams & MacKay, 2007) estimate the probability that the underlying process has changed. Prior work has examined these models individually (Mars et al., 2008; Kolossa et al., 2015; Ostwald et al., 2012), but they have not been compared head-to-head on the same dataset with single-trial methods. Here, we implement four hierarchical surprise estimators and benchmark their ability to explain trial-by-trial EEG prediction-error responses in the ERP CORE dataset (Kappenman et al., 2021). We test whether: (H1) adaptive surprise estimators will better explain single-trial ERP responses than static frequency-based surprise; and (H2) surprise-derived features will improve cross-subject decoding of stimulus class. 2. Methods 2.1 Dataset We used the ERP CORE dataset (Kappenman et al., 2021; N = 40, sub-012 excluded from original release, sub-007 excluded for excessive artifact rejection [85.4% rejection rate], yielding N = 38 for MMN analyses). We analyzed the MMN paradigm (auditory oddball; ~80% standards, ~ 20% deviants) and the P3 paradigm (visual oddball; ~80% non-targets, ~ 20% targets; sub-003, sub-005, sub-032 excluded for > 80% rejection rates, yielding N = 36). Data were recorded at 1024 Hz from 30 EEG channels plus 3 EOG channels. 2.2 Preprocessing All preprocessing was performed using MNE-Python 1.8.0 (Gramfort et al., 2013). Table 1 lists all parameters. Table 1 Preprocessing parameters and exclusion criteria. Parameter Specification High-pass filter 0.1 Hz (zero-phase FIR, Hamming window) Low-pass filter 30 Hz (zero-phase FIR, Hamming window) Sampling rate 256 Hz (downsampled from 1024 Hz) Reference Average reference Artifact rejection (ICA) FastICA, 15 components, automatic EOG detection Artifact rejection (epochs) Amplitude threshold: ±150 µV Epoch window −200 to 800 ms (stimulus-locked) Baseline correction −200 to 0 ms Exclusion criterion < 100 epochs (MMN) or 80% rejection rate After preprocessing and exclusion, the MMN dataset comprised 35,332 epochs across 38 subjects (mean 930 ± 48 per subject; 7.0% rejection rate). The P3 dataset comprised 5,865 epochs across 36 subjects. 2.3 Surprise Estimators All estimators operated on the binary stimulus sequence (0 = standard, 1 = deviant). (1) Static Shannon surprise: S_t = − log₂ p_global(x_t). (2) Adaptive Shannon surprise: S_t = − log₂ p_w(x_t) with sliding window w = 20. (3) Bayesian surprise: KL divergence between successive Beta-Bernoulli posteriors with flat prior. (4) Change-point predictive surprise: −log₂ P(x_t | model) under the Adams & MacKay (2007) framework with hazard rate h = 1/200. 2.4–2.5 Feature Extraction and Encoding Analysis Mean amplitude was extracted in the MMN window (100–250 ms, fronto-central ROI) and P3b window (250–500 ms, parietal ROI). Linear mixed-effects models were fit with each surprise model tested individually against a stimulus-class-only baseline (avoiding multicollinearity). Model comparison used AIC and likelihood ratio tests, with Holm–Bonferroni correction across 4 comparisons per ERP window. Variance inflation factors (VIF) were computed. Time-resolved regression used cluster-based permutation tests (5000 permutations). 2.6 Decoding Analysis Binary classification (standard vs. deviant) used L2-regularized logistic regression. Cross-subject leave-5-out CV was the primary evaluation. Surprise regressors were residualized against stimulus type to prevent label leakage. Metrics: ROC-AUC, PR-AUC, balanced accuracy. 2.7 Power Analysis Simulation-based power analysis (1000 simulations, N = 39, ~ 900 trials/subject) confirmed > 99% power to detect single-trial surprise–ERP correlations of r ≥ 0.10 at α = 0.05 in per-subject analyses. However, this addresses within-subject detection, not between-model discrimination, which depends on the difference in explained variance between models. 3. Results 3.1 ERP Replication Grand-average ERP waveforms replicated published ERP CORE results (Fig. 2 ). The standard–deviant contrast yielded Cohen’s d = − 0.16 for MMN amplitude at fronto-central sites. 3.2 Surprise Regressor Properties The four surprise models showed high multicollinearity (Fig. 1 C). VIF analysis confirmed: static Shannon (70.3), change-point (105.9), adaptive Shannon (17.3). Only Bayesian surprise (VIF = 1.1) was independent. 3.3 Encoding Results (H1) Table 2 presents the encoding model comparison results. Model Window ΔAIC p (uncorr.) p (Holm) Partial R² β [95% CI] Static Shannon MMN −1.4 0.066 0.131 9.5×10⁻⁵ 2.86 [− 0.20, 5.93] Adaptive Shannon MMN + 1.8 0.674 0.674 5.0×10⁻⁶ −0.03 [− 0.20, 0.13] Bayesian MMN −3.9 0.015 0.062 1.6×10⁻⁴ −0.06 [− 0.11, − 0.01] Change-point MMN −2.3 0.038 0.115 1.2×10⁻⁴ −0.41 [− 0.81, − 0.02] Static Shannon P3b + 1.3 0.394 1.000 2.0×10⁻⁵ 1.51 [− 1.98, 4.99] Adaptive Shannon P3b + 1.6 0.540 1.000 1.1×10⁻⁵ 0.06 [− 0.13, 0.24] Bayesian P3b + 1.8 0.679 1.000 4.4×10⁻⁶ −0.01 [− 0.07, 0.05] Change-point P3b + 1.7 0.557 1.000 9.7×10⁻⁶ −0.13 [− 0.58, 0.31] Table 2 . Encoding model comparison (MMN paradigm). Each model tested individually against stimulus-class baseline. Holm–Bonferroni correction applied within each ERP window (4 comparisons). MMN paradigm. Bayesian surprise showed the strongest association with MMN amplitude (ΔAIC = − 3.9, uncorrected p = 0.015), but did not survive Holm–Bonferroni correction (p_corrected = 0.062). Change-point predictive surprise was marginal before correction (p = 0.038, p_corrected = 0.115). All partial R² values were very small (< 0.02%), indicating that surprise explains a negligible fraction of single-trial variance beyond stimulus class. P3 paradigm (replication). In the P3b window, change-point surprise (uncorrected p = 0.017, p_corrected = 0.069) and Bayesian surprise (uncorrected p = 0.044, p_corrected = 0.131) showed trends but did not survive correction. Cross-validated prediction. Leave-one-subject-out cross-validation showed no significant improvement in out-of-sample prediction for any surprise model over the baseline (all p > 0.64), confirming the minimal explanatory benefit. Time-resolved analysis. All models showed significant clusters in the 100–230 ms window at fronto-central sites (cluster p < 0.001, Fig. 3 ). These clusters reflect the shared sensitivity to deviant-evoked MMN responses. 3.4 Decoding Results (H2) Table 3 presents the decoding benchmark results. Feature Set Evaluation ROC-AUC PR-AUC Balanced Acc. ERP-only Cross-subject 0.543 0.226 0.531 ERP+surprise (resid.) Cross-subject 0.450 0.186 0.474 ERP-only Within-subject 0.534 ± 0.041 — — ERP+surprise (resid.) Within-subject 1.000 ± 0.000* — — Table 3 . Decoding results (MMN paradigm). *Within-subject AUC = 1.0 reflects label leakage (see Section 4.3 ). Cross-subject decoding was modest (AUC = 0.543 for ERP-only). Adding residualized surprise features decreased performance (ΔAUC = − 0.093, p = 0.050). H2 is not supported. 3.5 Sensitivity Analyses Results were robust across adaptive Shannon window sizes (w = 10, 20, 50) and change-point hazard rates (h ∈ {1/50, 1/100, 1/200, 1/500}). Change-point regressors remained highly correlated with static Shannon (r > 0.97) across all hazard rates. 4. Discussion 4.1 Key Findings This paper compares four surprise formulations as predictors of single-trial EEG prediction-error responses. Bayesian surprise showed the strongest trend toward predicting MMN amplitude, but this did not survive correction for multiple comparisons. No model significantly improved out-of-sample prediction or cross-subject decoding. These results suggest that while computational models of surprise capture meaningful aspects of neural prediction error, the effect sizes in stationary oddball paradigms are too small to reliably distinguish between formulations. 4.2 Relation to Prior Work The finding that Bayesian surprise shows the strongest association (though non-significant after correction) with MMN amplitude fits with Mars et al. (2008) and Ostwald et al. (2012). The small effect sizes we observe (partial R² < 0.02%) are consistent with the difficulty of single-trial EEG analysis. 4.3 Methodological Contributions Multicollinearity. VIF values exceeding 70 for Shannon and change-point regressors demonstrate that stationary oddball paradigms cannot differentiate frequency-based from change-detection models. Only Bayesian surprise provides an independent signal. Label leakage. We document that surprise regressors produce trivially perfect within-subject classification (AUC = 1.0), even after residualization, because they are deterministic functions of the stimulus sequence. This confound has not been previously reported and has implications for future decoding studies using computational regressors. Multiple comparisons. The shift from p = 0.015 (uncorrected) to p = 0.062 (Holm-corrected) for Bayesian surprise highlights the importance of correction when testing multiple model families. We report both values for transparency. 4.4 Limitations First, the stationary oddball paradigm limits model differentiation. Roving oddball or volatile-environment paradigms would better test change-point and adaptive models. Second, amplitude-based artifact rejection was used instead of autoreject due to missing electrode positions in the ERP CORE files. Third, partial R² values were extremely small, suggesting that trial-to-trial surprise modulates only a tiny fraction of EEG variability. Fourth, the cross-validated prediction analysis showed no benefit for any surprise model, suggesting that the encoding-model improvements reflect overfitting to in-sample noise rather than genuine predictive power. 4.5 Future Directions Three follow-up directions stand out: (1) roving oddball paradigms with genuine non-stationarity; (2) naturalistic stimuli where surprise varies more continuously; (3) source-level or intracranial recordings to improve signal-to-noise. 5. Conclusion This paper reports a benchmark comparing four surprise formulations as predictors of single-trial EEG responses. Bayesian surprise shows the strongest trend, but no model survives correction for multiple comparisons. High regressor collinearity and trivial label leakage are identified as critical methodological challenges. These results set a baseline and point to non-stationary paradigms as the necessary next step. Declarations Data and Code Availability Data come from the ERP CORE dataset (Kappenman et al., 2021; https://erpinfo.org/erp-core; CC BY-SA 4.0). Code is available at https://github.com/brhanufen/surprise-eeg-benchmark Ethics Statement This study used publicly available, de-identified data from the ERP CORE dataset. No ethical approval was required for secondary analysis of de-identified public data. Conflict of Interest Statement The authors declare no conflicts of interest. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors Author Contributions (CRediT) B.F.Z. conceived and designed the study, performed all data processing and statistical analyses, developed the computational pipeline, and wrote the original draft of the manuscript. Z.A. contributed to the study design and methodology. P.D. contributed to manuscript writing and editing. All authors read and approved the final manuscript. References Adams, R. P., & MacKay, D. J. C. (2007). Bayesian online changepoint detection. arXiv:0710.3742. Friston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B, 360, 815–836. Gramfort, A., et al. (2013). MEG and EEG data analysis with MNE-Python. Frontiers in Neuroscience, 7, 267. Itti, L., & Baldi, P. (2009). Bayesian surprise attracts human attention. Vision Research, 49(10), 1295–1306. Kappenman, E. S., Farrens, J. L., Zhang, W., Stewart, A. X., & Luck, S. J. (2021). ERP CORE: An open resource for human event-related potential research. NeuroImage, 225 , 117465. Kolossa, A., Fingscheidt, T., Wessel, K., & Kopp, B. (2013). A model-based approach to trial-by-trial P300 amplitude fluctuations. Frontiers in Human Neuroscience, 6, 359. Maris, E., & Oostenveld, R. (2007). Nonparametric statistical testing of EEG- and MEG-data. Journal of Neuroscience Methods, 164(1), 177–190. Mars, R. B., et al. (2008). Trial-by-trial fluctuations in the event-related electroencephalogram reflect dynamic changes in the degree of surprise. Journal of Neuroscience, 28(47), 12539–12545. Näätänen, R., Paavilainen, P., Rinne, T., & Alho, K. (2007). The mismatch negativity (MMN) in basic research of central auditory processing. Clinical Neurophysiology, 118(12), 2544–2590. Ostwald, D., et al. (2012). Evidence for neural encoding of Bayesian surprise in human somatosensation. NeuroImage, 62(1), 177–188. Polich, J. (2007). Updating P300: An integrative theory of P3a and P3b. Clinical Neurophysiology, 118(10), 2128–2148. Rao, R. P. N., & Ballard, D. H. (1999). Predictive coding in the visual cortex. A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79–87. Additional Declarations The authors declare no competing interests. Supplementary Files SupplementaryMaterial.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9283955","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615501233,"identity":"a103172f-eb03-461d-a02a-fc03e60d612c","order_by":0,"name":"Brhanu Fentaw Znabu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIie3RMUsDMRTA8UjgTYFbX7BYP8KFQFQ88KvcUahLqINLh3KkHDgV5xuKn0HwC0QCuaXuB+dSBCfnw8Wi51xC3RzyH97weL/pERKL/cOSsWs+kS1OEkJgWKTDwBDhNeR4PvKSm0NJ2rJTnGe0SO2hhHSrH6Yhl13l3+aLUiaGPncsII7WL7aoN6OZevXXYuOdQguTyxChZJY7voJb1WrFDdiMWKaOQwSIFtXXjhZP9U3Pza7Mxjbpg4ShlgQZLR5RA1/eUZVaBkGCzE+HIbGdnonlvZPCgbxYB8hVU3ny+8p68r41fSkemmrbfgTInujfzmOxWCy2p2+Ux0uq2cPQmQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0009-7230-754X","institution":"University of Nebraska_lincoln","correspondingAuthor":true,"prefix":"","firstName":"Brhanu","middleName":"Fentaw","lastName":"Znabu","suffix":""},{"id":615501234,"identity":"be87992f-77df-4a62-8252-85aa80005846","order_by":1,"name":"Zohaib Atif","email":"","orcid":"","institution":"gwanju institute of science and technology","correspondingAuthor":false,"prefix":"","firstName":"Zohaib","middleName":"","lastName":"Atif","suffix":""},{"id":615501235,"identity":"58471c94-5fee-4679-a682-8bb331e6264d","order_by":2,"name":"Pradeep devkota","email":"","orcid":"","institution":"university of Kansas medical center","correspondingAuthor":false,"prefix":"","firstName":"Pradeep","middleName":"","lastName":"devkota","suffix":""}],"badges":[],"createdAt":"2026-03-31 19:54:37","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9283955/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9283955/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105976811,"identity":"6b228463-5275-4923-b6b9-7360f868dd40","added_by":"auto","created_at":"2026-04-02 05:31:26","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":147839,"visible":true,"origin":"","legend":"\u003cp\u003eStudy schematic and surprise model hierarchy. (A) Oddball paradigm. (B) Four estimators arranged by complexity. (C) Example surprise traces (z-scored). (D) Analysis pipeline.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9283955/v1/7053e415d40e5bb8e1b559ec.png"},{"id":106093669,"identity":"7db8123d-f267-43e2-87e9-1c8ce8a180c8","added_by":"auto","created_at":"2026-04-03 11:38:31","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":240891,"visible":true,"origin":"","legend":"\u003cp\u003eERP replication and quality control. (A) Grand-average waveforms at fronto-central sites, standard (blue) vs. deviant (orange). (B) Parietal sites. (C) Difference waveforms (deviant − standard). (D) Epoch counts per subject after rejection.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9283955/v1/ec4e3df33eb51216314aafdd.png"},{"id":105976812,"identity":"f2be5162-1c53-4c6e-af24-14f1292f747e","added_by":"auto","created_at":"2026-04-02 05:31:26","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":155379,"visible":true,"origin":"","legend":"\u003cp\u003eSurprise encoding results. (A) Time-resolved regression coefficients at fronto-central sites. (B–C) ΔAIC in MMN and P3b windows. (D) Variance explained.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9283955/v1/034e0732fd11efbeab8adf40.png"},{"id":105976815,"identity":"60b76cf3-bc88-4208-91e7-13e2b4b54ed9","added_by":"auto","created_at":"2026-04-02 05:31:26","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":94015,"visible":true,"origin":"","legend":"\u003cp\u003eDecoding benchmark. (A) ROC curves, cross-subject. (B) Feature ablation. (C) Cross- vs. within-subject comparison.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9283955/v1/3aa7b0004c4299b0746845e0.png"},{"id":106095591,"identity":"6f9799e5-b185-4e58-9817-ed79b8f45573","added_by":"auto","created_at":"2026-04-03 11:49:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1140948,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9283955/v1/61629c7c-25de-4422-96d7-1bfd9fab0c8e.pdf"},{"id":105976813,"identity":"9c95b51b-8bb2-4200-8d73-947d517443fd","added_by":"auto","created_at":"2026-04-02 05:31:26","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":754953,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-9283955/v1/4802d66f98d21d9b21f041ed.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eStochastic Surprise Signatures in Human EEG: A Reproducible Benchmark of Prediction-Error Models Using the ERP CORE Oddball Dataset\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe brain has been characterized as a prediction machine that continuously generates expectations about incoming sensory input and updates internal models when those expectations are violated (Rao \u0026amp; Ballard, 1999; Friston, 2005). This predictive processing framework provides a unifying account of perception, attention, and learning, where neural activity tracks the mismatch between expected and actual input.\u003c/p\u003e \u003cp\u003eOddball paradigms offer a direct window into neural prediction-error processing. Rare deviant stimuli appear among frequent standards, producing reliable electrophysiological responses to the deviants. The mismatch negativity (MMN) is an early fronto-central ERP component (100\u0026ndash;250 ms post-stimulus) reflecting automatic detection of auditory deviance (N\u0026auml;\u0026auml;t\u0026auml;nen et al., 2007). The P3b is a later parietal component (250\u0026ndash;500 ms) linked to context updating and surprise evaluation (Polich, 2007).\u003c/p\u003e \u003cp\u003eWhile these ERP components are known, \u0026ldquo;surprise\u0026rdquo; can be defined in several ways. Shannon surprise (S\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;log p(x)) quantifies event rarity. Bayesian surprise, defined as the KL divergence between successive posterior beliefs (Itti \u0026amp; Baldi, 2009), measures how much beliefs change. Change-point models (Adams \u0026amp; MacKay, 2007) estimate the probability that the underlying process has changed. Prior work has examined these models individually (Mars et al., 2008; Kolossa et al., 2015; Ostwald et al., 2012), but they have not been compared head-to-head on the same dataset with single-trial methods.\u003c/p\u003e \u003cp\u003eHere, we implement four hierarchical surprise estimators and benchmark their ability to explain trial-by-trial EEG prediction-error responses in the ERP CORE dataset (Kappenman et al., 2021). We test whether: (H1) adaptive surprise estimators will better explain single-trial ERP responses than static frequency-based surprise; and (H2) surprise-derived features will improve cross-subject decoding of stimulus class.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Dataset\u003c/h2\u003e \u003cp\u003eWe used the ERP CORE dataset (Kappenman et al., 2021; N\u0026thinsp;=\u0026thinsp;40, sub-012 excluded from original release, sub-007 excluded for excessive artifact rejection [85.4% rejection rate], yielding N\u0026thinsp;=\u0026thinsp;38 for MMN analyses). We analyzed the MMN paradigm (auditory oddball; ~80% standards, ~\u0026thinsp;20% deviants) and the P3 paradigm (visual oddball; ~80% non-targets, ~\u0026thinsp;20% targets; sub-003, sub-005, sub-032 excluded for \u0026gt;\u0026thinsp;80% rejection rates, yielding N\u0026thinsp;=\u0026thinsp;36). Data were recorded at 1024 Hz from 30 EEG channels plus 3 EOG channels.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Preprocessing\u003c/h2\u003e \u003cp\u003eAll preprocessing was performed using MNE-Python 1.8.0 (Gramfort et al., 2013). Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists all parameters.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePreprocessing parameters and exclusion criteria.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpecification\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHigh-pass filter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1 Hz (zero-phase FIR, Hamming window)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLow-pass filter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30 Hz (zero-phase FIR, Hamming window)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSampling rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e256 Hz (downsampled from 1024 Hz)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage reference\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArtifact rejection (ICA)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFastICA, 15 components, automatic EOG detection\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArtifact rejection (epochs)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAmplitude threshold: \u0026plusmn;150 \u0026micro;V\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEpoch window\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;200 to 800 ms (stimulus-locked)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline correction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;200 to 0 ms\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExclusion criterion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;100 epochs (MMN) or \u0026lt;\u0026thinsp;30 epochs (P3), or \u0026gt;\u0026thinsp;80% rejection rate\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAfter preprocessing and exclusion, the MMN dataset comprised 35,332 epochs across 38 subjects (mean 930\u0026thinsp;\u0026plusmn;\u0026thinsp;48 per subject; 7.0% rejection rate). The P3 dataset comprised 5,865 epochs across 36 subjects.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Surprise Estimators\u003c/h2\u003e \u003cp\u003eAll estimators operated on the binary stimulus sequence (0\u0026thinsp;=\u0026thinsp;standard, 1\u0026thinsp;=\u0026thinsp;deviant). (1) Static Shannon surprise: S_t\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;log₂ p_global(x_t). (2) Adaptive Shannon surprise: S_t\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;log₂ p_w(x_t) with sliding window w\u0026thinsp;=\u0026thinsp;20. (3) Bayesian surprise: KL divergence between successive Beta-Bernoulli posteriors with flat prior. (4) Change-point predictive surprise: \u0026minus;log₂ P(x_t | model) under the Adams \u0026amp; MacKay (2007) framework with hazard rate h\u0026thinsp;=\u0026thinsp;1/200.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4\u0026ndash;2.5 Feature Extraction and Encoding Analysis\u003c/h2\u003e \u003cp\u003eMean amplitude was extracted in the MMN window (100\u0026ndash;250 ms, fronto-central ROI) and P3b window (250\u0026ndash;500 ms, parietal ROI). Linear mixed-effects models were fit with each surprise model tested individually against a stimulus-class-only baseline (avoiding multicollinearity). Model comparison used AIC and likelihood ratio tests, with Holm\u0026ndash;Bonferroni correction across 4 comparisons per ERP window. Variance inflation factors (VIF) were computed. Time-resolved regression used cluster-based permutation tests (5000 permutations).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Decoding Analysis\u003c/h2\u003e \u003cp\u003eBinary classification (standard vs. deviant) used L2-regularized logistic regression. Cross-subject leave-5-out CV was the primary evaluation. Surprise regressors were residualized against stimulus type to prevent label leakage. Metrics: ROC-AUC, PR-AUC, balanced accuracy.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.7 Power Analysis\u003c/h2\u003e \u003cp\u003eSimulation-based power analysis (1000 simulations, N\u0026thinsp;=\u0026thinsp;39, ~\u0026thinsp;900 trials/subject) confirmed\u0026thinsp;\u0026gt;\u0026thinsp;99% power to detect single-trial surprise\u0026ndash;ERP correlations of r\u0026thinsp;\u0026ge;\u0026thinsp;0.10 at α\u0026thinsp;=\u0026thinsp;0.05 in per-subject analyses. However, this addresses within-subject detection, not between-model discrimination, which depends on the difference in explained variance between models.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.1 ERP Replication\u003c/h2\u003e \u003cp\u003eGrand-average ERP waveforms replicated published ERP CORE results (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The standard\u0026ndash;deviant contrast yielded Cohen\u0026rsquo;s d\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.16 for MMN amplitude at fronto-central sites.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Surprise Regressor Properties\u003c/h2\u003e \u003cp\u003eThe four surprise models showed high multicollinearity (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003eC). VIF analysis confirmed: static Shannon (70.3), change-point (105.9), adaptive Shannon (17.3). Only Bayesian surprise (VIF\u0026thinsp;=\u0026thinsp;1.1) was independent.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Encoding Results (H1)\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003epresents the encoding model comparison results.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWindow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eΔAIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ep (uncorr.)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ep (Holm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePartial R\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eβ [95% CI]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatic Shannon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMMN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;1.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e9.5\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e2.86 [\u0026minus;\u0026thinsp;0.20, 5.93]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdaptive Shannon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMMN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;1.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e5.0\u0026times;10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.03 [\u0026minus;\u0026thinsp;0.20, 0.13]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBayesian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMMN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;3.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e1.6\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.06 [\u0026minus;\u0026thinsp;0.11, \u0026minus;\u0026thinsp;0.01]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChange-point\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMMN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e1.2\u0026times;10⁻⁴\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.41 [\u0026minus;\u0026thinsp;0.81, \u0026minus;\u0026thinsp;0.02]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatic Shannon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP3b\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;1.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.394\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e2.0\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e1.51 [\u0026minus;\u0026thinsp;1.98, 4.99]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdaptive Shannon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP3b\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;1.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e1.1\u0026times;10⁻⁵\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e0.06 [\u0026minus;\u0026thinsp;0.13, 0.24]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBayesian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP3b\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;1.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.679\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e4.4\u0026times;10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.01 [\u0026minus;\u0026thinsp;0.07, 0.05]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChange-point\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP3b\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;1.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.557\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c6\"\u003e \u003cp\u003e9.7\u0026times;10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.13 [\u0026minus;\u0026thinsp;0.58, 0.31]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Encoding model comparison (MMN paradigm). Each model tested individually against stimulus-class baseline. Holm\u0026ndash;Bonferroni correction applied within each ERP window (4 comparisons).\u003c/p\u003e \u003cp\u003eMMN paradigm. Bayesian surprise showed the strongest association with MMN amplitude (ΔAIC\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;3.9, uncorrected p\u0026thinsp;=\u0026thinsp;0.015), but did not survive Holm\u0026ndash;Bonferroni correction (p_corrected\u0026thinsp;=\u0026thinsp;0.062). Change-point predictive surprise was marginal before correction (p\u0026thinsp;=\u0026thinsp;0.038, p_corrected\u0026thinsp;=\u0026thinsp;0.115). All partial R\u0026sup2; values were very small (\u0026lt;\u0026thinsp;0.02%), indicating that surprise explains a negligible fraction of single-trial variance beyond stimulus class.\u003c/p\u003e \u003cp\u003eP3 paradigm (replication). In the P3b window, change-point surprise (uncorrected p\u0026thinsp;=\u0026thinsp;0.017, p_corrected\u0026thinsp;=\u0026thinsp;0.069) and Bayesian surprise (uncorrected p\u0026thinsp;=\u0026thinsp;0.044, p_corrected\u0026thinsp;=\u0026thinsp;0.131) showed trends but did not survive correction.\u003c/p\u003e \u003cp\u003eCross-validated prediction. Leave-one-subject-out cross-validation showed no significant improvement in out-of-sample prediction for any surprise model over the baseline (all p\u0026thinsp;\u0026gt;\u0026thinsp;0.64), confirming the minimal explanatory benefit.\u003c/p\u003e \u003cp\u003eTime-resolved analysis. All models showed significant clusters in the 100\u0026ndash;230 ms window at fronto-central sites (cluster p\u0026thinsp;\u0026lt;\u0026thinsp;0.001, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). These clusters reflect the shared sensitivity to deviant-evoked MMN responses.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Decoding Results (H2)\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003epresents the decoding benchmark results.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeature Set\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEvaluation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eROC-AUC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePR-AUC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBalanced Acc.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eERP-only\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCross-subject\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.531\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eERP+surprise (resid.)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCross-subject\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.186\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.474\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eERP-only\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWithin-subject\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.534\u0026thinsp;\u0026plusmn;\u0026thinsp;0.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eERP+surprise (resid.)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWithin-subject\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.000\u0026thinsp;\u0026plusmn;\u0026thinsp;0.000*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Decoding results (MMN paradigm). *Within-subject AUC\u0026thinsp;=\u0026thinsp;1.0 reflects label leakage (see Section \u003cspan refid=\"Sec18\" class=\"InternalRef\"\u003e4.3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eCross-subject decoding was modest (AUC\u0026thinsp;=\u0026thinsp;0.543 for ERP-only). Adding residualized surprise features decreased performance (ΔAUC\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.093, p\u0026thinsp;=\u0026thinsp;0.050). H2 is not supported.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Sensitivity Analyses\u003c/h2\u003e \u003cp\u003eResults were robust across adaptive Shannon window sizes (w\u0026thinsp;=\u0026thinsp;10, 20, 50) and change-point hazard rates (h \u0026isin; {1/50, 1/100, 1/200, 1/500}). Change-point regressors remained highly correlated with static Shannon (r\u0026thinsp;\u0026gt;\u0026thinsp;0.97) across all hazard rates.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Key Findings\u003c/h2\u003e \u003cp\u003eThis paper compares four surprise formulations as predictors of single-trial EEG prediction-error responses. Bayesian surprise showed the strongest trend toward predicting MMN amplitude, but this did not survive correction for multiple comparisons. No model significantly improved out-of-sample prediction or cross-subject decoding. These results suggest that while computational models of surprise capture meaningful aspects of neural prediction error, the effect sizes in stationary oddball paradigms are too small to reliably distinguish between formulations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Relation to Prior Work\u003c/h2\u003e \u003cp\u003eThe finding that Bayesian surprise shows the strongest association (though non-significant after correction) with MMN amplitude fits with Mars et al. (2008) and Ostwald et al. (2012). The small effect sizes we observe (partial R\u0026sup2; \u0026lt; 0.02%) are consistent with the difficulty of single-trial EEG analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Methodological Contributions\u003c/h2\u003e \u003cp\u003eMulticollinearity. VIF values exceeding 70 for Shannon and change-point regressors demonstrate that stationary oddball paradigms cannot differentiate frequency-based from change-detection models. Only Bayesian surprise provides an independent signal.\u003c/p\u003e \u003cp\u003eLabel leakage. We document that surprise regressors produce trivially perfect within-subject classification (AUC\u0026thinsp;=\u0026thinsp;1.0), even after residualization, because they are deterministic functions of the stimulus sequence. This confound has not been previously reported and has implications for future decoding studies using computational regressors.\u003c/p\u003e \u003cp\u003eMultiple comparisons. The shift from p\u0026thinsp;=\u0026thinsp;0.015 (uncorrected) to p\u0026thinsp;=\u0026thinsp;0.062 (Holm-corrected) for Bayesian surprise highlights the importance of correction when testing multiple model families. We report both values for transparency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Limitations\u003c/h2\u003e \u003cp\u003eFirst, the stationary oddball paradigm limits model differentiation. Roving oddball or volatile-environment paradigms would better test change-point and adaptive models. Second, amplitude-based artifact rejection was used instead of autoreject due to missing electrode positions in the ERP CORE files. Third, partial R\u0026sup2; values were extremely small, suggesting that trial-to-trial surprise modulates only a tiny fraction of EEG variability. Fourth, the cross-validated prediction analysis showed no benefit for any surprise model, suggesting that the encoding-model improvements reflect overfitting to in-sample noise rather than genuine predictive power.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Future Directions\u003c/h2\u003e \u003cp\u003eThree follow-up directions stand out: (1) roving oddball paradigms with genuine non-stationarity; (2) naturalistic stimuli where surprise varies more continuously; (3) source-level or intracranial recordings to improve signal-to-noise.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis paper reports a benchmark comparing four surprise formulations as predictors of single-trial EEG responses. Bayesian surprise shows the strongest trend, but no model survives correction for multiple comparisons. High regressor collinearity and trivial label leakage are identified as critical methodological challenges. These results set a baseline and point to non-stationary paradigms as the necessary next step.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eData and Code Availability\u003c/p\u003e\n\u003cp\u003eData come from the ERP CORE dataset (Kappenman et al., 2021; https://erpinfo.org/erp-core; CC BY-SA 4.0). Code is available at https://github.com/brhanufen/surprise-eeg-benchmark\u003c/p\u003e\n\u003cp\u003eEthics Statement\u003c/p\u003e\n\u003cp\u003eThis study used publicly available, de-identified data from the ERP CORE dataset. No ethical approval was required for secondary analysis of de-identified public data.\u003c/p\u003e\n\u003cp\u003eConflict of Interest Statement\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors\u003c/p\u003e\n\u003cp\u003eAuthor Contributions (CRediT)\u003c/p\u003e\n\u003cp\u003eB.F.Z. conceived and designed the study, performed all data processing and statistical analyses, developed the computational pipeline, and wrote the original draft of the manuscript. Z.A. contributed to the study design and methodology. P.D. contributed to manuscript writing and editing. All authors read and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAdams, R. P., \u0026amp; MacKay, D. J. C. (2007). Bayesian online changepoint detection. arXiv:0710.3742.\u003c/li\u003e\n \u003cli\u003eFriston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B, 360, 815\u0026ndash;836.\u003c/li\u003e\n \u003cli\u003eGramfort, A., et al. (2013). MEG and EEG data analysis with MNE-Python. Frontiers in Neuroscience, 7, 267.\u003c/li\u003e\n \u003cli\u003eItti, L., \u0026amp; Baldi, P. (2009). Bayesian surprise attracts human attention. Vision Research, 49(10), 1295\u0026ndash;1306.\u003c/li\u003e\n \u003cli\u003eKappenman, E. S., Farrens, J. L., Zhang, W., Stewart, A. X., \u0026amp; Luck, S. J. (2021). ERP CORE: An open resource for human event-related potential research. \u003cem\u003eNeuroImage, 225\u003c/em\u003e, 117465.\u003c/li\u003e\n \u003cli\u003eKolossa, A., Fingscheidt, T., Wessel, K., \u0026amp; Kopp, B. (2013). A model-based approach to trial-by-trial P300 amplitude fluctuations. Frontiers in Human Neuroscience, 6, 359.\u003c/li\u003e\n \u003cli\u003eMaris, E., \u0026amp; Oostenveld, R. (2007). Nonparametric statistical testing of EEG- and MEG-data. Journal of Neuroscience Methods, 164(1), 177\u0026ndash;190.\u003c/li\u003e\n \u003cli\u003eMars, R. B., et al. (2008). Trial-by-trial fluctuations in the event-related electroencephalogram reflect dynamic changes in the degree of surprise. Journal of Neuroscience, 28(47), 12539\u0026ndash;12545.\u003c/li\u003e\n \u003cli\u003eN\u0026auml;\u0026auml;t\u0026auml;nen, R., Paavilainen, P., Rinne, T., \u0026amp; Alho, K. (2007). The mismatch negativity (MMN) in basic research of central auditory processing. Clinical Neurophysiology, 118(12), 2544\u0026ndash;2590.\u003c/li\u003e\n \u003cli\u003eOstwald, D., et al. (2012). Evidence for neural encoding of Bayesian surprise in human somatosensation. NeuroImage, 62(1), 177\u0026ndash;188.\u003c/li\u003e\n \u003cli\u003ePolich, J. (2007). Updating P300: An integrative theory of P3a and P3b. Clinical Neurophysiology, 118(10), 2128\u0026ndash;2148.\u003c/li\u003e\n \u003cli\u003eRao, R. P. N., \u0026amp; Ballard, D. H. (1999). Predictive coding in the visual cortex. A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79\u0026ndash;87.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"university of nebraska lincoln","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"prediction error, surprise, mismatch negativity, P3b, Bayesian inference, EEG","lastPublishedDoi":"10.21203/rs.3.rs-9283955/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9283955/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe brain continuously generates predictions about incoming sensory input and produces characteristic neural responses when those predictions are violated. In EEG oddball paradigms, these prediction-error responses manifest as the mismatch negativity (MMN) and P3b components. However, \u0026ldquo;surprise\u0026rdquo; can be formalized in multiple ways, and no prior study has systematically compared these formulations on the same dataset using single-trial methods. Here, we implemented four hierarchical surprise estimators and applied them to the ERP CORE dataset (N\u0026thinsp;=\u0026thinsp;39 subjects, auditory MMN and visual P3 paradigms). Using linear mixed-effects encoding models, we found that Bayesian surprise, quantifying the magnitude of belief revision, showed the strongest association with single-trial MMN amplitude among all models tested (uncorrected p\u0026thinsp;=\u0026thinsp;0.015), though this did not survive Holm\u0026ndash;Bonferroni correction for multiple comparisons (p_corrected\u0026thinsp;=\u0026thinsp;0.062). High multicollinearity among Shannon-based and change-point regressors (VIF\u0026thinsp;\u0026gt;\u0026thinsp;70) limited the interpretability of direct model comparisons. In a cross-subject decoding analysis, contextual surprise features did not improve classification of stimulus class beyond ERP amplitude features alone (ΔAUC\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.093). We conclude that Bayesian surprise shows the strongest trend among competing models, but that stationary oddball paradigms may lack sufficient power to definitively distinguish surprise formulations. All data, code, and analysis pipelines are publicly available.\u003c/p\u003e","manuscriptTitle":"Stochastic Surprise Signatures in Human EEG: A Reproducible Benchmark of Prediction-Error Models Using the ERP CORE Oddball Dataset","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-02 05:31:18","doi":"10.21203/rs.3.rs-9283955/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"97b8aeaa-1570-4d67-8ca3-bb39e33d0df2","owner":[],"postedDate":"April 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65583701,"name":"Computational Neuroscience"}],"tags":[],"updatedAt":"2026-04-02T05:31:18+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-02 05:31:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9283955","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9283955","identity":"rs-9283955","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}