Estimating the Event-Related Potential from Few EEG Trials
Authors: Anders Vestergaard Nørskov
Kasper Jørgensen
Alexander Neergaard Zahid
Morten Mørup
Venue: Accepted by TMLR ()

Abstract: Event-related potentials (ERP) are measurements of brain activity with wide applications in basic and clinical neuroscience, that are typically estimated using the average of many trials of electroencephalography signals (EEG) to sufficiently reduce noise and signal variability. 
We introduce EEG2ERP, a novel uncertainty-aware autoencoder approach that maps an arbitrary number of EEG trials to their associated ERP. To account for the ERP uncertainty we use bootstrapped training targets and introduce a separate variance decoder to model the uncertainty of the estimated ERP. 
We evaluate our approach in the challenging zero-shot scenario of generalizing to new subjects considering three different publicly available data sources; i) the comprehensive ERP CORE dataset that includes over 50,000 EEG trials across six ERP paradigms from 40 subjects, ii) the large P300 Speller BCI dataset, and iii) a neuroimaging dataset on face perception consisting of both EEG and magnetoencephalography (MEG) data. We consistently find that our method in the few trial regime provides substantially better ERP estimates than commonly used conventional and robust averaging procedures.
EEG2ERP is the first deep learning approach to map EEG signals to their associated ERP, moving toward reducing the number of trials necessary for ERP research. Code is available at https://github.com/andersxa/EEG2ERP.

Published in Transactions on Machine Learning Research (06/2025)
Estimating the Event-Related Potential from Few EEG Trials
Anders Vestergaard Nørskov*
oveno gveno@dtu.de
Department of Applied Mathematics and Computer Science, Technical University of Denmark
Kasper Jørgensen'
kusperjoergenseen@@@mla.coo
Department of Applied Mathematics and Computer Science, Technical University of Denmark
Alexander Necrgaard Zahid
alezander hwtpr/drreeeeeerrraaaadddssssso
Department of Applied Mathematica and Computer Science, Technical University of Denmark WS Audiology, Lamge, Denmark
Morten Mørup
mmor@ddu.cc dk
Department of Applied Mathematics and Computer Science, Technical University of Denmark
Reviewed on OpenReview: https: openreview. net/ forum? c6Lg
Abstract
Event-related potentials (ERP) are measurements of brain activity with wide applications in basic and clinical neuroscience, that typically estimated using the average of many trials of electroencephaloggaahh signals (EEG) to sufficiently reduce noise and signal variability. We introduce EEG2ERP, a novel uncertainty-awant arbitrary number of EEG trials to their associated ERP. To account for the ERP uncer- tainty we use bootstrapped training targets and introduce a separate variance decoder to model the uncertainty of the estimated ERP. We evaluate our approach in the challenging zero-shot scenario of generalizing new subjects considering three different publicly avail- able data sources; i) the comprehensive ERP CORE dataset that includes over 50,000 EEG trials across six ERP paradigms from 40 subjects, ii) the large P300 Speller BCI dataset, and iii) neuroimaging dataset on face porception consisting of both EEG and magnetoen- cephalography (MEG) data. We consistently find that our method in the few trial regime provides substantially better ERP estimates than commonly used conventional and robust averaging procedures. EEG2ERP the first deep learning approach to map EEG signals to their associated ERP, moving toward reducing the number of trials necessary for ERP research. Code available at httph: //ggt//ggbt/tt/t com/anddrrsxa//EG2ER
autoencoder approach that maps an
1 Introduction
Electronncohhalorrpply signals (EEG) represent summation of the electrical activity of neural processes in the brain. Isolating these processes in EEG data challenging due to poor signal-to-noise and therefore a common approach is to average many repeated stimulus-locked trials in order to extract the associated event-related potential (ERP) (Luck) 2014). Modern techniques often employ complex averaging and filtering methods to improve the extraction and clarity of ERPs (Lconowicz et al. 2005 Bailey al. 2023a bb. ERPs have been invaluable for invest.gating a wide range of topies in neuroscience (Luck) 2022) and psychology (Ha- jeak et al. 2019), and are relevant for brain-computer interface technologies, such spelling systems for disabled bled patients [Farwell & Donchin 1988 and control of humanoid robots, arms, and wheelchairs (Abiri
ct al. 2019
In recent years, deep learning has been widely applied EEG research to discern signals from noise across classification tasks such as emotion recognition (Jafari et al. 2023), sleep staging (Phan Mikkelsen 2022
Equua contribution.

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Published in Transactions on Machine Learning Research (06/2025)
detection of epileptic seizures Naaea & Ismail 2022), and classification of ERPs (Craik et al. 2019 Li
et al. 2020). Representation learning for EEG has also recently been substantially advanced by exploring transformer architectures and contrastive learning procedures (Kostas et al. 2021 Nørskov et al. 2023).
Our starting point will be the recently proposed transformer and contrastive learning based CSLP-AE framework (Norskov el al. 2023), an autoencoder model which uses a specialized reconstruction loss to encode EEG signals into two latent spaces split respectively to optimally characterize subject and task variability. This model has demonstrated strong performance in learning features useful for classifying both subjects and tasks and has shown promising generalizability and zero-shot capabilities.
In this work, we turn the CSLP-AE architecture into a novel EEG denoising framework. Given subject's few EEG trials, the aim is to estimate the corresponding subject-specific ERP with the ultimate aim of reducing the number of trials necessary to produce reliable ERP estimates. We call this EEG2ERP. This approach aims to make the process more efficient and less burdensome for both researchers and participants requiring fewer repcated trials. A key feature of the proposed framework is the additional uncortainty awareness. In addition to predicting the ERP for a given EEG signal, the model provides variance estimates learned under Gaussian likelihood while training on bootstrapped ERP targets, which naturally capture sampling variability.
Our objective is to recover interpretable, component-level event-related potentials that scientists routinely analyze to test hypotheses about cogmition, perception, and disease. These exploratory studies depend crit- ically on the quality of the ERP waveform, since its amplitude and morphology must. be cleanly measurable to serve as reliable dependent variables. For example, Kutas & Federmeier (2011) emphasize the utility of the N400 amplitude in indexing semantic memory retrieval and integration, Brouwer & Hoeks (2013) high- light how N400 and P600 amplitudes map onto distinct cognitive processes within language comprehension network, and Fields (2023) review the late positive potential predominantly in the context of its amplitude modulations linked to emotional processing and memory. Reliable access to these signal-level measures with fewer trials therefore directly benefits exploratory and analytic neuroscience.
Our research direction is aligned with best practices outlined for ERP research in clinical populations. As noted by Каррепman & Luck] (2016), ERP studies in patient groups face the dual challenge of limited trial numbers and the need for highly reliable mcasures. ERPs are only useful as biomarkers or dependent measures when their amplitudes and morphologies can be cleanly quantified, yet data constraints often compromise this. By improving ERP quality under reduced trial counts, our approach addresses these concerns, thereby supporting exploratory neuroscience and clinical applications in line with established methodological recommendations.
Furthermore, the well-documented dependence of ERP reliability on the number of trials an unsolved problem. Huffmeijer et al.] (2014) demonstrated adequate to excellent test retest reliability for multiple ERP components only when sufficient trial mumbers were available, recommending at least 30 trials for early components such as the VPP and more than 60 trials for later, broadly distributed components such as the P3. Similarly, developmental and lifespan studics have shown that crror-rolated components such as the ERN and error positivity can be reliably measured with as few as six lo eight trials, but only under favorable conditions and with carefully controlled tasks (Pontifex et al.] 2010)) Meyer et al.) 20144). Importantly, child ERP guidelines explicitly recommend minimizing trial numbers and building paradigms around the stability constraints of ERP components (Brooker et al.] 2019). These converging findings illustrate that ERP reliability is strongly trial-limited and that many populations, including children, clinical groups, and older adults, cannot realistically provide the large number of artifact-free trials typically required.
The proposed framework is evaluated on the ERP CORE dataset (Kappenman et al. 2021 under a challeng- ing zero-shot generalization setting, assessing the model's ability to estimate ERPs from a few FEG trials of unseen subjects. We further apply the EEG2ERP approach to a dataset on face perception (Wakeman & Henson 2015) considering both the modeling of EEG and magnetoenceplaalorappyy (MEG) trials. Finally, we evaluate it against strong baselines on the P300 Speller Brain-Computer Interfaces (BCT) dataset (Won) ct al.) 2 to assess its applicability in a practical setting where few repcated trials are essential to reduce the burden of using the system. We hypothesize that deep learning methodologies that explore the mullivari- ate structure of EEG signals accounting for subject and task variability can enhance ERP signal recovery
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using substantially fewer trials than conventional averaging procedures. To systematically investigate the proposed EEG2ERP in its capabilities of quantifying the ERP as function of trials, we consider unseen subjects not used during model training and split each subject's 's trials into two equal sets that are uniformly drawn among the available trials: one set is used to estimate the ERP with the models and basclines, while the other set is averaged conventionally. We then compare these two ERPs to quantify prediction quality.
In keeping with standard ERP methodology, treat the many-trial average from the held-out trials as a high signal-to-noise reference against which to evaluate prediction quality. This reference is not assumed to represent the true underlying ERP; it remains empirical estimate that is itself subject to jitter and artifacts. It nevertheless provides a strong benchmark because averaging across many repetitions is the accepted practice for approximating the underlying component with sufficient signal-to-noise ratio. Our evaluation therefore measures how well the model's few-trial estimate approaches this many-trial reference.
Target EEG trials
EEG2ERP Framework
ERP Prediction
X
CSLP-AE Architecture
Input EEG trials
Split + Bottleneck
Convolation
X
Subject space
Bootstrap inpul
Encoder
Decoder
space
Figure 1: The EEG2ERP model framework. In the top-right graph, the dashed line is the target ERP, and the blue line and is the model's estimated ERP and confidence respectively. The model maps input averaged over K2 EEG trials from one set to estimated ERP averaged over Ng trials from separate set. It is conditioned on K₁ and includes a decoder branch that estimates uncertainty. This visualization simplifies the prediction process to a single channel and demonstrates how bootstrapped ERPs replace the single-trial autoencoder targets of CSLP-AE while accounting for ERP uncertainty including a variance decoder.
2 Methods
We denote the set of EEG trials belonging to a specific subject and task 7 by
Da,r = (x(0 RCT lie {1 [J.
where C is the number of channels and T is the mumber of time points. We use X to denote the value of trial matrix X at the e'th channel and l'th time point.
The averaged ERP over K trials is denoted A s,r E RxT, and our model's denoised estimate of this ERP is written X K e gCxT
2.1 EEG2ERP
We develop an autoencoder framework based on CSLP-AE, that maps an ERP computed from small number of trials, K CxT, to the full ERP obtained from a larger number of trials X CXT where typically K < N.
5,7
3

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The model consists of an encoder, Eg, and decoder, Dy:
Eg : : RCTT_ R2x Dg : R2x + ROxT
where C' and T are the number of imput channels and time steps, and C22 T3 are the compressed latent dimensions. The bottleneck is split into two latent components: a subject-specific latent z E RC. xT. and a task-specific latent zT E CCx These are given as input lo the decoder to estimate the ERP. This split-latent structure enables the model to disentangle and retain subject- and task-specific information in the latent space.
Importantly, the encoder acts as an implicit conditioner, as it extracts both subject and task representations at inference time, without requiring explicit conditioning labels. This means that the subject and task information is inferred and embedded within the latent representation during encoding, and is later utilized by the decoder for ERP prediction. As a result, the model can generalize to unseen subjects during testing,
This implicit encoding of subject and task propertics makes the framework particularly suited for ERP denoising, where the goal is to preserve meaningful inter-subject and inter-task differences while reducing trial-level noise. We therefore adopt the CSL.P-AE. approach as the basis for F.G2ERP, with several modifications outlined in the following sections and the appendix.
We reformulate the training objective from conventional autoencoding, as in CSLP-AE, to instead map the average of an arbitrary number of input EEG trials to the associated subject ERP directly. We further augment the training process to account for the uncertainty of the ERP using bootstrapped target ERPs. In addition, we endow the modcling procedure with uncertainty quantification by incorporating a noise variance decoder to quantify the reliability of the estimated ERP. See Figure | for an overview of the EEG2ERP procodure.
Specifically, EEG trials are split into two halves: imput half and a target half, sampled uniformly from the available trials before training. Inputs to the model are derived solely from the input half, while target ERPs are constructed from the target half, preventing information leakage between input and target.
Our goal is to evaluate whether the model can predict an ERP that gemeralizes from trials that were not used to compute the target. Using the full set average as the target while the model sees a subset introduces dependence between prodictor and target. The same single trial fluctuations then appear on both sides of the evaluation. This shared noise inflates correlation and reduces error by construction, which produces optimistic estimate of performance that does not reflect generalization. Split-half evaluation avoids this optimism as the input half and the target half are disjoint, any agreement can not arise from shared single trial noise.
A further reason for the use of split-halves is parity of signal-to-noise ratio. Comparing one half to the other half equalizes the expected variance on both sides and the power of the average. In addition, when the same trials contribute both to the predictor and to the target average, any latency variability in those trials is shared. This overlap dampens the apparent impact of latency variability, because the predictor and the target are inffuenced by the same misaligned trials. In contrast, in the split-half setting, latency variability is independent across halves. The agreement in this case cannot be explained by shared jitter, so the evaluation is more sensitive to whether a method truly addresses latency variability rather than benefiting from overlap.
For subject s at task t, the EEG trials are partitioned into two halves each with No.- trials available. To model variability in ERPs, we use bootstrapping over trials during training (Mooney & Duval] 1993). From the input half, a bootstrap sample of K trials is averaged and encoded into a latent representation. The model then decodes this latent into predicted ERP and trains against bootstrap target obtained bootstrap sample of Ns.r harget-half trials.
The 5th bootstrap sample of K trials is denoted D, S Da,Ty and the corresponding ERP is denoted and computed with the point-wise average as follows:
X
Kg 8,7
X K
(1)
D
Xs.rEDs
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where [Dy] Kg. This bootstrap- based formulation acts regularization by exposing the model trial-level variability, helping it learn a distributional mapping instead of overfitting to fixed ERP.
We sample K3 out of the Nar available trials as follows
Kb ~ DiscreteWeighted (wee (wee x K.' k
NN..) ==1.....,,,,.
k= kl.........
(2)
which biases training toward using fewer trials on the input side.
This sampling strategy plays a similar role to noise scheduling in denoising autocncoders and diffusion models. By drawing K9 with probability proportional to 1/k, the model is exposed more frequently to low-triae trial-count inputs, where averaging provides only weak noise suppression. This emphasizes learning to recover ERPs under high noise conditions, which aligns with our goal of operating reliably when few trials are available. In preliminary experiments, we evaluated several alternative schedules but found that the inverse weighting yielded the strongest, performance in the low-tria regime.
In addition to the bootstrap-averaged signal X the model is conditioned on the trial count K' using a sinusoidal positional embedding (Vaswani et al. 2017); which is projected and added before the bottleneck transformer. We could also input the empirical pointwise standard deviation with the average, but this statistic depends heavily on K5, is unstable in the few-trial regime, and is undefined at Ky=1. Instead, the model learns the per-lime-point variance by maximizing the likelihood of bootstrapped larget ERPs.
Given an input bootstrap average and trial count, the full encoder decoder model computes the estimated ERP and uncertainty as follows:
23, Eg (X!r Ko) K, 8,7
(3)
K = (z )²
(4)
where z and Z are the latent representations for the subject and task latent space respectively, X the estimated ERP, and ohe CxT is the predicted point-wise standard deviation.
Kg is 5,7
The model is trained to maximize the following likelihood the bootstrap target ERP from the output half:
(&N. S.T.C.t
Z z" (
(...... & Kahe (o Ve,t
(5)
where N, is the 8th bootstrap ERP using Na.r trials from the target half.
This probabilistic formulation enables the model to learn not only the ERP but also an estimate of its variability over both channels and time for each trial. The noise scale is predicted using a dedicated convolu- tional branch in the decoder, transformed via the softplus activation to ensure positivity, following standard practice (Kingma & Welling 2014 Tomezak 2021).
2.2 Loss function
Following Nørskov et al. (2023), the total loss L given by combining the reconstruction loss LR, the contrastive learning loss LCI, and the latent permutation loss CrP:
CTOT LR LCL + CLP
(6)
These loss terms are substantially modified for the EEG2ERP framework as outlined below.
Reconstruction loss LR. To enable learning of the noise variance, the CSLP-AE L2 reconstruction loss is replaced with a negative log-likelihood loss as used in deep latent variable models. We use multivariate Gaussian distribution parameterized by the estimated mean X and standard deviation à:
C
T
[a,t - 8 + log dog
LR
(7)
2 2
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where X RCXT is the target ERP, X is the predicted ERP, and o is the predicted point-wise standard deviation. This loss enables learning both estimate of the ERP and its associated uncertainly.
In practice, we stabilize training by linearly annealing the predicted scale from one to ā over the first half of optimization. This variance annealing strategy is a heuristic generalization of the two-staged optimization approach proposed by (Stirn al. (2023). In that framework, the model first trained with squared error loss on the predicted mean, which equivalent up a multiplicative factor to fixing the variance one, and only afterwards is the variance estimator optimized using the negative log-likeihhodd. Our interpolation scheme replaces this discrete two-stage procedure with smooth transition, linearly annealing the variance contribution from a fixed value of one toward the model's predicted variance over the course of training. This can be seen as a heuristic extension of the faithful training principle, providing a more gradual training signal that stabilizes training.
Contrastive loss LCL This loss incorporates contrastive learning into each split-latent space (subject task). Pairs of subjects and tasks are sampled separately, and a contrastive loss is applied to each respective latent space to encourage specialization.
Let sum v) u |
u
denote cosine similarity. Given M latent pairs Z Z E R in latent space
I. E S. T), the full symmetric normalized temperature-scaled cross entropy loss (Sohn 2016 Oord et al.
2018
Radford et al. 2021 is:
M Σ m7
exp (sim ZZA, /T) sim Z Z
exp (sim( (Z //T)
log
log
(8)
M
exp
Σ exp (sim Z Z(1/T)
where T is the temperature. To support efficient training, we construct batch containing all combinations of subject-task pairs. Let Ns and Nr denote the number of subjects and tasks, respectively. All Ns x Ny combinations are encoded into tensors:
Z ZA n. RRNsNNxX
where H is the latent size, and IL denotes the latent space (subject S or task T). In cases where the number of subjects or tasks makes such a tensor infeasible (perhaps due to memory constraints), subsampling Ns subjects or NT tasks works explicitly in this setup.
Similaritics are computed by aggregating across the non-corresponding axis form the following similarity matrices:
Σ sim
A.3 Z
BBS))
Vi,j (I....,ss),
(9)
Ns
S sim (Z
ZBT)) Vi,j (1,.,,
(10)
The resulting subject similarity matrix aggregales similarities across lasks, and the task similarity matrix aggregates similarities across subjects. These matrices are then used within the contrastive loss by using cross-entropy on each similarity matrix and its transpose. This encourages subject representations that correspond the same individual cluster in subject-latent space, and likewise encourages task represen- tations that correspond to the same task to cluster in task-latent. space, while pushing apart mismatched pairs.
Latent permutation loss L.P The latent permutation loss adapted to support general permutations over the latent dimensions instead of fixed pairwise swaps. This generalizes the loss used in standard autoencoders, CSL.P-A,, and its quadruplet permutation variant (Norskov et al. 2023

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Let again Z ZA.1, B N denote two realizations of the encoding for all subject-task combinations, as similarly used in the contrastive loss. Permutations are applied along the axis not associated with the current latent space:
For L S (subject space), apply 02(+), random permutation over axis 2 (task dimension).
For L T (lask space), apply en e.),, random permutation over axis 1 (subject dimension).
Define 2:(:) as the random-penn permmmaatinttiioonn operator on axis i. Then the decoder Dg takes the permuted latents and outputs an ERP prediction. The permutation loss is then computed an instance-wise reconstruction loss against the original (non-permuted) ERP:
= CR(X, Do(es(ZA.), e (ZAAT)) + (X, Do(es(Zu.), e (z
(11)
This loss encourages disentanglement by forcing the model to produce consistent ERP estimates even when the subject and task latents are randomly mismatched ensuring consistent. extracted information across the two latent spaces.
Additional modifications Finally, we replace the rectified linear units and convolution strides in CSL.P- AE with gated linear units and linear interpolation. These changes are further detailed in Appendix and G respectively. Code is available at https: http///.tttuu.... http://.ogtuub.ooooooo. httggg/ha....aaarrrrr///////////
andersxa/EEG2En and hyperparameters for the
model are detailed in Appendix [
3 Baseline ERP estimation procedure
We evaluate three groups of baseline methods for estimating event-related potentials.
Sample averaging We first compare against conventional averaging across trials. This approach improves the signal-to-noise ratio by reducing random noise as more trials are included, but assumes that all trials are equally reliable and aligned. When noise varies across trials, the expected decrease in noise proportional to 1/VK may not hold. Trials containing outliers, artifacts other systematic noise distort the ERP, particularly when only few trials are available. Differences in subject-specific responses or slight timing variability can also produce misalignment, reducing representativeness of the true event- related signal. Robust averaging methods mitigate these effects by down-weighting outliers or aligning trials before averaging. As robust averaging baselines, we use the tanh weighting scheme introduced as a robust location estimator by Loonowicz et al. (2005) and Dynamic Time Warping averaging as described by Molina et al. 2024) (detailed descriptions are provided in Appendix H.1 and Appendix H.2). These methods are model-free and can be applied directly to the set of trials in a bootstrap sample.
Component aligning We include several algorithms that align and decompose trials before averag- ing. Woody's algorithm (Woody 1967 performs latency correction by iteratively aligning trials within component-specific latency windows. RIDE (Ouyang et al. 2014) extends this idea by decomposing each bootstrap sample into stimulns-locked, contral and response-lockes components and aligning the relevant component before averaging. Window definitions and component configurations follow ERP CORE and the RIDE base guide. Full settings are reported in Appendix H.3 and Appendix H.4 On the P300 Speller BCI dataset additionally apply xDAWN (Rivet et al.) 2009), spatial filtering method operating two more components to improve the signal-to-noise ratio. The xDAWN components are obtained from the
training data.
Template-based baselines Finally, we include template-based methods. The first baseline uses a task- specific global ERP template formed by the grand average of all training subjects and trials. In addition, we also include nearest-neighhor bascline where we compute per-subject ERPs across tasks on the training set and perform task-conditioned nearest-neighbor search in ERP space select the most similar ERP, which is then used the prediction.

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3.1 Performance assessments
To compare the predicted ERPs with the target ERP obtained from the second half of the data (i.e. test trials), we compute the root mean squared error (RMSE) across 200 bootstrapped input samples for a given subject and lask
RMSE (8KI xx)=
1 BBB
X x -
(12)
where X denotes the predicted ERP from the 6th input bootstrap of K trials, and XN is the full target ERP computed from N = Na,7 trials.
We compare this RMSE curve to that of conventional and robust averaging methods.
To enable comparisons across subjects and tasks with different ERP magnitudes, we also compute the coefficient of determination (R²), which normalizes the roconstruction error:
Σ
x Kg
XN
R2 ( x²) =1
(13)
Σ
X
N
This R² score is bounded above by (perfect estimation), with 1² corresponding to constant zero predictions. Negative values indicate predictions worse than zero-output baselines.
4 Experimental setup
4.1 Datasets
We developed and Lested EEG2ERP on the ERP CORE datasel (Kappenman el al. 2021 ), which consists of EEG signals recorded from C = 30 channels across 40 subjects, covering 7 different ERP components derivod from 6 distinct ERP paradigms: N170 from the Face Perception Paradigm, MMN from the Passive Auditory Oddball Paradigm, N2pc from the Simple Visual Search Paradigm, N400 from the Word Pair Judgment Paradigm, P3(b) from the Active Visual Oddball Paradigm, and both LRP and ERN from the Flankers Paradigm. Each ERP component is measured under two contrasting conditions (e.g., related vs. unrelated), resulting in a total of 14 distinct conditions (or tasks) across the dataset.
We applied minimal preprocessing to the trials, following the ERP cleaning procedures from Script #1 of each component, as outlined in the ERP CORE repository! H More information about the paradigms and preprocessing steps can be found Kappenman al. 2021).
EEG and MEG dataset originating from face perception experiments /Wakeman & Henson 2015 These datasets contain, respectively, 70 and 102 channels for the EEG and MEG data sampled at 200 Hz. Each trial belongs to one of three classes: Famous, Unfamiliar, or Scrambled. A detailed description of the preprocessing steps is provided in Appendix I.2
Additionally, investigated EEG2ERP
Finally, we evaluated EEG2ERP on the P300 BCI Speller dataset (Wo et al. 2022 & brain-computer interface (BCT) dataset. This dataset contains FEG recordings from 55 subjects performing a visual P300 spelling task based on and the resulting ERP is used to detect user intent based the P300 component. EEG was recorded from 64 channels at a sampling rate of 512Hx. The dataset provides testbed for assessing ERP estimation in a practical, real-world BCT context, particularly under trial-constrained conditions.
6 character matrix. Each trial involves stimulus flashes (rows and columns),
SSee the full ERP CORE procedure here: http:://tttt...cooo.o//////eete/ 20Procedures.pe

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4.2 Zero-shot generalization
For the framework to be practically useful, it must support zero-shot generalization: mapping EEG data from previously unseen subjects to their corresponding ERP signals. To this end, the ERP CORE dataset was split such that trials from 28 subjects were used for training, for validation, and the remaining 8 for testing. The Mokkman-Hensoon EEG and MEG datasets were divided into 11 subjects for training, 2 for validation, and 3 for testing. Finally, the P300 BCI Speller dataset split into 38 subjects for training, 5 for validation and 12 for lesting. The exact subject splits are provided in Appendix 1.1
During ERP comparisons, we focus exclusively on the task-relevant EEG channel identified by Kappenman ct al. 2021 for the ERP CORE data, and on EEG channel 065 and MEG channel 098 for the Wakeman- Henson data, as these are reported exhibit the strongest component-specilte responses.
5 Results
5.1 Evaluation of the extracted ERPs from the ERP CORE data
In Table D compare the performance of ERP estimation using conventional averaging, robust averaging procedures, and the EEG2ERP approach. Our findings indicate that for K K= and K 5 trials, as well as for K corresponding to 10% of the total trials, the EEG2ERP method provides the best ERP estimates, as quantified by prediction quality measured using R². Notably, EEG2ERP demonstrates strong performance even with as few as K- = trials.
Additionally, we observe that EEG2ERP outperforms simple averaging even when using 100% of the trials. However, the dynamic time-warping (DTW) averaging procedure proposed by Molina et al. (0224 achieves the best performance when 100% trials are available.
Test set results on the ERP CORE dataset. Standard deviations are computed across 10 initializa- tions of the EEG2ERP model.
Table 1:
R (%)
Model / Method
K=1
K=5
10%
100%
EEG2ERP
5.0 + 1.6
31.7 + 0.6
36.1 + 0.5
47.7 + 0.4
Simple Averaging
-1696.6
-382.1
-193.0
34.4
Weighted (Leonowicz et al.
2005
-234.1
-109.6
47.1
DTW Mollna et al. 2024
-124.9
-56.7
50.6
Woody's s Algorithm
-424.1 + 153.9
-236.3
77.7
-009 + 15.3
RIDE
-35..5 + 106.6
-207.4
+ 54.6
-29.8 - 15.9
Nearest Neighbor
14.5 - 7.0
12.0 - 7.0
42.5 + 4.4
Global Template
1.71
To account for the high degree of task variability in ERP estimation, the left panel of Figure presents boxplots comparing FEG2ERP (at K = 5) and simple averaging at K 5 and at 100% against the target ERP estimated from the other half of the test trials. These boxplots, which illustrate performance across the eight test subjects, reveal substantial variability in ERP recovery quality. In many cases, the ERPs poorly replicate those derived from the other half of the trials (as shown by the green boxplots for simple averaging with 100% of trials). At K = 5, EEG2ERP generally yiclds more reliable ERP estimates, whereas conventional averaging, even with all available trials, sometimes fails as seen, for instance, with the MMNN/Devinnts and N2pe/ Cantralateral components.
In the right panel of Figure we assoss how well the ERP uncortainty estimates are calibrated the actual variances of the ERPs. We generally observe that relatively low and high estimated variances correspond low and high true variances, indicating good calibration.
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Figure 2: Left panel: Boxplots comparing R values of the obtained ERPs against the test ERP. Com- parisons include the simple average of all trials (100%), simple average over K 5 trials, and EEG2ERP applied at K outside the bounds (below R² -3)- Right panel: Variance estimates given by standard deviation function of root mean squared error (RMSE) to the ground truth test ERP. Points represent the RMSE of denoised ERPs using K = 5 trials to the test ERP for specific subject-task pairs, alongside the noise standard deviation estimates of the denoised trials.
trials. The missing boxes of simple average K 5 for the MMN paradigm appear
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10-
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100
25
50
100
25
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-10
500
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10
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500
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ooraage (H4)
20-
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Time tma)
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Figure 3: Left panel: Root Mean Squared Error (RMSE) as function of the number of trials included, com- paring conventional averaging, Dynamic Time Warped averaging (Molina et al.) 2024). and the EEG2ERP procedure, Results are shown for three test subjects across one specific task from each of the six paradigms. Right pancl: Estimated ERP signals based K 5 trials, comparing conventional averaging, robust averaging, and EEG2ERP. Confidence bands show bootstrapped estimates of the true ERP; with variance estimates from EEG2ERP predictions displayed as +2 times the standard deviation.
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The left panel of Figure systematically investigates the ERP estimation quality function of the mum- ber of trials used. We compare FEG2ERR to both conventional ERP averaging and robust ERP estimation procedures, across three randomly selected test subjects. We find that our denoised estimates (blue curves) outperform both conventional averaging and the best-performing robust method by Molina et al. (2024) particularly in the low-trial regime (vertical black lines mark K = 5). Furthermore, the robust. estimation methods generally outperform conventional averaging. In the right panel of Figure g we also present ex- amples of the corresponding estimated ERPs, including the associated bootstrapped uncertainties and the estimates by the EEG2ERP model.
We examine how well key ERP signal mcasures reported for the ERP CORE datasct are recovered by EEG2ERP and baseline averaging methods in Appendix A We also visualize the extracted latent task and subject representations and evaluate their utility for classification in Appendix [ The results indicate that the structure of the latent space improves substantially when using K = trials compared to ==
To further compare spatial characleristics of the recovered activity, Figure | shows topographic maps for a representative (unseen) subject in the N170 Faces paradigm. We visualize scalp potentials at 170 ms and 320 ms after stimulus onset using either one trial, five trials, or all available trials. This allows direct comparison of how EEG2ERP and simple averaging capture physiologically meaningful spatial patterns when little data is available.
Topographic Comparison: N170/Faces (Subject 22)
Avg 170
Simple
170
520
K-5
100% (n-36)
100% target (n=37)
Figure 4: Topographic comparison of EEG2ERP and simple averaging for subject 22, which was not seen during training, under the N170 Faces paradigm 170 ms and 320 ms. Rows show results using one trial, five trials, all available trials on the model input half, and all available trials on the unseen target half. EEG2ERP recovers the characteristic N170 pattern with very limited data, while simple averaging degrades under low trial counts. Color scale is the same for all plots and indicates scalp potentials in microvolts.
5.2 Evaluation of extracted ERPs from the Wakeman-Henson EEG and MEG data
In Table 2 we report the prediction performance for the Wakeman-Henson EEG and MEG datascts. As with the ERP CORE data, EEG2ERP shows favorable performance at K = 1, K = 5, and when using 10% of the trials, outperforming both conventional and robust averaging methods. However, for the MEG data, the DTW method by MMolna et al. (2024) outperforms EEG2ERP when 10% of the trials are used, and all conventional averaging methods outperform EEG2ERP when 100% of the trials are available except the Global Template procedure producing inferior estimates.
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Table 2: Test set results on Wakeman-Henson for EEG (top) and MEG (bottom) datasets. Standard
deviations are computed across runs of EEG2ERP. Wakeman Henson EEG Channel EEG065:
R (%)
Model
K=1
K=5
10%
100%
EEG2ERP (Ours)
16.3
1.6
26.7 + 2.4
33.2 + 2.4
38.5 + 4.0
Simple Averaging
-807.6
-219.7
-48.0
62.8
Weighted (Leonowicz et al.
2005
-208.7
-42.3
64.4
DTW (Molina et al. 2024
-36.8
42.3
68.8
Global Template
19.3
Wakeman Henson MEG Channel MEG098:
R² (%)
Model
K=1
5=5
10%
100%
EEG2ERP (Ours)
13.6 + 2.3
19.7 + 2.2
21.8 + 2.5
27.8 + 5.0
Simple Averaging
-878.6
-243.0
-65.8
55.5
Weighted [Lconowicz et al. 2005
246.2
-67.2
56.7
DTW Moolina et. al. 2024
-95.1
5.7
44.2
Global Template
3.1
5.3 Evaluation on the P300 BCI Speller Dataset
To further assess the practical utility of EEG2ERP, particularly in the context of Brain-Computer Interfaces (BCIs), we evaluated its performance on the P300 BCI Speller dataset (Won el al. 2022). We compared EEG2ERP against several established ERP estimation and denoising techniques: simple averaging, Dynamic Time Warped (DTW) averaging (Molina et al. 2024). global ERP template (Template) derived from the training set, and the xDAWN algorithm (Rivet et al. 2009) For xDAWN, spatial components were learned from pooled epochs of all training subjects to enable zero-shot evaluation on the test subjects. The results, measured in terms of R² (%) against target ERPs constructed from all available trials in a held-out portion of the data, are presented in Table
The results Table demonstrate that REG2ERP consistently outperforms other methods low-trial conditions (K = 5 and 10% of trials) for estimating target character ERPs. For instance, at K 5 trials, EEG2ERP achieves R² of 33.08 6.80%, substantially outperforming DTW at -333.25 = 112.61% and simple averaging at -609.79 + 181.70% Even compared to xDAWN, strong spatial filtering baseline, EEG2ERP yields superior performance at low trial counts for target character ERPs. Notably, the Global Template procedure again fails in producing performant ERP estimates.
While xDAWN performs best on non-target ERPs at 100% of trials, EEG2ERP achieves competitive or better R scores few-trial conditions. These results highlight EEG2ERP's robustness in low-data regimes, which are typical in many BCI applications.
5.4 Model ablations
In Appendix C compare EEG2ERP to set of ablated variants in order to assess the contribution of key components. These include: (i) CSLP-AE trained on few-trial averaged inputs, (ii) EEG2ERP with single-trial inputs (K = 1), (iii) EEG2ERP without uncertainty modeling, and (iv) EEG2ERP without both uncertainty modeling and the trial-count. embedding. The single-trial FEG2ERP variant, can additionally
use ERP variance estimates to weight individual predictions (Appendix E
Across ablations, CSLP-AE performs poorly when required to estimate ERPs from few-trial averages. The single-trial FEG2ERP variant performs similarly to the full model at K 5 trials but degrades at larger trial
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Table 3: Test set R2 (%) results on the P300 BCT Speller dataset (Won et al. 2022
EEG2ERP compared
against Dynamic Time Warped (DTW) averaging, Simple Averaging, a global ERP Template, and xDAWN. K denotes the number of trials used for eslimation. Higher R² values are better.
Spelling Target Character
Model
K = 5
10%
100%
EEG2ERP (Ours) DTW (Molina et al., 2024)
33.08 + 6.80
34.99 + 5.85
37.28 + 5.64
-333225 + 112.61
-65.51 + 36.43
21.30 + 12.04
Weighted Leonowiez et al.
2005
656.42 + 193.27
-232.16 + 84.65
11.40 = 23.55
Simple Averaging
609.79 + 181.70
-202.72 76.71
12.61 + 23.06
Global Template
32.77 6.80
xDAWN (Rivel et al. 2009
129.38 + 38.02
20.10 + 17.20
36.46 + 7.04
Spelling Tan-Target Character
Model
K
10%
100%
EEG2ERP (Ours)
2282.62 + 74.91
-8.86 + 15.75
- 13.69 + 20.86
DTW Molina et al. 2024)
-3111.61 + 903.81
-128.78 + 53.74
Weighted Leonowicz al.
2005)
-5723.25 + 1438.91
-422.03 + 123.66
-15.59 26.00
Simple Averaging
-5275.53 1271.46
-386.58
111.59
-14.82 25.78
Global Template
-10.23 = 16.65
xDAWN [Rivet et al. 2009
856.37 = 206.62
49.37 = 25.90
10.04 14.19
counts. Removing uncertainty modeling or both uncertainty modeling and trial-count conditioning leads reduced performance overall, indicating that both components contribute meaningfully to estimation quality.
Finally, to assess temporal consistency, conducted an additional experiment where trials were evaluated in chronological order rather than randomly sampled (see Appendix DJ, confirming that EEG2ERP remains robust under more realistic temporal sampling conditions.
6 Discussion
In this work, we introduced EEG2ERP, a deep learning framework for estimating event-related potentials from a small number of EEG trials. This approach enables zero-shot generalization unscen subjects and incorporates uncertainty estimation by design.
6.1 Key Findings
Our experiments consistently showed that EEG2ERP outperforms both conventional and robust averaging methods in the low-trial regime. Remarkably, even with just K = 5 trials, EEG2ERP estimated ERPs with higher R² than conventional averaging using all available trials. This highlights the model's ability to extract meaningful signal representations from noisy input data.
The success of EEG2ERP appears be driven by two key innovations: (1) introducing bootstrap-bassd training strategy that enables robust ERP estimation from varying numbers of trials, with an emphasis low-trial scenarios, and (2) incorporating uncertainty quantification in the decoder to estimate predictive variability. These components improve robustness and reliability in trial-scarce settings. Combined with the underlying CSLP-AE framework, which enables zero-shol generalization by disentangling subject- and task- specific variability in a split-latent representation, these innovations make possible to perform low-trin towatrial, uncortainty-awark ERP estimation even for subjects unscen during training. Thus, FEG2ERP reduces the number of trials needed to obtain reliable ERPs while generalizing to unseen individuals, offering a powerful and flexible tool for data-efficient. neural signal analysis.
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6.2 Comparison with Prior Work
While previous efforts in ERP estimation have largely focused signal averaging spatial filtering (e.g. xDAWN, Template-based Methods), EEG2ERP uses fundamentally different approach: it learns encoder- decoder mapping from noisy EEG to clean ERPs in an end-to-end fashion. Unlike robust averaging, which remains model-free and task-agnostic, EEG2ERP benefits from task-aware representation learning and ex- plicit uncertainty modeling. Our results show that this leads to stronger generalization in both EEG and MEG scttings, particularly when data scarce.
Notably, EEG2ERP outperformed established methods like xDAWN and DTW in low-data scenarios but surpassed by DTW on the MEG data when all trials were used. This suggests that data-rich scenarios may still favor flexible alignment-based methods and traditional denoising, while in contrast, deep models like EEG2ERP remain elfective and robust even when trial counts are low and with minimal preprocessing.
We also compared the EEG2ERP procedure to a simple global ERP template. Across the datasets, this template-basse ERP estimation consistently produced lower R values. This further emphasizes the diffi- culty of ERP estimation and the advantage of more advanced methods such the proposed EEG2ERP; particularly in low trial scenarios.
6.3 Implications
The ability to estimate ERPs from very few trials opens the door to faster, more efficient EEG-basod studios. This could reduce experimental duration, lower participant burden, and enable ERP analysis in populations where many repeated measurements are impractical, such as in children, elderly patients, or individuals with neurological conditions.
Moreover, EEG2ERP provides per-sample uncertainty estimates, which can guide downstream decisions, such selecting trials for further analysis or identifying unreliable ERPs. This uncertainty-wwarr feature is especially relevant in clinical and BCI contexts where interpretability and reliability are crucial.
Although EEG2ERP substantially improves amplitude estimation relative to baseline averaging procedures, the gains in latency estimation are more modest. This reflects the fact that our model operates on averagod trial inputs, which partially obscure trial-to-trial lateney variability. As result, latency structure that is misaligned before averaging cannot always be fully recovered. Existing alignment procedures, such DTW or RIDE, explicitly address latency variability at the trial level, and combining such alignment- based preprocessing with EEG2ERP may produce complementary benefits. Future extensions could also incorporale explicit latency estimation or per-trial encoding, enabling the model to account for variability in timing before aggregation. These directions are promising avenues for improving latency-sensitive ERP charactorization..
6.4 Limitations
A key limitation of this work is the variability in model performance across tasks and subjects. Although EEG2ERP performed well on average, specific components (e.g. MMN and N2pc) remain challenging to predict, especially when trial numbers are low or inter-subject variability is high.
Another limitation lies in dataset scope. The datasets presently considered, while comprehensive, represents controlled laboratory settings with well-defined paradigms. Real-world EEG often more variable and noisy. Future work should test EEG2ERP more diverse datasets and under naturalistic conditions.
6.5 Future Directions
In this work, we built. EEG2ERP on top of the CSLP-AE architecture due to its strong zero-shol perfor- mance (Nerskov et al. 2023 Future research should explore alternative model architectures, particularly those leveraging sclf-supervised pro-training or recent EEG foundation models such as BENDR, Neuro-GPT, or LaBraM (Kostas et al.) 2021 Cui al. 2023 Jiang et al., (0244). These approaches could further en- hance generalization and robustness, especially in low-data regimes. We presently used sampling scheme
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proportional to the inverse of the number of trials used to emphasize learning in the low trial regime. Ex- ploring alternative sampling schedules that improve performance across the full range of K9 is an interesting direction for future work. Importantly, our work introduces ERP prediction as a novel downstream task for such foundation models emphasizing efficient recovery of cvoked responses from very few trials.
7
Conclusion
We presented EEG2ERP, novel deep learning framework for estimating event-related potentials (ERPs) from small number of EEG trials, with strong generalization to unseen subjects. The method leverages bootstrapped training largets and learned noise variance decoder to estimate both the ERP and its as- sociated uncertainty. EEG2ERP achieved state-of-the-al performance in few-shot ERP estimation across multiple datascts and modalitics, consistently outperforming conventional and robust averaging approaches in low-trial scenarios.
EEG2ERP is the first method to map EEG signals directly to their associated ERPs in a zero-shot setting, Its integration of predictive uncertainty enables more reliable ERP recovery and supports trial selection based on model confidence. As such, EEG2ERP provides not only powerful new tool for data-efficient ERP estimation but also valuable benchmark for future EEG representation learning approaches.
We view this work as a foundational step toward more advanced deep Icarning methodologies in noural signal processing. In particular, the uncertainty-awar design of EEG2ERP is likely to become a key feature in future efforts to reduce the number of trials required for ERP research, enabling broader applicability both experimental and clinical contexts.
Broader Impact Statement
This work introduces approach for estimating ERPs from few EEG trials, which may lower data collection demands and broaden access to high signal-to-noise neural measurements. More efficient ERP extraction could support research in populations that are difficult to study with long repeating protocols and may help enable future applications in adaptive neurotechnology, clinical monitoring, or real-world cognitive assessment.
As with many data-driven models, benefits depend on careful validation and appropriate deployment. Models trained on limited datasets may not capture the full diversity of neural responses, and downstream use should therefore consider the possibility of reduced reliability in underrepresented groups. Continued work on diverse datasets and transparent reporting will help ensure that such tools support inclusive and responsible development across scientific and technological domains.
Acknowledgments
V. N. was supported by Danish Data Science Academy, which funded by the Novo Nordisk Foundation (NNF21SA0069429) and VILLUM FONDEN (40516). A. N. Z. has received funding from the Lundbock Foundation (R347-2020-2439).
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A ERP CORE metrics
In Table we invostigate how well respectively peak latency and amplitude is recovered by the EEG2ERP and traditional averaging procedures, and in Table 5 the recovery of mean amplitude, area latency and onset latency when compared to the reported values Kappenman et al. (2021).
Table 4: Recovery of peak latency and amplitude EEG2ERP at K=5 and ERP Core statistics, and s.d. over subjects
Paradigm
Peak Latency (ms)
Peak Amplitude (uV)
EEG2ERP
ERP Core
REG2ERP
FRP Core
ERN
62.18 (12.14)
54.47 (12.63)
-12.31 (4.91)
13.86 (7.01)
LRP
-61.88 (13.77)
-49.9 (15.66)
-1.62 (1.93)
-3.41 (1.15)
MMN
174.66 (12.01)
187.60 (19.13)
-1.63 (0.24)
-3.46 (1.71)
N170
128.99 (9.81)
131.4 (12.56)
-2.20 (0.72)
-5.52 (3.32)
N2pc
231.13 (13.85)
253.24 (18.51)
-0.96 (0.81)
-1.86 (1.60)
N400
372.89 (27.03)
370.09 (49.43)
-9.29 (1.81)
-11.04 (4.65)
P3
461.72 (37.06)
408.89 (70.48)
6.90 (3.43)
10.15 (4.53)
Traditional averaging and Molina et al. averaging for K=5, mean and s.d. over subjects
Paradigm
Peak Latency (ms)
Peak Amplitude (nV)
Simple Avg.
Molina al.
Simple Avg.
Molina et al.
ERN
55.22 (13.27)
55.70 (16.16)
-66.15 (9.48)
-20.46 (9.07)
LRP
-59.93 (12.37)
-63.34 (11.42)
-8.71 (3.60)
-4.99 (3.75)
MMN
177.94 (7.18)
176.73 (8.89)
-9.55 (2.67)
-5.05 (1.59)
N170
132.47 (7.89)
132.75 (7.82)
-8.33 (2.52)
-5.64 (2.39)
N2pc
234.43 (7.51)
230.30 (6.13)
-4.79 (1.71)
-2.02 (1.55)
N400
375.99 (34.16)
375.85 (36.71)
-1.550 (5.71)
-11.56 (4.83)
448.23 (30.72)
441.20 (33.83)
15.21 (5.21)
10.89 (4.90)
Table 5: Recovery of mean aplitude, latency, area latency and onset latency REG2ERP at K=5 and ERP Core, mean and s.d. over subjects
Paradigm
Mean Amplitude (μV)
50% Area Latency (ms)
Onset Latency (ms)
EEG2ERP
ERP Core
EEG2ERP
ERP Core
EEG2ERP
ERP Core
ERN
-9.31 (3.94)
-9.26 (5.90)
50.60 (4.42)
54.36 (9.99)
10.08 (6.91)
2.50 (27.53)
LRP
0.58 (2.61)
-2.40 (0.94)
-53.43 (3.35)
-49.99 (9.72)
-88.68 (7.65)
-96.50 (19.85)
MMN
-0.58 (0.17)
-1.86 (1.22)
172.22 (1.67)
185.20 (14.44)
148.35 (9.32)
146.94 (30.33)
N170
-1.09 (0.83)
-3.37 (2.71)
126.58 (1.74)
131.84 (8.58)
117.89 (4.45)
95.76 (29.05)
N2pc
0.08 (0.87)
-1.14 (1.15)
237.66 (1.99)
246.43 (8.81)
210.21 (4.66)
213.63 (30.85)
N400
-6.02 (1.77)
-7.61 (3.27)
390.52 (10.70)
387.72 (17.85)
316.02 (13.77)
284.86 (44.92)
P3
3.64 (3.48)
6.29 (3.39)
453.18 (11.04)
436.47 (32.77)
357.00 (25.67)
327.44 (61.98)
Traditional averaging and Molina et averaging for K=5, mean and s.d. over subjects
Paradigm
Mean Amplitude (nV)
50% Area Latency (ms)
Onset Latency (ms) Molina et al.
Simple Avg.
Molina et al.
Simple Avg-
Molina et al.
Simple Avg.
ERN
14460 (9.29)
-12.44 (8.30)
48.99 (4.18)
48.37 (4.05)
16.48 (8.51)
13.93 (7.99)
LRP
0.13 (4.12)
-0.15 (3.97)
-54.69 (3.44)
-54.00 (3.45)
-82.93 (7.90)
-89.11 (6.73)
MMN
-1.23 (2.43)
-1.21 (0.83)
173.84 (0.75)
173.99 (1.51)
149.68 (6.71)
145.01 (9.17)
N170
-3.72 (1.81)
-2.83 (1.89)
128.41 (2.08)
128.75 (2.26)
121.41 (6.46)
120.62 (6.40)
N2pc
0.62 (1.73)
0.70 (1.61)
236.11 (1.47)
236.21 (1.89)
215.56 (5.07)
210.11 (3.55)
N400
-6.86 (5.20)
-5.46 (4.45)
395.46 (8.06)
397.57 (5.81)
323.48 (11.69)
320.11 (11.92)
P3
4.34 (4.02)
4.32 (3.69)
456.30 (9.87)
454.79 (9.40)
355.33 (20.58)
353.90 (24.78)
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B
Model latent space
Figure contains confusion matrices from encoding every trial as singlo-trial in the test datasct using the encoder and using the XGBoost Classifier (Chen & Guestrin 2016) just as in Nørskov et al. (2023] The corresponding subject and latent spaces are shown using I-SNE plots in Figure
Subject
Took Accuracy:
Paradigm Acturacy:
6:11 0.23
0.42
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0.07 0.12
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2099
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9111
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622
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523
(1.09 6:06 0.10 3:00 0.56
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526
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0.07 9.28 2.0 0.00 0.11
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011
142000cck0ed
M420
0195
9107
0.5
1.10
001
057
529
6.31
6.07 0.22 9.1L
0.23
8
8
NA00
Presidied
Prokited
Figure 5: Confusion matrix on subject, task and paradigm labels using XGBoost Classifier with 5-fold Cross- Validation splits as in CSLP-AE. Latents encoded using single-trial samples only.
514
520
10peCantra
523
526
1-SNE7 2
t.SNE
t-SNE 1
t-SNE 1
Figure 6: t-SNE plot on the subject latents (left) and task latents (right) from single-trial samples.
Figure 7 contains confusion matrices from encoding bootstrap samples of five trials each, without replacement for all available trials to keep samples independent,, on the test dataset and using XGBoost to classify. The corresponding subject and latent spaces are shown Figure
Figure contains confusion matrices from the EEG2ERP model trained with single trial input. Here encoding single trials the test dataset and using XGBoost to classify. The corresponding subject and latent spaces are shown in Figure 10
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Tisk
Ba anced Accuracy: 68.49%
Balanced Accuracy: S3. 73.77%
Balanced Accuracy: 78.345
0:71
6:05
0.33
0:3
0.05
HRNY
53/
0.00
0:02
0.83
0/23
0.04
PPP
0.07
0.02
0.03
0.54
0.00
0.04
0.00
505
0.00
6:07
0.67
5.06
0.06
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006
0.00
500
0.05
5.05
0.00
2:63
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0.03
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p:pp
0.00
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0.00
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502
6.00
8.06
0.00
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622-
0.07
6:02
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N400
0.02
0.02
0.00
PAltare
0.05
0.00
0.01
0.00
0:01
0.19
55
Predected 182el
Preskted
Figure 7: Confusion matrix subject, task and paradigm labels using XGBoost Classifier with 5-fold Cross- Validation splits as in CSLP-AE. Latents are encoded using five independent trials that are also independent of other samples.
514
520
522
523
526
1-SNE 2
t:SNE
str 12po laland TO TOPPos
t-SNE 1
t-SNE 1
Figure 8: t-SNE plot on the subject latents (left) and task latents (right) from latents with five independent trials that are also independent of other samples.
Tesk
3b anced Accuraty: 39.46%
Balanced Accuracy: 28 26%
Ealanced Accuracy: 54.55%
0:30
0:2 2.00 0.66 D47 0.1
532
0.30
0:21
033 2.00
8/6 0.11
UnPrpolistere
13P
0.22
332
0.11
0.05
0.11
0.04
0.07
KI5 0.13
0.12
0.33 518 0.25 0.05 0:05
0.11
500
M..1
9.18
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1.5 031 0.09 0/33
0.10
0.09
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0.00
0.40
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M173/7acee
0.05
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140021 talited
M820
0.93
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8:04
PAMare
P3
0.07
9.04
0.03
0.66
6:02
0.11
0.66
8
2
E20
Preditted
Figure 9: Confusion matrix on subject, task and paradigm labels using XGBoost Classifier with 3-fold Cross- Validation splits as in CSLP-AE. Latents are encoded using single trials using the EEG2ERP trained with single trial input instead of bootstrap.
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514
520
522
523
526
Actolars
MATOO and
E-SNE 2
E-SNE
t-SNE 1
t-SNE 1
Figure 10: I-SNE plot the subject latents (left) and task latents (right) from latents with single trials using the EEG2ERP trained with single trial input instead of bootstrap.
C Results of CSLP-AE and ablations of EEG2ERP on denoising
We evaluate how different components EEG2ERP contribute ERP reconstruction by comparing the full model to several ablated variants. First, we consider standard CSLP-AE model trained on ERP CORE and evaluated by averaging its single-trial reconstructions the test sct. This bascline does not incorporate uncertainty modeling, trial-count information, trained a variant of REG2ERP using only single-trial inputs (Kinput = 1). Although this version is not exposed to averaged imputs during training, it can produce an ERP estimate for each trial and combine them using uncertainty-base weighting (Appendix This variant is denoted EEG2ERP w/ Single Trial.
bootstrapped averaging during training. We additionally
In addition to the single-trial ablations, we include two ablations on the uncertainty decoder and the trial- count conditioning. The first removes the uncertainty decoder (EEG2ERP w/o Unc.), which prevents the model from estimating per-time-point variance but retains trial-count conditioning. The second removes both uncertainty modeling and trial-count conditioning (EEG2ERP w/o Unc. w/o Emb.), ), isolating the effect of the latent-conditioning mechanism on performance. Finally, we evaluate CSLP-AE when the input consists of few-trial averages instead of single trials (CSLP-AE w/ Avg. Input), to assess whether CSLP-AE can learn the mapping without the architectural changes and the uncertainty modelling.
Quantitative results are presented in Table The standard CSLP-AE bascline performs poorly across all conditions, and providing few-trial averaged inputs does not resolve this and only seems to exacerbate it. The single-trial variant of EEG2ERP performs comparably to the full model at K = trials but degrades at larger trial counts, reflecting that the full model benefits from being trained on inputs spanning range of K. Removing uncertainty modeling or both uncertainty and trial-count conditioning leads to consistent decreases in performance, particularly when few trials are available. These comparisons indicate that both uncertainty estimation and trial-count conditioning play meaningful roles robust ERP prediction.
A boxplot showing R² K for each of the models above and in Table is shown in Figure
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Table 6: Test results for CSLP-AE with averaging, EEG2ERP with single-trial input, and EEG2ERP.
Model
R (%)
n
K = 5
10%
100%
CSLP-AE
-37.3
-25.0
-8.6
CSLP-AE w/ Avg. Input
4
124.4 0.7
119.0 0.8
99.8 + 0.8
REG2ERP w/ Single Trial
6
32.6
0.9
33.5
37.6+
EEG2ERP
10
0.6
3.5
47.7
EG2ERP w/o Unc.
5
2.2
2.90
38.5
EG2ERP w/o Unc. w/o Emb.
5
10.8
1.9
24.5 1.9
41.2
10
-15
Metic CSUME 6-5
al Single
-3.0
(M/COMMMMNE wopportent
MURA
Tel
Figure 11: Box-plot the ablations on the EEG2ERP model, showing the standard CSLP-AE as used for denoising. EEG2ERP trained with single trial input, and the EEG2ERP model.
Chronologically sequential trials
We performed an additional experiment evaluating all methods chronologically sequential trials rather than random samples. In practice, this setting more closely reflects the real-world use case of reducing the number of trials by omitting later ones, thereby preserving their temporal order. Specifically, FEG2ERP was trained as before using randomly ordered bootstrap samples but evaluated using sequentially ordered trials. The results on the ERP CORE dataset are summarized Table
Table 7: Performance on ERP CORE when using chronologically sequential trials rather than randomly sampled trials. Higher R² indicates better ERP estimatiion. ion.
Model
K
10%
100%
EEG2ERP
32.7+2.7
43.7.0.8
50.410.5
DTW
-65.6
-66.7
59.9
Weighted
-17.99
-135.0
65.3
RIDE
-22..5
-133.5
-16.7
Woody's alg.
-226.3
-209.1
18.6
Nearest neighbor
25.7
13.3
47.7
Simple avg.
-171.6
-159.0
60.7
Overall, results show improved performance across most methods compared to random sampling, which is expected since temporally adjacent trials are less affected by non-stationarities such as changes in attention or fatigue. Importantly, EEG2ERP maintains strong performance under this temporally ordered evaluation, confirming its robustness across different sampling strategies.
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E Estimation of average ERP from denoised single-trial EEG estimates
To obtain final ERP prediction from a set of N estimated ERPs obtained from single trial EEG signals by the EEG2ERP, we employ an estimator that maximizes the likelihood of all of the produced single trial ERP estimates (below denoted ( (c, for the 7th trial for subject at task 7 for channel at time t with associated estimated uncertainty - (c, ()). For the ERP estimate of channel at timepoint we obtain
II $1 ( (c (o.6))((((.)))) (d!9(c.1))
(c, arg max
(14)
Pa,s (e.t)
The solution to this maximization reduces to calculating a weighted average of the estimated ERPs, where the weights are the inverse variances (precisions) of the signals as given by
E 60! (c,t) (c,t)
Po. (c,
(15)
E @ (c,t(ctt)
This inverso-variance weighted average can be shown have the least variance among all weighted aver- ages (Hartung et al. 2008); and the variance of this weighted average estimator is given by:
(c, = Var (cr(
(16)
EN (ol.
As the variance of the mcan is reduced by factor of 1/N we can multiply this variance of the mean by N to oblain an estimate of the average variance of this weighted average ERP estimate. Notably, this averaging procedure thereby accounts for the precision each individual ERP estimate and gives more weight to single trial estimates with low as opposed to high variance.
F Gated Linear Units as opposed to ReLU
The CSLP-AE model architecture utilizes ReLU activations within the convolutional blocks. While ReLU activations are widely used for their simplicity, effectiveness, and fast implementation, recent advancements suggest that Gated Linear Units (GLUs) can provide improved performance in sequence modeling tasks by introducing clement-wisc gating mechanisms that allow more expressive control over the flow of informa- tion (Dauphin et al.] 2017 Shazeer 2020). Consequently, the ReLUs in the ConvBlocks of the CSLP-AE architecture have been replaced with GL.Us instead.
The ReLU activation function defined as:
(e,)( = max(za,j,0 0) Vi Vj
(17)
where ž,j represents the output of the convolution operation, C₂ is size of the latent dimension and T, is the time-resolution of the latent space.
In contrast, the GLU activation function utilizes gating mechanism. The convolution output is split into two parts: onc-half represents the feature signal, and the other half functions the modulating gate. For input X E RCXT the convolution is expressed as:
(18) However, in practice, this is computed with a single convolution operating with double the filters and with the output channels split evenly. The modulation gate, 2(0), normalized using affine instance normal- ization (Ulaanov al., 2016) before applying the activation: z(o) (nstanceNormi((((00) The GLU activation function is then applied as:
Conv1D(X)xs) and (g) 2.
ConviD(X)
(1) GLU(=
(19)
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where (f)) is the standard logistic sigmoid function.
In the CSLP-AE architecture, instance normalization is applied directly to the feature signal after each convolution. While this improves training stability by normalizing the input distribution, it also removes scale information from the feature signal. This can adversely affect signal representation. The normalization is applied on an instance basis. This means that normalization is performed each timestep in the resolution of the latent space. Relative magnitude information between representations in time is thus being removed from the signal by normalizing each such instance.
Applying the normalization function in the gating function is contribution of this work. By moving instance normalization to the gating mechanism, the derived GLUs maintain scale information in the feature signal through the feature signal path. Here scale information refers to the relative magnitude of features, which can be critical for encoding the strength or importance of specific EEG signal components. For example, the amplitude of an ERP signal reflects physiological characteristics and contributes to its interpretability. Normalization ion eliminates this magnitude by standardizing feature values for each instance. This loss of scale can hinder the model's abilitt to leverage amplitude- baaed patterns in the data.
Instance normalization in the derived GLUs includes lcarnable affine paramcters that can control the behavior of the sigmoid gating function. This enables the model to dynamically modulate the location, sharpness and width of the sigmoid gating function, allowing finer control over information flow and being able to adapt to varying data distributions during training.
With non-linearity confined the gating operation, the derived GLUs ensure a linear pathway for the residual feature signal between network layers which enhances signal propagation and gradient flow. The feature signal z(f) remains unaltered by non-linear transformations, allowing it to retain structure and scale, This preserves the integrity of the input signal while enabling selective attemuation or amplification in the network by the modulating gate.
G Interpolated Residual Connections
The CSLP-AE architecture (Norskov et al. 2023 is based loosely on the ResNet architecture from He et al. (2016) with residual connections between blocks of convolutions. Residual connections are a core component of deep learning architectures which enables better gradient flow and improved training of deep networks.
In the original ResNet design, when the feature maps of the input and output have different sizes (c.g.. during down-sampling of 2 (He et al.] 2016). This ensures that the dimensions of the input and output match. These are marked as dashed lines in Figure 3 of the original paper by He et al. (2016).
up-sampling), the shorlcut connection is adapled using convolution with stride
However, this breaks up the direct connection backbone that flows through the model and introduces addi- tional complexity, as the convolutionn modifies the residual path and introduces non-linear transformations, disrupting the direct signal flow. The residual connections can be viewed from different perspective entirely, as in Veit et al. (2016), where they act as the main pipeline. From this perspective, the convolutional blocks are ensemble shallow networks extracting and adding information to this main pipeline. Breaking up this pipeline with a convolutionn and activation makes this signal pipeline no longer linear.
The original ResNet design also applies a convolution between blocks with differing number of channels He et al., 2016). However, this is not necessary for the CSLP-AE, architecture where all blocks have the same number of filters.
Rather than using a convolution with stride 2 for the residual connection, interpolation can be used to resize the residual connection to match the target feature map dimensions. This approach retains the simplicity of identity mappings and the direct linear connection while also minimizing additional computational overhead.
Given the one-dimensional nature of the data, the choice of interpolation method is simply the piecewise lincar interpolation of the signal to match the size of the down- or up-sampled signal in the time dimension. During down-sampling the main convolutional layer reduces the feature map resolution, while the residual path is resized using linear interpolation to match the new resolution. Similarly, during up-sampling, the
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residual is resized to match the expanded dimensions of the feature map, ensuring compatibility for the element-wise addition.
Let the input feature map be defined as Z E RCxi2 where C is the number of channels and Tz is the size
of the time dimension, and let the output feature map after the convolution and activation be U E RCxT where Ty different from Tz. The residual connection is interpolated to match the time resolution Tv of the output as follows:
V = (i,terp(Z,TT)) + (et(oonv(2) Z)) = interintt,.... Z, Tb) + +U
(20)
where conv(2) is the convolution operation applied to the input Z, act(.) is the non-linear activation function, interp( Z, Tu) is an interpolation function that resizos along the time dimension to match Tu, and functions as element-wise addition of the interpolated residual and the output of the convolutional block.
H Robust averaging procedures
H.1 Tanh Weighting
tanh weighting scheme by Leonowicz et al. (2005) The tanh weighting scheme, introduced as a robust location estimator in Leonowicz et al. (2005), is applied across trials to improve ERP mcasurement by adaptively reducing the influence of outliers and non-stationary noise in the data. Unlike simple averaging, which treats all trials equally, the tanh method assigns weights based the extremity of trial values (the amplitude). using a hyperbolic tangent function to down-weigh extreme deviations, In cases with small number of trials, this scheme provides a significant advantage by dynamically optimizing weights in a data-dependent manner. This enhances the signal-to -oll-t---iiieeee ratio (SNR) and yields a more accurate and representative ERP [eonooicz ct al. 2005).
Denote a bootstrap sample of EEG signals in the most prominent channel as X E R consisting of K trials and T timepoints. The weighting scheme is applied time-wise to estimate the best mean (location estimate) at each timepoint. First, the data for each time point t is sorted in ascending order, producing permutation pr( that maps indices from the original order to the sorted order as follows
[p,(1). S Tp.(2). S ... S (K)(K). Vt E {I....,T]
(21)
(i) is the index in the original order that corresponds to the i-th smallest value in the sorted order. Specifically, P {l...., K} + {1,...,K) K) such that (p)( is the i'th smallest value of X,, The columns of the data matrix X are thus sorted in ascending order at each timepoint. After sorting, the rows no longer represent original trial indices but instead correspond to low-to-high voltage measurements. The weighting scheme is applied as follows
K
R. =
W. E (1...,,T)
(22)
where we are weights per trial time t. Applying a piecewise tanh-function the new indices enables assigning lower weights to extreme voltages and higher weights to central values, improving the robustness of the location estimate. Such a function can be defined as follows
tanh (e(i + 1)) - v. 1 tanh (c(i- K)) +v,
if K T (I..,. K) (1....,,T) K
(23)
if
>> 0 is a constant offset and > 0 is a scaling parameter. The constant offset value is used to remove extreme values entirely from the equation by setting any negative weights to zero. The scaling parameter controls the curvature of the weighting function. For high values of e the weighting approaches the uniform simple average and for lower values it approaches a linear scaling as a distance from the middle point. We use the default parameters from the original paper (c = 0.1, v = 0). Finally, the weights are obtained by normalizing the matrix such that each column vector sums to one:
max 0)
Wi.t = Σ/K max 0)
(24)
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H.2 Dynamic Time Warped Averaging
Dynamic Time Warping (DTW) for ERP estimation, as introduced in Molina el al. (2024), is technique adapted from speech and sound processing (Berndt & Clifford 1994 Müller 2007] to address latency and jitter variability in EEG signals. Variations in trial timing and amplitude can distort averaged ERP wave- forms, leading to blurred peaks and high ERP waveform variability (Ouyang et al., 2016; Murray et al., 2019). DTW aligns individual trials to a reference signal by minimizing temporal differences, improving ERP quality by reducing latency variability. This method particularly useful for cases where latency jitter and amplitude variability across trials make simple averaging suboptimal.
Let X E RKXT denote bootstrap sample of EEG signals for specific channel, where K is the number of trials and T is the number of timepoints. Let v E g² represent the reference signal, which is obtained using traditional simple averaging:
K K
2
(25)
The DTW process dynamically adjusts each trial Wh E RR (k: 1lk=1 I....,K) by finding an alignment path p = (Pi, P21.P2...... . pas) where Pm = (Pim PJm) maps the indices of and æk.
The alignment path minimizes a total cost function defined by the sum of distances between the aligned elements:
cxii,) d(v,, Vi,j E {I)
(26)
where d(:;-) can be any distance function. In the present work the Euclidean distance d(a, b) = (a b) is used while in Molina et al. (2024) the Manhattan distance was used d(a.b) = la b). The path p must satisfy the following two conditions:
1. The boundary condition P1 = (1, and PM = (T,T).
2. Steps must be limited to (1, 0), or (0, 1).
The first condition guarantees that the total length of both signals is considered avoiding partial matching, The second condition ensures that the path only moves in the down-right direction and prevents backtracking. These conditions ensure that the path starts in the upper-left corner and flows to the lower-left corner of the cost matrix.
The alignment path is found using dynamic programming (Snnin 2008 Using the alignment path p warped version of each trial, xy E R can be constructed. However, the signal has length M which does not correspond with the length of each trial which is T. To ensure the warped trial has the same length as v, steps in the alignment, path p that do not advance the index of the reference signal (i.e. (0, steps) are discarded. The warped signal with these path elements discarded is denoted as ox E R", Essentially, this looks each index in the reference signal and takes the corresponding value of the trial of the path. In cases where there are multiple steps for the same reference index, Molina et al. (2024) opts to discard these, Another solution would be to take the average. In the present work these steps are discarded as well.
The estinated ERP is found by laking the average of the warped trials:
ak
(27)
By first matching and warping the signals to a common reference signal the temporal precision and amplitude consistency of the ERP is greatly improved and the influence of latency and jitter variability is reduced.
H.3 Woody's Algorithm
Woody's algorithm (Woody 1967 was implemented as a latency correction baseline. For each ERP com- ponent, we used the ERP CORE-defined measurement windows expanded in both dircctions to allow for broader alignment. The windows used are defined in Table The algorithm iteratively aligned each trial the evolving average until convergence, maximizing cross-correlation within the specified latency window.
27

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Published in Transactions on Machine Learning Research (06/2025)
Table Woody Component Windows
Component
Window (ms)
N170
-10 to 350
MMN
125 425
N2pc
to 475
N400
100 to 700
P3
100 to 800
LRP
-300 to 200
ERN
-200 to 300
H.4 RIDE
We implemented the Residue Iteration Decomposition (RIDE) method OOyang et al. 2014) in Python based on the publicly available MATLAB toolbox RIDE separates EEG signals into separate components: stimulus-locked (S), central (C), and response-locked (R) components. We used a three-component model (S, C, R) for all conditions except LRP and ERN, which were modeled with an R-only component. Window definitions followed the RIDE base guide, with main component windows set according to ERP CORE's reported significance intervals, see Table
Table 9: RIDE Component Settings
Component
S window (ms)
C window (ms)
R. window (ms)
N170
110 to 150
100 to 900
300 to 300
MMN
125 to 225
100 to 900
-300 to 300
N2pc
200 to 275
100 to 900
-300 to 300
N400
0 to 500
300 to 500
-300 to 300
P3
0 to 500
300 to 600
-300 to 300
LRP
-100 to 0
ERN
0 to 100
H.5
Implementation validation
To verify that our Python implementation of the Woody latency correction baseline (Woody 1967 and the RIDE decomposition baseline (Ouyang et al. 2014) behaved as expected, we validated both implementations on simulated ERP data with known single-tria latency variability. The simulated dataset consisted of 50 single-channel trials sampled at 500 Hz from 200 to 800 ms. Each trial contained two components with realistic morphology: a positive P300-like peak and a negative N200-like peak that preceded the P300 by 100 ms. The P300 latency varied uniformly between 300 and 500 ms across trials, and moderate additive noise, amplitude variation, and bascline drift were included.
Both methods estimated per-trial latency shifts, allowing direct comparison to the known ground-truth latencies. We quantified accuracy using the correlation between true and estimated latencies and the root mean square error after centering. Woody's algorithm recovered latencies with correlation 0.995 and RMSE 5.77 ms. RIDE achieved correlation 0.998 and RMSE 4.93 ms.
Figure 12 illustrates the unaligned and aligned trials, the recovered templates, and the correspondence between true and estimated latencies for both methods.
2 toolbox for residue iteration decomposition (RIDE): https://cns. edu. ww/.RIEE.E.........
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Published in Transactions on Machine Learning Research (06/2025)
Original Maal clest
Weody's Alggncd Wills
HIDE Al gredd Trias
Weaty's figned Pog
Amp LoV
Time-tii
ERP Comportion
Labincc Necovary Compar son
Error Comp parison
Weaty
Woore
Racoratucted Thu Templats
"orfect condiatin
Raadbakk
-100
Tran
Figure 12: Validation of Woody's algorithm and RIDE simulated ERP data with known latency jitter. Top panels show trial waveforms before alignment, after alignment with Woody, and after alignment with RIDE, together with the corresponding averages. Bottom panels show the averaged waveforms compared to the ground-truth template, the relationship between true and estimated latencies, and the residual estimation error. Both methods recover single-trial latency variability with high accuracy.
Experimental setup
We train EEGERP for Emax = 200 epochs, annealing the predicted standard deviation over the first Etarget 100 epochs, and employ a learning rate of x 10-4 with a OneCycle learning-rate scheduler. Complete parameter values and experimental settings are detailed in the associated source code, which is provided as supplementary material and hosted at lattps://githii com/ Indersxa/EEG2EN
1.1 Data partitioning
We evaluated EEG2ERP on three publicly available M/EEG datasets. For each dataset, subjects were partitioned into mutually exclusive training, validation (development). and test splits, and all experiments for that dataset used the same split. Table 10 summarizes the exact subject IDs per split.
Table 10: Data partitioning for all datasets.
Dataset
Set
# subjects
Subject IDs
Training
28
1, 2, 3, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 21,
24, 25, 28, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40
ERP CORE (40)
Validation
4
4, 7, 27, 33
Test
8
14, 15, 20, 22, 23, 26, 29
Training
11
2, 3, 5, 7, 8, 9, 10, 11, 13, 14
Wakeman Henson (16)
Validation
2
12, 15
Test
3
0, 4, 6
Training
38
0, 1, 3, 4, 5,
6,
7,
8, 9, 10, 11, 13,
14,
15, 17, 18,
20, 21, 23,
27,
28,
34,
35,
36,
37,
38,
39,
41, 42,
P300 BCI Speller (55)
44, 45, 46
47,
49,
50,
51,
52,
53
Validation
5
12, 29,
33,
40,
43
Test
12
16,
19,
22,
24,
25,
26, 30, 31, 32, 48, 54
29

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Published in Transactions on Machine Learning Research (06/2025)
1.2
M/EEG data preprocessing pipeline
All M/EEG recordings were preprocessed in FrepdTrip (Oostenveld et al. 2011).
EEG and MEG were
handled separately, following the steps summarized in Table 11
Table 11: M/EEG preprocessing steps.
Step
Operation
Details
Bad channel
Channels with relative bandpower 49.75-50.25 Hz 15% were markod bad and interpolated from spatially neighboring channels.
detection & interpolation
High-pass filtering
FIR high-pass filter, 1 Hz cutoff, to remove baseline drifting. 50 Hz notch to remove power-line interference. Continuous data segmented into trials time-locked to task stimuli.
Notch filtering
Segmentation
(epoching)
Artifact trial
(1) reject trials with trial-level z-score> 20 (jump artifacts); (ii) reject trials with EOG channels band-pass 2-15 Hz and 2-score> 6. Subtract mean in -000 ms to pro-stimulus window.
rejection
Baseline correction
7
EEG re-referencing
EEG only: average reference across EEG channels.
Resampling
Resampled to 200 Hz.
Trial cropping
Keep -00 ms to 800 ms per trial.
30


Reviews:
[{"review_id": "GJAyDs69V9", "reviewer": "Reviewer_Tsca", "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- Clear writing\n- The modeling decisions all make sense\n- Experiments are strong for fewer trials\n- Methodological contribution is good\n\nWeaknesses:\n- I'm not convinced that the \"split all trials into two non-overlapping sets for input/output\" setting is the best one one. Why not just use the (boostrap) of the non-split full trial as the target? You cited \"leakage\", but is that the right way to think about this here? If I have a mean of 10 numbers, and I want to use it to approximate the mean of 100 numbers, which include the 10 numbers as a subset, what's the problem? \n- Your input is the pointwise-average signal of K trials and K, the number of trials. Then you estimate the variance on the output. I don't understand how it's hypothetically possible to get a good variance estimate without also using the pointwise-variance signal of K trials as well. Is the argument that K is sufficient somehow? Can you please do this experiment and ablate that adding the pointwise-variance (probably point-wise standard deviation in practice for numerical stability) to the input doesn't help?", "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 introduces EEG2ERP, a deep learning approach for estimating ERPs from a smaller number of EEG trials. The strength EEG2ERP method is its performance when only a few EEG trials are available.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Ablate the concatenation of the pointwise strandard deviation to the input.\n- Please add additional latency-jitter baselines, like RIDE. https://pubmed.ncbi.nlm.nih.gov/25455337/", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "9j8bRKi8Fo", "reviewer": "Reviewer_BojW", "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": "**Strength:** The approach of performing non-linear denoising/prediction from bootstrapped average ERPs is interesting. It could connect to wider literature on denoising auto-encoders.  \n\nThe included experiments and figures are clear and seem well defined. \n\n**Weaknesses:**\n\nThe major gap is the lack of connection between the problem that is solved and the ultimate aim of reducing trials for a specific purpose. The approach aims to reduce number of trials to get reliable ERP estimates. But the ultimate aim, what can you do with a ERP estimate is under-explored, which undermines the paper.  The big question is whether the estimate of ERP with fewer samples sufficient information to act on. It is not clear if it help neuroscience studies or enhance the classification in brain-computer interfaces.\n\nThere is a need for a discussion regarding whether the few trial R^2 (possibly combined with the variance estimates) is sufficient to support scientific hypothesis testing.\n\nNote that the Molina et al. paper uses classification in the end to justify their approach. Also xDAWN also examines the accuracy of classification as a function of the number of repetitions. For the P300 speller, the problem is to classify the ERP as being target or non-target. It's not clear if the improved reconstruction in low trial regime supports that. \"The ability to estimate ERPs from very few trials opens the door to faster, more efficient EEG-based studies.\" This is a possible implication but it should be justified.\n\nIt should be made more clear early on that the ERP estimate from the many trials (second half of the trials) is considered the gold standard / ground truth.  However, this assumption is not clear given the fact that there could be temporal jitter and/or artifacts. I.e. for training and testing different versions of what is considered ground truth ERP could be used. \n\nRegarding jitter, a classic baseline for ERP estimation with misaligned trials is Woody, Charles D. \"Characterization of an adaptive filter for the analysis of variable latency neuroelectric signals.\" Medical and Biological Engineering 5, no. 6 (1967): 539-554. This is arguably simpler than the dynamic time warping. \n\nA base assumption is that the EEG trials are partitioned into two halves... I assume these halves are chronological. It is idealistic to consider that there is a single 'ERP' as the brain adapts. Habituation can happened after only a few trials.  Early and late trials may be distinct, which is in itself interesting. This is not discussed.  Looking at the results, could the ERP \"ERN/Correct\" in Subject 20, be an example of habituation?\n\nClarity is also issue at times with the formulation, there are some mistakes and ambiguities. \n\nAnother weakness is the heuristic choice of annealing the variance estimate in the Gaussian negative log-likelihood as this specific problem has been addressed in the literature (Beta-NLL paper): \nSeitzer, Maximilian, Arash Tavakoli, Dimitrije Antic, and Georg Martius. \"On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks.\" In Tenth International Conference on Learning Representations (ICLR 2022). 2022.", "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": "The paper introduces a methodology for predicting the EEG event-related potentials (ERP) in the latter half of trials from a few initial trials. To do this it adapts an auto-encoding network trained to disentangle the subject and task specific information to handle the case of ERP input and outputs. In addition to the mean, the variance is also estimated and a negative log likelihood is used in lieu of mean squared error for the reconstruction. Results show that with just 1 or 5 trials the model often has positive R^2 for predicting the average ERP, which is much better than baselines.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "The paper should be revised to address weaknesses above (critical). \n\nThe phrasing \" it also provides variance estimates that are learned during training using associated bootstrapped ERP training targets accounting for the ERP uncertainty.\" is hard to parse. The confusion is that the uncertainty estimates use a Gaussian likelihood model, which is independent of the bootstrapping. The way it was written I was anticipating that the bootstrap variance estimates were going to be used. \n\nLast sentence before Figure 1 \"ERPs to quantify reconstruction accuracy.\" I'm not sure that the choice of 'reconstruction' should be used. It is actually misleading because the target is not reconstructed per sea. It is rather a prediction problem given the chronological split between initial and final trials.  \n\n\n**Issues with formulation (critical)**: \n\"To support efficient training, we construct a batch containing all combinations of subject-task pairs.\" Taken literally, this doesn't seem possible for a large number of subjects and tasks. The aggregating in (9) and (10) means subjects are paired and then tasks are paired. Is that correct, rather than all combinations. Also, the verbal description before and after equation 9 and 10 is not clear. As I think 'non-corresponding axis' should be corresponding axis, i.e., same task in (9) or same subject in (10). Also do $A$ and $B$ denote disjoint set of $N_S$ subjects? Otherwise, why not use the same tensor for both? Furthermore, there must be a mistake in indexing because $j$ is undefined in (9) and $i$ is undefined in (10). Also the term \"opposing axis\" isn't clear.\n\nIt is rather confusing, what the pairs are in relation to $\\bar{\\mathbf{Z}}^{A,\\mathbb{L}}$ compared to without the bar defined before equation 9. The operation of the random permutation is not clear in (11), I guess $\\bar{\\mathbf{X}}$ denotes a single realization case, but it is not clear what it corresponds to given that $A$ and $B$ are different tensors. Also it is not clear if there should a sum over it. That is, is this is an instance wise loss like (7)? Or a batchwise loss like (8)? \n\nWhat is the 'pre-latent embedding space'?\n\n**Additional results**: (possibility to strengthen the work)\nI'd request to compare the linear annealing of predicted scale with the Beta-NLL approach for learning the uncertainty estimate. Also the uncertainty estimate can be quantified using expected calibration error (i.e., binning the variance estimates and looking at the squared error compared to the bin-center variance for points assigned to each variance bin). \n\nA simple baseline would be to find the nearest neighbor (considering ERPs from full set of trials) of the training set, and retrieve that. This could be more meaningful than global average template.   \n\nI'd also like to see Woody's jitter based approach. \n\nThere is description in Appendix E and Appendix F about the changes from the CSLP-AE baseline.  The additional modifications of using gated linear units is quite substantial, but it is not clear the impact of these choices compared to overall formulation of the problem.\n\nThe results are impressive for K=1 and K=5, but its not clear to me if that is the first and first 5 trials respectively, or it if is across all sets of 1 or 5 trials. But in Table 2, at 100% the results are well below simple averaging. Perhaps the Zipf law on the number of trials overemphasizes learning from a few trials at the expense of performing well when many trials are given. This is related to the issue of noise scheduling in denoising auto-encoders that has lead in part to  diffusion models. There is no simple answer but it seems that different priors on $K_b$ could be compared. \n\nSimilarly, given the training over different numbers of trials in (2), wouldn't it be better to test? Also I don't see how information leakage during training is a problem as long as the splits are chronological. Meaning that the if the input average is based on a boostrap average of the first K trials, couldn't the remaining N-K trials be used? \n\n\n**Questions**\n\nIt would be useful to describe the baseline methods with more detail. Is the \"global template\" the average across other subjects?  The exact phrase only appears in the tables.\n\n\"EEG2ERP is the first method to map EEG signals directly to their associated ERPs\" is this correct? Besides $K=1$ isn't it operating on averages also? \n\nHow are the tanh parameters optimized? Original paper uses Nelder-Mead. Is the same adopted? Nothing is mentioned in Appendix G.\n\nIn tables 1 and 2, for $K=1$ the entry for Weighted should be dashed out, as there is no sense in this.  Also what is the sense of DTW for $K=1$? That is DTW warping to itself? I feel that DTW with its own reference should also be grayed out. \n\nWhy isn't the Weighted (Leonowicz et al. 2005) included in Table 3.\n\n\n**Minor notes:** \n\nFigure 1, internal notation of superscripts with parentheses and subscripts b and n do not match the equations. \n \nUsing calligraphic D for both the dataset and the decoder can be confusing. I'd avoid calligraphic for the encoder and decoder. \n\nLast sentence before Section 3. \"Hyperparemeters\" misspelled.\n\nWhy would xDAWN \"acts on two or more components reducing the SNR\"? I think this is a typo.\n\nI find it odd that Table 1 appears at top of page in the midst of Section 4 well before its reference in Section 5.", "broader_impact_concerns": "The broader impact statement appears to be too broad for this scope of this study.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "vCKOEU7pfQ", "reviewer": "Reviewer_mTSH", "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": "Strength: The writing is clear. The study design is solid. The topic is important and has practical applications.\n\nWeakness: Some of the experimental design can be further improved.", "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 introduces a novel deep learning framework to map a few EEG trials to a denoised ERP waveform with uncertainty prediction. The main architecture is the existing CSLP-AE. The authors propose a bootstrap training scheme, a variance decoder, and new losses for the EEG2ERP framework. Experiments are performed on three public datasets and the model shows large gains over simple averaging, robust averaging and DTW, on unseen subjects. Additional analysis including ablation on the “averaging” procedure, visualization and analysis of the latent space, detailed evaluation of the output ERP features, are performed to enhance the rigorousness of the study. In sum, this is well-written, solid work with huge potential for various downstream applications and contributions to the neuroscience community.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. The ablation study is not complete, and the paper should ablate all differences vs CSLP-AE, which means studies of EEG2ERP w/o uncertainty, EEG2ERP w/o uncertainty w/o trial number embedding, and CSLP-AE with few trial averaged input should be included.\n2. Technically speaking, we will not be able to get the “ground truth ERP” in real life experiments. Although the author designed a rigorous experiment paradigm, it would make the paper stronger if a simulation study can be performed to quantitively evaluate the model’s ability to recover ERP components (Latency, amplitude, topological map, etc). \n3. I am particularly interested in the topography map in the real data as well as it also shows the spatiotemporal modeling abilities. \n4. As shown in table 4-5, the latency metrics are not improving vs benchmarks but the amplitude estimates has a huge improvement. A discussion could be added on this point.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)