Bayesian Test-Time Adaptation via Dirichlet feature projection and GMM-Driven Inference for Motor Imagery EEG Decoding
Authors: Huan LUO
Na Lu
Xiaopeng Wang
Xu Niu
Venue: ICLR 2026 Poster (2026)
Keywords: Brain-computer interface
motor imagery
test-time adaptation
Dirichlet distribution
Bayesian inference
Primary area: applications to neuroscience & cognitive science
TL;DR: BTTA‑DG is a lightweight, gradient‑free Bayesian test‑time adaptation framework that projects EEG model sequential embeddings into a compact Dirichlet space and uses GMM‑driven Bayesian inference to robustly calibrate motor imagery predictions.

Abstract: Generalization in EEG-based motor imagery (MI) brain-computer interfaces (BCIs) is hampered by cross-subject and cross-session variability. Although large-scale EEG pretraining has advanced representation learning, their practical deployment is hindered by the need for costly fine-tuning to overcome significant domain shifts. Test-time adaptation (TTA) methods that adapt models during inference offer a promising solution. However, existing EEG-TTA methods either rely on gradient-based fine-tuning (suffering from high computational cost and catastrophic forgetting) or data alignment strategies (failing to capture shifts in temporal predictive embeddings). To address these limitations, we propose BTTA-DG, a novel Bayesian Test-Time Adaptation framework that performs efficient, gradient-free adaptation by modeling the distribution of temporal predictive embeddings. Our approach first employs a lightweight SincAdaptNet with learnable filters to extract task-specific frequency bands. We then introduce a novel Dirichlet feature projection that maps temporal embeddings onto a compact and interpretable parameter space, effectively capturing the concentration of time-varying predictive evidence. Adaptation is achieved via a GMM-driven Bayesian inference mechanism, which models the historical distribution of these Dirichlet parameters and fuses this evidence with the model's prior predictions to calibrate outputs for the target domain. Extensive experiments show that BTTA‑DG significantly outperforms previous EEG‑TTA methods, achieving state‑of‑the‑art accuracy while running at real‑time speed. Furthermore, visualizations confirm the physiological interpretability of our learned filters and the robust class separability of our Dirichlet feature space.

Published as a conference paper at ICLR 2026
BAYESIAN TEST-TIME ADAPTATION VIA DIRICHLET FEATURE PROJECTION AND GMM-DRIVEN INFERENCE FOR MOTOR IMAGERY EEG DECODING
Huan Luo', Na Lu²; Xiaopeng Wang", Xu Niu²
"School of Future Technology, Xi'an Jiaotong University
Sccooo of Automation Science and Engineering, Xi' an Jiaotong University luchuan12300 200stu xjtu. edu. cn, Lvna20090xjtu. edu. cn
ABSTRACT
Generalization ERG-based motor imagery (MI) brain-computer interfaces (BCIs) is hampered by cross-subject and cross-session variability. Although large-scale EEG pretraining has advanced representation learning, their practical deployment is hindered by the need for costly fine-tuning overcome significant domain shifts. Test-time adaptation (TTA) methods that adapt models during inference offer a promising solution. However, existing EEG-TTA methods either rely on gradient-basee based fine-tuning (suffering from high computational cost and catastrophic forgetting) or data alignment strategies (failing to capture shifts temporal pre- dictive embeddings). To address these limitations, Bayesian Test- Time Adaptation framework that performs efficient, gradient- free adaptation by modeling the distribution of temporal predictive embeddings. Our approach first employs lightweight SincAdaptNet with learnable filters to extract task-specific frequency bands. We then introduce novel Dirichlet feature projec- tion that maps temporal embeddings onto a compact and interpretable parameter space, effectively capturing the concentration of time-varying predictive evidence. Adaptation is achieved via GMM-driven Bayesian inference mechanism, which models the historical distribution of these Dirichlet parameters and fuses this evi- dence with the model's 's prior predictions to calibrate outputs for the target domain. Extensive experiments show that BTTA-DG significantly outperforms previous EEG-TTA methods, achieving state-of-the-an accuracy while running at real-time speed. Furthermore, visualizations confirm the physiological interpretability our learned filters and the robust class separability of our Dirichlet feature space.
propose BTTA-DG, novel
INTRODUCTION
Electroenncephalograahy (EEG) based compuer interfaces (BCIs) decode cortical activity to
control external devices (Clerc 2013). Among them, motor-imagery (MI) BCIs leverage sensorimotor rhythms (SMRs) (Neuper et al. 2006) and have shown promise in stroke rehabilitation (López-Laarre
(et al. 2018) and assistive control (Fernánde7-Rodriguee et al.] 2016 Noda et al. (2012). Recent advances in large-scale EEG pretrained models (Wang et al. [2024] Jiang et al. [224]] Kim et 2024),
trained on massive datasets, have demonstrated unprecedented capabilities in learning general and reliable representations. However, deploying such models in real-world scenarios remains challenging due to significant data shifts in EEG recordings (Huang et al., (023). These shifts stem primarily from the non-stationarity of EEG signals, driven by cross-subject cross-session neurophysiological differences (Apicella et al. 2024). Consequently, bridging these distributional gaps requires robust adaptive strategies beyond pretraining alone (Xu et al. 2020 Wimpff al. 2025 Liu et al. 2025).
Test-time adaptation (TTA), which adapts models during inference using online unlabeled data (L) al. 2023). presents a promising solution for practical BCI deployment. However, existing EEG- TTA methods fall into two paradigms with critical trade-offss Gradient-based approaches update model parameters through techniques such entropy minimization (Wang et al. 2020), pseudo-
"Corresponding author.

---

Published as a conference paper at ICLR 2026
label optimization (Lee et al.) 2013 Wang et al. 2022), and consistency regularization. While effective, these methods suffer from high computational overhead due to gradient backpropagation and risk catastrophic forgetting when continuously updating pre-trained representations. For in- stance, OTTA (Wimpff et al. 2024) integrates data alignment with entropy-based batch normalization finetuning, while T-TIME (Li et al. 2023) employs ensemble learning with conditional entropy mini- mization, both requiring substantial computational resources. Conversely, non non-gradient approaches avoid parameter updates by recalibrating domain-specific statistics, such batch normalization layer recalculation (Schneider et al., (020)) or data alignment (Wimpff et al., 2024 Bakas et al. 2025). While computationally efficient, these methods rely on shallow alignment techniques that inadequately capture the complex, domain shifts inherent in EEG representations across subjects and sessions. This creates a fundamental challenge: to develop a TTA framework that is both computa- tionally efficient and capable of modeling deep distributional changes, all while being theoretically grounded and avoiding destructive model updates.
To address these challenges, propose BTTA-DG, Bayesian Test-Time Adaptation framework that achieves nigh-performance, gradient- free adaptation via Dirichlet feature projection and GMM-driven inference. Our approach introduces the Dirichlet distribution to EEG-TTA, treating it as a "distribution over categorical distributions" to model prediction uncertainty (Wong) 1998). Our method first employs Sinc-based adaptive network (SincAdaptNet) extract powerful, task-specific features. We then introduce a novel Dirichlet feature projection, which maps temporal predictive embeddings onto a compact, interpretable parameter space. Unlike conventional EEG-TTA methods that rely on heuristic data (Zanini et al. 2017 He & Wul 2019) or shallow statistics aligmment (Schneider et al., 2020). this probabilistic representation effectively models the concentration of the model's 's time-varying predictive distribution, allowing us to capture shifts in temporal predictive embeddings in the new domain, which is a sigmificant advance. To ensure stable and efficient adaptation, we design Gaussian Mixture Model (GMM)-driven Bayesian inference mechanism. A GMM models the historical distribution of Dirichlet parameters from the target domain, and Bayesian inference fuses this likelihood with the deep model's prior predictions. This entire process is gradient-free calibrating the model's 's outputs without destructive updates to its pre-trained weights, thereby preventing catastrophic forgetting. Our contributions include:
We construct Sinc-based adaptive network (SincAdaptNet) that leverages learnable Sinc- filters to extract task-specing frequency bands. It enhances the representation of temporal embeddings by isolating the most informative spectral components.
We are the first introduce the Dirichlet distribution EEG-TTA, creating low- dimensional projection that provides a robust and interpretable representation of deep distributional shifts, overcoming the limitations of prior heuristic and shallow alignment methods.
We propose novel GMM-driven Bayesian inference mechanism that enables gradient- -ree adaptation. By modeling the historical Dirichlet parameter distribution, the GMM retains gl lobal-neighhorhood knowledge of the test data. Bayesian inference then combines the GMM likelihood with prior predictions to yield calibrated posterior predictions.
Across public MI datasets, BTTA-DG achieves oftte-of- accuracy with real-time speed. Visual- ization analyzes confirm the physiological interpretability of our learned spatial and spectral filters, which isolate MI-specific scalp topographies (frontal, central, parietal, and occipital regions) and frequency bands (mu, beta, gamma). Furthermore, we show that our Dirichlet feature space yields robust class separability, evidenced by low intra-class covariance (<0.27) and high inter-class KL divergence (>31.85). These results validate BTTA-DG as a lightweight, robust, and theoretically grounded framework for practical test-time adaptation in BCIs.
2 METHODOLOGY
Notations In MI-TTA research, a cross-subject setting is commonly considered, where leave- one-subject-out (LOSO) cross-valle volsddvali is widely adopted (Altaheri et al.) 2023). Each subject in turn serves as the unlabeled target, with all other subjects' data forming the source. Let [D( V. denote the source domain containing labeled EEG trials from L subjects, where D sxe = {(s). yř 1 ===1 consists of !o trials for subject 1. Each trial sf E CxT is C-channel EEG signal of length T.
2

---

Published as a conference paper at ICLR 2026
with class label yj L. The target domain Deg {s*} Nu contains Nig unlabeled test trials arriving sequentially from one single subject. deep classification model fo = fels 9ane. with parameters 0, is pre-trained on {D Here, the encoder Jenc RCCT - RRC xf maps the EEG trials to embeddings of dimension [C] T, and the classifier fas R - R produces predictions for [C] classes. The goal is to adapt fe to Dug via online MI-TTA framework without requiring target labels source data. In addition, within-subject adaptation across sessions is also discussed in Appendix H
2.1 SINC-BASED ADAPTIVE BANDPASS FILTERING NETWORK
We propose a lightweight Sinc-based Adaptive Bandpass Filtering Network (SincAdaptNet) to serve the deep classification model So within the MI-TTA framework. The network comprises: Spat- Conv + Sinc-Conv - IncCh-Conv + Cls-Conv, with layer normalization inserted after temporal filtering and channel expansion avoid batch-statistics dependence when the online batch size is one (Ba ct al. 2016).
Spat-Conv performs spatial filtering with F'pp kernels of size (C' x 1), reducing channel redundancy while retaining task-relevant spatial patterns, akin to data-driven CSP (Blankertz et al. 2007). Sinc- Conv is an interpretable, parametrized temporal convolution inspired by SincNet (Ravanelli & Bengio 2018: Zhang et al. (0024) rather than learning free-form kernels, it learns low cutoff flow and bandwidth Jhand (thus Jhigh = foo + fbana), from which a windowed-sinc band-pass kernel is generated. This yields MI-relevant mu (8-13 Hz), beta (13-30 Hz) McFarland et al. (2000); Pfurtscheller et (2006), and gamma (> 30 Hz) Darvas et al. (0110) rhythms with few parameters and clear spectral interpretability. The Sinc-Conv layer comprises Fsine adaptive bandpass filters of size (1 x Nsime) and uses "SAME" padding to preserve temporal dimension. IneCh-Conv expands channels to Fine to enrich representation, and Cls-Conv maps features
[C] x T embeddings, where C denotes the number of motor imagery classes and T denotes the temporal length.
Critically, inspired by the SwAV framework (Caron al. 2020p, normalized probability spaces enable more stable and interpretable representation learning under domain shift. For each EEG trial, its temporal predictive embeddings are mapped through softmax function follow time-varying
categorical distributions. denoted by X = Gene (s) [21, 22........ ØT] E KT Each Øy E R encodes an instantaneous class probability vector at timestep j. collectively forming a trajectory of time-vane varying uncertain predictions. The model's prior prediction is obtained through temporal averaging: (X) T E 3, E RICI This averaging process integrates the dynamic prediction information over time, providing robust and informative prior for subsequent Bayesian inference. Complete architectural details of AdapANet are provided Appendix B
2.2 BAYESIAN TEST-TIME ADAPTATION VIA DIRICHLET FEATURE PROJECTION AND GMM-DRIVEN INFERENCE
To address challenges in current MI- TTA methods catastrophic forgetting from gradient-based up- dates and insufficient modeling of deep feature shifts-we propose a probabilistic test-time adaptation framework that integrates Dirichlet feature projection with GMMM-driven Bayesian inference. This approach dynamically calibrates the deep model's prior predictions fo(s) through Bayesian inference, enabling efficient, gradient-free and theoretically grounded online test-time adaptation.
Overall, the Dirichlet feature projection method first projects the post-softmax temporal predictive embeddings X to the low-dimensional Dirichlet parameters. It preserves the prior concentration towards each class for temporal predictive embeddings that follow time-varying categorical dis- tribution. Second, in GMM-driven Bayesian inference, the Dirichlet parameters estimated from historical EEG trials are clustered by GMM, which efficiently encodes both global information of the historical test trials and the neighborhood information of the current calibrating trial. Bayesian inference is then used to combine the GMM likelihood with the prior prediction of deep model to obtain the calibrated posterior.
1) DIRICHLET FEATURE PROJECTION FOR DEEP-FEATURE MODELING
The core of our method is the Dirichlet feature projection. The Dirichlet distribution, as a "dis- tribution distributions (Wong. 1998)", is probability distribution over the parameter space
3

---

Published as a conference paper at ICLR 2026
(a)
Duricletti..2 0.2, 0.2)
(b)
Dirichlettk,
(c)
Dirichlet(S,
(d)
DirschletrL,
Sumples
Sumples
1.0
1.0
1.0
1.0
0.0
0.0
0.0 0.2 1.4.0. 4...0. 4.9..
10 Ra R 22
1 aa 2
16 R
Dirichlet distributions for varying parameter settings. Each subplot displays 1000 samples (blue points) and the mean (red points) within the probability simplex (red lines). (a)-(c) illustrate that increasing the total scale oo yields lower uncertainty (lower variance). Comparing (b) and (d) illustrates that elevating a component a, shifts the prior concentration toward its corresponding class.
Figure I:
of categorical distribution. It can encode temporal predictive embeddings of categorical distri- butions for EEG trial rather than fixed categorical distribution. Let the temporal predictive embeddings output from SincAdaptNet's encoder be X = [2) 22, ,,, E RI4[xT, where each 2; (#ij; F22 "......., c1y)) E - represents instantaneous categorical probability vector timestep j. The probability simplex A AlCI is defined
A 1
Σ
Jzj =
1, Jaj 2 0
The Dirichlet distribution offers interpretable parameter a, where each component a; reflects the concentrated prior probability towards class of temporal predictive embeddings, and the scale og -Ee Og indicates the overall uncertainty across T time steps (Ng al. 201 1) (see Figure [ important to note that a (and thus 0g) is obtained by meximum-likellinee estimation via a fixed-point algorithm rather than by manual tuning.
Assume that the temporal predictive embeddings X Dir(a),, with parameter vector (a1 ... o ) E R Each categorical probability vector zj is an i.idd sample from Dir(a). The support of Dir(a) is also confined A 141-1
X follow a Dirichlet distribution, denoted as
We define projection that maps the temporal predictive embeddings X R into its low-dimensional Dirichlet parameters a E R via maximum likelihood estimation (MLE),
T
P P
RI X ÔMLE = arg max
log D(æ a))
(2)
J=1
where the Dirichlet probability density function is given by
CC
T(ao) [(a)) i=1
D(z
II 2
(3)
C
Here, I(-) is the Gamma function.
This projection effectively compresses the temporal dynamics the deep features into single, semantically rich vector that parameterizes the model's predictive distribution for that trial. The Dirichlet parameter estimate, ÓMMLE, could be efficiently computed using a established fixed-point iteration algorithm (Minka 2012), detailed in
0 1/-1 (agi))
1 T
Σ
log Tij
where vi (u) = d (w) denotes the Digamma function. Full algorithmic details for computing the post-projection Dirichlet parameters are provided in Appendix
4

---

Published as a conference paper at ICLR 2026
2) GMM-DRIVEN BAYESIAN INFERENCE FOR GRADIENT-FREE CALIBRATION
For historical test EEG trials 8, we compute their Dirichlet parameters via the projection OMMLE P(gene (8)) and store parameters of high-confidence trials in a memory bank M, organized by their (calibrated) predicted label. This Dirichlet feature projection is performed independently for each trial and depends only on its own temporal predictive embeddings. A Gaussian Mixture Model (GMM) (Reynolds et al., 2009) is then employed to cluster the historical Dirichlet parameters in My for each class to build a canppaaametric density estimate of the historical Dirichlet parameters accumulated from the target domain, yielding a class-specific GMM likelihood:
PCMM v) = Σ Tykk N((c; Hy.ks Dy,k),
where K is the number of mixture components for class y, Ty.k are the weights satisfying Ek Ty.k = 1 and Ty.k >> O, and My,k and Eg,s are the mean and covariance of the 1tth Gaus- sian component, respectively.
The GMM encodes the global distribution of the historical test EEG trials and each component model preserves the neighborhood information of the current test trial to be calibrated. Any proximity of the current test trial to particular cluster results in a relatively large GMM likelihood.
For a current test EEG trial s with parameter ÓEMLE. the calibrated posterior is computed by combining the GMM likelihood PGMM (ÓrMLE y) with the deep model's prior prediction po (y) fo()") via Bayesian inference:
PGMM (&WLL y) po po(y)
(y (MLL))
(6)
=y
y') po po()
Thus, the historical GMM influences only the posterior through the term PGMM( y). while the Diriehlet-rrojectedd feature MLE itself remains purely trial-specific. The final calibrated prediction is then obtained via deal = arg maX Peal(y âMLLE). Subsequently, the Dirichlet parameter âMLE of the current test EEG trial is updated into the memory bank according to its confidence and predicted label. We maintain a fixed-size memory bank and discard the oldest entries when full, while only inserting trials that satisfy both a confidence threshold Tronf and an entropy threshold Tent- In this way, highly uncertain or noisy recent trials are prevented from entering the memory. very old trials are gradually forgotten. Each inserted trial contributes at most 1/M to the GMM fitting, so a small set of recent trials cannot dominate the GMM posterior fusion. After each insertion, we refit the class-specific GMM on the corresponding memory bank using standard Expectation-Maxinn -Mxximization (EM). This is feasible because the Dirichlet features are very low-diment dimennnnsi,nal, so full EM refitting incurs only small overhead, whereas more sophisticated incremental or online clustering would introduce unnecessary complexity without empirical benefits in our setting.
Algorithm T summarizes the pseudo-code of the proposed BTTA-DG framework (see Appendix D)
M f- Mas U {âMLE).
3) THEORETICAL ANALYSIS FOR ENHANCED TEST-TINE ADAPTABILITY
The central innovation of our work is the shift from adapting on point estimates (i.e., pseudo-labels) to adapting on probabilistic distributional representations. Conventional TTA methods are highly sensitive to the noise and uncertainty inherent in single predictions from domain-shifted model. Furthermore, shallow alignment techniques fail to capture how the complex space of temporal predictive embeddings deforms in a new domain. Our key insight is that the domain shift is more reliably expressed in the distribution of the model's sequential predictions rather than in any single prediction.
Instead of directly using the model's s output point estimates, we introduce Dirichlet feature projection to model the entire distribution of the sequential categorical embeddings for each trial. This yields a cow-dimensional Dirichlet parameter vector a. The vector a provides a richer representation of trial's predictive characteristics than simple class prediction. Each component a, reflects the "concentration" " or evidence for class i, while the total scale og relates to the predictive uncertainty or variance throughout the trial. When encountering new domain, inherent signal differences cause
5

---

Published as conference paper at ICLR 2026
shifts in these predictive distributions. Our Dirichlet projection explicitly captures this distributional shift in a compact parametric form. This a more robust and informative feature for adaptation, as encodes not just what the model predicts. but also how confident and consistent that prediction is across time, which is crucial for characterizing a new domain.
This principled representation is what enables high test-time adaptability. By capturing the essence of the domain shift a low-dimensional parameter space, we can perform effective calibration using well-established density estimation (GMM) and inference (Bayesian) techniques. This completely bypasses the need for gradient-based optimization, thus circumventing catastrophic forgetting and computational inefficiency. The theoretical soundness empirically validated through visualization analysis (Figure B demonstrating well- sell-separaeed class clusters with high inter-class KL divergence (231.85) and low intra-class covariance (<0.27), confirming successful mapping of domain-shifted signals into discriminative latent space.
Pilter 3.1-7.9 11z
Intra-class Aug. Cov Clasters
31.85
Left hand Right Error
12
Fitter 6.9-1100 Hz.
20.0:25.0
10
Fiiter 13: 22:622.626. Hz
RighT
Fiiter 17: 29.7-3333
Amplttade
8
Filter 21:
Fiterr 24: 53.8.68.5 Hz
BLay
6
Response
Hight
4:h .
4
n2 1055
Right
2
0
20
40
80
100
Prequency (1tz)
Figure 2: Frequency responses of the 24 learned SincConv filters (color-coded) and their cumu- lative response (black), which shows spectral energy concentration.
Figure 3: Scatter of Dirichlet parameter estimated for test EEG trials, color-coded by class with mis- classified trials outlined in red. GMM ellipses reveal weight and covariance of clusters.
EXPERIMENTAL RESULTS
3.1 IMPLEMENTATION
Datasets The BTTA-DG framework was evaluated on three MOABB (Jayaram & Barachant 2018)
motor imagery datasets BNCI2014001, BNCI2014002 and BNCI2015001, and SHU MI dataset (Ma et al. 2022). Key characteristics are summarized in Table For BNCI201 4001, only two classes (r/l hand imaginations)
used. For all datasets, cross-subject deave-one-subject-on (LOOS) protocol was adopted, using only the first session from each dataset. The source model was pretrained on the training set, and during test-time adaptation, test trials arrived sequentially one-by-one in the online adaptation setting. Preprocessing included only a 1-48 Hz bandpass filter and Euclidean Alignment (He & Wu 2019).
Table 1: Summary of the four MI EEG datasets
Number of subjects
Number of channels
Sampling rate (Hz)
Trial length (s)
Number of sessions
Trials 1st session
Types imaginations
Datasel
RNC12014001
250
288
hand, feet, tongue
BNC12014002
14
160
right hand. both feet
BNC12015001
12
512
400
right hand, both feet
SHU MI Dataset
25
32
512
4
5
100
left hand, right hand
BCT C TV 2h
9
250
4
5
120
left hand, right hand
To comprehensively assess the performance of BTTA-DG, we compared it against traditional classification methods, Transformer-based method, optimal transport-bai based method and
Baselines

---

Published as a conference paper at ICLR 2026
Table 2: Cross-subject adaptation accuracy (%) on BNC12014001, with asterisk(*) denoting the significance level (*: p=0.05).
Setting
Method
S0
S1
S2
53
S4
S8
S6
S7
S8
Avg.
CSP
83.33
52 08
97.92
75.00
56.25
67.36
72. 22
88.19
71.53
73.77
Source
EEGNet
83.19
60.28
92.08
67.92
57.22
72.50
64.86
86.11
79.44
73.73
EEG conformer
81.18
64.16
96.80
74.44
58.47
70.76
64. 17
92.71
79.03
75.7519.15
SincAdaptNet
84.97
63.95
97.68
77.13
56.22
72.68
67.26
93.86
79.56
L.
BN-adape
84,97
63.93
97.68
77.13
56.22
72.68
27.26
93.86
79.56
g..0
Tent
75.97
57.92
94.51
68.54
52.22
65.21
59.38
90.14
68.19
70. 23.228
PL
76.46
56.67
97.92
70.34
52.29
66.32
60.42
93.89
72.15
71.83+a.21
Online TTA
COTTA
85.00
63.68
98.05
76.32
57.22
72.08
67.64
94.63
80.48
77. 77.24
SAR
84.24
63.40
97.36
76.25
54.72
69.10
67.50
93.54
80.28
76. 76.27+1.00
TTIME
84.44
94
69.38
63.13
15.90
OTTA
84.43
63.60
97.14
77.63
57.63
73.04
66.44
95.26
83.14
77.55 77.58
BTTA-DG
87.51
66.67*
98.61
77.08
57.64
73.61
68.75*
95.83*
82.64
78.70%
Table 3: Cross-subject adaptation accuracy (%) on BNC12014002, with asterisk(*)) denoting the
significance level (*: p=0.05).
Setting
Medhod
56
51.0
512
CSP
62.00
52.00
99.20
70.00
54.00
950.00
68.000
53.00
59.00
41.00
72,71
Source
HLGNNe
65.00
80:00
53.00
903.20
74.20
08:20
$5..00
54.00
91.33
15.000
72.00
59.20
51.00
73: 73.17a3.0
HEG conforeer
66.50
80.50
55.00
75.10
90.50
47.44
23.000
79.50
75.80
18.20
47.90
StucAdayoNet
67.90
90.10
99.00
79.30
81.00
72.30
93.30
76.10
94.00
25.90
51.20
50.90
60.40
51.60
75.05.1..0
BN-a
67.90
80.10
39.20
79.30
61.00
72.20
93.30
76.10
94.00
75,90
81.20
50.90
60.40
$1.60
78.05
Teett
$7.20
70:40
90.30
70.70
67.10
08:30
$5.10
06:30
91.00
64.10
77.10
70:40
52:30
49.200
70 70.08.44
PI
57.20
73.40
99.80
75.00
71.50
67.30
92.10
65.80
03.69
64.80
74.70
68:40
55.10
49.20
72.0 23
Online TTA
CHTTA
SAR
66.90
60.20
90.10
70:00
99.00
99.90
77.20
79.40
81.50
80.50
72.70
72.10
91.90
03:80
75.50
74.40
94.00
95.00
24.10
76.90
81. 50
$1.30
79.40
50.50
57.00
59.30
49.10
$2.00
77. 77:0213:00
78: 1211.7
TTIME
07.10
78. 50
40
79.00
K3.70
70:30
91.33 30
74.20
92.38 90
73.90
79. 10.00
57.20
48.60
76, 38.85
83.000
98.50
74.40
94.50
70.00
77.30
63.90
$1.90
BTTA-DG
69.00*
83.00
100.00
$2.00*
73.00
95.00
$4.00
$3.00
63.40
54,40*
30.20 07
state-of-thee thr- TTA methods, including CSP (Blankertz et al. 2007). EEGNet (Lawhern et al. 2018
EEG Conformer (Song et al.) 2022). BN-adapt (Schneider et al., 2020), Tent (Wang et al. 2020). PL (Lee et al. 2013), SAR (Niu et al. 2023), CoTTA (Wang al. 2022 T-TIME (Li et al. 2023). and OTTA (Wimpff et al. 2024). All experiments were run independently 10 times, and the average results are reported. Detailed experimental settings, including dataset descriptions, baseline methods, and hyperparameters, are provided in Appendix
3.2
MAIN RESULTS
Table reports the cross-subject accuracies on BNCI2014001, including the source model and online TTA techniques. Our proposed BTTA-DG achieves state-of-the-art performance with an average accuracy of 78.70%. Notably, BTTA-DG excels most subjects, highlighting its robust generalization capabilities across different subjects. We also observe that several gradient- based TTA basclines drop after applying TTA. Because in EEG's 's online single-trial adaptaion (batch size 1), noisy trials induce misleading gradients that update BN weights and overwrite pre-trained structure-i.e. -ie catastrophic forgetting. BTTA-DG avoids this failure mode by freezing the network and adapting in probabilistic parameter space, yielding gradient-free calibration without destructive updates. Table 3 and Table 4 summarize LOSO cross-subject accuracies on BNCI201400
and B0C12015001. Results on SHU MI dataset and detailed statistical significance analysis are presented in Appendix F Given the practical constraints of portable EEG hardware, we further evaluated BTTA-DG on BCI Competition IV 2b, which contains only three EEG channels. (Appendix G
In addition, we also assessed the performance of BTTA-DO DD in a within- ment. We pretrained the model on the first session and tested on the second session of BNC1201 simulating session shifts in the same subject's 's motor imagery. The results of this cross- cross-session adap- tation are presented in Table demonstrating that BTTA-DG effectively adapts to different sessions too (86.50% + 2.49%). Statistical significance analysis are presented in Appendix H Additionally, a sliding-window window experiment on BNCI201400 4001 further shows that BTTA-DG also improves over the source model in online BCIs requiring low latency and continuous feedback. (Appendix Ip. Furthermore, to relate the cubse-subject TTA gains to each subject's 's intrinsic "decodeability", we report three-fold within-subject k-fold adaptation accuracies BNC12014001 in Appendix
cross-session experi-
7

---

Published as a conference paper at ICLR 2026
Table 4: Cross-subject adaptation accuracy (%) on BNC12015001, with asterisk(*) denoting the significance level (*: p=0.05).
Setting
Method
Avg.
CSP
91. 30
93.50
86.50
85.00
70.00
62.00
65.00
59.00
59.50
65.00
59.
56. 16.50
72.00
Source
BEGNet
91.50
95.00
15.70
85. 15.90
81.30
65.60
65.20
64.30
63.00
66.50
57.50
55.20
72. 22.08=n..2
EEG conformer
94.00
95.20
83,10
86.50
84.80
66.40
68.50
64,10
63.50
65.00
56.
56.40
75 62
SincAdupiiNrr
87.65
59
BN-adage
72.30
64.75
75, 25
Tent PL
80.30
68.65
73.75
68.05
68.30
55.15
56.60
57.15
54.45
55.55
50.25
61.09 11.09:4.55 4.30
97.85
90.50
77.30
80.10
70.30
$6.30
58.00
56.75
54.25
55.70
51 10
49.50
66. 06.555.. 2.115
Online TTA
CWTTA
SAR
97 90
96.85
87.75
95.35
90.80
88.45
73,30
88.00
87.65
63.65
64.60
72.65
72.10
65.20
64.80
65.75
65.25
62.75
63.45
60.70
58 30
58. 50
57.45
73.70-3.32
75,
FTIME
T6. 76.02:22.0
OTTA
98.95
57.20
67.55
59.00
1..0
BTIA-UL DG
98.50
96.00
92.00
90.80
$8.50
05.30
75.50
67.50
65.75
65.50
64.50
65.00'
77.922. 922..22.7.
Table 5: Cross-session adaptation accuracy (%) on BNCI2014001, with an asterisk(*) denoting the significance level (*: pc0.05).
Setting
Method
50
S1
Avg.
CSP
88.19
54,17
97.22
65.97
48.6
70.14
68.06
94.44
90.97
75.31
Source
EEGNet
86.81
63.54
94.65
70.97
72.92
68.61
13.26
93.47
92.71
79.66
Conformer
87.92
58.75
75.83
77.77
95.63
80.13
AincAda
84.69
56.64
98.51
70.32
86.22
72.06
82.47
97.54
92.47
82.33
BN adapt
84.69
$6.64
98.51
70.32
86.22
72,06
82.47
97.54
92.47
82.33
Tent
80.35
62.22
64.51
93.06
73.72.1.77
PL
77.71
51.74
98.75
58.13
75.28
64.58
68.75
97.01
91.46
75.933
Online TTA
CoTTA
54.51
72.36
82.71
98.33
82.39 02.00+220
SAR
86.32
55.00
99.24
71.11
86.11
70.49
82.92
96.53
91.88
82.18
F-TIME
78.40
54.03
98.33
69.79
81.94
70.49
80.69
97.50
91.53
80.30=3.42
OTTA
89.71
55.89
96,79
72.42
91.58
73.67
87.49
96.03
91.58
83.91
BTTA DG
85.42
62.50
100.000
76.39
91.67
77.78*
90.97
100.00
93.75
86.50"
Table 6: Quantitative alignment of learned Sine filter passhands with known MI-EEG rhythms BNC12014001. Values denote, for each subject, the percentage (%) of filters whose passbands overlap each band.
Frequency band
SO
S1
S2
S3
S4
S5
S6
S7
S8
Avg.
/4 (8-13 Hz)
24.17
25.83
25.83
23.33
24.17
27.50
24.17
24.17
25.00
24.91
99 (13-30 Hz)
32.50
35.00
28.33
28.33
43.33
25.83
30.00
28.33
29.17
31.20
7 (30-45 Hz)
35.83
30.83
34.17
40.00
26.67
40.00
40.00
40.00
36.67
36.02
Other
7.50
8.33
11.67
8.33
5.83
6.67
5.83
7.50
9.17
7.87
To verify that SincAdaptNet's Sinc-Conv layer learns meaningful bandpass filters, Figure illustrates the frequency responses of each learned filter BNC12014001 and their cumulative response in cross-subject LOSO setting (training set: $1-S8; test set: SO). Learned filters partition into three physiologically meaningful ranges mu rhythm (8-13 Hz, Filters 1-7), beta rhythm (13-30 Hz, Filters 8-17), and gamma rhythm (30-68.5 Hz, Filters 18-24). Cumulative response (black curve) peaks in the mu (11.2 Hz), beta (30.5 Hz), and gamma (55.3 Hz) bands, demonstrating significant energy concentration of MI EEG. Similar spectral patterns emerge across different test subjects (see a quantitative alignment analysis for calculation details). On average, about 25% of filters align
Appendix K). Beyond these qualitative plots, on BNC12014001 (see Appendix D with the f band, with the 3 band, and 36% with the low-y band, leaving fewer than 8% outside these MI rhythms. This concentration on well-established sensorimotor frequencies further supports the physiological interpretability of the SincAdaptNet front-end.
Figure 14 (in Appendix M presents the 16 spatial kernels learned by Sinc AdatANds Spat-Conv
layer as scalp topographies, each displaying a distinct electrode weighting akin to those produced by the CSP (Blankertz et al.) (007). The range of frontal, central, parietal, and occipital patterns (Decety) 1996; Lesser et al. 1998) highlights the model's capacity to learn multiple spatial representations of EEG activity.
8

---

Published as a conference paper at ICLR 2026
(a)
(b)
(c)
0.790
0.790
0.790
Adapted Accuracy
Adapted Adapted Accuracy
0.785
0.785
Adapted
0.785
0.780
0.780
0.780
5
10
0.55
0.60
0.65
0.66
0.68
Components
Entropy Threshold
Figure 4: Sensitivity of BTTA-DG to key hyperparameters.
Figure visualizes the low-dimensional Dirichlet parameter estimated from test EEG trials and GMM clustering outcomes on BNC1201400 in cross-subject LOSO setting (training set: S1-S8; test set: S0). The low-dimensional Dirichlet parameter of EEG representation exhibits good class separability, with misclassified samples predominantly located near class boundaries. Moreover, a high inter-class KL divergence (31.85) and low intra-cluster covariance (0.27) indicate that GMM effectively captures both global and local information of Dirichlet parameter distribution, providing a robust statistical foundation for Bayesian inference. The geometry of Dirichlet parameters and cluster remains stable for other test subjects (see Appendix
Computational efficiency To assess the computational efficiency of BTTA-DG, we measured the average inference time and the number of floating-por ppint operations (FLOPs) per trial for each method on the BNCI201400) dataset. As presented in Table 7 BTTA-DG achieves real-time performance with average inference time of 15.77 per trial 17.8% faster than T-TIME (Li et al. 2023) and 24.2% faster than OTTA (Wimpff et al., 2024), which are the recent baselines for EEG-TTE TTA. BN- adapt is the fastest method because merely recomputes batch-normalization statisties without any tradient-based optimization or probabilistic inference. Detailed computational complexity analysis and memory usage are Appendix
To dissect the contributions of our proposed components, we conducted an ablation study, with the results summarized in Table We start with the SincAdaptNet (Source Only) model as our baseline. We then incorporate Euclidean Alignment (+ EA) establish the performance of standard domain alignment technique. We further evaluate BTTA-DG w/o EA, which removes EA but retains the Dirichlet feature projection and RLMM-driver inference. We also include Sin- cAdaptNet + EA GMM, which performs GMM-driven inference directly the time-averaged plosabiooyy vector. The crucial next step isolates the effectiveness our Dirichlet projection by applying the Dirichlet Projection without the GMM-driven inference (+ Dirichlet Projection), instead using a simple classifier on the projected parameters. Finally, our BTTA-DG (Full Model) integrates all components. Across all datasets and settings, EA provides initial improvement AdaptNe,, and BTTA-DG w/o EA also yields gains over the source-only model, indicating that the Dirichlet+GMM module has standalone adaptation capability. Introducing GMM calibration on the mean class probbabryyy (+ EA GMM) leads to marginal improvements over + EA. Consistently, SincAdaptNet + EA + Dirichlet outperforms both + EA and + EA GMM, while the full BTTA- -DG. which combines EA, Dirichlet projection and GMM-baser Bayesian inference, achieves the best performance in every setting, with absolute gains of roughly 2 2-6% over the source-only baseline.
Ablation study
Sensitivity analysis To assess the robustness of BTTA-DG, sensitivity analyzes were conducted on three key hyperparameters: the number of GMM components K, the minimum confidence threshold Toonf and the maximum entropy threshold Tent Teanf and Tem govern the conditions under which Dirichlet parameters of test trials are stored in the memory bank: Dirichlet parameters are retained if the confidence of trials exceeds Tconf and their entropy is below Tents ensuring that only high-certainty, low-uncertainty test data contribute to the adaptation process. As shown in Figure 4 BTTA-DG exhibits robustness across parameter variations. Accuracy remains stable (78.2%-78. 7%) for K [2, 12). Higher thresholds (0.53-0.65) improve accuracy from 78.0% 78.7%, filtering low-confidence trials to reduce noise in adaptation. Low entropy (0.65-0.7 0.70) sustains accuracy at 78.0%-78.8 7,, ensuring only high-certainty trials enter the memory bank.

---

Published as a conference paper at ICLR 2026
Sensitivity to Online Class Imbalance To evaluate the robustness of BTTA-DG in practical scenarios where data flow may not be uniformly distributed, we conducted an experiment on the BNCI2014001 dataset under artificially induced online class imbalance. We systematically varied the class ratio in the test set from a balanced 1:1 distribution to severely imbalanced 1:0.25. Table 9 reports the class-wise and overall accuracies under these ratios. While the overall accuracy gracefully degrades with increasing imbalance, we observe that the accuracy for the minority class (Class I) conversely improves as its prevalence decreases. These results indicate that STTA-DG does not collapse under imbalance but instead specializes to rare events, which is desirable for many real-wor world BCI scenarios. more detailed interpretation is provided in Appendix
Table 7: Average inference time and FLOPs per trial on BNCI2014001.
Method
BN-adapt
Tent
PL
CoTTA
SAR
T-TIME
OTTA
BTTA-DG
Time (ms)
5.1
18.4
17.8
23.0
32.5
18.5
19.5
15.7
FLOPs (M trial)
133.3
266.7
266.7
333.4
466.9
266.7
330.5
141.6
Table Ablation Study across settings and MI datasets. Mean s.d. accuracy (%).
BNC12014001
BNCI2014002
BNC12015001
SHU MI
Method
cross-session
cross-subject
cross-subject
cross-subject
cross-subject
SincAdaptNer (Source Only)
80.62 + 2.70
75.30 + 1.82
76.40 + L.62
73.92 + 1.95
61.02 1.70
BTTA-DG w/o EA
81.88 2.58
76.85 + 1.65
77.55 1.59
75.06 1.88
61.90 1.68
SincAdaptNet EA
82.33 + 2.62
77.03 + 1.31
78.05 + 2.48
75.48 + 1.84
62.42 1.72
SincAdaptNet EA + GMM
82.47 + 2.59
77.55 + 1.35
78.25 2.36
75.62
1.82
62.58 = 1.70
SincAdap(Net EA Dirichlet
84.04 + 2.55
77.61 + 1.43
78.88 + 1.47
76.36 4: 1.78
63.24 1.78
BTTA-DG (Full Model)
86.50 2.49
78.70 + 1.32
80.29
1.07
77.92 1.76
64.06 1 1.92
Table 9: Performance of BTTA-DG under varying online class imbalance ratios the BNCI2014001 dataset. As imbalance increases, the model specializes, improving minority class accuracy.
Class Ratio (0: 1)
Accuracy Class (%)
Accuracy Class (%)
Overall Accuracy (%)
1:1
77.01 1.53
80.40 1.45
78.70 + 1.32
1 0.75
74.07 1.44
80.45 1.34
76.81 +\2 1.25
0.5
69.75 + 1.52
83.02 + 1.42
74.17 = 1.28
0.25
64.67 1.18
85.19 1.64
68.77 + 1.19
4 CONCLUSION
In this paper, we presented BTTA-DG, a novel gradient-free and efficient TTA framework for MI-EEG decoding. By projecting temporal predictive embeddings into compact Dirichlet parameter space, our method captures predictive uncertainty and models the target domain's feature distribution. A GMM is employed summarize historical Dirichlet parameters, preserving global and neighborhood information of test trials. Subsequent Bayesian inference integrates learned historical evidence with the network's priors, effectively bridging domain gaps without the risk of catastrophic forgetting. Our extensive experiments validate that BTTA-DG achieves state-of-the-art adaptation performance, significantly outperforming existing EEG-TTA methods while operating real-time speeds. Although density estimation on the memory buffer benefits from reasonably balanced EEG data, our online class-imbalance study indicates that BTTA-DG remains robust even under imbalanced class ratios. The explicit handling more extreme or non-stationary imbalance is an interesting direction for future work. Beyond MI-EEG, the same principle of Dirichlet feature projection plus GMM-based Bayesian calibration could in principle be transferred to other neural modalities (e.g., INIRS, ECoG) and to broader BCI settings. future work, we also commit to integrate BTTA-DG with large pretrained EEG models to explore whether the gains are additive. By enabling nigh-performance adaptation without requiring new labeled data, our framework reduces user burden and represents a significant step towards the development of practical, real-world BCI systems.
10

---

Published as a conference paper at ICLR 2026
ETHICS STATEMENT
The authors adhere to the ICLR Code of Ethics. The datasets utilized in this research are publicly available for all researchers subjects for this study. The original data collection was conducted by its respective creators under appropriate ethical protocols, including institutional review board (IRB) approval and informed consent from all participants. Our work is confined to the analysis of this existing, anonymized data and does not introduce new ethical concerns regarding human subjects.
Brain-Compius Interface. No new data was collected from human
REPRODUCIBILITY STATEMENT
We are committed to ensuring the reproducibility of our research. All experiments were conducted on the publicly accessible datasets. Comprehensive implementation details, including data preprocessing steps, model architecture, optimizer settings, and the full set of hyperparameters along with the strategy for their selection, are thoroughly documented in Section 3.1 and Appendix E
REFERENCES
Hamdi Altaheri, Ghulam Muhammad, and Mansour Alsulaiman. Physics-informedd attention temporal eeg-based
convolutional network for eeg- based motor imagery classification. IEEE transactions industrial informatics, 19(2):2249- 2258, 2022.
Hamdi Altaheri, Ghulam Muhammad, Mansour Alsulaiman, Syed Umar Amin, Ghadir Ali Altuwaijri, Wadood Abdul, Mohamed Bencherif, and Mohammed Faisal. Deep learning techniques for classification of electroencephalogram (eeg) motor imagery (mi) signals: A review. Neural Computing and Applicationn, 14(20):14681-1777)) 2023.
Andrea Apicella, Pasquale Arpaia, Giovanni D' Errico, Davide Marocco, Giovanna Mastrati, Nicola Moccaldi, and Roberto Prevete. Toward cross-subject and cross-session generalization in eeg-based emotion recognition: Systematic review, taxonomy, and methods. Neurocomputing, pp- 128354, 2024.
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv: 2016.
Stylianos Bakas, Siegfried Ludwig, Dimitrios A Adamos, Nikolaos Laskaris, Yannis Panagakis, and Stefanos Zafeiriou. Latent alignment in deep learning models for eeg decoding. Journal of Neural Engineering. 2025.
Benjamin Blankertz, Ryota Tomioka, Steven Lemm, Motoaki Kawanabe, and Roburt Muller. Optimizing spatial filters for robust eeg single-trial analysis. IEEE Signal processing magazine, 25 (1):41-56, 2007.
Dhanajit Brahma and Piyush Rai. A probabilistic framework for lifelong test-time adaptation. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 3582-3591, 2023.
Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning of visual features by contrasting cluster assignments. Advances in neural information processing systems, 33:9912-9922 2020.
Chi-Sheng Chen, Ying-Jung Chen, and Aidan Hung-Wer Wen Tsai. Large cognition model: Towards pretrained eeg foundation model. arXiv preprint arXiv:2502. 17464, 2025.
Maureen Clere. Brain computer interfaces, principles and practise: Oxford university press usa, jonathan wolpaw and clizabethwinterwolpaw:; 2012: 424 pages. isbn: 978-019538885-5 (hard- cover), 2013.
Felix Darvas, Reinhold Scherer, Jeffrey G Ojemann, RP Rao. Kai J Miller, and Larry B Sorensen. High gamma mapping using eeg. Neuroimage, 49(1):930-993 2010.
11

---

Published as a conference paper at ICLR 2026
Jean Decety. The neurophysiological basis of motor imagery. Behavioural brain research, 77(1-2): 45-52, 1996.
Pauline Dreyer, Aline Roc, Léa Pillette, Sébastien Rimbert, and Fabien Lotte. A large eeg database with users' profile information for motor imagery brain-computer interface research. Scientific Data, 10(1):580, 2023.
Álvaro Fernández- Femmández-Rodriuuzz, Francisco Alvarco-Alvarzz, and Ricardo RoneAngevin, Review real brain-controlled wheelchairs. Journal of neural engineering. 13(6):06101,, 2016.
Amparo Gil, Javier Segura, and Nico M Temme. Numerical methods for functions. SIAM, 2007.
He He and Dongrui Wu. Transfer learning for brain-computer interfaces: euclidean space data alignment approach. IEEE Transactions Biomedical Engineering, 67(2):399 410, 2019.
Gan Huang, Zhiheng Zhao, Shaorong Zhang, Zhenxing Hu, Jiaming Fan, Meisong Fu, Jiale Chen, Yaqiong Xiao, Jun Wang, and Guo Dan. Discrepancy between inter-and intra-subject variability in eeg-based motor imagery brain-computer interface: Evidence from multiple perspectives. Frontiers in neuroscience, 17:1 122661, 2023.
Yusuke Iwasawa and Yutaka Matsuo. Test-time classifier adjustment module for model-agnostic domain generalization. Advances in Neural Information Processing Systems, 34:2427-2440, 2021.
Vinay Jayaram and Alexandre Barachant. Moabb: trustworthy algorithm benchmarking for beis. Journal of neural engineering, 15(6)1066011, 2018.
Wei-Bang Jiang, Li-Ming Zhao, and Bao-Liang Lu. Large brain model for learning generic represen- tations with tremendous eeg data in bci. arXiv preprint 2rXiv:2405.18765 2024.
Jonathan W Kim, Ahmed Alaa, and Danilo Bernardo. Eeg-gpt: exploring capabilities of large language models for eeg classification and interpretation. arXiv preprint arXiv:2401. 2024.
Demetres Kostas, Stephane Proca-Ouellete and Frank Rudzicz. Bendr: Using transformers and a contrastive self-supervised learning task to learn from massive amounts of eeg data. Frontiers in Human Neuroscience, 15:653659, 2021.
Vernon J Lawhern, Amelia Solon, Nicholas Waytowich, Stephen M Gordon, Chou Hung, and Brent Lance. Eegnet: a compact convolutional neural network for eeg-basee train-computer interfaces. Journal of neural engineering, 15(5):056013, 2018.
Dong-Hyun Lee et al. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on challenges in representation learning, ICML, volume 3, pp. 896. Atlanta, 2013.
Ronald P Lesser, Santiago Arroyo, Nathan Crone, and Barry Gordon. Motor and sensory mapping of the frontal and occipital lobes. Epilepsia, 39:569-$80, 1998.
Ang Li, Zikai Wang, Liuyin Yang, Zhenyu Wang, Tianheng Xu, Honglin Hu, and Marc M Van Hulle. Comet: A contrastive-maskee masked brain foundation model for universal ceg representation. arXiv preprint arXiv:2509.00: 00 2025.
Siyang Li, Ziwei Wang. Hanbin Luo, Lieyun Ding, and Dongrui Wu. T-time: Test-time information maximization ensemble for alu--nn--paa beis. IEEE Transactions on Biomedical Engineering, 71 (2):423-432, 2023.
Jian Liang, Ran He, and Tieniu Tan. A comprehensive survey test-time adaptation under distribu- tion shifts. International Journal of Computer Vision, 133(1):31 64, 2025.
Yifci Liu, Hengwei Ye, and Shuhang Li. Llms help alleviate the cross-subject variability in brain signal and language alignment. arXiv preprint arXiv:2501.02621 2025.
Eduardo López-Larraz, A Sarasola-Sanz, N Irastorza-Landa Landa, N Birbaumer, and A Ramos- Murguialday. Brain-machine interfaces for rehabilitation in stroke: a review. NeuroRehabilttation 43(1)::7~97, 2018.
12

---

Published as a conference paper at ICLR 2026
Jun Ma, Banghua Yang, Wenzheng Qiu, Yunzhe Li, Shouwei Gao, and Xinxing Xia. A large eeg dataset for studying cross seoss-n variability in motor imagery brain-computer interface. Scientific Data, 9(1):331, 2022.
Dennis J McFarland, Laurie A Miner, Theresa M Vaughan, and Jonathan R Wolpaw. Mu and beta rhythm topographies during motor imagery and actual movements. Brain topography, 12:177-186. 2000.
Thomas Minka. Estimating dirichlet distribution, 2012. DRL.ittpss//bminnaaa.iiitt io/ papers/dirich wtwprrihhhemtmiaaaaaaaeaaaaaa ch pdf
Christa Neuper, Michael Wörtz, and Gert Pfurtscheller. Erd/ers patterns reflecting sensorimotor activation and deactivation. Progress in brain research, 159:211-222, 2006.
Kai Wang Ng. Guo-Liang Tian, and Man-Lai Tang. Dirichlet and related distributions: Theory, methods and applications. 2011.
Shuaicheng NIu, Jiaxiang Wu, Yifan Zhang, Zhiquan Wen, Yaofo Chen, Peilin Zhao, and Mingkui Tan. Towards stable test-time adaptation in dynamic wild world. arXiv preprint arXiv:2302. 12400, 2023.
Tomoyuki Noda, Norikazu Sugimoto, Junichiro Furukawa, Masa-aki Sato, Sang-Ho Hyon, and Jun Morimoto. Brain-controlled exoskeleton robot for bmi rehabilitation. In 2012 12th ieee-ras international conference on humanoid robots (humanoids 2012), pp. 21-27. IEEE, 2012.
Standard Electrode Position Nomenelature. American electroenceehaalorrapicc society guidelines for. Journal of clinical Neurophysiology, 8(2):200-202, 1991.
Yiheng Peng, Li Chen, Shijie Guo, Yuzhu Guo, Yang Li, et al. A fully test-time adaptation method for motor imagery. Li and Guo, Shijie and Guo, Yuzhu and Li, Yang, A Fully Test-Time Adaptation Method for Motor Imagery, 2025.
Gert Pfurtscheller, Clemens Brunner, Alois Schlögl, and FH Lopes Da Silva. Mu rhythm (de) synchronization and eeg single-trial classification of different motor imagery tasks. Neurolmage, 31(1):153-159, 2006.
Yiyang Qin, Banghua Yang. Sixiong Ke, Peng Liu, Fenqi Rong, and Xinxing Xia. M-fanet: Multi- feature attention convolutional neural network for motor imagery decoding. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 32:401-411, 2024
Mirco Ravanelli and Yoshua Bengio. Interpretable convolutional filters with sincnet. arXiv preprint arXiv:1811.0972 2018
Douglas A Reynolds et al. Gaussian mixture models. Encyclopedia of biometrics, 761(669-663))3, 2009.
Cédric Rommel, Joseph Paillard, Thomas Moreau, and Alexandre Gramfort. Data augmentation for learning predictive models on eeg: a systematic comparison. Journal of Neural Engineering, 19 (6):066020, 2022.
Christina Sartzetaki, Panagiotis Antoniadis, Nick Antonopoulos, Ioannis Gkinis, Agamemnon Kra- soulis, Serafeim Perdikis, and Vassilis Pitsikalis. Beyond within-subject performance: A multi- dataset study of fine-tuning in the eeg domain. 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 4429 4435, 2023.
Steffen Schneider, Evgenia Rusak, Luisa Eck, Oliver Bringmann, Wieland Brendel, and Matthias Bethge. Improving robustness against common corruptions by covariate shift adaptation. Advances in neural information processing systems, 33: 1539-11551. 2020.
Yonghao Song, Qingqing Zheng, Bingchuan Liu, and Xiaorong Gao. Eeg conformer: Convolutional transformer for eeg decoding and visualization. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 31:710-719, 2022.
13

---

Published as a conference paper at ICLR 2026
Michael Tangermann, Klaus-Robert Müller, Ad Aertsen, Niels Birbaumer, Christoph Braun, Clemens Brunner, Robert Leeb, Carsten Mehring, Kai Miller, Gernot R Miller-Putzz et al. Review the bei competition iv. Frontiers in neuroscience, 6:55, 2012.
Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell. Tent: Fully test-time adaptation by entropy minimization. arXiv preprint arXiv:2006. 10726, 2020.
Guangyu Wang, Wenchao Liu, Yuhong He, Cong Xu, Lin Ma, and Haifeng Li. Eegpt: Pretrained transformer for universal and reliable representation of eeg signals. Advances in Neural Information Processing Systems, $7:39249-392888 2024.
Jiquan Wang, Sha Zhao, Zhiling Luo, Yangxuan Zhou, Haiteng Jiang, Shijian Li, Tao Li, and Gang Pan. CBramod: A criss-cross brain foundation model for EEG decoding. In The Thirteenth International Conference Learning Representations, 2025. URL /tttpps://oeereeeie.e
Bet//forumidddNPNUEE
Qin Wang, Olga Fink, Luc Van Gool, and Dengxin Dai. Continual test-time domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp- 7201-7211, 2022.
Martin Wimpff, Mario Döbler, and Bin Yang. Calibration-free online test-time adaptation for electroencephalography motor imagery decoding. In 2024 12th International Winter Conference Brain- Coii--Comuuter Interface (BCI), pp. 1-6. IEEE, 2024.
Martin Wimpff, Bruno Aristimunha, Sylvain Chevallier, and Bin Yang. Fine-tuning strategies for continual online eeg motor imagery decoding: Insights from a large-scale longitudinal study. arXiv preprint arXiv:2502.06828. 2025.
Tzu-Tsung Wong. Generalized dirichlet distribution in bayesian analysis. Applied Mathematics and Computation, 9711 1998.
Zehao Xiao and Cees GM Snoek. Beyond model adaptation at test time: A survey. arXiv preprint arXiv:2411 1.t-22411.0087... 2024.
Lichao Xu, Minpeng Xu, Yufeng Ke, Xingwei An, Shuang Liu, and Dong Ming. Cross-dataset variability problem in eeg decoding with deep learning. Frontiers in human neuroscience, 14:103, 2020.
Chaoqi Yang, M Westover, and Jimeng Sun. Biot: Biosignal transformer for cross-data learning in the wild. Advances Neural Information Processing Systems, 36:78240-78260, 2023.
Liuyin Yang, Qiang Sun, Ang Li, and Marc M. Van Hulle. Are EEG foundation models worth it? comparative evaluation with traditional decoders in diverse BCI tasks. In The Fourteenth International Conference on Learning Representations, 2026. URL htttps://opprreviee
net/Forum2ld=-Xomtee
Yao Yuxuan, Wang Hongbo, Chen Li, Peng Yiheng, and Jingjing Luo. Foundation models for eeg decoding: current progress and prospective research. Journal of Neural Engineering, 2025.
Paolo Zanini, Marco Congedo, Christian Jutten, Salem Said, and Yannick Berthoumieu. Transfer learning: A riemannian geometry framework with applications to brain-computer interfaces. IEEE Transactions Biomedical Engineering, (5(5):1107-1111 2017.
Xiaoli Zhang, Yongxionga Wang, Yiheng Tang, and Zhe Wang. Adaptive filter of frequency bands based coordinate attention network for eeg-based motor imagery classification. Health Information Science and Systems, 12(1):11, 2024.
Bowen Zhao, Chen Chen, and Shu- Tho Xia. Delta: degradation-free fully test-time adaptation. arXiv preprint arXiv:2301.1300 13018, 2023.
14

---

Published as a conference paper at ICLR 2026
A RELATED WORK
Recent years have witnessed remarkable progress in large-scale EEG pretrained models trained on massive datasets. Representative models include BENDR (Kostas et al. 2021). BIOT (Yang al. 2023), LaBraM (Jiang et al., 2024), EEGPT (Wang al., 2024). CBraMod (Wang al.
2025 and CoMET (Li al. 2025). These foundation models demonstrate impressive capabilities learning general representations across diverse EEG paradigms. However, their effectiveness in
MI decoding remains limited despite their scale. As shown in Table TO lightweight architectures achieve competitive or superior performance compared to large-scale models while being orders of magnitude more parameter-efficien For instance, SincAdaptNe matches or surpasses all considered large-scale models, and it trails EEGPT by less than 1% on BCIC-IV-2a while outperforming on BCIC-2b, despite using roughly four orders of magnitude fewer parameters.
Table 10:
Comparison large-scale pretrained EEG models and lightweight models on BCIC-IV-2a- 4class and BCIC-2b (LOOS)).
Scale
Methods
Number Params (M)
BCIC-IV-2a-class BCIC-2b
Large-scale foundation models
BENDR
4.0
0.4899
0.7067
BIOT
3.2
0,4590
0.6409
LaBraM
5.8
0.5613
0.6851
EEGPT
25.0
0.5846
0.7212
CBraMod
4.0
0,5585
0.6735
Lightweight models
EEGNet
0.003
0.5685
0.7429
EEGConformer
0.55
0.5341
0.7361
SincAdaptNet
0.0015
0.5764
0.7632
This performance gap stems from fundamental challenges. First, MI-induced EEG signals are inherently weak and highly variable compared to other paradigms like visual evoked potentials. Unlike P300 or SSVEP which show consistent patterns across subjects, MI relies on subjective imagination to trigger sensorimotor rhythm ERD/ERS. This results in subtle power changes in specific bands (e.g. μ:: 8-13 Hz, 3: 18 30 Hz) that are often masked by noise. Moreover, these subtle power changes vary significantly across subjects. Some subjects demonstrate clear p-rhythh ERD/ERS while others show only minimal changes, which the "BCI illiteracy" phenomenon Dreyer et al. (2023). This extreme weakness and variability make unified feature extraction challenging. Large- models may not capture these subtle subject-specific nuances without task-aligned pretraining.
Second, current pre-training strategies for EEG foundation models may face limitations. Most foundation models are trained with objectives like masked reconstruction or contrastive learning that are inherited from NLP and vision tasks, to learn general representations from unlabeled EEG data Yuxuan et al. 2025). However, these objectives may not align with task-specific requirements. For instance, masked reconstruction encourages the model to recover missing signal segments based on contextual patterns. These patterns may emphasize global temporal structure that relates to noise rather than task-relevant features. In addition, many models mix diverse data without task/subject differentiation Chen et al. (2025), leading to "averaged" representations of unclear utility. This explains why simple linear classifiers perform poorly on these pretrained representations in certain case, where the features lack linearly separable task-relevant information Yang et al. (2026). Consequently, they require substantial non-linear adaptation during fine-tuning, which can negate the benefits of pretraining and risk overfitting limited downstream datasets.
These limitations highlight the need for specialized adaptation approaches that can handle MI's inherent variability. Online test-time adaptation (TTA) methods adapt source models and make simultancous predictions during inference, utilizing unlabeled online target data (Liang et al. 2025 Xiao & Snoek 2024). Over the past year, TTA methods have been extended from computer vision to MI EEG signal decoding.
Traditional TTA techniques (batch normalization calibration (Zhao et al. 2023) entropy minimiza- tion (Wang et al. 2020; [Nu et al. 2023), pscudo-labeling (Lee et al. 2013 wasawa & Matsuo (202T) and consistency regularization(Brannl BBrahaa & Rai 2023)) can be broadly categorized into parameter
15

---

Published as a conference paper at ICLR 2026
finetuning and non-finetuning methods. Non-finetuning methods adjust domain-specifer statistics without gradient backpropagation, offering high computational efficiency but limited adaptability. For example, BN-Adapt (Schneider al. (2020) recalculated BN layer statistics in target domain to mitigate distribution shifts. Parameter finetuning methods, on the other hand, include partial and full finetuning. Partial finetuning methods update only subset of the network's parameters to balance adaptability and efficiency. For instance, Tent (Wang et al. (220)) minimized entropy by updating only the BN affine parameters. SAR (Niu et al. 2023) further introduced sharpness-aware entropy minimization technique to suppress noisy test samples with large gradients, stabilizing TTA. Full finetuning methods update the entire network using losses calculated by pseudo-labels. For example, Pseudo-Label (Lee et al., 2013) employed the model's 's high-confidence predictions as pseudo-labels for self-training, whereas CoTTA (Wang et al.] 2022) utilized data augmentation to generate pseudo-labels and incorporates weight stochastic restoration to alleviate error accumulation and forgetting.
In MI decoding domain, to address the complexity of EEG signals, state-of-the-art MI-TTA frame- works integrate data alignment techniques with multiple parameter finetuning techniques. Specifically, OTTA (Wimpff al. 2024) integrated Euclidean Aligmment (EA) (Zanini et al., 2017) Rieman- nian Alignment (RA) (He & Wu 2019) techniques with entropy minimization of BN finetuning to reduce cross-subject domain shifts. MI-FTTA (Peng al. 2025) combines teacher-student mutual learning and constrandt sample selection to filter noisy pseudo labels, and employed BN statistics recalculation and prototype-basee contrastive learning to enhance adaptation performance. T-TIME (Li et al., 2023) used ensemble learning for label prediction and finetuned classifiers by conditional entropy minimization and adaptive marginal distribution regularization, achieving higher performance. Latent alignment method (Bakas et al. (025) introduced deep sets to EEG decoding and aligned distributions in the deep learning model's s feature space. For large-scal online MI decoding, continual finetuning strategies (Wimpff et al.) 2025) combined with TTA methods have been also explored to improve BCI performance in real-world applications. In addition to these unsupervised TTA approaches, Sartzetaki et al. (Sartzetaki et al., 2023) present comprehensive multi-dataset study une-tuning. showing that even a small amount of labeled target data can boost MI decoding performance and highlighting the potential of supervised adaptation when such labels available.
Despite the advancemenss, critical challenges persist. 1) Computational efficiency: Full finetuning methods incur high cost due to gradient updates, limiting real-time applicability. 2) Catastrophic forgetting: Continuous parameter updates risk overwriting pre-traines knowledge for MI decoding. 3) Shallow statistics-based adaptation: Methods lack theoretical modeling of deep feature shifts across domains. Therefore, developing lightweight, robust, and theoretically grounded MI-TTA methods remains a challenge.
16

---

Published as a conference paper at ICLR 2026
B SINCADAPTNET DETAILS
Hamming
Reshapot-11 1.1)
LN
Reshspejorginaj)
120
200
samplel(i)
samplel(n)
commlee(n)
moan
Transpose
Moduule
LN Modullo
ZFf
Squeeze
Tranepose
Softmax
T
Spat-Conv
Sinc-Conv
IncCh-Conv
Cls-Conv
Figure 5: Architecture of SincAdaptNet. A compact four-layer encoder for MI EEG: Spat-Conv (spatial filtering) > Sinc-Conv (learnable, sinc-parameterized bass-pass) - IncCh-Conv (channel expansion) + Cls-Conv (per-time class embeddings). Layer normalization is applied after temporal filtering and channel expansion to avoid reliance on batch statistics in online inference.
AdaptNe has only four convolutional layers. From statistical perspective, MI decoding is largely governed by low-dimensional structure in the tmme-frequnncy domain (e.g.. μ/ rhythms over small set of motor channels), very deep architecture is more likely to increase variance than to capture additional task-relevant structure under limited MI-EEG data. SincAdaptNet imposes strong inductive bias by parameterizing each temporal filter with only spectral parameters (low cut-off and bandwidth), favoring band-limited solutions aligned with known MI neurophysiology and yielding favorable bias-variance trade-off. Empirically, this lightweight encoder does not weaken representation capacity. Across all datasets in our experiments, Sinc AdaptNet matches or outperforms deeper backbones such as EEG Conformer while remaining computationally efficient for online TTA.
Moreover, the explicit frequency-banc extraction of the Sinc-Conv layer directly benefits our Bayesian TTA framework. The learnable Sine filters isolate physiologically critical and B bands and suppress irrelevant spectral noise raw EEG, producing more stable and less ambiguous sequence of predictive embeddings over each trial. This cleaner input leads more robust fixed- exed-point Dirichlet estimation, improving the quality of the probabilistic representation that our GMM-based TTA module adapts on, and thereby enhancing robustness to non-stationarity in realistic online BCI scenarios while keeping the overall system efficient and interpretable.
The Sinc-Come layer is not standard convolution but is parametrically defined by the sinc function with learnable cutoff frequencies, making it highly interpretable. Full hyperparameter settings for the network are detailed in Appendix E We have ereated an architecture diagram to visually clarify the network structure (Figure 5). Besides, we added the following SincAdaptNet architecture equations. Let CCxT be an input EEG trial with C channels and T time points. The four-layer AincAda processes the input as follows:
Spat-Cony Spatial filtering with Fxpa filters of size (C' x 1): 8xpat F xxx are the spatial convolution kernels.
W spat * 8, where W W
Sinc-Comt Adaptive bandpass filtering with Fsinc sinc-based filters: 8sinc = Isinc S The sinc
kernel hime is parametrically generated from learnable cutoff frequencies flo and bandwidth foand, with fnigh = flow + foand- The frequency response of the ideal bandpass filter is:
H() = rect
rect
(8)
2
2.
The time-domain impulse response is derived via the inverse Fourier transform,
h(n)) 2 2nigh sine(2 (1igh))))
2ho (2nT(2/ < co.
17

---

Published as a conference paper at ICLR 2026
Since this ideal response is infinitely long, it is truncated and Hamming window w(n) is applied to mitigate spectral leakage, resulting in the convolution kernel,
Wwindowed (n) hn)) w()). Nsinc
Nsine
(10)
2
2
where Nine denotes the truncated length and f, is the sampling frequency. The Sinc-Com layer comprises Fsinc adaptive bandpass filters of size x Nsme)) and uses "SAME" padding preserve temporal dimension.
IncCh-Conv Channel expansion with 2 filters of size (Fepu x 1): 8inc W inc Ssinc where Wine E IR P
x1, yiclding output X E Rl4xxr, Each column is passed through softmax to form time-varying categorical vector, and the temporal average provides robust prior for Bayesian calibration in our TTA framework.
Cls-Conv Final layer with [c] filters: X
Wels Sinc where Wels E II
C DIRICHLET PARAMETER ESTIMATION DETAILS
This section details the efficient algorithm used to compute the Maximum Likelihood Estimate (MLE) of the Dirichlet parameters a from sequence of categorical probability vectors X ( ØT] with Φ; A Cl-1, The method is based the well-established fixed-point iteration algorithm by Minka ka 2012) which we implement for our online TTA framework.
Fixed-point iteration for MLE Let X = [x1 T2.... Tyl be set of T samples, where each , c15)
is categorical probability vector sampled from a Dirichlet distribution with parameters (an, (on,.... ........
2; (Tij, #2j....j..... .
()))). ). The goal is estimate P(X) ÔMLE, the MLE of The log-lik log-likelihood function for the Dirichlet distribution is employed.
T
L(a)= Σ log D))
(11)
The maximum likelihood estimator ÔMMLF can be obtained by iteratively computing
T
Og
now 1/=
(((00)) old
+
log Fij
(12)
T
where vi (u) du (u) denotes the Digamma function.
Thus, if the inverse Digamma function 1 can be obtained, the iterative rule (12 is used to estimate the Dirichlet parameters for temporal predictive embeddings each test EEG trial.
To accelerate convergence, we initialize the Dirichlet parameters a init using the empirical mean T; and variance of of the categorical probability vectors from temporal predictive embeddings. From the properties of the Dirichlet distribution, the mean and variance satisfy:
ΣT
2
j==
Fij
a
(13)
T
a
T
1
E (1 Zz)
of
(xi x,)²
(14)
T
a0 +1
Therefore, an initial estimate a can be computed as,
I; F.) 1)
(15)
0
ag Zi.
(16)
By iterating rule 112 with these initial estimates and solving for e via Newton's method (described below), efficiently converge to the Dirichlet parameters â
18

---

Published as a conference paper at ICLR 2026
Newton's iteration for calculating inverse Digamma
The Digamma function is defined by
v (u) = d (w)=
-
Σ
1
(17)
du
12 +
72 +
m=0
where Euler constant 7 = - (1). To solve for u (1) from the equation (²()) - v = 0, we
employ Newton's iteration (Gil et al. 2007). Given (((a +
Σ log Taj rule 12 the
Newton iteration is formulated as,
(2ald)
new
16 old
(18)
(wald)
where v'(u) denotes the Trigamma function.
To further accelerate convergence of Newton's iteration, the initial value unt is initialized using an approximate inverse function &i -1 (v), where
(u) (u) llog (u 1/2)
if 0.6,
(19)
?
if 0.6,
Yelds,
exp (u+ 1
if 2 2222 if v < -2.22
1
(20)
Once convergence is reached, we substitute + (v) (v) w into fixed-point iteration rule
12 to
update a."h ueww Iterating this process yields the estimated Dirichlet parameters ÔMLE-
Numerical stability. We clip Rij [10-7, 10-7] to avoid zeros, and early-stop when |o < 10-4, In all datasets, the method converges within O iterations per trial, where Jier typically remains under 5-10.
19

---

Published as a conference paper at ICLR 2026
D
THE PSEUDO-CODE OF BTTA-DG
Algorithm summarizes the pseudo-code of the proposed BTTA-DG framework.
Algorithm 1: BTTA-DG Framework
Input: Pretrained model fo. memory banks My. test trial tolerance E, K GMM components, the minimum confidence threshold Tconf and the maximum entropy threshold Tent- Output: Calibrated label Deal-
I/ Feature extraction
X <
Genc (9)
po(y) (X)
// Obbaain priori
// Accelerated Dirichlet parameter estimation
// Initialize a init
for
C do
T; f 1 Σ}= j=== Øij
7
of + T 2
(Iij F:)
a0 nit
[2] >i=1
[2
2:(1 Et)
a + ag
Iz
end
a new f- a 0
0g
// Fixed-point iteration for MLE
while llarew ald
do
old + a new
for i to [ do
v (agid) 2j=1 log Zij
a NewtonSolver(x..) aow k
// Using Equations
18)
19
and
20
end
ag
new
21=1 a
end
O'LL
new
// GMM-driven Bayesian inference
y E L
Fit GMM: (Ty 1yy E Ly, 1K EM K)
PGMM (DMLE 1)
ER=l Ty (CEMLE Myyke gg.
PeMM ónvanly
po (v)
Peal (LMLE)
Elel
axsa v' polv')
end
Final prediction and memory bank update
daa arg maxyec Peal ÔEMLE
confidence Peal Hcal âMLE)
entropy - - Pea ÓMML)) log Pea âMLL) if confidence 2 Teonf and entropy I Ten then Drop oldest if [M buffer_sizee
Mase Mynn U (
end
return Dcal
20

---

Published as a conference paper at ICLR 2026
E IMPLEMENTATION DETAILS
This appendix provides further details on the datasets, baseline methods, and experimental configura- tions.
Dataset descriptions
BNC12014001: Derived from BCI Competition IV-2a Tangermann al. (2012). this dataset includes data from 9 subjects performing four-class MI tasks (left hand, right hand, feet, tongue) recorded using 22 EEG electrodes at 250 Hz. Each subject completed two sessions (288 trials per session) with trial duration of 4 seconds. Only trials of left hand and right hand were used for analysis.
BBCC20140022 This dataset contains data from 14 subjects performing two-class MI tasks (right hand vs. feet) recorded using 15 EEG electrodes at 512 Hz. Each subject participated in one session comprising 160 trials, with a trial duration of seconds. Only the first 100 trials per subject were used for analysis.
BNCI2015001: This dataset comprises data from 12 subjects performing two-class MI tasks (right hand vs. feet) recorded using 13 EEG electrodes at 512 Hz, each subject completed three sessions with 400 trials per session and a trial duration of seconds.
SHU MI Dataset (Ma et al., 2022). This dataset is particularly relevant as was specifically designed to study long-term variability, containing data from 25 subjects recorded over different days. Following the evaluation protocol provided with the dataset's 's official code, we performed rigorous Leave-One Ceeee-nnnSuuee--OOOS (LOSO) experiment on the last 10 subjects.
Baselines
To comprehensively evaluate BTTA-DG, we compared it against:
CSP et al. (2007): ) A traditional machine learning method that constructs spatial filters to maximize the variance of one class while minimizing that of another, thereby enhancing class separability.
EEGNet Lawhern et al. (2018): A compact convolutional neural network that integrates spatial-temporal feature extraction from EEG signals. BN-adapt Schheider et al.) (2020): Adjusts BN statisties to better adapt the target distribution.
EEG Conformer (Song al.) 2022): A Transformer-basee
architecture designed to capture complex temporal dependencies in EEG signals. This baseline tests whether architectural advances alone are sufficient to overcome the domain shift challenge.
Tent Wang et al.
2020): Optimizes affine parameters of BN via entropy minimization.
PL Lee et al.
2013): Uses high- high-confidence predictions as pseudo-labels for self-training.
SAR Niu al. (023): Incorporates reliable entropy minimization and sharpness-aware
optimization to suppress noisy samples with large gradients.
CoTTA Wang et al. (2022); Adapts the model using pscudo-labels generated through data augmentation and stochastic weight restoration to mitigate catastrophic forgetting.
Data augmentation techniques implemented include Gaussian noise, time shift, frequency shift, phase perturbations. time dropout, channel dropout, channel shuffle, bandstop filter, and channel symmetry Rommel et al. (2022).
T-TIME Li et al. (2023): Uses ensemble learning where multiple classifiers predict each unlabeled test EEG sample, updating classifiers via conditional entropy minimization and adaptive marginal distribution regularization.
OTTA Wimpff et al. (024)): Integrats Euclidean Alignment or Riemannian Alignment techniques with entropy minimization of BN finetuning to reduce cross-subject domain
shifts.
Pre-training and test-time adaptation configurations The SincAdaptNet was pre-trained on train set using the AdamW optimizer with learning rate of 1e-3, batch size of 32, for 100 epochs. For fair comparison, all TTA methods (except CSP and EEGNet) used SincAdaptNet as the backbone and applied EA preprocessing. SincAAdapNNet processes EEG trials E R BxxxXXX through:
21

---

Published as a conference paper at ICLR 2026
(1) Spatial filtering via 2D convolution (kerne__se size (C, Fsper 16 outputs), (2) Temporal filtering with Sinc FIR bandpass filters (4-30Hz) via SincConv (kerne size = (1,51), Fsicc = 16 outputs), (3) Layer normalization, (4) Increasing-Chant Channel convolution with ELU activation, (5) Layer normalization, and (6) Classifing convolution with LogSoftmax activation.
During test-time adaptation, the model was adapted using batch size of for epoch. Compared with mini-batch settings, this single-trial setting is both more realistic and more challenging, because many TTA methods (e.g., batch-norm-based approaches like BN-adapt) rely batch statistics and degrade or fail when only one sample is available. In contrast, our method works robustly with batch size of thanks to the use of layer normalization and probabilistic GMM over Dirichlet features instead of batch statistics. The same adaptation mechanism can be directly applied to larger mini-batches without any modification.. The memory bank size was set to 1000. The convergence tolerance for Dirichlet parameter estimation was set to & = l 3. As shown in the sensitivity analysis F our method is robust moderate variations in hyperparameters of our adaptation process. The final values for GMM components, confidence threshold, and entropy threshold were determined based on a grid search over reasonable range, with the optimal values selected based on the average performance standard validation procedure ensures that the hyperparameter tuning is fair and does not use any information from the target domain. The GMM configured with 8 components. The minimum confidence threshold Tconf was set to 0.596, and the maximum entropy threshold Tem was set to 0.673.
held-out validation set created from the source domain subjects. This
Experiments were implemented via Python 3.10 and Py' 2.1.0, and on server with NVIDIA TITAN V GPU and an Intel(R) Xcon(R) Gold 6230 CPU @ 2.10GHz.
F TABLES OF CROSS-SUBJECT ADAPTATION ACCURACY AND STATISTICAL SIGNIFICANCE ANALYSIS
Table 11 summarize LOSO cross-subject accuracies SHU MI dataset for online adaptation methods. Our BTTA-DG framework consistently outperforms all competing TTA methods. However, the performance gain is not statistically significant. We have investigated this and believe it stems from the lower EEG quality and higher complexity (5 sessions) of this particular dataset. This has limited the effectiveness of the feature extractors. When the baseline feature discriminability lower, becomes inherently more difficult for any TTA method to demonstrate large, statistically significant gains.
We assess statistical significance by conducting pairwise one-way ANOVA tests between BTTA-DG and each baseline. Table 12 [3 and 14 list per-subject and overall ANOVA p-values comparing BTTA-DG against each baseline. In most subjects, BTTA-DG demonstrated a significant difference from the baseline method (p < 0.05), further validating the statistical superiority of the BTTA-DG.
Table 11: Cross-subject adaptation accuracy (%) on SHU MI dataset.
Setting
Method
Avg. (%)
CSP
59.24
Source
EEGNet
61.07=1.10
EEG conformer
61.36g1165
SincAdapiNet
62.42.1172
BN-adapt
62.42 12.422-1.72
Tent
56.23+22.6
PL.
50.65
COTTA
62.73.1.75
Online TTA
SAR
58.33+2.37
T-TIME
62.37
OTTA
63.22 03.29
BTTA-DG
64.06 1.00-...22
22

---

Published as a conference paper at ICLR 2026
Table 12: Pairwise ANOVA p-values comparing BTTA-DG each baseline on BNC12014001 for
cross-subject adaptation.
Method
S0
S1
S2
S3
S4
S5
S6
S7
S8
Overall
SincAdu
3.5c-07
1.2c-08
8.4c-11
9.0c-01
6.2c-02
5.1c-02
2.2c-02
1.2c-04
1.7c-04
L.c-03
BN-adapt
3.5e-07
1.2c-08
8.4e-11
9.0e-01
6.2e-02
5.1e-02
2.2e-02
1.2e-04
1.7e-04
1.1e-03
Tent
14c-06
6.1e-08
6.8c-04
1.6c-10
2.5e-07
6.9c-07
9.7e-12
7.6c-05
2.0c-08
4.6c-05
1.5c-07
7.4c-11
2.7e-06
8.5c-07
4.6c-04
2.1e-06
1.c-066
3.7c-03
3.9c-05
4.9c-04
CoTTA
9.5c-07
2.9c-05
1.1c-05
1.9c-11
5.7c-01
L.6c-03
8.3e-02
8.0c-03
2.9c-03
1.2c-03
SAR
9.9c-06
7.3c-05
9.0c-05
4.4e-02
3.1e-07
7.6c-05
7.2c-02
6.6c-03
3.0c-02
2.7c-04
T-TIME
1.1e-05
4.1e-05
4.4e-04
1.3e-01
2.6e-01
2.0e-07
1.3e-07
4.1e-03
1.4e-03
1,5e-03
OTTA
2.3e-06
4.7c-07
1,7e-08
3.8c-01
9.9c-01
1.4e-01
1.ee03
2.4e-04
4.1e-02
4.8c-02
Table 13: Pairwise ANOVA p-values comparing BTTA-DG each baseline BNC12014002 for
cross-subject adaptation.
Methed
Overall
NincAdapNeer
4.5e-12
2Me-10
0.00
1.0e04
1.5e-07
3.7e-0
1/0-07
0100
1.76-04
9.0e-0h
5.5o-D4
9.5e-15
3.2e407
4.4r-17
BN-adet
6.5p00
2.M-100
0.00
5.5-415
1-c-04
1.5p-07
37e-09
1/K-07
0.00
1.7o-44
9.0e0h
5. 5.8o-li
9-4e-05
3.7p00
4 4.40-0
Tex
8.2 11
1.3c 05
1.3c.4
5.9
9.36.05
1.3e-00
6.7c 04
2.0e008
1.2e-02
6,0c 08
9.7c
6.0e-06
6.42 13
1.9e-1
2.3e-07
PL
1.30 05
6.3g 07
0.
1.6e
1.9 04
3.
1.1e
0.5e
9:0e
5.7e
2.5e
2.0e-0
li 05
1.9e 13
1.8 05
COTTA
388 03
1 05
31
1.38 02
5.0e
1:4e-05
1:
3.5.05
1.0e-00
1.5e 02
9.5e
1.3e-00
8ile 04
5:4e-0
4.
SAR
232-00
3.1:08
8.7-02
S.4-04
12:-02
1.9-08
232-05
2.6-06
3.7c00
2.0-44
2.2-07
3.1c-0
19c-06
4.0-04
7:2-06
T-TME
3.c-00
9.4-00
3.7c-02
2.6e-0
7.3-01
1.4-04
6.8c
244-04
5.9-08
3.9--6
26c-06
3.0-04
6.42 06
246-05
5.0-06
OTTA
2.0g 02
1,0+000
2.76-06
2.6e 34
8.8 03
4.5e001
1.5c 01
6.9-08
6.5e-02
4.2c 04
2.1e-11
3.3e.01
1.2c 01
2.36-05
3.76-02
Table 14: Pairwise ANOVA p-values comparing BTTA-DG to each baseline on BNC12015001 for
cross-subject adaptation.
Method
80
82
53
85
S6
87
88
89
S10
S11
Overall
SincAdaptNet
5.8c-08
4.6c-07
2.9c-02
3.8c-08
8.3c-02
6.2c003
3.1e-02
4,8c-03
3.2c-01
2.9c005
2.8c-05
7,4c-11
5.5e-0r
BN-atapt
3.8e-08
3.1e02
3.2c-01
299-05
83e-06
1.5e-10
2.2c-06
6.0c-11
1.1e499
7.7c-10
4.4c-10
7.0e-11
5.5c49
1.3c-08
8.4e-18
2.0c-21
7.0-077
PL.
1.3e42
27e-02
2.7c05
8.8c004
16s-12
1.4e417
4:2-066
1.8-11
9.8--1
8.5e.08
3.0e-17
4.76-22
8.0c-06
CATTA
93e-03
3.7e402
1.9-01
1.3c-04
5:7e-01
16c-02
28c-00
29a-02
7.c-01
2.5c-02
1.1e07
1.8e-99
4.62-03
SAR
122-02
6.2e03
1.5e-02
3.9e006
6.6c-02
3.6e.1
1.1e02
5.0c-03
5.7-01
7.3e:04
2.0c-03
4.3e-07
1.2e-02
TTIME
0.
5.4e077
1.2c04
1.c-01
4.2s-05
7.0-03
5.5c-07
2.7c-07
OTTA
19c-02
07
03
1.9e006
4.3c-02
5.5c-14
1.3e006
8.9-01
2.2c077
4.4e022
2.2c-03
2.8e-12
5.0c-02
G ADAPTATION ON LOW-CHANNEL EEG
Given the practical constraints of portable EEG hardware, we further evaluated BTTA-DG on BCI Competition IV 2b, which contains only three EEG channels. We followed the same LOSO cross-subject protocol as the main experiments. All architectural, training, and adaptation hyperpa- rameters were kept identical, except for adjusting the input channel dimension.
Table 15 reports subje-t accuracies for source models and online TTA baselines. Despite the extremely low sensor density, BTTA-DG achieves the highest average accuracy of 78.76%, with statistically significant gains over the AdapNNe source model. These results confirm that the proposed Dirichlet-GMI. adaptation mechanism remains effective under minimal channel configurations, supporting its practical relevance for low-density BCI systems.
Table 15: Cross-subject adaptation accuracy (%) on BCI Competition (3 channels). An asterisk (*) denotes statistical significance leverl (*; p < 0.05).
Setting
Method
So
S1
S2
S3
S4
S5
S6
S7
S8
Avg.
CSP
70.09
61.25
63.68
77.17
78.21
68.21
74.20
73.82
72.51
71.01
BEGNet
74.28
63.90
68. 32
82.35
80. 16
70.05
77
76.61
75.10
74.29
Source
EEG conformer
72.23
62.45
83.12
69.10
76.30
76.56
76.56
73. 73..6122.02
SincAdaptNet
74.57
64.73
72.07
89.67
80.93
71.32
79.72
80.00
73.85
76.3220..0
BN adat
74.57
64.73
72.00
89.67
80.93
71.32
79.72
80.00
73.85
76.32,.o.a
67.27
65.22
60
69.75
67.42
66.18
68.27
71.58
67.85
67. 67.79+1.24
PL.
67.77
65.48
67.08
70.52
70.33
66.57
73.17
72.70
68.45
69.12 199.1.11.00
Online TTA
C6TTA
74.78
64.73
72.30
90.05
82.02
71.93
80.38
80.30
74.65
76.7911.00
80.48
75.01
T-TIME
75.92
64. 18
72.00
91.68
80.53
72.85
81. 02
79.78
72.92
76.77.1.53
OTTA
78.55
67.60
70.78
84.78
81.42
67.70
81.98
79.00
75.32
g6.34
BTTA-DA DG
77.50
67.00
74.33'
91.50
84.17'
76.50'
83.58
82,83'
76.50
78. 78.76
23

---

Published as a conference paper at ICLR 2026
H WITHIN-SUBJECT CROSS-SESSION EXPERIMENTS
To verify that BTTA-DG can adapt not only across subjects but also across sessions for the same subject, conducted within-subjer cross-session study BNCI2014000 4001. Specifically, pretrained SincAdaptNet on 1st session of each subject and then performed test-time adaptation that subject's 2nd session, simulating session shifts different days. Table S reports the classification accuracies for cross-session adaptation. BTTA-DG achieves an average of 86.50% + 2.49%, significantly outperforming all competing TTA methods (asterisks denote p 0.05 by pairwise ANOVA against each baseline).
Table 16 presents the corresponding pairwise ANOVA p-values comparing BTTA-DG each baseline across subjects S0-S8, as well as an overall y-value computed on per-subject mean accuracies. Most comparison reach statistical significance, confirming that our gradient-free Bayesian calibration maintains its advantage even under within-subjed cross-session drift.
Table 16: Pairwise ANOVA p-values comparing BTTA-DG to each baseline on BNC1201400) for
cross-session adaptation.
Method
So
S1
82
S3
S4
S5
S6
S7
S8
Overall
SitcAdaptNet
1.7c-01
3.2c-07
8.6c-09
3.1c-04
1.6c-03
2.2c-06
6.2c-04
1.1c-11
1.9c-06
1.8c-03
BN-adapt
1.7c-01
3.2c-07
8.6e-09
3.1c-04
1.6c-03
2.2c-06
6.2c-04
1.1c-11
1.9c-06
1.8c-03
Tent
1.6e-01
1.0c-14
6.5e-04
1.3e-11
1.1e-15
2.4e-11
1.e-10
3.6e-02
8.7e-03
4.5e-03
PL
3.2c-06
3.8c-14
1.0c-06
4.2c-12
4.7c-05
1.7c-07
L9c-05
1.1c-03
5.6c-02
3.0c-03
CoTTA
7.8c-01
9.8c-09
8.4c-04
3.8c-05
3.4e-03
9.4c-06
1.6e-33
2.5c-09
3.5c-03
7.2c-03
SAR
2.8c-01
1.6e-05
8.9e-04
8.3e-04
9.6c-05
3.2e-06
3.1e-04
1.3e-07
7.6e-04
3.7e-03
T-TIME
9.7e-06
1.5e-08
2.5e-05
5.6e-04
2.9e-07
9.6e-06
3.0e-04
5.4e-07
9.6e-03
4.8e-04
3.1e-10
3.0e-08
6.9e-17
3.3e-02
8.4e-01
4.0e-06
1.le01
3.0e-13
3.0e-09
3.7e-02
I SLIDING-WINDON ONLINE ADAPTATION
To directly address the concern about whole-trial processing versus low-latency online BCIs, we evaluated BTTA-DG in a sliding-window setting BNC12014001 under the same cross-subject setting as the main experiments. Each 4 trial was segmented into non-overlapping s windows, and adaptation and inference performed per window, while all other training and adaptation settings were kept identical.
Table 17 reports window-level accuracies for the source models and online TTA baselines. As pected, overall accuracies are lower than in the full-trial setting. Nevertheless, BTTA-DG still achieves the best average performance (76.49%) and provides clear improvement
the SincAdaptNet source model (74.5%%). This shows that the proposed Dirichlet-GMe GMM adaptation mechanism compatible with online windows (batch size 1) and can effectively operate in a low-latency, continuous-feedbacc regime, mitigating the practical limitation that the main experiments use full trials.
Table 17: Sliding window
diddng-windoww adaptation accuracy (%) on BNC12014001 with I-s windows. An asterisk (*) denotes statistical significance level (*: p < 0.05).
Setting
Approach
SO
S4
S6
S7
S8
Avg.
CSP
74.17
66.48
79.02
61 61.25
55.44
74.44
67.99
83.78
83.95
71.84
BEONe
$7.60
69.90
85.95
Source
EEGCouformer
75,80
67.63
80.91
62.04
$7.80
75 75.94
70.40
86.55
86.03
73.68
1.94
SincAdaptNer
76.60
68.33
81.81
62.64
58.40
76.74
70.90
87.85
87.43
74.52
1.30
adaa
76,60
68.33
81.81
62.64
58.40
76.74
70.90
87.85
87.43
74.52
1.30
PL
73.40
63.89
78.47
58.33
54.10
72.29
66.18
81.25
85.00
70.32
3.26
Online
CoTTA
76.83
68.85
63.08
$7.94
76.97
70.93
88.22
SAR
76.86
66.24
79.01
60.54
56.86
74.22
70.61
83.39
84.01
72.
T-TIME
76.00
67.53
83.01
62.60
57.04
76.97
69:61
89.89
87.73
74
1.68
76.63
67.42
81.58
63.39
70.06
74.001
1.96
DG
77.39
72.53"
83.64
64.89
60.03
78.08
73.22"
90.58
87.81
76.49"
1.41
24

---

Published as a conference paper at ICLR 2026
J WITHIN-SUBJECT K-FOLD ADAPTATION ON BNCI2014001
To understand the intrinsic "decodeability" of each subject and its relationship with TTA effectiveness, conducted a three-fold within-subject cross-validation on BNC1201 4001. For each subject, merged the two sessions, split trials into three folds, and performed within-subject training and testing. This setting enables direct comparison with the cross-subject TTA results in the main text.
summarizes within-subjec accuracies across source models and online TTA baselines. Overall, within-subjec training yields high decodeability for most subjects (e.g., SincAdaptNet reaches an average of 84.46 84.46%) while BTTA-DG further improves performance to 87.30%. For some subjects (e.g.. $1, S2 and S3), the crose-subject SincAdaptNet accuracy in Table exxeeds their within-subjert baselines. This observation is consistent with the hypothesis that pretraining other subjects can benefit "bad-performing" subjects. For the majority of subjects, however, within-subject accuracies remain higher than cross-subject baselines, indicating that inter-subject variability can induce negative transfer and highlighting that the gains from BTTA-DG primarily stem from effective test-time adaptation.
Table 18
Table 18: Within-subjeet k-fold adaptation accuracy (%) BNCI2014001. An asterisk (*) denotes statistical significance over the SincAdaptNet source model (paired I-test, p < 0.05).
Setting
Method
S0
S1
S2
53
S4
S5
S6
S7
S8
Avg.
CSP
90.26
51,53
95.81
67.48
70.65
74.23
72.80
93.55
88.41
78.30
HEGNet
95.24
72.88
83.20
89.15
82.41
Source
EEGConformer
92.19
52.81
96.14
73.56
86.27
75.83
84.51
97.24
89.80
13.15....0
SincAdaptNet
93.38
54.66
96.64
74.66
88.58
76.92
86.81
97.82
90.67
8-1 $1.4662..6
BN-adapt
93.38
54.66
96.64
74.66
88.58
76.92
86.81
97.82
90.67
84 26.46642.08
Tent
52.60
97.01
79.62
89.69
62.15.13.04
PL
93.37
51.94
97.57
67.70
89.76
73.26
83.65
98.58
90.80
82.96+3..0
Online TTA
CoTTA
94.20
54.82
97.60
74,90
90.14
77.81
87.81
98.65
91.35
85, 85.25
SAR
94.13
53.75
97.05
72.99
75.83
86.39
89.72
83.90
T-TIME
92.53
52.60
97.29
72.19
89.65
76.42
85. 69
98.68
89.90
83. $3.8013.40
OTTA
93.00
57.84
97.38
77.18
92.28
76.41
91.86
98.08
90.68
86.08 12.35
BTTA-DG
96.49"
58.64
98.57
78.78"
90.24
92.32
87.30+a.50
K FIGURES OF FREQUENCY RESPONSES OF THE LEARNED SINCCONV FILTERS
To provide a comprehensive view of how SincAdapiNetts learnable band-pass filters operate across all subjects, this appendix presents the complete frequency responses of each of the 24 Sinc-Cony filters for every LOSO test fold. These figures substantiate the interpretability and effectiveness of Sinc-Conv as a data-driven substitute for hand-crafted bandpass filtering in EEG analysis.
15.0
8.812.99
1:
Pilter 31-7.8 Hz
12
Fitter S: 7.7:12.0
Filter 15.7/20..2
Fiber 20.3
Pilter 13: 25.9-0.1
10
Pilter 23.0-27.
10.0
Filter 37:11-33 Hz
Fitter 17: 29.7-33.33 Ha
Amplitude
39.7-44.0000
Amplitude
Filter 24: 6-.6-53.7 7 Hz
Fiiter 24: 54.3-58.4444 Hx
Cumulative Respense
Cumulative
5.0
2.5
0.0
20
40
100
20
60
100
Frequency (Hz)
Brequency (Hi))
Figure 6: Training set: others; test set: S1
Figure 7: Training set: others: test set: S2
25

---

Published as a conference paper at ICLR 2026
Pilter 9,816144 l1s
Filter 1: 5.4-9.9 l1s
12
Filter 7:1:11.3
12
Pilter 23.2:27.7 11z
Filter 9t 16.6-20. 1iz
10
Füter 13: 30.2-34.3 H2
10
Fiiter 13: 24.1-28.1
31.335.
32.3-37.44
Amplitatte
8
Pilter 21: 29 8-34, 1 tte
Amplitede
Filter 21: 44.5-48.. thr
Filter 24: 48.1663.0
Filber 53.3 67.7
6
Cumulative Rergonse
Cumulative Response
4
2
20
40
80
100
0
20
40
60
80
100
Prequency (ltz)
Prequency (1tz)
Figure 8: Training set: others; test set: S3
Figure Training set: others; test set: S4
Pilter 1: 3.9.8.7 1lz
Filter 1: 9.5-14.0 1lz
12
Pilter
12
Fiiter 21.1/25.3 Hz
Filter 9: 14.1-18.1
10
Pilter 13: 22.2-26.
10
Filter 23.4-26.00
29.23333
Amplitado
Pilter 21: 44.5-60. liz
Vilter 21: 31.3-33336622 Liz
Fiiter 49.4-53.4
43.5-57.3
6
Cumulative Response
Cumulative Response
2
20
40
80
100
0
20
40
60
80
100
Brequency (1tz)
Brequency (ttz)
Figure 10: Training set: others; test set: S5
Figure 11: Training set: others; test set: S6
Filter 5.7.0.55
1:
12
Fittrr 30:1-14.... Hz
2000
Filter 5: 5.2.9.6
Filter 2..88255.6
12
16.6-22.3
10
Fülter 13: 13:223.-28.44 4 Hz
Filter 13: 30.3-000555..0 Hi
Pilter 17,3333336
10
Filber 33.1-33115
Amplitude
8
64.4-58.0
Fiterr 26: 54.2 58.2 Hiz
Filter 24: 48.8 63.0 Ei
6
Cumulative
Cumulative Response
4
2
0
Fraquenccy
Frequency (Hx)
Figure 12: Training set: others; test set: S7
Figure 13: Training set: others; test set: S8
26

---

Published as a conference paper at ICLR 2026
L QUANTITATIVE ALIGNMENT OF SINC FILTER PASSBANDS WITH MI-EEG RHYTHMS
To complement the main-text analysis in Table 6 we briefly describe how the quantitative alignment was computed. For each learned Sinc filter on BNCI2014001, we first obtained its lower and upper cut-off frequencies and then checked whether its passhand overlapped +2 Hz tolerance around the standard (8-13 Hz), 3 (13-30 Hz), and low-y (30-45 Hz) bands. For each subject, we then calculated the proportion of filters whose passbands fell into each of these bands outside them, yielding the percentages reported in Table 6
M TOPOGRAPHIC VISUALIZATION OF THE LEARNED SPATCONV KERNELS
The use of spatial convolution is standard and effective technique in EEG deep learning models (e.g.. EEGNet (Lawhern al. 2018), ATCNet (Altaheri et al.) 2022h, EEG conformer (Song et al. 2022). M-FANet (Qin et al., 2024). and etc.) to learn spatial filters. While EEG channel ordering arbitrary, the "C convolution learns weighted sum of all channels (not only local adjacent channels), effectively creating data-driven spatial filters that can capture relationships between physically distant but functionally related brain regions (e.g., bilateral motor cortices). Our topographic visualizations in Figure T4 show that the learned kernels are not limited to local neighbors but capture diverse and physiologically meaningful scalp-wide patterns, confirming its ability to learn non-local inter-channel relationships.
Figure 14 shows all 16 spatial kernels from SincAdaptNet's Spat-Conv layer, rendered on a standard 10-20 montage Nomenclature (191)) scalp map. Together, these topographies span frontal, central, parietal, and occipital cortices, demonstrating that SincAdaptNet automatically learns multiple physiologically meaningful spatial filters Mulers-muuh like CSP but in fully data-driven, end-to-end fashion.
Scalp topographles spatial convolution weights tperciue
Squi Geen
Opel Care
LIVE 90990
0.0
Spa
SpatC Sarmet
Sant Aocnal
Spal
Figure 14: Topographic visualization of Spat-Conv kernels for SincAdaptNet trained on BNC12014001 (22 channels). Each subplot displays one spatial kernel mapped onto the 2D electrode layout (standard 10-20 montage), where the color scale indicates the weight amplitude.
27

---

Published as a conference paper at ICLR 2026
N FIGURES OF DIRICHLET PARAMETER DISTRIBUTION WITH GMM CLUSTERING
To provide comprehensive view of how our Dirichlet-GMi pipeline captures class-specific structure in the www-dimensional embedding space across all subjects, this appendix presents the complete scatters of Dirichlet parameter representation and GMM clustering outcome for every LOSO test fold. These figures illustrate the stability and separability of the Dirichlet parameter representation across test trials, and how a Gaussian mixture model (GMM) clusters these parameters into coherent groups. This analysis validates our choice of Dirichlet projection to compactly encode prediction uncertainty and our use GMM to preserve both global and local neighborhood information in BTTA-DG.
6
Inter-cluss KL. Div 41.61 Intra-class Avg. Cov Clasters 0.0
Left hane
land
12
Inter-class KL. Div 35,60
Intra-class Avg. Cov of Clasters
Lett hand hand
Highs
5
Balk
9.11
8
T0
Maga
5,10
3
Riets
Sagh
4
8
10
Figure 15: Training set: others; test set: $1
Figure 16: Training set: others; test set: S2
9
Inter-class KL Dir 31.53
Inter-class KL Div > 23 23.86
Avg.
Right hand Error
Ang.
Right hand Eccor
8
7
6.07
Riyha
6
3,2
Intate
Fib
Raba
5
0.22
Yy
A6007
4
3
Ty. 0.
5
5
d1
Figure 17: Training set: others; test set: $3
Figure 18: Training set: others; test set: $4
28

---

Published as a conference paper at ICLR 2026
7
Inter-class KL Dir 7:31.16
Intru-class Aug. Cov Clasters 0.1
Lef hand
Right hond
Intru-class Auy. Cov of Clusters x 00.1
Inter-class KL Dly $7.19
Left hand Right hond
6
Hust
0.02
mi 0392
Ran
8
5
2/14
4
Righ
3
Righ:
3
4
5
8
5
6
7
8
81
Figure 19: Training set: others; test set: S5
Figure 20: Training set: others; test set: S6
Inter-class KL. Div 44.35 Intri-class Ang. Cov Clasters 0.2
Left hand Right hond
Inter-claas KL. Div 77 Intra-class Auy. Coy of Clusters < 0.2
Lec't land Right hone
8
No 0.5
1
7
patt
6
ng Rale
5
02
4
Frr
Rid
3
4
6
8
10
4
8
10
41
Figure 21: Training set: others; test set: S7
Figure 22: Training set: others; test set: S8
29

---

Published as a conference paper at ICLR 2026
O COMPUTATIONAL COMPLEXITY
This appendix summarizes the space and time complexity of BTTA-DG's test-time pipeline, covering Dirichlet parameter estimation, memory maintenance, and GMM-based calibration. Let M be the size of the memory bank, |C| the number of classes (i.e., the Dirichlet dimension d = [C) and K the number mixture components per class.
Space complexity. For each trial we store only its low-dimensional Dirichlet parameter vector E Rd so the memory bank costs (M GMM parameters per class add ( d) for means and (())) for diagonal variances (plus ((K) for weights). Since M is fixed and d (2,4) in our MI-EEG settings, the overall cost minimal.
Concretely, in a 2-class MI task (d = 2) with a memory bank size of M = 1000 trials per class, the bank stores buffers x 1000 trials 2 floats/trial 4 bytes/float32 values, corresponding roughly 16 KB per subject. Even for d = 4 classes with the same M, the total memory remains the order of KB per subject. The GMM parameters with a small number of components additional kilobytes. Since BTTA-DG is instantiated per target user at deployment, this memory cost scales linearly in the number of adapted users rather than in the size of the pre-trie pre-training source user.
add at most few
Time complexity.
Dirichlet MLE. For trial with T time steps, computing sufficient statistics = log.ray costs O(dd); the fixed-point updates with Newton refinement for g then cost Tier), where the number of iterations Juer is typically 5-10 (see Appendix C Hence, Dirichlet projection: O + d Ine) = O(Td).
Memory update. Appending a single vector (and evicting the oldest when full) a queue operation with (1))
GMM re-fitting. Re-fitting by EM over the memory bank has per-EM-iiee EM-ieratiion cost OdM) For JEM iterations, the per-trial overhead O MKd).
Given that d S 4, K is small, and M is bounded, the end-to-end end overhead is negligible in practice while enabling robust, gradient-free adaptation. In terms of FLOPs, the Dirichlet projection and GMM steps contribute only a small fraction of the total cost relative SincAdaptNet forward pass, which is reflected in the modest increase from 133.3M to 141.6M FLOPs per trial reported for BN-adapt and STTA-DG in Table 7
P DETAILED ANALYSIS OF CLASS IMBALANCE SENSITIVITY
This appendix provides additional interpretation of the class-imbalance experiment reported in Table in the main text.
As noted there, while the overall accuracy gracefully degrades with increasing imbalance, we observe that the accuracy for the minority class (Class 1) conversely improves as its prevalence decreases. For the minority class, our confidence and entropy thresholds ensure that only high-certainty trials of the rare class are added to its memory bank. This creates highly "pure" and compact GMM, which becomes exceptionally good at identifying these specific, ideal minority-class trials.
Conversely, the GMM for the majority class must account for much larger and more diverse set of trials, causing its distribution to become more diffuse. This can lead to a decrease its own classification accuracy as the decision boundary shifts. Taken together, this finding highlights that our method does not simply fail under severe online class imbalance: instead, it adapts by specializing its model for rare events, which is desirable robustness property for real-world applications.
Q DECLARATION OF LARGE LANGUAGE MODEL (LLM) USAGE
The LLM is used only for writing, editing, or formatting purposes and does not impact the methodology, scientific rigorousness, or originality of the research.
30


Reviews:
[{"review_id": "cyd5k3qFkU", "reviewer": "Reviewer_4sdH", "summary": "This paper presents a Bayesian test-time adaptation framework for EEG motor imagery decoding that addresses cross-subject and cross-session generalisation challenges. It leverages Euclidean Alignment (EA) to align EEG trials into a common domain, followed by a gradient-free Bayesian adaptation on low-dimensional Dirichlet-distributed sequential embeddings, extracted from pretrained SincAdaptNet models.  This method offers a gradient-free approach that avoids catastrophic forgetting and adapts robustly during test time.", "questions": "Given the practical constraints on EEG hardware, benchmarking performance on datasets with fewer EEG channels is advisable. While BNCI and SHU datasets are well established, inclusion of standard datasets like BCI Competition IV Dataset 2b (3 channels) or datasets with low-density configurations would strengthen practical relevance.\n\nFor more realistic online BCI applications, investigating windowing or sliding window strategies, which segment data into shorter temporal windows for quick iterative adaptation and inference, would address practical BCI applications.\n\nA recommended discussion point to include in the paper is addressing scalability and memory cost concerns for large-scale deployment across thousands of individuals, given the fact that each trial from each participant is represented and stored.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The method emprically demonstrates its consistent outperformance across four well-known and diverse motor imagery EEG datasets with rigorous leave-one-subject-out and cross-session validation.\n\nThe projection of high-dimensional sequential EEG embeddings onto a compact Dirichlet-distributed parameter space is an innovative approach to capture predictive uncertainty and temporal evidence concentration.\n\nThe learned filters and Dirichlet feature spaces align with neurophysiological expectations, which supports the model’s interpretability and trustworthiness", "weaknesses": "The lack of an ablation study without EA precludes understanding of the standalone adaptation capabilities. This reliance could limit practical application scenarios where EA cannot be applied, e.g., variable or missing channels, high artifact environments.\n\n\nThe current approach processes entire trials for adaptation and inference, which is less practical for online BCIs requiring low latency and continuous feedback.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "YGfh8t8Wgf", "reviewer": "Reviewer_Av96", "summary": "The paper proposes BTTA-DG, a Bayesian Test-Time Adaptation (TTA) framework for motor imagery (MI) EEG decoding. The method aims to address cross-subject and cross-session variability by enabling gradient-free adaptation during inference. It consists of three core components:\n(1) a Sinc-based adaptive network (SincAdaptNet) for frequency-selective representation learning,\n(2) a Dirichlet feature projection that probabilistically models deep feature uncertainty, and\n(3) a GMM-driven Bayesian inference mechanism that calibrates model predictions without updating weights.\n\nThe framework is theoretically motivated and computationally efficient. By introducing Dirichlet modeling into the EEG-TTA setting, the paper provides a probabilistic view of feature dynamics and uncertainty estimation. Experiments demonstrate competitive accuracy and improved interpretability compared with prior TTA approaches.", "questions": "- The paper claims that BTTA-DG achieves lower computational overhead than existing EEG-TTA methods. Quantitative evidence—such as comparisons of inference time, FLOPs, or memory usage—would be helpful to substantiate this claim.\n\n- The proposed online TTA framework appears to operate only with a batch size of 1. It would be useful to clarify whether this is a methodological constraint or a design choice, as well as the rationale for this setting and its consistency with real-world BCI scenarios where input configurations may vary.\n\n- Further clarification is needed on how the “historical distribution” in the GMM-based Bayesian inference is estimated and updated during test time. If this distribution is continuously adapted, it may lead to potential distribution drift or overfitting toward recent samples.\n\n-The paper presents visualizations of learnable Sinc filters and claims physiological interpretability. A quantitative evaluation of whether the learned frequency bands align with known EEG rhythms (e.g., μ, β, γ bands) would strengthen the interpretability argument.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The authors successfully introduce Dirichlet modeling into the EEG-TTA decoding paradigm and achieve strong results on four public datasets, validating the method’s empirical effectiveness.\n\n- The proposed BTTA-DG framework leverages GMM-driven Bayesian inference to avoid parameter updates during test time, achieving fast inference speed and making it suitable for real-world BCI deployment.\n\n- The model effectively mitigates cross-subject and cross-session variability, demonstrating that a single model can generalize to new subjects and sessions at test time without gradient updates.", "weaknesses": "- The paper employs SincAdaptNet for pretraining, which contains only four convolutional layers. Given the limited size of EEG datasets, it remains unclear how such a lightweight backbone can ensure strong representational capability. If the contribution mainly lies in “extracting task-specific frequency bands,” this may be insufficient as a novel methodological point. The authors are encouraged to clarify the specific purpose and benefits of frequency-band extraction in the context of TTA and practical BCI applications.\n\n- The Dirichlet distribution is introduced to parameterize the probabilistic distribution over class predictions. However, since the scale parameter α₀ significantly affects the concentration of the distribution, the authors should explain how α₀ is chosen or tuned, and analyze its impact on model stability and uncertainty estimation.\n\n- Although Table 7 reports the average inference time, it would be beneficial to include a comparison of runtime and memory usage, to quantitatively demonstrate the computational efficiency of the Dirichlet modeling and strengthen the claim of practical advantage.\n\n- While the GMM-driven Bayesian inference is theoretically sound, the interaction between Dirichlet feature projection and GMM posterior fusion remains insufficiently explained. The authors should further clarify how the historical GMM distribution influences the Dirichlet-projected features during test time, and whether it could cause bias toward recent samples. Providing additional conceptual explanation or visualization would help improve clarity.\n\n- The ablation study is not sufficiently comprehensive. A more systematic evaluation, such as testing under cross-session and cross-subject settings and examining whether the improvements are consistent across multiple datasets, would substantially strengthen the empirical validity and generalizability of the proposed framework.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "T96wg5v2EO", "reviewer": "Reviewer_G2CU", "summary": "This paper proposes a novel method for cross-subject (and cross-session) Test Time Adaptation (TTA) of motor imagery BCIs, that is based on Bayesian-inference calibration of predictions, with the likelihood being given by the (GMM) distribution of test trials in the Dirichlet parameter space of their class probability distributions across time. This method is not gradient-based, avoiding high computational cost and catastrophic forgetting. Compared to other non-gradient-based methods in prior literature, authors claim that this approach can adequately capture high-dimensional (deep feature distribution) domain shifts. Results show state-of-the-art performance (+0.8%-2.6% absolute accuracy improvement) in cross-subject and cross-session accuracy compared to prior TTA methods, evaluated in an online setting across 4 public motor imagery datasets. Computational efficiency is the second best among all compared methods, and visualization of the GMM clusters of test trials in Dirichlet space shows good separation of classes. Finally, additional ablation studies are provided concerning the comparison of probability calibration vs. projection only and the impact of hyperparameters in estimating the GMM likelihood, thus explaining performance and design choices.", "questions": "Please address the points outlined above in the “Weaknesses” section. If those are substantially addressed with a change in the paper’s content or with a convincing reason why this change is not feasible / desirable, the paper will be recommended for acceptance. \n\nEspecially addressing the 1st point is necessary for recommendation of acceptance. Depending on how the rest of them are addressed, the rating could be increased to either 6 or 8.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "This paper offers substantial novelty to the field of TTA in BCIs, through creative combination and application of existing statistical modeling methods (Dirichlet distribution + GMM estimation + Bayesian inference) which advances the state of the art considerably on multiple datasets, while being interpretable and efficient at the same time.\n\nThe paper is of high quality; the methods proposed are well thought out and well explained, the experiments and figures provided support (most of) the claims well, and figures are both pleasant and informative (especially figure 1). Writing is very clear, convincing, and easy to follow, even when going through complex technical details.", "weaknesses": "1. **High-level statements misaligned with method details.** In various instances throughout the paper it is either implied (lines 20, 61, 63, 70, 74, 250) or directly stated (line 22) that the method “directly models the distribution of deep features”. However, this is not true from this reviewer’s understanding of the method - the Dirichlet parameter space, although reflecting the distribution of class probabilities across trial time (which is indeed more than just static trial predictions), is still only modeling low dimensional class probability features and not high-dimensional deep features of the trials as stated (or implied). If by “high-dimensional” the authors referred to the temporal dimension, that should be made more clear as the current phrasing can be misleading (usually when saying high-dimensional / deep features of a DNN this cannot be the output layer even if it makes predictions per token).\n2. **DNN model choice not well motivated.** While the introduction states that “recent advances in large-scale EEG pretrained models [cited: labram, egg-gpt, etc.] trained on massive datasets have demonstrated unprecedented capabilities in learning general […] representations”, these models are not used as the backbone model or as baselines in the current paper’s experiments. Instead, a much shallower model is used (only 4 layers) and it is trained from scratch in the down-stream datasets. This choice should be better motivated (ideally also showing the performance of those large-scale pretrained models as baselines), and depending on what that motivation is, it could also be good to show TTA results using those models as backbones.\n3. **Useful additional comparisons desired.** First, it would be useful to be able to compare the TTA performance with the performance achieved with full fine-tuning to the target subject, to quantify how much this gap is starting to close; for example EA+Fine-tuning achieves 82.6 in BNCI2014001 (see [1]). Additionally, it would be informative to know the (k-fold) within-subject performance of each of the subjects here (perhaps in the Appendix), to provide insights into the “decodeability” of each subject’s data and how it may relate to the effectiveness of TTA with this data. For example in [1], pretraining on the rest of the subjects was shown to especially benefit “bad-performing” subjects compared to their within-subject performance - here it could conversely be that those subjects are not very effective for TTA. Second, an additional ablation that performs the GMM-BTTA without the Dirichlet projection, using instead the feature space of the mean class-probability across trial time (red dot in Figure 1; e.g. (d) would be represented by (0, 0.5, 0) instead of (1, 5, 1)) would also be good to demonstrate the usefulness of the projection (uncertainty modeling) in the calibration.\n4. **Presentation issues.** The conclusion paragraph needs some more work. Sentence “While the framework assumes” (line 481) is either left unfinished or has some grammatical error. Sentence “our framework demonstrates robustness under mild departures” (line 484) is not evidenced in the results (or is not made clear which result this refers to). Same line, “would” does not make sense. Figure 4 would benefit from having the scale of all y axes be the same so that the difference in fluctuations is more clear and comparable. The order of tables and figures in that page is also inconsistent with the flow of the text, should be Table 7, Table 6, Figure 4. The paper would benefit from having Table 13 in the main text. There should also be some comment in the text on why “BN-adapt” is that much faster (Table 7) than all others. On line 173 there is a mistake in the figure caption, “(b) and (d) illustrate” should be just “(d) illustrates”.\n\n[1] Sartzetaki, C., Antoniadis, P., Antonopoulos, N., Gkinis, I., Krasoulis, A., Perdikis, S. and Pitsikalis, V., 2023. Beyond Within-Subject Performance: A Multi-Dataset Study of Fine-Tuning in the EEG Domain. In 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC) (pp. 4429-4435). IEEE.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)