Main contributions

• We introduce the BELT architecture, a modular BCI design paradigm that separates general-purpose communication decoding from application-specific logic, enabling broader reusability.
• We propose a Bayesian two-phase decoding strategy that combines a general prior model with user-specific posterior adaptation, improving accuracy while reducing the need for extensive individual training.
• We emphasise practical deployment by enforcing strict design rules: lightweight classification for embedded hardware, task-aware data compression, and an Edge-Cloud infrastructure to balance computation, bandwidth, and privacy.
• We present BELT-lite, a deep learning-based model for MI tasks within the BELT framework, tailored for resource-constrained environments and demonstrating the feasibility of our approach in real-world settings.

Related work and current challenges

The challenges facing portable BCI systems are well documented and directly motivate the design choices in BELT. We organise our review around four key areas: signal variability and adaptation, embedded deployment constraints, edge–cloud communication, and data privacy. For each area we briefly survey relevant literature and indicate how BELT addresses the identified challenge—fully or partially.

Architecure

The proposed pipeline is illustrated in Fig 1 and consists of eight steps. In this section of the paper, the description and mathematical definition of steps are given. All symbols used in the equations throughout this section are summarized in Table 1, along with their corresponding types.

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Table 1. Mathematical notation used in the BELT architecture.

https://doi.org/10.1371/journal.pone.0354976.t001

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Fig 1. The BELT architecture pipeline.

The framework consists of eight steps organized into three phases: (1) Prior phase (Steps 1-3): Prior data collection, prior model training, and compression–decompression pair training. These components are embedded in the device during production. (2) Adaptation phase (Steps 4-7): New EEG data are compressed and transmitted to the cloud (Step 4), stored and combined with existing user history (Step 5), used for posterior model training (Step 6), and the personalized posterior model is transferred back to the device (Step 7). (3) Update phase (Step 8): Optional continuous updates with explicit user consent, balancing personalization with privacy and scalability. Mathematical definitions for each step are provided in the accompanying text.

https://doi.org/10.1371/journal.pone.0354976.g001

The first step involves collecting prior data. This is a critical stage, and we emphasize its importance as fundamental to the realization of BCI technologies. Therefore, we dedicate a distinct step exclusively to this process. We denote EEG signals as and the user’s target intention—referred to as the symbol or message in telecommunication terminology—as y. The complete set of prior data is represented by and is defined in (1) where N is the total number of signal segments in prior dataset.

(1)

With the prior data collected, the next step is to construct the prior model. However, before model training, we emphasize the importance of prior data augmentation, as it has been shown to yield a non-negligible improvement in final classification accuracy. For example, Fahimi et al. used Deep Convolutional Generative Adversarial Networks (DC-GANs) to improve classification accuracy by 3.57% in motor imagery (MI) tasks [37]. Similarly, Al-Saegh et al. applied CutCat [38] —a technique that cuts and concatenates EEG signals from inter- and intra-subject trials—and demonstrated improved performance with smaller datasets. Another study adapted SpecAugment, a data augmentation technique originally developed for speech recognition, to steady-state visually evoked potentials (SSVEP) and reported improved classification performance [39]. Therefore, we incorporate data augmentation into the framework and denote the augmented dataset as .

Using the augmented data, we train the prior model. This model receives EEG input and estimates the corresponding target symbol . Following telecommunication terminology, we refer to this model as the detector, denoted by D, as defined in (2):

(2)

Accordingly, the optimization objective to find the optimal prior model is expressed in (3). This is a probabilistic minimization problem, where denotes the parameter space of the detector D. The term as condition implies that , and this abstraction is used for readability and brevity.

(3)

The next step is to find the compression pair denoted by (Comp, Decomp). Comp will be applied over EEG data and gives us the compressed data as shown in (4) and later by applying the decompressor on , we get the decompressed signal depicted in (5). However, for , we will prefer to use the reconstructed term instead of decompressed, for better mathematical formulation.

(4)

(5)

The detector plays a crucial role in the development of the task-aware compression and decompression pair, as it is required for computing the task-aware penalty. The overall optimization objective is shown in (6). Solving this optimization problem gives us Comp and Decomp by simultaneously minimizing and which represent the data reconstruction loss and the task-specific compression penalty, respectively. The scalar j serves as a trade-off parameter between reconstruction fidelity and task relevance. and are compressor and decompressor model parameters to be found.

We expect to encourage the compressor to act as a form of task-oriented preprocessing. We expect the optimization to result in a compression pair that preserves task-relevant information (via ) while reconstructing a signal as close as possible to the original in the mean squared error (MSE) sense (via ).

(6)

We define the reconstruction loss as the mean squared error (where E denotes the expectation operator), given in (7), and the compression task penalty as the detector’s error when given the reconstructed EEG signal, shown in (8).

(7)

(8)

In the third step, once the prior model and compression–decompression pair are trained, the device can be programmed accordingly in the production pipeline. Steps 4–7 constitute the user adaptation phase.

In Step 4, the user’s EEG signal is acquired, compressed, and transmitted to the cloud via the internet. In Step 5, the cloud first stores the received data in a dedicated cloud storage space. However, performing posterior training on this newly received data alone may be insufficient and result in overfit due to its limited size. Therefore, the second operation in this step is to query all previously stored data belonging to the same user from the cloud storage database (DB).

It is important to note that all stored data is maintained in compressed format. This design reduces storage costs and enhances data privacy, as the decompressor—required to reconstruct the raw EEG signal—is not deployed on user devices. Additionally, the task-aware penalty is expected to discard redundant and user-agnostic features, thereby improving privacy and promoting a more ethical data-handling approach.

Step 6 involves posterior training, which is performed on the cloud. First, the compressed posterior data is decompressed into reconstructed signals . Then, the posterior model is trained according to the objective in (9). The first term on the right-hand side represents the direct posterior training loss, where the condition is a shorthand notation for . However, training exclusively on this limited posterior data may lead to overfitting, potentially resulting in degraded performance—even for that specific user.

To address this, a second regularization term is introduced. This term acts as a constraint by referencing the prior dataset, preventing the model from deviating too far from generalizable features. The scalar is a balancing factor; when the user-specific dataset is sufficiently large, a smaller value of may lead to improved personalization without overfitting.

Once trained, the resulting personalized model is denoted as .

(9)

It is important to note that the prior model is trained on augmented data and is also evaluated on raw EEG signals . In contrast, the posterior model is fine-tuned using decompressed data and thus is optimized for evaluation on reconstructed signals , rather than raw data. This distinction justifies the use of instead of in the left-hand side of the optimization objective in (9).

There are two approaches for deploying the posterior detector on the device:

1. Evaluate on raw data : Since the reconstruction loss in (6) forces the decompressed data to resemble the raw input, it is feasible to apply the posterior detector directly on raw signals. The trade-off between reconstruction fidelity and task-specific alignment is controlled by the factor j. In this scenario, the device uses as a suboptimal approximation of the posterior detector.
2. Evaluate using the optimal posterior detector : This approach resolves the sub-optimality by explicitly passing the raw input through the learned compression–decompression pipeline before detection. The formulation is given in (10). Here, the task-aware penalty effectively acts as a preprocessing objective, which may improve classification accuracy. However, this setup requires deploying the decompressor on the device, thereby revealing its parameters and compromising the privacy benefits discussed earlier.

(10)

Therefore, we recommend adopting the first approach for public applications, where privacy and scalability are priorities. In contrast, the second approach is more suitable for private, controlled, and limited-use cases where maximizing accuracy is critical. This distinction mirrors the paradigm of public cloud versus private cloud in conventional cloud computing frameworks.

Finally, the trained posterior model weights are transferred to the device and stored in its persistent memory. As a result, by the end of Step 7, the personalized posterior model becomes available locally on the device for real-time inference.

Even with the posterior model deployed, further improvements remain possible. However, to uphold ethical and privacy standards, explicit user consent is required before initiating additional updates, as illustrated in Step 8 of Fig 1. If the user agrees to participate, the system re-enters the adaptation cycle starting from Step 4, enabling continuous refinement of the posterior model.

The key characteristics of the proposed architecture are outlined below:

1. The architecture adopts a Bayesian perspective, emphasizing the importance of both the prior and posterior models. The prior model is not merely a pre-training artifact—it plays a vital role in device setup, connectivity, and post-factory deployment.
2. A Cloud-Edge architecture is targeted, which we consider a promising paradigm for BCI systems. In this design, the cloud handles computation-heavy and storage-intensive tasks, while the edge device is responsible for data compression and real-time model evaluation.
3. The use of lightweight models with transferrable weights is emphasized, considering that the evaluation is performed on embedded systems with limited computational resources.
4. Task-aware data compression is a key component, both for enhancing efficiency and for offering a degree of privacy by minimizing exposure of user-specific raw data—thereby contributing to the resolution of ethical challenges.

Therefore, we designate this architecture as Bayesian Edge-cloud architecture with Lightweight classification and Task-aware compression (BELT).

Model

Although the BELT architecture provides a conceptual framework for addressing key challenges in current BCI systems, it is not directly deployable without practical instantiation. In this section, we present our proposed implementation within the BELT architecture, built upon deep learning principles. Given the emphasis on lightweight design, we refer to this model as the BELT-lite model.

Despite being deep-learning-based, the BELT-lite model is optimized for embedded systems and is suitable for resource-constrained environments. An overview of the model is provided in Fig 2. As illustrated, we adopt an autoencoder architecture for data compression. The detector module consists of four core components: LTI time filters, linear spatial filters, a Network Tuning Block (NTB), and a dot-product classifier. The remainder of this section provides a detailed explanation of the detector design.

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Fig 2. Overview of the BELT-lite model.

The model consists of two main subsystems: a detector (bottom) for classification and an autoencoder (top) for data compression. The detector is optimized for embedded deployment and comprises four components: (i) linear time-invariant (LTI) temporal filters that extract frequency-specific features, (ii) linear spatial filters that combine information across channels, (iii) a Network Tuning Block (NTB) that computes log-power features and enables efficient two-phase training, and (iv) a lightweight dot-product classifier. The autoencoder compresses EEG signals for efficient edge–cloud transmission and can be used independently when compression is required. Together, these components realize a lightweight instantiation of the BELT architecture suitable for resource-constrained environments.

https://doi.org/10.1371/journal.pone.0354976.g002

Implementation

To support reproducibility and address the well-documented challenge of re-implementation in BCI research, we provide the complete source code for the BELT framework. The implementation is archived and publicly available at: https://github.com/adanayi/BELT.

Cross validation strategy.

To ensure statistical reliability and reproducibility, we fixed the random seed before any data splitting. Shuffling is essential in this dataset because each subject’s recordings span five sessions, and later segments may be more informative as subjects improve with visual feedback. Standard k-fold splits that preserve session order could unintentionally bias certain folds; shuffling yields k independent realizations of the MI-EEG process and mitigates this risk.

We employ two complementary cross-validation (CV) strategies, each serving a distinct evaluation goal.

Subject-dependent 10-fold CV (full prior training): All 9112 segments from all 18 subjects are pooled, shuffled, and randomly split into 10 folds, each containing approximately 90% training and 10% validation segments. This procedure is repeated identically for every experiment, using the same pre-computed fold assignments. Per-subject accuracy is then computed on the validation segments belonging to each subject. Because training and validation folds may contain different segments from the same subject, this strategy evaluates the model’s capacity to fit the population under identical training conditions, not its ability to generalise to completely unseen subjects. It is used for all comparisons of architectures, augmentation levels, and compression methods, where the primary interest is relative performance.

Leave-one-subject-out with repeated folds (new-subject prior training): To explicitly measure generalisation to new users, we conduct a separate experiment in which one subject is held out entirely. The prior model is trained on data from the remaining 17 subjects, and the held-out subject serves exclusively as the validation set. To obtain robust performance estimates despite the small per-subject sample size, this training-validation split is repeated 10 times for each held-out subject, using different random shuffles of the 17 subjects’ data (still under the fixed random seed for consistency). This yields a mean and standard deviation of the prior accuracy for each subject when treated as unseen. Posterior fine-tuning is subsequently performed using only the held-out subject’s data, mirroring a real-world onboarding scenario.

In both strategies, the validation segments are strictly excluded from the training set in each fold, so there is no data leakage. The term validation accuracy throughout the paper refers to the metric computed on these held-out segments.

Fig 3 summarises the complete analysis pipeline from raw data to statistical inference, highlighting both CV branches.

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Fig 3. Complete data analysis pipeline.

The flowchart illustrates the end-to-end experimental workflow from raw data to statistical inference, including dataset combination, segmentation, cross-validation, evaluation scenarios (full training and new-subject testing), posterior fine-tuning, and statistical testing methodology. Details of each stage are provided in the accompanying text.

https://doi.org/10.1371/journal.pone.0354976.g003

Detector.

The detector was implemented using the Keras framework [45]. The network input is a tensor of shape , where denotes the variable batch size. The first layer applies LTI time filtering, implemented as a grouped Conv1D layer with 9 kernels and a groups parameter of 3. This configuration yields 3 filters per EEG channel (3 channels total). The kernel size is 25 samples, corresponding to at a sampling frequency of . Using ‘same’ padding, this layer outputs a tensor of shape .

Following this, the linear spatial filtering block is another Conv1D layer with 16 kernels of size 1 sample. Both the LTI time and spatial filter layers have no bias terms and employ linear (identity) activation functions. Consequently, the output of the spatial filtering block has shape , which is then passed to the Network Tuning Block (NTB).

The NTB begins with an element-wise square operation defined as

(11)

followed by a 1D average pooling layer, and finally a logarithmic transform given by

(12)

where is set to 10⁻⁸ to ensure numerical stability.

The average pooling layer uses a window size of 20 samples with a stride of 13 samples, resulting in smoothed power estimates over approximately frames with overlap.

The choice of signal power as a classification feature is motivated by findings that the power in the mu rhythm and central bands conveys MI information [8,46].

As shown in our prior work [13], this log-power structure enables a two-phase training procedure: during early stages with larger errors, backpropagation modifies the weights of preceding layers (prior training phase), whereas in later stages with smaller errors, backpropagation is effectively suppressed to minimize changes in these layers and focus training on the subsequent classifier layers (posterior training phase). This behavior aligns well with the intended training regime of the BELT-lite model.

This log-power structure fulfills the two additional objectives outlined for the NTB. While the use of log power is common in MI-BCI literature, its effectiveness is often empirically noted without a clear explanation. Our analysis clarifies that the superior performance stems from the fulfillment of these specific training objectives. Although integrating more recent physiological insights into the NTB may further enhance performance, this work focuses on emphasizing the importance of these objectives rather than exploring alternative architectures.

It is worth mentioning that allocating three LTI filters per channel is also motivated by findings regarding the rhythm [8] and central sub-bands [46] in MI classification. Accordingly, two of the filters are expected to approximate bandpass filters for the and frequency bands, while the third filter provides an additional degree of freedom for data-driven adaptation.

The use of overlapping frames for power smoothing is motivated by the need to reduce the number of classifier parameters in small-dataset scenarios—such as ours—to mitigate overfitting during training.

The output of the NTB is a tensor of shape , which is then flattened into a vector of shape before being fed into the classifier’s first layer. Through the combined processing of the LTI filters, spatial filters, and NTB, the input signal size is effectively reduced to approximately 40.5% of its original dimensions ().

The classifier itself is a two-layer perceptron comprising 4 neurons in the first layer and 2 neurons in the second. The first layer uses a ReLU activation function, while the second layer employs a sigmoid activation, making it suitable for one-hot encoded classification tasks.

Given the limited size of the dataset, we employed several strategies to mitigate overfitting. Batch normalization layers were applied both before and after the NTB. Additionally, an l₂ regularization term with a penalty coefficient of 0.01 was applied to the first dense layer of the classifier. A dropout layer with a dropout probability of 0.2 was inserted between the classifier’s dense layers.

We contend that the most complex layer in the model is the first dense layer of classifier, where each neuron connects to 1216 inputs from the previous layer. This high connectivity increases the risk of overfitting given the limited dataset. However, as discussed earlier, this layer is intended to learn the signal space or domain transformation; thus, we allow it substantial representational capacity while relying on l₂ regularization to control overfitting.

Since the final classifier layer performs a distance-like measurement in the transformed space, we prefer the preceding layer to maintain expressive power rather than excessive compression to preserve generalization. Consequently, the dropout layer placed between the classifier layers plays a critical role in balancing expressiveness and regularization.

The structure of the detector is summarized in Table 2. The layers are listed in order, along with their Keras naming conventions, to facilitate reproducibility and ease of reimplementation by the reader.

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Table 2. BELT-lite detector layer structure.

https://doi.org/10.1371/journal.pone.0354976.t002

For prior detector training, we used batch size 32, learning rate 10⁻³, and 100 epochs with 10-fold cross-validation (the same folds were used across all levels).

Compressor.

We have used an AutoEncoder for the compression task. While AutoEncoders are already widely adopted in EEG signal processing, the value of our approach lies in its alignment with the practical-friendly architecture of BELT via BELT-lite. Specifically, we rely on a convolution-only structure, which, as discussed earlier, is well-suited for embedded systems and real-time cloud applications. We emphasize that the current AutoEncoder design is not intended as an optimal solution, but rather as a functional and extensible starting point within the scope of this work.

The Encoder network consists of three Conv1D layers. The first layer uses 32 kernels of size 3 and stride 1, enabling it to extract 32 short temporal-spatial patterns without compressing the time dimension. The second layer has 16 kernels of size 25 (i.e., ) and a stride of E₁, introducing compression in the time domain. The third layer applies N kernels of size 2E₂ with stride E₂, further compressing the temporal axis. Notably, the number of parameters in this final layer grows with N, allowing greater expressivity when compression is high.

Letting C denote the number of EEG channels, the overall compression ratio CR is calculated as:

(13)

For instance, with C = 3, N = 9, E₁ = 5, and E₂ = 2, we achieve a compression ratio of CR = 3.33. In contrast, we checked the ZIP standard compression and it yields a much lower ratio of 1.04 for this dataset while being unsuitable for real-time use, and being inefficient for implementation on low-cost embedded systems. Although our method is lossy, unlike ZIP, this is not inherently a drawback—it necessitates evaluating the impact of compression on final task performance.

The Decoder consists of two deconvolution (Conv1DTranspose) layers. The first layer uses 32 kernels of size and stride , effectively upsampling the compressed representation back to the original temporal resolution. The second layer applies C kernels of size 3 to reconstruct the multi-channel EEG signal. The first layer performs the main decompression, while the second maps the output to the original channel dimensionality.

Kernel size in the first layer is deliberately set proportional to the compression parameters, as higher compression typically demands greater capacity for accurate reconstruction. All encoder and decoder layers use linear activation, and unlike the classifier, we allow bias terms in all layers. This added complexity is acceptable because (1) compression is not always required in BELT, and (2) when compression is active, classification is bypassed, allowing us to tolerate this trade-off for improved reconstruction quality.

Comparative baseline model: EEGNet

To evaluate the computational efficiency and accuracy of BELT-lite, we selected EEGNet [47] as a baseline model. EEGNet is a compact convolutional neural network specifically designed for EEG-based brain–computer interfacing. It employs depthwise and separable convolutions to achieve high classification performance with a minimal parameter count ( parameters), making it a widely adopted benchmark for lightweight BCI decoding architectures. Its balance of accuracy and efficiency makes it an appropriate reference point for assessing BELT-lite’s suitability for embedded deployment.

While EEGNet’s inference latency is acceptable for many laboratory setups, on ultra-low-power platforms such as the ARM Cortex-A7 it still consumes significant CPU time; further reduction is desirable for prolonged battery-operated use.

For all pairwise comparisons between BELT-lite and EEGNet, we employed the Wilcoxon signed-rank test as the primary statistical measure. This nonparametric test was chosen because it makes no assumptions about the normality of the underlying data distribution and is appropriate for paired observations (same subjects or same experimental runs). For accuracy comparisons, the test was applied to the mean accuracies of each subject across 10 cross-validation folds. For runtime comparisons, we performed 100 independent measurement runs, each consisting of 100 consecutive inferences, and used the Wilcoxon test to compare the resulting latency distributions. All tests were two-tailed with a significance threshold of . Results are reported as mean standard deviation unless otherwise noted, and effect sizes are discussed in the context of practical significance.

Prior detector

We trained the prior detector on all 18 subjects using the augmentation scheme described in the Data Augmentation subsection. Table 3 reports the per-subject accuracy (mean std) for each augmentation level.

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Table 3. Prior model accuracy across augmentation levels.

https://doi.org/10.1371/journal.pone.0354976.t003

To assess whether augmentation significantly influences performance, we conducted a Friedman test on the mean accuracies across all subjects, treating each fixed level (0–4) as repeated measures. The test indicated a significant overall effect of augmentation intensity (, p = 0.017). A Nemenyi post-hoc test was then performed to identify which specific conditions differed.

The pairwise comparisons revealed that significantly outperformed the baseline (adjusted p = 0.019), and showed a borderline significant improvement (p = 0.048). No other fixed augmentation level differed significantly from the baseline (all p > 0.05), and none of the non-zero levels () differed significantly from each other (adjusted in all cases).

These findings lead to two nuanced conclusions:

1. Simply applying a fixed augmentation level across all subjects does not guarantee a statistically significant improvement over using only real data. While levels (and, to a marginal extent, ) provided reliable gains, other intensities – particularly and – did not reach significance. The variability across folds and subjects dampens the effect of many augmentation strengths, so the choice of intensity matters.
2. There is no evidence that any single fixed augmentation level is universally superior; the optimal intensity likely varies per subject. The significant improvement seen with suggests that moderate augmentation is beneficial, and subject-specific tuning remains a promising direction for future work.

Notably, even the best fixed augmentation level () remained below the highest single-subject accuracy observed in this study (e.g., subject S4 achieved ). This underscores that inter-subject variability remains a more fundamental challenge than the choice of augmentation intensity, and that real-world BCI systems will still require careful per-subject calibration.

Posterior detector

The prior detector is then fine-tuned individually on each subject’s own data to get the posterior detector. While this follows the standard train-then-fine-tune paradigm in transfer learning and operates on point estimates rather than full probability distributions, we retain the terminology of prior and posterior to suggest the possibility of extending this framework into a fully Bayesian formulation in future work. Although this is not true Bayesian inference, the terminology anticipates the integration of Bayes’ rule as envisioned in the BELT architecture.

Please note that this fine-tuning approach does not explicitly implement the optimization defined in (9). However, the selection of training epochs and learning rates during the prior and posterior phases can be interpreted as implicit controls similar to the factor, balancing the influence of subject-specific data against general prior knowledge. Accordingly, no fixed numeric value is assigned to in our experiments. In our setup, the prior model is trained with a learning rate of 10⁻³ on data from all 18 subjects (or 17, depending on the experiment), whereas posterior fine-tuning uses a higher learning rate of on a single subject’s data. The drastically reduced dataset size inherently limits the influence of the subject-specific loss and, together with the learning rate, provides a regularising effect analogous to a small .

Table 4 reports the posterior model accuracies for all 18 subjects under two prior augmentation conditions: no augmentation () and moderate augmentation (). Fine-tuning used the same fixed prior checkpoint obtained from training with the respective augmentation level. To assess whether augmentation during prior training influences posterior performance, we applied a Wilcoxon signed-rank test to the per-subject accuracies. The test revealed a significant difference between the two conditions (W = 30.0, p = 0.0139). Concretely, fine-tuning from the moderately augmented prior yielded a mean posterior accuracy of 84.3% across all subjects, compared to 82.6% for the no-augmentation prior — an average improvement of approximately 1.7 percentage points. On Dataset A the benefit is more pronounced: mean accuracy rose from 77.4% to 80.6%, while on Dataset B the means were identical (87.9%). This result shows that even a modest amount of synthetic prior data can provide a statistically reliable benefit for subject-specific adaptation, although the effect varies by dataset.

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Table 4. Posterior model accuracy across augmentation levels.

https://doi.org/10.1371/journal.pone.0354976.t004

Once again, we emphasize that our use of the term posterior does not refer to Bayesian posterior in the strict sense. However, we argue that a two-stage approach—either explicitly Bayesian or inspired by Bayesian reasoning—is essential. Both models serve distinct purposes: the prior model is useful for initial deployment or onboarding new users, while the posterior model is crucial for long-term use, as subject-specific fine-tuning significantly boosts accuracy.

Comparing prior and posterior results (Table 3 vs. Table 4) confirms that posterior training is essential for achieving high accuracy and should not be omitted in practical applications. The substantial gap between prior and posterior accuracies across all subjects underscores the necessity of user-specific adaptation. This is also shown in Fig 4.

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Fig 4. Mean prior and posterior classification accuracy for each subject ().

Bars represent mean accuracy across 10 cross-validation folds, with error bars indicating standard error of the mean (SEM). Results are shown for all 18 subjects (Subjects 1–9 from Dataset B, Subjects 10–18 from Dataset A). Posterior fine-tuning consistently improves accuracy across every subject, with gains ranging from approximately 5 to 25 percentage points. Notably, Subject 4 (Dataset B) approaches near-perfect accuracy () after adaptation, while Subject 12 (Dataset A) reaches , demonstrating the effectiveness of subject/user training. The substantial gap between prior and posterior accuracies across all subjects underscores the necessity of user-specific adaptation in practical BCI deployment.

https://doi.org/10.1371/journal.pone.0354976.g004

To formally assess the value of posterior training relative to prior models, we conducted a Friedman test across four conditions:

• Prior ()
• Prior ()
• Posterior ()
• Posterior ()

The test revealed a highly significant overall difference (, ). Fig 5 presents the Nemenyi post-hoc results as a significance heatmap. Three key findings emerge:

1. Both posterior conditions significantly outperform both prior conditions (all adjusted p < 0.01, see heatmap). This confirms that subject-specific fine-tuning is essential for maximizing accuracy, regardless of the prior augmentation level.
2. The two prior conditions ( and ) do not differ significantly from each other (p > 0.05). While the dedicated augmentation analysis in previous subsection indicated that some augmentation levels (e.g., ) can significantly improve prior performance, the more limited difference between and is not detectable in this four-condition comparison after correction for multiple testing.
3. The two posterior conditions ( and ) did not differ significantly in the Nemenyi post-hoc test (p > 0.05). This appears to contradict the earlier Wilcoxon test restricted to the two posterior groups (which gave p = 0.0139), but the discrepancy arises because the Nemenyi test applies a conservative correction for all pairwise comparisons across the four conditions. The effect of prior augmentation on posterior performance, while detectable in a focused pairwise comparison, is modest and does not remain significant under this broader correction. We therefore conclude that once fine-tuning is applied, the choice of prior augmentation level has at most a small benefit, which should be weighed against the simplicity of using no augmentation.

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Fig 5. Nemenyi post-hoc test results comparing prior and posterior models under different augmentation conditions.

The heatmap compares four conditions: Prior (), Prior (), Posterior (), and Posterior (). Each colored cell indicates that the row condition does not significantly outperform the column condition (p < 0.05) based on the Nemenyi test following a significant Friedman test (, ). Key findings: (i) both posterior conditions significantly outperform both prior conditions, confirming that subject-specific fine-tuning is essential; (ii) the two prior conditions do not differ significantly; (iii) the two posterior conditions do not differ significantly after correction for multiple comparisons, though a direct pairwise Wilcoxon test indicated a modest significant difference (p = 0.0139); thus the effect of prior augmentation on posterior accuracy is small and not robust in all statistical contexts.

https://doi.org/10.1371/journal.pone.0354976.g005

To illustrate the findings, Fig 6 shows the mean prior and posterior accuracies across all 18 subjects for the two augmentation levels and , with error bars representing the standard error of the mean (SEM). The figure confirms that posterior accuracies consistently exceed prior accuracies for both augmentation levels, consistent with the significant effect of fine-tuning reported above.

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Fig 6. Mean prior and posterior accuracies across all 18 subjects for augmentation levels and .

Error bars indicate standard error of the mean (SEM). Posterior accuracies substantially exceed prior accuracies for both conditions, while the difference between the two augmentation levels is small and discussed in the text.

https://doi.org/10.1371/journal.pone.0354976.g006

Training optimization

In order to reduce the computational load on the cloud, we propose to partially limit fine-tuning by freezing parts of the model. This section presents the implementation of this approach along with its results. Before presenting the results, we highlight the potential advantages of freezing parts of the model during training:

1. Reduced computational load: Fewer parameters are updated, leading to lower back-propagation overhead, which reduces processing demand on cloud infrastructure.
2. Lower memory requirements: The end device requires less programmable memory, as it no longer needs to store the coefficients of the LTI filter layers.
3. ASIC compatibility: Fixed LTI filter coefficients allow for hardware implementation using ASICs, which can significantly improve efficiency.
4. Improved generalization with limited data: A simpler model, resulting from partial freezing, is less prone to overfitting when the posterior training data is scarce. While this advantage may diminish with larger datasets, in practice, the posterior data must be collected during the initial user setup. Therefore, minimizing the required data collection enhances the user experience.

Frozen LTI filter layers.

As a first step, we freeze only the LTI filters layer of the model, allowing the spatial and classifier layers to be fine-tuned. This choice is motivated by the fact that LTI filters are generic task-dependent temporal feature extractors and may not require subject-specific adaptation, whereas spatial and classifier layers can benefit from personalization. By freezing only the LTI layers, we aim to balance model adaptability with computational efficiency.

The results are shown in Table 5. A Wilcoxon signed-rank test comparing the two prior augmentation levels ( vs. ) revealed a significant improvement when fine-tuning from the augmented prior (W = 7.0, ). Concretely, the dataset-wise means increased from 86.4% to 87.2% on Dataset B and from 75.5% to 78.8% on Dataset A.

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Table 5. Posterior accuracy with frozen LTI filter fine-tuning.

https://doi.org/10.1371/journal.pone.0354976.t005

Classifier only.

In the next step, both the LTI filters and the spatial linear filters are frozen during posterior training, allowing only the classifier layers to adapt. This configuration aims to further reduce the computational load while evaluating whether the remaining trainable layers can compensate for reduced flexibility. The results are presented in Table 6.

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Table 6. Posterior accuracy with classifier-only fine-tuning.

https://doi.org/10.1371/journal.pone.0354976.t006

A Wilcoxon signed-rank test between the two prior augmentation levels ( vs. ) revealed a significant improvement when fine-tuning from the augmented prior (W = 7.0, ). Concretely, the dataset-wise means increased from 85.9% to 86.3% on Dataset B and from 74.5% to 76.2% on Dataset A.

Summary of fine-tuning depth

To compare the three posterior adaptation strategies, we fixed the prior augmentation level at —the intensity that yielded the highest mean accuracy in the previous analyses—and evaluated each subject’s accuracy after full fine-tuning, frozen LTI, and classifier-only training. Fig 7 shows the mean accuracy for Dataset B and Dataset A under all four conditions, including the prior model for reference. Error bars denote the standard error of the mean (SEM) across subjects.

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Fig 7. Effect of fine-tuning depth on posterior accuracy.

Paired bars show mean accuracy across 18 subjects for BCI Competition IV-2a and IV-2b datasets. All posterior results use the augmented prior (). The prior bar is included for visual reference. Error bars indicate SEM. A Friedman test on the three posterior conditions reveals a significant effect of fine-tuning depth (, ); full fine-tuning significantly outperforms classifier-only training, while frozen LTI does not differ significantly from full fine-tuning (see Fig 8).

https://doi.org/10.1371/journal.pone.0354976.g007

A Friedman test on the three posterior conditions across all 18 subjects confirmed a significant effect of fine-tuning depth (, ). Nemenyi post-hoc tests (Fig 8) revealed that full fine-tuning significantly outperforms classifier-only fine-tuning (adjusted ), while the frozen LTI configuration does not differ significantly from full fine-tuning (p = 0.16). Notably, frozen LTI is significantly better than classifier-only training (p = 0.013).

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Fig 8. Nemenyi post-hoc test results for fine-tuning depth.

The heatmap compares three posterior conditions (all using ): full fine-tuning, frozen LTI layers, and classifier-only fine-tuning. Colored cells indicate that the row condition significantly outperforms the column condition (p < 0.05) after a significant Friedman test (, ). Full fine-tuning significantly outperforms classifier-only (); frozen LTI is not significantly different from full (p = 0.16) but significantly better than classifier-only (p = 0.013).

https://doi.org/10.1371/journal.pone.0354976.g008

These results indicate that freezing only the LTI filters preserves most of the accuracy of full fine-tuning, whereas restricting adaptation to the classifier alone incurs a statistically significant but practically modest penalty of 2–5 percentage points. Given the substantial computational savings—classifier-only fine-tuning updates only a fraction of the network parameters—this trade-off is acceptable for resource-constrained deployment scenarios, while frozen LTI provides an intermediate configuration that is statistically indistinguishable from the full model.

New subject performance

In this experiment, we evaluate the architecture’s ability to generalize to new and unseen subjects. Due to limited data, we adopt a leave-one-subject-out approach: each time, one subject is excluded from the prior model training, and the system is later fine-tuned (posterior) using only the excluded subject’s data. Additionally, to better understand the generalization behavior, we measure the performance of subject 4 (as a good performing subject due to Fig 4) across all trained models. To reduce complexity and save time, we disable the data augmentation step and report results only for .

The performance of the prior model is reported in Table 7 and depicted in Fig 9. To quantify the cost of encountering a new subject, we compared each subject’s prior accuracy when treated as unseen (from the leave-one-subject-out procedure) against their own prior accuracy when they were part of the full prior training, as reported in Table 3 (column ). A Wilcoxon signed-rank test on these 18 paired observations revealed a significant drop in performance (W = 35.0, p = 0.027, N = 18). The mean accuracy decreases were 3.3 percentage points for Dataset B and 1.5 percentage points for Dataset A. This confirms that excluding a subject from the prior training introduces a small but statistically significant penalty, even though subsequent fine-tuning can partially compensate, as will be discussed.

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Table 7. Performance of prior models in the new subject test in percent ( format).

https://doi.org/10.1371/journal.pone.0354976.t007

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Fig 9. Comparison of prior model accuracy on seen vs. unseen subjects across 18 subjects.

Bars represent mean accuracy with error bars indicating standard error of the mean (SEM). “Seen” refers to models trained with the target subject’s data included (results from Table 3), while “Unseen” refers to leave-one-subject-out evaluation where the target subject was excluded during prior training. Results show a statistically significant accuracy drop for unseen subjects (Wilcoxon signed-rank test: W = 35.0, p = 0.027, N = 18), with mean decreases of 3.3% for Dataset B and 1.5% for Dataset A. This demonstrates the generalization limitations of BCI models and underscores the necessity of subject-specific data exposure even in the prior training phase.

https://doi.org/10.1371/journal.pone.0354976.g009

We do not make a conclusion regarding the effect of each individual subject on the model at this point, but we strongly indicate the necessity of having larger prior datasets. We also expect that more generalized models with fewer parameters can reduce the dependency on certain subjects beyond the current level although they open the challenge of under-fitting.

The results for posterior training are presented in Table 8 and illustrated in Fig 10. On average, accuracy decreased by 1.1% for Dataset B and, surprisingly, increased by 0.8% for Dataset A when subjects were unseen during prior training and subsequently fine-tuned in the posterior phase. However, a Wilcoxon signed-rank test revealed that these differences are not statistically significant (W = 70.0, p = 0.523). This indicates that posterior training performance does not degrade significantly for new subjects—a desirable outcome that supports the robustness of the proposed approach.

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Table 8. Performance of posterior models in the new subject test in percent ( format).

https://doi.org/10.1371/journal.pone.0354976.t008

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Fig 10. Comparison of posterior model accuracy on seen vs. unseen subjects across 18 subjects.

Bars represent mean accuracy after posterior fine-tuning, with error bars indicating standard error of the mean (SEM). “Seen” refers to models where the target subject’s data was included in prior training before fine-tuning; “Unseen” refers to models where the target subject was excluded during prior training and fine-tuned only on their own held-out data. On average, unseen subjects showed a 1.1% decrease in accuracy for Dataset B and a 0.8% increase for Dataset A compared to seen subjects. A Wilcoxon signed-rank test revealed that these differences are not statistically significant (W = 70.0, p = 0.523), indicating that posterior fine-tuning is robust to new subjects and does not degrade significantly even when prior exposure is absent—a desirable outcome supporting the practical viability of the BELT architecture.

https://doi.org/10.1371/journal.pone.0354976.g010

Compressor

We implemented the AutoEncoder with different architectural parameters. Denoting compression configuration as , we systematically varied N, E₁, and E₂ across (1, 5, 9, 13), (2, 5, 10, 20), and (2, 5), respectively, yielding 32 combinations in total. For each configuration, an AutoEncoder was trained with a learning rate of 10⁻³ for 50 epochs using MSE loss and the ADAM optimizer. The comparison evaluation metric is the classification accuracy of the reconstructed signal () using the prior detector, with the reported accuracy drop representing the average across all k-folds. Importantly, the AutoEncoder training was performed on data from all subjects, since the focus here is on the impact of compression rather than subject transferability.

As shown in Fig 11, configurations with N = 1 consistently result in severe accuracy degradation. This outcome is expected, as collapsing all spatial information into a single mixed channel eliminates task-relevant features, forcing the optimization to prioritize reconstruction quality under the MSE penalty irrespective of classification requirements. By contrast, configurations such as (N/2/2) and (N/5/2) show minimal or no accuracy loss for N = 9 and N = 13, with occasional slight improvements observed.

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Fig 11. Compression configuration comparison.

Positive values indicate accuracy drops (worse performance after compression), while negative values indicate accuracy improvements. An autoencoder was trained for each configuration , and the reconstructed signal was evaluated using the prior detector. The accuracy drop is defined as the change in detector performance between the original signal and the reconstructed signal ; all changes shown are therefore attributable to the compression–reconstruction process. Parameters and were varied, yielding eight configurations per N value ().

https://doi.org/10.1371/journal.pone.0354976.g011

Therefore, we adopt the (9/5/2) configuration (with CR = 3.3 and negligible accuracy gain) as the baseline for subsequent experiments. As discussed eailier, a parameter j was defined to control the trade-off between reconstruction fidelity and task accuracy. Based on this, we designed three model variants:

1. Task-Unaware (TU): j = 0. The model focuses solely on signal reconstruction, without regard to the classification task.
2. Task-Only (TO): . The model disregards reconstruction and optimizes exclusively for classification accuracy during compression.
3. Task-Aware (TA): . The model balances reconstruction and classification objectives, with j determining the trade-off.

A 10-fold experiment was conducted per subject, and average accuracy drops are reported in Fig 12, with error bars representing the standard error of the mean (SEM) across subjects. Prior and posterior detectors without compression serve as baselines.

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Fig 12. Comparison of average accuracy drop for different compression approaches.

TA = Task Aware, TU = Task Unaware (MSE only). F = Full posterior training, C = Classifier-only fine-tuning. Error bars indicate standard error of the mean (SEM) across subjects. Prior models are compared to the detector-only system without compression; posterior models are compared to the posterior model without any compression and with full fine-tuning. Among posterior C models, TU achieves the smallest accuracy drop overall, with a mean reduction of only even under classifier-only fine-tuning—a statistically significant but practically modest penalty (W = 2.0, ).

https://doi.org/10.1371/journal.pone.0354976.g012

Contrary to our initial expectations, the TU model consistently achieved the best overall performance. On prior data, TU outperformed both TO and TA, likely because the larger parameter count of TO (due to chaining the autoencoder and detector) increases overfitting risk, while the multi-objective optimisation of TA introduces additional complexity that may hinder reconstruction quality. For posterior models, TU with full fine-tuning exhibited a negligible accuracy drop relative to the no-compression baseline. Even under the more constrained classifier-only fine-tuning, TU maintained a small average drop of approximately 3%. A Wilcoxon signed-rank test confirmed that this drop is statistically significant (W = 2.0, ), yet the absolute decrease remains modest—about 3% on average—indicating that TU compression remains viable for resource-limited deployment scenarios, such as private clouds where only classifier-side fine-tuning is feasible.

In summary, the TU model demonstrates the following:

1. Minimal degradation of prior model performance, and in some cases slight improvements.
2. An average accuracy drop of less than 0.5% when used with full posterior fine-tuning.
3. A statistically significant but practically small () drop under classifier-only fine-tuning, making it suitable for privacy-assured but resource-constrained private cloud deployments.

These findings highlight that for our experimental setting, a simple reconstruction-based compression (TU) is more effective than task-aware or task-only alternatives, offering an attractive trade-off between accuracy and computational efficiency.

Computational efficiency and embedded suitability

In addition to accuracy, practical deployment of BCI models depends critically on computational efficiency and hardware compatibility. To this end, we benchmarked BELT-lite—a constrained instantiation of the BELT architecture with only 1.65k parameters—against EEGNet [47], a widely adopted lightweight CNN for EEG decoding with 2.23k parameters. While EEGNet serves here as a strong compact baseline, it should be noted that the BELT framework is not tied to a specific feature extractor and could in principle integrate EEGNet-style blocks if desired.