## 3 Proposed Method
### 1D-CNN Backbone Model  
The convolutional neural network (CNN) has achieved superior performance in many applications among the different deep learning models. A CNN is a type of artificial neural network with two main advantages: local connectivity and weight sharing. These advantages make the (CNN) appropriate for high-dimensional signals such as EEG brain signals. Unlike hand-engineered feature extraction techniques, it automatically learns a rich hierarchy of multi-scale features from the data in an end-to-end manner using optimizers like the stochastic gradient descent (SGD) algorithm and back-propagation algorithm. Different CNN architectures have been proposed in the literature. We proposed a simple and lightweight 1D CNN model motivated by the CNN architectures proposed in [30; 31], as shown in Figure 2; its architecture depends on the pyramid approach. Two important factors in the design of the architecture of a CNN model are width (the number of filters in Conv. layers) and depth (the number of learnable layers in a CNN model). The common approach is to increase the width with increasing depth; it excessively increases the number of learnable parameters, leading to overfitting for applications where we encounter a scarcity of annotated data; it also gives rise to a large number of redundant features, which unnecessarily adds to the complexity of the model. In the pyramid approach, the width decreases as the depth of the network increases. It has two advantages: (i) firstly, it keeps the number of learnable parameters small, allowing the model to train with a limited amount of data, avoiding overfitting; (ii) it inherently applies feature selection and removes the redundant features. For these reasons, we designed a 1D CNN based on the pyramid approach; the model's width decreased from 16 (filters) to 4 (filters); see Figure 2.  
The model consists of five temporal convolutional blocks (\(TConvB\)), one spatial convolutional block (\(SConvB\)), four max-pooling layers, and two fully connected layers (FC). Each \(TConvB\) and \(SConvB\) block consists of three layers: batch normalization, 1D temporal/spatial convolutional, and ReLU layers. The first \(TConvB\) implements the mapping \(\phi_{1}:\ R^{\mathbb{C}\times T}\to R^{\mathbb{C}\times T\times 16}\) that takes input EEG trial \(x\in R^{\mathbb{C}\times T}\) as input, filters each of \(C\) channels with each of the 16 filters using temporal convolution, and yields the output \(z^{1}\in R^{\mathbb{C}\times T\times 16}\) i.e., \(\phi_{1}(x,\theta_{1})=z^{1}\), where \(\theta_{1}\) represents the parameters of the filters of this block. Each input channel is decomposed into 16 frequency bands using the temporal filters of size 1 \(\times\) 11. It is equivalent to the  
Figure 2: Backbone 1D-CNN model [Conv-B (no. of filters)]. It consists of five temporal blocks, one spatial convolution block, and two FC layers. spectral decomposition of the input EEG trial \(x\), with a filter bank consisting of 16 filters. Further, the bands of the same frequency across \(C\) channels are linearly combined using \(SConvB\), which uses spatial filters of size \(C\times 1\) for this purpose. In other words, \(SConvB\) implements the mapping \(\phi_{2}\big{(}z^{21},\theta_{2}\big{)}=z^{2}\), where \(\theta_{2}\) denotes the parameters of the filters of this block; this mapping aggregates the frequency bands originating from different brain locations and reveals the correlation between EEG channels. The output \(z^{2}\) is passed to the mapping \(\phi_{3}\big{(}z^{2};\theta_{3}\big{)}=z^{3}\) realized by the second \(TConvB\) block, which reveals the second-order information along the temporal dimension from the fused frequency bands. Then, the output \(z^{3}\) is processed by the mapping \(\psi_{1}\big{(}z^{3}\big{)}=z^{4}\), realized by the first max-pooling layer, which reduces the size of \(z^{3}\) to half by eliminating redundant information.