## 3 Experimental Set-Up  
This paper examines the proposed approach for improving the post hoc interpretability of Deep and Wide convolutional neural networks based on the Class Activation Maps of GradCam++ to characterize the inter/intra-subject variability of the brain motor-elicited potentials. This purpose is addressed with an evaluation pipeline that includes the following stages (see Figure 2): (_i_) Preprocessing and feature extraction of the time-frequency representations from raw EEG data to resemble the FBCSP algorithm and the CWT method. Then, the extracted multi-channel features are converted onto a 2D surface through a topographic interpolation to feed the CNN: (_ii_) Bi-class discrimination of motor-evoked tasks within a D&W CNN framework and estimation of the resulting weighted feature representations through the generalization version of Class Activation Mapping. For simplicity, gray-scale images and a binary classification problem are considered; and (_iii_) Group-level relevance analysis is performed across the subject groups through a CKA projection of the relevant spatial activations obtained from the GradCam++ maps. **Database of Motor Imagery Potentials**  
_GigaScience_ (publicly available at [[http://gigadb.org/dataset/100295](http://gigadb.org/dataset/100295)]([http://gigadb.org/dataset/100295](http://gigadb.org/dataset/100295)) (accessed on 1 August 2021)): This collection holds EEG data obtained from fifty-two subjects (though only fifty are available) according to the BCI experimental paradigm of MI. As shown in Figure 3, the paradigm begins with a fixation cross presented on a black screen within 2 s. Then, a cue instruction appeared randomly on the screen during 3 s to ask each subject to imagine moving the fingers, starting to form the forefinger, and proceeding to the little finger touching each to their thumb. Then, a blank screen appeared at the start of the break, lasting randomly between 4.1 and 4.8 s. For either MI class, these procedures were repeated 20 times within a single testing run. Data were acquired by a 10-10 placement \(C\)-electrode system \(C\!=\!64\) with 512 Hz sampling rates, collecting 100 trials per individual (each one lasting \(T\!=\!7\) s) in two labeled tasks \(\Lambda\!=\!0\)--left hand, or \(\Lambda\!=\!1\)--right hand. **Preprocessing and Feature Extraction of Image-Based Representations**  
At this stage, each raw channel is bandpass-filtered within [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30] Hz using a five-order Butterworth filter. Further, as performed in [44], we carry out a bi-domain short-time feature extraction, namely, using two approaches: continuous wavelet transform and Filter Bank Common Spatial Patterns. In the former extraction method, CWT coefficients provide a compact representation of the EEG energy distribution, resulting in a time-frequency decomposition with components distinct from conventional Fourier frequencies. A feature set of CWT is extracted by using the Complex Morlet function commonly used in the spectral analysis of EEG, fixing the scaling value to 32. According to the second approach, a multi-channel EEG dataset can be mapped to a subspace with a lower dimension, or latent source space, to enlarge the class separation by maximizing its labeled covariance. Here, we set the amount of CSP components as 3\(\Lambda\) (\(\Lambda\!\in\!\mathbb{N}\) is the number of MI tasks), utilizing a regularized sample covariance estimation. For comparison purposes, the parameters of both extraction techniques are adjusted to the set, optimizing the accuracy performance of FBCSP [52]. That is, fixing the sliding short-time window length parameter \(\tau\!=\!2\) s with an overlapping step of 1 s, resulting in \(N_{\tau}\!=\!5\) EEG segments. For implementing the filter bank strategy, the following bandwidths of interest: \(\Delta f\!\in\!\{\mu\!\in\![8;\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\!\!