Objective. Brain–computer interfaces (BCIs) decode information from neural activity and send it to external devices. The use of Deep Learning approaches for decoding allows for automatic feature engineering within the specific decoding task. Physiologically plausible interpretation of the network parameters ensures the robustness of the learned decision rules and opens the exciting opportunity for automatic knowledge discovery. Approach. We describe a compact convolutional network-based architecture for adaptive decoding of electrocorticographic (ECoG) data into finger kinematics. We also propose a novel theoretically justified approach to interpreting the spatial and temporal weights in the architectures that combine adaptation in both space and time. The obtained spatial and frequency patterns characterizing the neuronal populations pivotal to the specific decoding task can then be interpreted by fitting appropriate spatial and dynamical models. Main results. We first tested our solution using realistic Monte-Carlo simulations. Then, when applied to the ECoG data from Berlin BCI competition IV dataset, our architecture performed comparably to the competition winners without requiring explicit feature engineering. Using the proposed approach to the network weights interpretation we could unravel the spatial and the spectral patterns of the neuronal processes underlying the successful decoding of finger kinematics from an ECoG dataset. Finally we have also applied the entire pipeline to the analysis of a 32-channel EEG motor-imagery dataset and observed physiologically plausible patterns specific to the task. Significance. We described a compact and interpretable CNN architecture derived from the basic principles and encompassing the knowledge in the field of neural electrophysiology. For the first time in the context of such multibranch architectures with factorized spatial and temporal processing we presented theoretically justified weights interpretation rules. We verified our recipes using simulations and real data and demonstrated that the proposed solution offers a good decoder and a tool for investigating motor control neural mechanisms.