Electroencephalogram-based brain-computer interface (BCI) has potential applications in various fields, but their development is hindered by limited data and significant cross-individual variability. Inspired by the principles of learning and memory in the human hippocampus, we propose a multi-task (MT) classification model, called AM-MTEEG, which combines learning-based impulsive neural representations with bidirectional associative memory (AM) for cross-individual BCI classification tasks. The model treats the EEG classification of each individual as an independent task and facilitates feature sharing across individuals. Our model consists of an impulsive neural population coupled with a convolutional encoder-decoder to extract shared features and a bidirectional associative memory matrix to map features to class. Experimental results in two BCI competition datasets show that our model improves average accuracy compared to state-of-the-art models and reduces performance variance across individuals, and the waveforms reconstructed by the bidirectional associative memory provide interpretability for the model's classification results. The neuronal firing patterns in our model are highly coordinated, similarly to the neural coding of hippocampal neurons, indicating that our model has biological similarities.