A technical solution is described for implementing a computer-executed system of association memory matrices to replace the proximal layers of a convolutional neural network (CNN). An example method includes configuring one Associative Memory Matrix (AMM) for each configured layer in the CNN. This one-to-one conversion method motivates the name to the product: the Joint Proximity Association Template (JPAT) for Neural Networks. The invention is a numerically stable soft-ware based implementation that (1) reduces the long training times, (2) reduces the execution time, and (3) produces bidirectional intra-layer connections and potentially, inter-layer connections as well. The method further includes, potentially, forming a single AMM, from the multiple AMMs corresponding to the multiple and proximal layers of the CNN, in anticipation of the well-known Universal Approximation Theorem.