This work introduces a novel generative continual learning framework based on self-organizing maps (SOMs), a brain-inspired natural computing model, extended with learned distributional statistics and encoder--decoder models for class incremental continual learning. These extended SOMs enable exemplar-free replay with fixed-capacity statistical memory, eliminating the need to store raw data samples. For high-dimensional input spaces, the SOM operates over the latent space of the encoder--decoder, while for lower-dimensional inputs, the SOM operates in a standalone fashion. Our method stores a running mean, variance, and covariance for each SOM unit, from which synthetic samples are then generated during future learning iterations. For the encoder--decoder method, generated samples are fed through the decoder to be used in subsequent replay. Experimental results on standard class-incremental benchmarks show that our approach performs competitively with state-of-the-art memory-based methods and outperforms memory-free methods, notably improving over the best state-of-the-art single-class incremental performance without pretrained encoders on CIFAR-10 and CIFAR-100 by nearly 10% and 7%, respectively. We also achieve the best performance on single-class incremental CIFAR-100 using a foundational encoder-decoder and present the first baseline results for single-class incremental TinyImageNet. Our methodology facilitates easy visualization of the learning process and can also be utilized as a generative model post-training. Overall, the results demonstrate that SOM-based statistical replay offers a scalable, label-free, exemplar-free approach to class-incremental continual learning under standard task-boundary protocols.

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