An MNIST digit is placed at the centre of an 80×80 grid. One update rule — 8,768 parameters, applied at every cell, seeing only its own 3×3 neighbourhood — is iterated for 45 steps. Ten circular regions sit on a ring around the digit, and the model is trained so that at the end of the rollout the region belonging to the digit's class has the highest mean activation while the other nine stay dark. The prediction is therefore read off as a location on the grid, not from a classification head: the grid has to change shape until the answer is visible in its form. This reaches 95.5% on the MNIST test set, which is well below what an ordinary small convnet gets. The interest is in the mechanism, not the score — the signal has to travel from the digit to the right region using nothing but local communication.
The leading circle is outlined in white; a dashed green circle marks the true class when the model gets it wrong. “Lead” is the gap between the top region and the runner-up.
Accuracy sits at chance (11.4%) until roughly step 25,000, then reaches 55% at the next validation point and 84% by step 30,000. Validation runs every 5,000 steps, so the change is only localised to within one interval, and this is a single seed — we did not test whether the timing is consistent across seeds.
Alive masking leaves the model at chance. Lowering the fire rate costs most of the accuracy. Initialisation and loss choice make a few points of difference at most.
This checkpoint was fine-tuned on a state pool, and holds its answer when the rollout is run 5× longer than it was trained for, losing 0.4 pp. Without that fine-tuning the state drifts and accuracy at T=250 is markedly worse.
Fashion-MNIST holds up. CIFAR-10 reaches 50.5% — better than chance, but routing colour images through 16 channels of local traffic is clearly much harder.