Sixteen skills. Nothing forgotten.

The setup

Sixteen small control skills, introduced one at a time on a shared stream, each cued by its own signal and revisited forever. Every learner must pick up the new skill without dropping the old ones. This is the stability–plasticity problem, live.

Each grid cell is one skill: green if that learner can still perform it when tested, red if it has lost it, gray if not yet taught. The grid is re-tested continuously against the real kernel; nothing is remembered by the page.

What to watch

1. Frozen holds its first skills and never gains another, the shipped-model status quo.
2. Linear RNN learns until its weights run away. Its row turns red and its label reads DIVERGED, with the tick it happened on. That is the reason nobody ships live learners.
3. Contractive is bounded like us by design, so “you just clamp” is off the table. But its memory lives in its weights, so new skills overwrite old ones. Red creeps in. That is overwrite, not a shortage of neurons.
4. Synapse keeps learning and keeps what it learned, and cannot diverge while doing it. Memory lives in the network’s physics, not the trained weights, so learning new skills doesn’t overwrite old ones.

Scope

Capacity is finite and measured. Skills per neuron is a budget, not magic. Extra neurons raise that budget here because learning is additive below it. For the contractive rival, size is the wrong lever: memory lives in the weights, so new skills overwrite old ones whether the net is this size or larger.

The claim is not that a huge model, trained offline on a closed set, can never hold sixteen. It is that on this live sequential stream, at matched size, boundedness does not buy retention. The conjunction is a small network that can’t diverge and doesn’t have to overwrite what it already knows, with no replay buffers or task boundaries.