Structure learning — expansion + Bayesian model reduction live
The learner starts with ONE hidden state. The observation stream cycles through three regimes (with deterministic off-regime noise every 11th step). When an observation arrives that no current state explains above threshold, the learner grows a state — watch the orange "grew state N" events fire at each regime boundary. Every 150 steps it scans state pairs with the Bayesian-model-reduction evidence test (closed-form in log-Beta functions) and merges any pair whose merger increases model evidence — the green events. The heatmap is the learned likelihood P(obs | state) assembling itself from Dirichlet counts. No gradients anywhere; replaying the same stream reproduces the same model bit-for-bit.
About this exhibit
This ingests the architecture behind VERSES' AXIOM result — the object-centric active-inference agent that beat a state-of-the-art deep-RL world model on the Gameworld benchmark with roughly 99% less compute. The load-bearing trick is not a bigger network; it is that there is no network. Three closed-form moves replace gradient descent:
- Conjugate count learning — likelihood and transition matrices are Dirichlet-distributed; observing data adds posterior-weighted counts. One addition per cell.
- Online expansion — when maxs P(obs | s) falls below threshold, add a state rather than distort the ones that already work.
- Bayesian model reduction — merging two states is accepted only when the model-evidence change, computed exactly in log-Beta functions, is positive. Statistical redundancy, not heuristics, decides.
Every step emits the standard substrate receipt. Growth and merge events are typed entries in the trace, so the entire structural history of the model is replayable — same stream in, same model out, every time.