The Octonionic Trie¶
A self-organizing hierarchical memory where octonionic algebra replaces gradient-based learning entirely.
How it works¶
The trie routes inputs through a tree structure using the algebraic properties of octonions:
- Routing: At each node, the product \(n \cdot x\) is decomposed along the 7 quaternionic subalgebras. The child whose subalgebra has the largest projection is selected.
- Compatibility check: The associator \([x, c, n]\) is computed. If its norm is below the threshold, the input descends into child \(c\).
- Novelty detection: If no child is compatible (all associator norms exceed the threshold), a new branch is created.
- Content update: At the leaf, the node's content is updated by octonionic composition: \(o' = o \cdot x\).
Key results¶
| Experiment | Result |
|---|---|
| MNIST (CNN encoder, 60K training) | 95.2% accuracy (no gradients in classifier) |
| 7-category stability-plasticity | 97.7% accuracy, 0% forgetting |
| Novelty detection | 5x spike ratio at category transitions, zero false negatives |
Threshold policies¶
The associator compatibility threshold is the single most consequential parameter. The library provides 7 pluggable policies:
| Policy | Strategy |
|---|---|
GlobalPolicy |
Fixed threshold at all nodes |
PerNodeEMAPolicy |
Exponential moving average of observed associator norms |
PerNodeMeanStdPolicy |
Welford's online mean + k*std |
DepthPolicy |
Threshold decays (or grows) exponentially with depth |
AlgebraicPurityPolicy |
Variance of associator norms and similarities in node buffer |
MetaTriePolicy |
A second trie optimizes thresholds via ratio-feedback signal |
HybridPolicy |
Blends two policies (mean, min, max, or adaptive transition) |
See the API Reference for full documentation of OctonionTrie, TrieNode, and all threshold policies.