Research line: the August geometric intelligence programme
In August the project asked a basic question: can the geometry it likes, rotations in four dimensions (R4/Spin coordinates) and hyperbolic (Lorentz) space, carry the work of attention in a language model? The programme (issue #973) reproduced ordinary attention exactly inside these coordinates, which is a useful parity check, but never found a case where the geometry did better than a plain control. This line holds its nine records. Its questions moved into the September native model.
| Catalog id | geometric-intelligence-aug |
| Time span | 25 to 30 Aug 2026 (1 record undated) |
| Milestone | None recorded (9 of 9) |
| Records | 9 |
| Outcomes | negative 3 · plan 2 · positive 2 · diagnostic-stop 1 · inconclusive 1 |
| State | Closed; superseded by the September native model. Configurations are closed, the ideas are not |
Counts: archive/catalog.jsonl. Terms follow the glossary; ACTIVE, READY and PARKED are defined on the mechanism board.
flowchart LR A["25 to 26 Aug<br/>Decoder plan; mixer<br/>test and spike"] --> B["28 to 29 Aug<br/>Lorentz attention and<br/>retention tests"] B --> C["30 Aug<br/>Learned manifold;<br/>score localisation"] C --> D["Softmax decoder in R4<br/>coordinates: exact parity,<br/>no advantage"]
Parity was achieved; advantage was not.
What it set out to do
Replace or enrich the standard transformer's attention with geometry from the project's own toolbox, using a small donor model (SmolLM2) as the reference. A positive result would have meant a measurable gain over a matched control that uses the same parameters and no geometry.
What happened, in order
- 25 to 26 Aug: a decoder plan and a mixer. A one-layer mixer distilled from a donor layer beat a coordinate-permuted control by 4.44% against a 5% gate, verdict REDESIGN_REPRESENTATION (record). A layer-29 geometric spike passed its first gate with 32 cycle-free tokens and 4/5 on a control review, promoted to the next gate with no quality claim (spike). The decoder roadmap records that its next gate (G1) ended in REDESIGN_REPRESENTATION (plan).
- 28 Aug. Retention with a geometric gate scored 16/28 against 23/28 for plain gated delta on a synthetic fixture (record).
- 29 Aug. Intrinsic Lorentz attention was stopped before held-out data. Its covariance residual was 9.12e-8 against a frozen ceiling of 1e-8, and the curved arm trailed the flat one (record). A learned Lorentz manifold had cross-entropy 7.71 against 4.48 for a flat Euclidean arm and 3.67 for the donor (record).
- 30 Aug. A tangent value readout was 1.0644 times worse than a normalised-centroid readout, and a plain Euclidean score beat the Lorentz score as a diagnostic (record). A preflight for finite Lorentz score radii was parked and never run (record).
- Undated. The full decoder with ordinary causal softmax run through coherent R4/Spin frames matched the donor's logits to a maximum absolute difference of 1.05e-5 over 196,608 logits, with no R4 advantage (record).
Key results
| Result | Kind | Source |
|---|---|---|
| R4/Spin softmax decoder matches the donor: maximum logit difference 1.05e-5 over 196,608 logits | measurement | record |
| One-layer mixer beats a permuted control by 4.44%; gate 5% | measurement | record |
| Geometric retention 16/28 against plain 23/28 | measurement | record |
| Learned Lorentz manifold cross-entropy 7.71 against 4.48 Euclidean and 3.67 donor | measurement | record |
What it taught
Exact algebra reproduces ordinary behaviour perfectly but carries no meaning on its own (lesson 8 in what the project knows). Fixed geometry usually tied or lost to a matched control (lesson 6). The Lorentz idea returned in September, where a Lorentz read beat a dot read by 0.018 nats on code in 3 of 4 seeds before it lost when adapted (stack line). Each negative closes only its exact configuration (decision D22).
Current state
Closed. The programme record survives as inactive evidence.
Go deeper: the generated catalog page lists all 9 records.