docs: accessible figure legends (README.md) for all figures
One self-contained README.md per results/ figure folder (Layer 1 E1-E6 and Layer 1.5 bridge/collapse/grounding/architectures/recombination): plain-language claim, setup, a compact symbol glossary, a panel-by-panel walkthrough, and the takeaway + falsifier. Auto-renders when browsing the folder; carries the honest caveats (grounding's ruler reframing, the excluded VAE). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
parent
b8da418034
commit
3b9f4f7893
11 changed files with 369 additions and 0 deletions
32
results/bridge/README.md
Normal file
32
results/bridge/README.md
Normal file
|
|
@ -0,0 +1,32 @@
|
|||
# bridge — the histogram model reproduces Layer-1 E2 exactly (the HARD GATE)
|
||||
|
||||
**Claim tested (a plumbing check, not science):** does the neural experiment harness, when run with a
|
||||
*trivial* model, reproduce the Layer-1 math exactly? If not, no later neural result could be trusted.
|
||||
|
||||
**Setup (Layer 1.5).** Same generational loop as every neural experiment — each generation, draw the
|
||||
parent's samples, optionally mix in real data, retrain, measure — but the "model" is a **histogram**:
|
||||
it just counts which modes appeared and resamples them (no neural net, no smoothing). This reduces the
|
||||
neural setup *exactly* back to Wright–Fisher drift. `K = 200` modes, `n = 200`, 200 generations,
|
||||
60 repeats, grounding swept `g ∈ {0, …, 0.4}`.
|
||||
|
||||
### Symbols
|
||||
- **mode** = one of the `K` items (Layer-1.5 word for "item"); read off each generated sequence by a zero-error oracle.
|
||||
- **`g`** grounding fraction, **`g*`** its critical value, **`H`** diversity, **`H_eq`** the exact closed-form equilibrium diversity.
|
||||
|
||||
### The four panels
|
||||
1. **Trajectories.** Diversity `H` per `g`. `g = 0` collapses; `g > 0` plateaus — the E2 picture,
|
||||
now produced by the *neural runner*.
|
||||
2. **Bridge = Layer 1 (the gate).** Dots = the neural histogram runner's stationary `H` vs `g`; the
|
||||
black dashed curve = the exact `H_eq` closed form from Layer 1. The dots sit **on** the curve, and
|
||||
the recovered critical grounding is **`g* = 0.047` (CI [0.045, 0.052])** — matching Layer-1's
|
||||
0.048. This equality is what licenses every trained-model result to be read against the analytic
|
||||
core.
|
||||
3. **Tail survival.** Fraction of the rare tail retained vs `g` (item-count red, truth-mass purple) —
|
||||
rises with grounding, deep tail lags, exactly as in E2.
|
||||
4. **Per-rarity band.** Survival by rarity band vs `g`; deep bands need more grounding
|
||||
(`m·p*ᵢ ≳ 1`).
|
||||
|
||||
### Takeaway
|
||||
The harness is faithful: with a memoryless model it reproduces Layer 1 to the decimal. **This is a
|
||||
gate, not a finding** — passing it is the precondition for the RNN/MLP experiments
|
||||
(`collapse`, `grounding`, `architectures`, `recombination`), where the *model* is what changes.
|
||||
Loading…
Add table
Add a link
Reference in a new issue