Giorgio Gilestro
3b9f4f7893
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>
38 lines
2.7 KiB
Markdown
38 lines
2.7 KiB
Markdown
# grounding — the grounding response in real weights (and why the ruler matters)
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**Claim tested:** does the E2 result — a small dose of real data (`g* ≈ 0.05`) rescues diversity —
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reproduce in a trained GRU? The honest answer reframes the question.
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**Setup (Layer 1.5).** Autoregressive GRU, `K = 256` modes, `n = 200`, 30 generations, grounding
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swept over 9 values `g ∈ {0, 0.005, …, 0.2}`, **18 repeats** (many repeats are needed because each
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lineage's fate is genuinely noisy under `n = 200` drift). The falsifier was pinned in the config
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*before* running.
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### Symbols
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- **`g`** grounding fraction (share of real data), **`g*`** its critical value.
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- **forward-KL** distance from truth (the operative neural collapse metric here).
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- **tail survival** `tail_truth_mass_alive` — truth-weighted fraction of the rare tail retained. **`H`** diversity.
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- **recovery fraction** — how much of the achievable forward-KL reduction a given `g` has bought (0 = dry, 1 = best observed).
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### The four panels
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1. **Trajectories.** Forward-KL over generations per `g`: grounding suppresses the climb.
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2. **Phase boundary.** Stationary forward-KL vs `g` **falls monotonically** (dry ≈ 2.08 → `g = 0.2`
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≈ 0.75); the effect is statistically significant (paired *t* up to 3.3; 89% of lineages improve at
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`g = 0.2`). **The SIGN is confirmed.**
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3. **Recovery curve.** Fraction of the divergence gap closed vs `g`. **Half the gap closes by a
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median-recovery grounding of `g ≈ 0.04`** (CI [0.004, 0.116]) — a striking echo of Layer-1's 0.048
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(black dashed) — **but full recovery needs `g ≈ 0.19`**, far more than the exact histogram: the
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GRU's smoothing both caps the collapse and slows the rescue.
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4. **Why forward-KL (the key methodological panel).** Normalised responses of three rulers vs `g`:
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`H/H*` (flat ~0.8) and **tail survival (flat / non-monotone — dry is as high as grounded!)** both
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fail to register the effect, while **forward-KL recovery** responds cleanly. A smoothing model keeps
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*spurious* tail support alive, so counting surviving modes is misleading; only distance-from-truth
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is honest.
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### Takeaway (an honest reframing)
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Two results: **(1)** the operative neural collapse metric is **forward-KL**, not `H` or tail-survival —
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smoothing decouples "modes alive" from "close to truth." **(2)** The *sharp* threshold `g* ≪ 1` is a
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property of the exact operator, carried quantitatively by the histogram **bridge** (`g* = 0.047`); the
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trained GRU confirms grounding's **direction** and **softens** its sharpness. The pre-registered
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95%-of-`H*`/tail falsifier is *not* met — but because those are the wrong rulers for a smoothing
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model, not because grounding fails; the blueprint §3.5 directional claim holds robustly.
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