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>
32 lines
2.2 KiB
Markdown
32 lines
2.2 KiB
Markdown
# E1 — Distillation without grounding collapses, tail-first
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**Claim tested:** if a model is trained only on the previous model's output, generation after
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generation, does it lose knowledge — and does the *rare* knowledge go first?
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**Setup (Layer 1, pure math).** A "population" of `K = 500` items with a fixed true frequency
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`p*` shaped like a Zipf curve (a few common items, a long tail of rare ones). Each generation we
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draw `n = 100` samples from the current model and refit — **no real data is ever added** (`g = 0`).
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Run for 600 generations, averaged over 100 independent repeats.
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### Symbols
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- **`p*`** — the true frequencies (fixed reality). **`p_t`** — the model's frequencies at generation *t* (drifts).
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- **`H`** heterozygosity = diversity (1 = everything equally likely, 0 = one item left). **`H*`** = diversity of the truth.
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- **forward-KL** `D(p*‖p_t)` — how far the model has drifted from truth (0 = perfect, grows without bound as the tail is forgotten).
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- **support** = how many items still have any probability. **head/tail** = common/rare items.
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### The three panels
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1. **Geometric decay.** Blue = the simulated diversity `H`; black dashed = the exact textbook law
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`H₀·(1 − 1/n)^t`. They sit on top of each other — the loss of diversity is *exactly* the
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population-genetics drift law, not an approximation. (This is the validation gate: if these two
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curves disagreed, the simulator would be wrong.)
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2. **Tail dies first** (log axis). Red = fraction of *rare* (tail) items still alive; green =
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fraction of *common* (head) items still alive. The red curve plunges far faster — rare knowledge
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is lost roughly an order of magnitude sooner than common knowledge.
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3. **Collapse.** Purple (left axis, log) = number of distinct items surviving, falling from 500
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toward ~1 (everything collapses onto a single dominant item). Orange (right axis) = forward-KL to
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truth, diverging as the tail vanishes.
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### Takeaway
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Unchecked model-on-model training is a ratchet: diversity decays on a precise mathematical schedule,
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and the rare tail is destroyed first. **Falsifier (not triggered):** if `H` had stayed flat, the
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whole thesis would fail. It didn't.
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