Giorgio Gilestro
ab3dc10587
- paper/pnas -> paper/manuscript (venue-neutral)
- configs/layer1 -> configs/inheritance, src/knowledge -> src/inheritance
(imported as `inheritance`), make layer1 -> make inheritance; layer2 alias dropped
- inheritance and trained-network bundles named after the manuscript figure
they feed (fig2_grounding_sweep, figS3_rebaselining, ...), or descriptively
where they feed none; configs keep their `experiment:` value so parquet
hashes are unchanged, only output.dir moves
- figure scripts, SI figure sources, notebooks, REPRODUCING.md, README and the
SI Methods/tables updated; make clean no longer deletes tracked manifests;
reproduce.sh hashes the s{seed}/ layouts too
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm
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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