Giorgio Gilestro
871bc39ec6
Revisiting Layer 1 against Layer 1.5 (and Riis 2026, arXiv:2604.08554):
neutral Wright-Fisher is a null that BOTH neural architectures deviate
from, in opposite directions. Add a learning kernel to the refit step,
p_{t+1} = T_theta(counts/n), with two population-genetics knobs -- reset u
(mutation toward a prior = smoothing) and temperature tau (sharpening =
mode-competition) -- both identity by default, so the histogram bridge and
all 68 scientific-validation/correctness tests are unchanged.
Result: neutral drift fails both neural models, oppositely.
- VAE regime (n=6000, K=30): neutral drift is inert (no collapse), yet the
real VAE collapsed to one mode. Sharpening tau=0.8 reproduces it -- the
estimator ADDS collapse pressure.
- RNN regime (n=200, K=256): neutral drives H->0, but the real RNN only
partially collapses. Mutation u=0.006 reproduces the H-floor -- the
estimator REMOVES collapse pressure. Honest caveat: uniform-mutation
overshoots the RNN's forward-KL, evidence its smoothing prior is
truth-like, not uniform (future refinement).
This mechanistically explains the architecture-generality result and the
softened neural g*, and develops the estimator axis Riis names as future
work. New: knowledge/kernel.py, configs/layer1/kernel_{sharpen,smooth}.yaml,
figures/plot_kernel.py (overlays analytic arms vs committed neural
endpoints), READMEs, tests/test_kernel.py (+6, 105 total green). Strategic
Riis positioning recorded in CLAUDE.md: concede "collapse=drift" as prior
art; lead with recombination, the kernel axis, and the Lamarckian society.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
42 lines
2.9 KiB
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42 lines
2.9 KiB
Markdown
# kernel — the learning kernel: why real learners deviate from neutral drift
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*(This legend covers both `results/kernel_sharpen/` and `results/kernel_smooth/`; the figure
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`kernel.png` is written into both.)*
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**Claim tested.** Neutral Wright–Fisher drift (the histogram bridge, and the baseline of Riis
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2026) is the *null* model of collapse. But Layer 1.5 showed real trained models deviate from it —
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and in **opposite directions**. Can a single extension of Layer 1 — a parameterized *learning
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kernel* on the refit step, `p_{t+1} = T_θ(counts/n)` — reproduce both deviations, and does neutral
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drift genuinely fail without it?
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**Setup.** The kernel (`knowledge/kernel.py`) has two population-genetics knobs, both reducing to
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neutral drift at their defaults (so the histogram and every scientific-validation test are
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unchanged): **reset `u`** — mutation toward a prior (`p ← (1−u)p + u·π`), i.e. smoothing; and
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**temperature `τ`** — sharpening (`p ∝ p^{1/τ}`, `τ<1` concentrates), i.e. mode-competition. Two
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matched-to-neural regimes, 24 replicates each.
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### The four panels (`kernel.png`; blue = neutral, red = kernel-on, green dashed = the real neural model)
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**Top row — VAE regime (`n=6000`, `K=30`), pro-collapse:**
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1. **Heterozygosity.** Neutral drift is **inert** — at `n=6000` it barely moves (`H` stays at
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`H*`). Yet the real VAE (green) collapsed to `H≈0`. **Sharpening (`τ=0.8`) reproduces the
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collapse.** Neutral drift is *falsified*; the estimator's mode-competition is required.
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2. **Support.** Neutral holds ~all 30 modes; sharpening → 1 mode, matching the VAE.
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**Bottom row — RNN regime (`n=200`, `K=256`), anti-collapse:**
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3. **Heterozygosity.** Neutral drift drives `H → 0`, but the real RNN (green) only *partially*
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collapses (`H` floors at ~0.68). **Mutation `u=0.006` reproduces the floor.** The estimator here
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*removes* collapse pressure.
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4. **Forward-KL.** Neutral diverges; smoothing plateaus. Honest caveat: uniform-mutation plateaus
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*above* the RNN's KL (~5 vs ~2) — evidence the RNN's smoothing target is **truth-like, not
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uniform** (a refinement for future work). The *sign* is unambiguous.
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### Takeaway
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Model collapse in real learners = **neutral drift ⊕ an architecture-specific estimator-bias
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operator that can point either way.** The histogram sits at the neutral null (`u=0, τ=1`); the VAE
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**sharpens** (adds collapse); the RNN/MLP **smooth** (add a diversity floor). This mechanistically
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explains the Layer-1.5 architecture-generality result and the softened neural `g*`, and develops
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the exact axis Riis (2026) names as future work ("different smoothing schemes… each induce their
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own fixed-point geometry… a natural direction for further work"). `u`/`τ` are calibrated from a
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single neural diagnostic and pinned in the configs. **Falsifier (not triggered):** if neutral drift
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had already reproduced the neural curves, the estimator axis would be superfluous — instead it fails
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in *both* regimes, oppositely.
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