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>
Confirms model collapse and its arrest by grounding on REAL images, not
just the synthetic sandbox. A conv VAE (the canonical generative-collapse
model) is retrained each generation on its own generated digits, with a
fraction g of fresh real MNIST mixed in. Modes = digit class x stroke-
thickness bin (K=30, Zipf, ~18 tail modes); the oracle is a frozen CNN +
deterministic thickness at 98.5% mode accuracy (30x30 confusion matrix
recorded in the manifest as the measurement-noise floor).
Result (4 reps): dry (g=0) collapses to a single mode -- forward-KL
0.5->18, support 30->1, tail 1.0->0.06, H->0 -- while 10% grounding holds
all 30 modes (KL~0.6, full tail, H~0.9). Signs, not magnitudes (blueprint
3.5); the exact synthetic oracle stays the quantitative anchor. The VAE
needs ~10% grounding vs the synthetic histogram's ~5%, consistent with the
grounding finding that trained nets need more than the exact operator.
Plugs into the existing data-agnostic contract (metrics/grounding/output
reused verbatim): mnist_data (thickness bins, class x thickness bijection,
MnistSampler), mnist_oracle (ClassifierOracle + confusion matrix),
mnist_vae (ConvVAEGenerator), mnist_loop (run_mnist_lineage), kind=
mnist_lineage dispatch, MnistCfg/OracleCfg. Figures: plot_mnist (parquet-
only) + mnist_montage (eyeball diagnostic showing digits degenerate to one
blurry mode). make mnist / make env-mnist, kept out of the make neural
loop. 99 tests green (+5 torchvision-gated).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Grounding refinement (18 reps): forward-KL is the operative neural
collapse metric, not H or tail-survival. The RNN's smoothing keeps
spurious tail modes alive, so tail_truth_mass_alive is flat/non-monotone
in g and H stays ~0.8 of H*; only forward-KL falls monotonically (dry
2.08 -> g=0.2: 0.75, paired t up to 3.3). The sharp g* << 1 is an
exact-operator feature carried by the histogram bridge (0.047); the
trained RNN confirms the SIGN and softens the sharpness (half the KL gap
closes by g~0.04, but full recovery needs g~0.19). Blueprint 3.5's
directional claim holds; the pre-registered 95%-of-H*/tail falsifier is
not met because those are the wrong metrics for a smoothing model.
Robustness: a fully-degenerate RNN can emit only invalid codewords, so
measure_distribution now returns a terminal-collapse sentinel (fixation
on the dominant mode) instead of crashing a long sweep. Edge test added
(94 tests green).
Figures: plot_{bridge,collapse,grounding,architectures,recombination}.py,
each a pure function of its committed bundle, wired into `make figures`
(glob plot_*.py minus plot_E[1-6]/_*). bridge sits on the exact H_eq
curve (g*=0.047); recombination shows max-merge rising while mean-distill
stays flat; architectures shows the collapse/rescue signs across
histogram/GRU/MLP.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Finishes the Layer 1 analytical core. All six experiments run with honest,
publication-quality figures; 71 tests green.
- E3 region-matched grounding: `grounding.exercised` knob + per-region tail
survival. Matched holds the exercised region's tail (0.49) where uniform
spreads thin and lets it collapse (0.07).
- E4 multi-teacher recombination: `run_coverage` runner. Union coverage matches
U(K_T,rho,q) exactly. Finding: mean-mixture distillation shows NO surviving
benefit (a conservation law — 1/K_T dilution cancels the union gain); a
union-preserving max-merge (M2N2-style) does. E4 reports both operators.
- E5 QD vs greedy: greedy drives fixation (H~0.01); QD holds H at 0.48-0.88,
rising with the novelty exponent.
- E6 re-mint gate: `arm` multi-override sweep. Re-minting a collapsed lineage
locks in divergence of KL-to-original; gating on diversity prevents it.
- E2 analysis add-ons (from the companion work order, numbers verified): new
analysis.py (reduce_to_stationary, critical_grounding with bootstrap CI ->
g*=0.048, 95% CI [0.047,0.050]); tail_band_metrics + per-band logging; the
E2 figure rebuilt as a 2x2 (defined g*+CI, g=0 flagged as a finite-time
artifact, tail item-vs-mass, per-rarity-band panel). Uses truth-mass-weighted
tail coverage rather than the raw (martingale) tail_mass.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Scaffold plus the Layer 1 analytical core and the first two experiments.
- knowledge/: truth, metrics, teachers (2.7.1 shared-switch construction),
step, lineage, experiment, config, seeding (imported as `knowledge`).
- Validation spine green: neutral decay (Pred 1), fixation (Pred 2), exact
mutation-drift equilibrium (Pred 3), union coverage (Pred 5). 68 tests pass.
- E1 reproduces tail-first collapse. E2 delivers the headline: a grounding
phase boundary g* << 1, with stationary H tracking the exact H_eq closed
form (g=0.005 -> 68% of truth diversity; g=0.05 -> 96%).
- Reproducibility: uv venv from a hash-pinned uv.lock is the source of truth;
every run writes results.parquet + resolved_config.yaml + manifest.json
(lib versions, git commit, sha256). Figures and manifests tracked; the
large regenerable parquet is gitignored.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
