Clarity pass over the main text (36-item audit), Discussion rewrite and cut,
acknowledgements, Souly et al. as ref 62, lettered SI panels, model section
moved under Results; plus the untracked curriculum/society/compose/smol
configs, runners, figures, stats and tests that the SI already cites.
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm
The five priority fixes, in the PNAS draft and propagated to the
long-form document and results documentation:
1. The averaging proposition now proves what it claims: a FIRST-ORDER
cancellation of the multi-parent retention gain under output-mean
inheritance in the rare-item regime (n·p/K << 1), with the convexity
boundary stated (averaging's variance reduction can reduce extinction
outside that regime — the reviewer's argument) and the union
operator's renormalisation + oracle requirement explicit. "Adding
parents cannot help" deleted everywhere.
2. Grounding: g*~=0.05 restated as an operational threshold (equilibrium
smooth in g — no phase transition); m·p floor restated as
1−exp(−m·p) per-batch observation probability with
retention/occupancy/reintroduction distinguished; the deep-tail rule
de-categoricalised (stratified sampling; recombination recovers only
what parents retain).
3. Grounded INHERITANCE (data channel) separated from grounded
EVALUATION (fitness channel) in the society section; retitled to
"complementary contributions"; general joint necessity disclaimed.
Table 1 + v6 ledger updated.
4. Alignment contradiction removed everywhere ("cannot be an alignment
failure" -> the reviewer's formulation); abstract says "remaining
after permutation-and-rescaling alignment"; group = search space,
control recovery != global optimality; "specialisation is merge-safe"
-> "do not treat divergence/specialisation alone as evidence of
incompatibility".
5. Significance headline matched to the bounded evidence; seed-
dependence sensitivity added (per-seed rho stable +0.37..+0.53 for
functional measures, ~0 for geometry, gradient alignment
seed-UNSTABLE −0.11..−0.55 — reported as its own caveat; LOSO ranges
in stats script).
Presentation: review-process meta-language stripped; "exact" reserved
for closed forms ("analytic model" labels); headroom rule qualitative;
directed-sex phrasing per review; ratchet = consequence-level
correspondence; compact results table (Table 2) added. Response letter:
paper/response-to-review-3.md. Both PDFs rebuilt; 151 tests green.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
The decisive experiment from the external review. 39 LoRA parent pairs
(0.5B, 3 seeds) on three axes decorrelated by construction: conflict
(contradictory conventions on shared prompts, private budgets fixed),
compat (same prompts, SAME convention — overlap without conflict), and
duration (weight divergence, zero conflict). Six pre-merge predictors;
primary outcome = merge penalty (parent potential − merged achieved).
League table (Spearman vs penalty, n=39): functional measures predict
(dis_raw +0.460, epi_conf +0.446, p<0.005); geometry collapses
(delta_cos +0.03, delta_l2 +0.17 n.s.); gradient alignment weak (−0.35);
performance ~0. The first grid's apparent geometry win (+0.60) was an
overlap/volume artifact — the compat control axis (added for exactly
this) exposed and killed it: same overlap and data volume, zero penalty.
Honest riders in the README: confidence weighting does not beat raw
disagreement as a rank predictor (pre-registered internal prediction not
confirmed; it does double the conflict/compat level contrast), and
|rho|~0.45 is bounded by 0.5B merge-outcome noise (7B is the firm-up).
Also: micro-batched gradient accumulation (OOM fix on the shared 16GB
GPU), exact r-space LoRA-delta geometry (brute-force-verified test,
151 green), systemd-run runbook lesson (tmux dies with the SSH session
scope on this box).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
llm_speciation (new kind; src/llm/speciation.py): E13 in LLM weights.
LoRA children share the frozen base's coordinates, so merge failure is
functional by construction. CONFLICT (ambiguous sort prompts learned
under opposite conventions — the BDM structure): function-specific
hybrid breakdown — merged coherence 0.02-0.08 falls below BOTH parents
(~0.2) on the conflicted function; and in the de-confounded `add` design
(private budget fixed, conflict added on top; 3 seeds after a
single-seed pilot showed one anomalous point) the merge's private-family
accuracy shows NO trend with conflict — the damage is surgical, not
global. DURATION (over-trained disjoint specialists, 1->12 epochs): the
merge improves (0.84->0.94) and stays above the best parent — the MLP
"no emergent isolation" null generalises; relevant to the
expert-training-duration report (2607.11997), with the epistasis
prediction left to the decisive experiment.
Multi-seed firm-up (seeds threaded into specialist caches; `seeds:` list
support in the runner; fixed test sets): all three recombination claims
hold with CIs — merges beat every specialist (5 seeds, ties
0.647±0.027 > best spec 0.592±0.009; worst-family 0.28 vs <=0.16); union
0.274±0.026 > fusion 0.174±0.102 on hard (3 seeds); directed 0.221±0.026
> soup. NEW finding: fusion is seed-FRAGILE where headroom exists
(CI ±0.10) while routing/directed selection are stable (±0.026) — the
union/selection operators win on reliability, not just mean.
Figures (llm_speciation 3-panel; llm_seeds 3-panel with 95% CI), READMEs,
+1 convention test (150 green), make llm-speciation / llm-seeds targets.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
E13c (the symmetry defense): alignment now runs modulo the FULL
function-preserving unit symmetry group of a ReLU MLP (per-unit positive
rescaling via canonicalise_scale, composed with Re-Basin permutations;
sanity gate recovers a permuted-and-rescaled copy exactly). Verdict: the
full group removes the independent-init barrier (residual 0.001) and
essentially none of the conflict barrier (0.502 -> 0.497) — the residual
is functional, not a missed symmetry (answers arXiv:2606.23607). The
cliff gains a hybrid-fitness readout: merged accuracy 0.97 -> 0.03 with
conflict. Floor proposition drafted (paper/si-notes.md S1): endpoint
invariance + max(eps_A, eps_B) >= mu(S)/2 for any merged model under any
alignment group.
E13b (emergent divergence): pre-registered second reading — with NO
conflicting training signal (disjoint class specialists; rolled-input
conventions), residual is 0.000 at every divergence to t_div=3200, and
the merge RESCUES the forgetting specialists (parents 0.535/0.474 ->
merged 0.955; a sustained Fisher-Muller rescue at zero barrier).
Speciation in real weights requires functional conflict; it does not
emerge from compatible specialisation on shared ancestry. LLM-scale
over-specialisation (cf. 2607.11997) deferred to Phase-3 llm_speciation.
3-panel figure, READMEs, +2 tests (149 green), make mnist wired.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
A new analytic experiment on an orthogonal evolution-of-sex axis: not the
recombination RATE (E9) but the population's mating STRUCTURE. Agents on a
ring recombine with a second parent drawn from a window of breadth b
(b->0 monogamous/isolation-by-distance, b=1 promiscuous/panmictic), under
local selection, swept against NK ruggedness K.
Finding: the optimal mate-pool breadth SHRINKS as skills get more
entangled. Wide/promiscuous merging wins the champion on additive
landscapes (K<=3, b=0.6), but on rugged ones (K>=6) it prematurely
converges to a worse champion and an intermediate breadth (b~0.35) wins;
pure monogamy over-fragments. Throughout, promiscuity monotonically lifts
the population MEAN but destroys diversity and parallel exploration. The
design rule extends E9: merge widely for additive skills, keep
island-structured sub-populations for entangled ones — a merging-native
axis the panmixia-assuming literature lacks.
- src/knowledge/mating_system.py + experiment.py dispatch (kind: mating_system)
- configs/layer1/E14.yaml (breadth x K sweep, 20 reps, bitwise-reproducible)
- figures/plot_E14.py; results/E14/ (figure, README, manifest, resolved config)
- tests/test_mating_system.py (+5, 147 green); make layer1 wired
- folded into both papers (full + accessible) as the third §5 result
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
The real-weight image of E12, and the answer to the mode-connectivity reviewer.
Small no-BN MLPs on MNIST, forked from a shared base and trained independently,
are weight-averaged; we measure the linear-mode-connectivity barrier before and
after in-house deterministic Git Re-Basin permutation alignment (neural/rebasin.py,
scipy linear_sum_assignment), decomposing it into removable (coordinate artefact)
and residual (reproductive isolation). kind: speciation_real.
Result (3 reps):
- shared (same task, shared fork): no barrier — trivially mergeable.
- independent (same task, different init): naive 0.056, alignment removes 98%
(residual 0.001) — the incompatibility is a coordinate artefact.
- conflict (conflicting label maps): naive 0.496, alignment removes 0% (residual
0.496) — genuine reproductive isolation. Because alignment demonstrably works on
the independent case, the conflict residual is real, not a failure to align.
- Isolation cliff (speciation_real_cliff): residual rises 0.00->0.13->0.19->0.28->
0.40->0.49 with the fraction of conflicting classes — the real-weight mirror of
E12's cliff; residual==naive throughout (functional, not coordinate).
rebasin.py sanity-gated (recovers a known permutation exactly). plot_speciation_real.py
(2-panel), +4 pure-NumPy tests (142 green), README with honest positioning vs
Git Re-Basin / Entezari / Frankle / Pari 2024 / Zhou 2026. Wired into make mnist
(needs torchvision).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
New analytic result for the evolution-of-sex paper: how far can two lineages
diverge before recombination (model merging) stops working? Frames merge failure
as biological reproductive isolation via Bateson-Dobzhansky-Muller
incompatibilities. src/knowledge/speciation.py, kind: speciation, on the E7-E11
genotype machinery (pure seeded NumPy, bitwise-reproducible; no external
simulator whose separate RNG would break that).
- BDM construction (E12.yaml): ancestor + two lineages substituting disjoint loci
(each parent adaptive, incompatibility-free), a fraction rho of cross-lineage
pairs are BDMIs. Sweeping divergence d reproduces the predicted
compatible -> outbreeding depression -> hybrid inviability curve; the isolation
cliff moves to lower d as epistasis density rises (iso at d=20: 0.00/0.03/0.50
for rho 0.1/0.25/0.5); incompatibilities snowball ~ (d/2)^2 (Orr-Turelli).
- NK variant (E12_nk.yaml): parents = hill-climbed local optima; the epistasis
wedge — recombination gain flips 0 -> -0.13 and OD rate 0 -> 0.90 as ruggedness
K rises. At matched divergence, mergeability is governed by epistasis, the axis
no divergence-only ML merge predictor captures.
plot_E12.py (3-panel), +7 tests (138 green), README with honest positioning
(concedes the empirical phenomenon to Pari 2024 / Zhou 2026 + permutation
artefacts to Git Re-Basin; claims the predictive theory + the epistasis wedge).
Wired into make layer1.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
The easy task families saturated 7B (strings & arith at 1.00), so the earlier
7B nulls — moe: fusion 0.87 > union 0.84; directed ~= soup — could not separate
"refinements don't help at scale" from "tasks too easy at 7B". Adds a hard task
variant (hard: true in tasks.py: multi-step lists, Caesar ciphers / letter
transforms, multi-step & larger arithmetic; same family labels and answer
formats, threaded through make_tasks/train_specialist/runners; hard specialists
cache separately as spec_*_hard) and re-runs both experiments at 7B on Imperial
CX3 (one L40S, 24 min, unsaturated: arith ~0.48, strings 0.67, lists 0.34).
Both nulls flip back to the 0.5B ordering:
- Union beats fusion again: routing 0.500 > fusion 0.40 (soup 0.392 / ties
0.400), the same 10-pt margin as 0.5B. Fusion dilutes the fragile strings
specialist so hard (0.665 -> soup 0.300) that soup even trails the best single
specialist (0.425); routing keeps it intact (0.670).
- Directed selection beats soup again: 0.492 > 0.392 (+10 pts), recovering most
of routing's benefit from one deployable merged model (lifts strings to 0.630).
Correction to the earlier interpretation: the llm_moe_hpc "regime flip" and the
llm_directed_hpc "no headroom" null were driven by TASK SATURATION, not base
capability. The operative variable is headroom — "merge, don't average" (union >
fusion) and "directed sex" (selection > single blend) hold whenever there is room
to lose to dilution: a weak base (0.5B) OR hard tasks at a strong base (7B-hard).
Fusion only wins in the degenerate corner where easy tasks let a strong base
compose to the 1.00 ceiling. Vindicates E8's max > mean in real 7B weights once
saturation is controlled.
Default (easy) task behaviour is unchanged (hard defaults False). +1 hard-task
test (131 green). Excludes the 0.5B smoke bundle (a pipeline gate, not a
deliverable). Results in results/llm_{moe,directed}_hard_hpc/ (parquet gitignored).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Adds the "directed sex" operator (E10) the moe regime-flip pointed to: don't
commit to one a-priori blend — breed a population of recombinant offspring
(specialists merged at Dirichlet-sampled weights), score each on a held-out
validation split with the verifier, and keep the fittest, reported on a fresh
test split. Two breeding objectives: best-overall and best-worst-family.
src/llm/directed.py + kind llm_directed, reusing the cached specialists.
Result — refinements pay off in proportion to how far the uniform soup is from
optimal:
- 0.5B (soup dilutes): directed selection beats soup on the bred objective —
directed_overall 0.69 > soup 0.64; directed_balanced worst-family 0.37 > 0.26.
Riders: single-objective selection trades off the other axis (overall-breed
tanks lists to 0.17); a global blend still trails per-input routing (0.74).
- 7B (Imperial CX3, soup already composes to ceiling on near-saturated families,
strings/arith 1.00): directed ~= soup (0.868 ~ 0.873, marginally below via a
val/test overfit gap) — no fitter offspring to breed.
Through-line across all four LLM runs: "merge, don't average" and its refinements
(routing, directed selection) are weak-base / suboptimal-default phenomena — they
help at 0.5B and are inert at 7B. Honest limitation kept in the writeup: the 7B
families are near-saturated, which caps the headroom; a harder unsaturated
benchmark is the fair next test.
Also folds in the two llm_moe local manifest/config files missed in 8da0dac.
+3 directed unit tests (130 green). Results in results/llm_directed{,_hpc}/
(parquet gitignored).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Adds the union-preserving recombination operator that llm_merge lacked (E8's max,
not mean): keep each specialist LoRA intact and SELECT the right one per prompt
(MoE router: oracle, or training-free nearest-centroid over base embeddings) or
per module (max_merge = winner-take-all by delta norm). src/llm/moe.py, kind
llm_moe, reuses the cached specialists.
Result — a clean regime boundary for "merge, don't average":
- 0.5B: union wins. Routing 0.74 / worst-family 0.43 > soup 0.64 / 0.26, with no
dilution (recovers each specialist's own-family peak). E8's max > mean in real
weights, because at a weak base averaging dilutes.
- 7B (Imperial CX3, L40S, 9 min): the ordering INVERTS. Fusion wins — soup 0.87 >
routing 0.84 > max_merge 0.78. Routing is capped at the best parent per family;
fusion blends and, given a capable base, COMPOSES beyond any parent (soup lists
0.62 > spec 0.57). Selection can't synthesise better than its best component;
averaging-that-composes can.
So "merge, don't average" (E4/E8) is a weak-parent / small-model law, not
universal: union wins under dilution, fusion wins under composition. Refines E8
(its additive-landscape max>mean assumed no compositional headroom). The operator
to want is fusion-that-composes + offspring selection = the directed-sex ideal
(E10) — the natural next experiment.
Honest riders: the learned router is trivially perfect (lexically-distinct
families), and router-free max_merge is the weakest union (not input-adaptive).
+2 router unit tests (127 green). Results in results/llm_moe{,_hpc}/ (parquet
gitignored per the reproducibility contract).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Re-ran the specialist-merge experiment at a capable base (Qwen2.5-7B-Instruct,
200 tests/family) on one L40S GPU of Imperial's CX3 HPC (8 min walltime). The
two caveats the 0.5B prototype left marginal are now resolved:
- "exceeds every parent overall" is clean: both merges 0.87 vs best specialist
0.77 (+10 pts), and above every specialist on every family.
- dilution vanishes: at 0.5B averaging diluted the lists-specialist
(0.43->0.26); at 7B the merge beats it (0.62>0.57). Dilution was a
small-model artefact -- a capable base composes rather than dilutes, which
softens E4's "merge, don't average" once the parents are strong.
The figure title is now data-driven (reports ">" for 7B, "~" for 0.5B).
Adds the hpc/ smoke job script and the llm_merge walltime trim. Results synced
to results/llm_merge_hpc/ (parquet gitignored per the reproducibility contract).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
First step from toy models toward real language models, on one 16 GB GPU.
New src/llm/ package: procedural task families + exact-match verifier
(tasks.py), batched eval (evaluate.py), LoRA specialisation (specialise.py,
manual answer-only SFT), weight-space merge via peft add_weighted_adapter
(merge.py: soup = averaged deltas, ties = sign-reconciled union), runner
(experiment.py, kind llm_merge). Base Qwen2.5-0.5B-Instruct (Apache-2.0);
three disjoint hard families (lists/strings/arith); one LoRA specialist each
(~90s total).
Result (seed 1), reported honestly:
- STRONG/robust: the merges are the ONLY models competent across ALL
families -- worst-family ~0.25 vs <0.16 for every single specialist (the
Fisher-Muller "generalist assembled from specialists" signature, in real
LoRA weights).
- MARGINAL: "exceeds every parent overall" is only marginal at this scale
(soup 0.64 vs best specialist 0.63; ties 0.61 below it).
- CAVEAT VISIBLE: averaging dilutes peaks (lists specialist 0.43 -> merge
0.26) -- Layer-1's "merge, don't average" (E4) appearing in real weights.
The pipeline works end-to-end; the balance/retention half reproduces; the
strict overall-exceeds and soup-vs-ties distinction need scale (bigger base,
more/cleaner families, seeds, a dilution-resistant / offspring-selected
merge) -- the HPC step. Env: Python 3.14 + transformers 5.13 works;
note transformers-5.x apply_chat_template returns a dict. make env-llm /
make llm; adapters under gitignored models/llm/, base in the HF cache.
figures/plot_llm_merge.py, README, tests/test_llm.py (+3, 125 green).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
The culmination. A finite population of agents (genotypes, L loci) evolves
on a rugged NK landscape that IS reality (knowledge/dynamic_society.py),
composing the four operators the whole study built toward: grounding,
directed recombination (sex), quality-diversity selection, and mutation.
Grounding is made load-bearing via the consensus-conformity (self-
consumption) mechanism (GG decision): selection acts on
g*true_fitness + (1-g)*conformity, where conformity = agreement with the
population's own consensus, so at g=0 the society optimises fitting-the-
crowd rather than reality.
4-arm ablation (12 reps), each breaking distinctly, only the full society
climbing (global_opt ~ 0.79):
- full 0.78 climbs to the optimum, diversity maintained longest
- no_sex 0.77 can't recombine to escape local optima
- no_diversity 0.74 greedy: collapses diversity fastest, worse local optimum
- no_grounding 0.48 self-consumption collapse to an unfit consensus
(trains on the crowd -> confident-but-wrong mean;
conformity-true gap ~ 0.5)
This integrates E1-E6 + the learning kernel + E7-E10 into one system and
shows the Lamarckian society needs ALL of grounding + directed sex +
diversity: on a rugged landscape you need diversity to explore basins, sex
to recombine them, and grounding to select on reality -- remove any one and
you fail differently. Closes the C3 vertical claim analytically; the LLM
rung remains the eventual empirical instantiation.
New: knowledge/dynamic_society.py, configs/layer1/E11.yaml, figures/
plot_E11.py, README, tests/test_dynamic_society.py (+5). kind:
dynamic_society dispatch; make layer1 wired. 122 tests green.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Deepen the sexual-reproduction frame before entering the full society, on
the two facets GG chose: landscape robustness and directed recombination.
Adds a Kauffman NK landscape (genotype.nk_fitness, tunable ruggedness),
finite n-parent crossover (genotype.crossover, per-gap recombination rate),
and hill-climb (parents = local optima = trained models).
E9 (recomb_landscape) -- the "why sex?" test: E8's dramatic super-parent
result used an ADDITIVE landscape. On rugged/epistatic landscapes, blindly
recombining local optima causes OUTBREEDING DEPRESSION -- offspring fall
below the parents, worse with both ruggedness and recombination rate (K=8,
free recomb: ~ -0.23), and the optimal recombination rate shrinks as
ruggedness grows. Design rule: merge freely when skills are complementary/
additive; sparingly (and with selection) when entangled.
E10 (directed_sex) -- directed sex beats biological sex: biology is stuck
with 2 random-mating parents and no offspring preview; an AI can choose
complementary mates, evaluate many recombinant offspring, keep the fittest,
and use unbounded parents (iterated recombine-then-select). Random
("biological") sex craters with ruggedness (0.66->0.51); directed sex
tracks/exceeds the best parent at every ruggedness -- converting the
outbreeding-depression catastrophe into a win. No biological analog.
Complete sexual-transmission picture: dramatic super-parent offspring when
skills are complementary (E8); outbreeding-depression risk when entangled
(E9); directed sex resolves the risk (E10). configs/layer1/{E9,E10}.yaml,
figures/plot_{E9,E10}.py, READMEs, +5 tests (117 green).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Enter the Lamarckian society with a robust theoretical frame. The single-
locus, fixed-p* model can only express recovery toward a ceiling; the
society's load-bearing claim is vertical -- capability that EXCEEDS any
component. Generalize knowledge to a distribution over genotypes (L
biallelic loci, K=2^L, additive fitness = # correct loci), reusing all the
K-mode machinery. The one new operator is recombination: free recombination
sends p -> product of per-locus marginals (linkage equilibrium).
E8 (star, kind: society) -- the vertical claim / Fisher-Muller: decorrelated
PARENTS (specialists, expert on their loci, agnostic elsewhere) are
recombined; sexual merge assembles a genotype fitter than any parent,
climbing to the optimum (12/12, a genotype no parent had) as parent count
grows and rho->0, while the best single parent (~8.7) and the mean-mixture
"model soup" (~11.6) plateau below. Reuses make_retention_matrix (locus
mastery replaces tail-item retention).
E7 (kind: genotype_lineage) -- the advantage of sex: a single population
adapts toward the optimum; the sexual lineage adapts faster than asexual
(clonal interference) by keeping loci in linkage equilibrium (LD->0 vs LD
spike). Honest scope: a speed advantage, not a permanent Muller's-ratchet
gap (subtle to force); E8 carries the headline.
Metaphor shift (per GG): the society is sexual reproduction with UNBOUNDED
parents, not teacher->pupil. Teacher->pupil caps at the ceiling; n-parent
recombination is combinatorial and generative, and unlike biology there is
no two-parent limit. Collapse = asexual degradation; the cure = sex. This
unifies E4 (merge != average) + E6 (irreversibility) under evolution-of-sex
theory and reaches ground Riis's single-locus n-grams cannot.
New: knowledge/{genotype,genotype_lineage,society}.py, configs/layer1/{E7,
E8}.yaml, figures/plot_{E7,E8}.py, READMEs, tests/test_genotype.py (+7).
experiment.py dispatch (kind in {genotype_lineage, society}); make layer1
wired. 112 tests green.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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>
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>
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>
src/neural/recombine.py mirrors Layer-1 run_coverage but trains K_T specialist RNNs on
assignments from the exact shared-switch retention construction (K_T/rho/q clean; union
matches the closed form), then recombines the measured teacher distributions two ways:
mean (naive pooling) vs oracle-guided max-merge (per-mode strongest teacher, M2N2-style),
each followed by size-n resampling.
Result (8 reps): at rho=0, union rises 0.49->0.96 (supply matches closed form); analytic
surviving_max rises 0.043->0.087 while surviving_mean stays flat ~0.045 — the conservation
law (averaging cancels the union gain, max-merge realises it). At rho=1 (identical
teachers) union and max are flat. The lesson holds in the neural setting; trained-weight
columns show the same signs but noisier (smoothing inflates baseline; deep tail barely
clears n=200 resampling). torch-gated test added. 93 tests green.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
configs/neural/{N0,N1,N2,N5}.yaml -> {bridge,collapse,grounding,architectures}.yaml,
results dirs likewise. Updated experiment/output.dir fields, comments/docstrings, and
docs; regenerated the four result manifests (now carrying the real git commit). No
functional path resolution referenced the codes (the Makefile globs configs/neural/*.yaml
and tests use inline configs), so nothing breaks. 92 tests green.
Co-Authored-By: Claude Opus 4.8 (1M context) <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>
