# Work order — PNAS submission: "The Evolution of Sex for Artificial Intelligence"

*Created 2026-08-11. Target: PNAS Direct Submission research article (~6 pp main + SI Appendix),
preceded by an arXiv preprint (q-bio.PE × cs.LG). Decision basis: 2026-08-11 literature + venue scan
(see memory/competitive-landscape.md, August addendum). GG approved PNAS + the analysis.*

**Governing constraints.** (1) Dual audience: every claim stated so a computer scientist and a
biologist can each follow it — keep the "two statements of the same fact" device and the
dictionary table; define every term at first use. (2) Honesty ledger: concede Riis +
First-Extinction + quantitative-trait collapse up front; claims are the *cure* and its theory, not
the diagnosis. (3) Reproducibility is the differentiator: every figure from committed artifacts,
code+data DOI at submission.

---

## Phase 1 — Referee-proof the headline (E13 hardening) — Week 1

The speciation result (E12+E13) is both our most novel and most exposed claim
(arXiv:2606.23607, June 2026: a symmetry group larger than permutations removes most transformer
barriers). Patch before the preprint goes up.

- [x] **E13c — scale-aware alignment (the symmetry defense).** *(Done 2026-08-11: canonicalise_scale
  + gated tests; decomposition & cliff regenerated — conflict residual 0.502→0.497 under the full
  group, independent 0.001; floor proposition drafted in paper/si-notes.md S1. Hybrid-fitness
  readout added: cliff accuracy 0.97→0.03.)*
  - Extend `neural/rebasin.py` with per-unit **positive rescaling** canonicalisation: for the
    no-BatchNorm ReLU MLP, the full function-preserving unit symmetry group is permutation ∘
    positive diagonal scaling. Canonicalise both nets first (rescale each hidden unit to
    ‖in-weights‖=1, pushing the norm into the out-weights), *then* permutation-match. Sanity gate:
    a randomly permuted **and rescaled** copy must realign to functional identity (extend
    `tests/test_rebasin.py`).
  - Re-run `speciation_real` + `speciation_real_cliff` reporting `residual_perm` vs
    `residual_perm_scale`. Expected: independent-init residual stays ≈0; conflict residual
    unchanged. Update figure/README.
  - Write the **theoretical floor proposition** (SI): two models with low loss on *contradictory*
    label assignments over the same inputs cannot both be matched by any function-preserving
    transformation — any single merged function errs on at least the disagreement mass, so the
    conflict-condition barrier has an information-theoretic floor independent of the symmetry
    group. Cite 2606.23607 and position: their result strengthens ours (the *removable* part may
    grow with richer groups; the *functional* residual cannot vanish). Also cite the two June-2026
    LMC papers found in the direct arXiv sweep (2026-08-11): "Beyond Structural Symmetries: Linear
    Mode Connectivity via Neuron Identifiability" (2606.03…) and "Functional Equivalence in
    Attention … Applications to Linear Mode Connectivity" (2606.16…) — same objection family, same
    defense. Direct arXiv API sweep also re-confirmed: speciation/DMI/Fisher–Muller/ratchet/
    evolution-of-sex/mating-for-models have zero ML hits on arXiv itself as of the newest listings.
- [x] **E13b — emergent speciation (the decisive missing experiment).** *(Done 2026-08-11: the
  pre-registered SECOND reading — residual 0.000 at every t_div ≤ 3200 in both `disjoint` and
  `augment`; the merge RESCUES the forgetting specialists (parents 0.535/0.474 → merged 0.955,
  sustained Fisher–Muller). Speciation requires functional conflict in this regime; LLM-scale
  over-specialisation deferred to Phase-3 llm_speciation. Figure panel C + READMEs updated.)* Current E13 *imposes*
  contradiction; a true Dobzhansky–Muller incompatibility is *emergent* (each change harmless
  alone, bad only in combination). Design (`speciation_real` new conditions, CPU/torch, cheap):
  - `disjoint`: fork from the shared MNIST base; child A continues on classes 0–4 only, child B on
    5–9 only (no contradiction anywhere). Sweep divergence time `t_div`. Measure naive barrier and
    scale+perm-aligned residual on the full task, **and merged-model accuracy vs best parent**.
  - `conventions` (optional, purer DMI): same task, different augmentation conventions (A:
    rotations, B: inversions) — representational drift with zero output conflict.
  - **The money curve:** merged accuracy vs `t_div` should trace E12's *compatible →
    outbreeding-depression → inviability* trajectory emergently: at low divergence the merge
    *rescues* the two forgetting specialists (Fisher–Muller), at high divergence it fails
    (speciation). If it comes out, this is a headline panel. Either outcome is publishable
    (no growth ⇒ "models are safer to merge than biology predicts" — an honest bound).
  - Tests + README + fold into figure. Pre-register the falsifier language before running.

## Phase 2 — arXiv preprint package (GG decision 2026-08-11: DO NOT POST until all experiments
and analysis are complete — the preprint goes up after Phase 3, with the final analysis folded in;
re-run md2tex + tectonic at that point)

- [x] Citation refresh in `paper/the-evolution-of-sex-for-ai.md` *(done 2026-08-11; author names verified against arXiv API)*: **new concessions** —
  First-Extinction Law (2509.20101), quantitative-trait collapse (2407.17493), verifier-injection
  (2510.16657); **precursor** — Livnat & Papadimitriou, *Sex as an algorithm* (CACM 2016);
  **adjacent-to-differentiate** — merge-collapse theory (2603.09463), mergeability prediction
  (2601.22285), non-local merging (2410.12766), model kinship (2410.12613), expert-duration
  (2607.11997), symmetry-scaling (2606.23607), Harris (2604.05142), in-context diversity collapse
  (2604.18005, 2603.24676).
- [x] Fold E13b/c results into the speciation section (whatever they show — honestly). *(Done: full-symmetry residual + hybrid-fitness cliff + the emergent converse, in abstract, §5, §13 and the accessible version.)*
- [x] LaTeX conversion: `paper/arxiv/` (md2tex.py block-based converter from the Markdown source of
  truth; main.tex; 3 figures; builds clean under tectonic, 20 pp; arXiv pdflatex hint guarded).
- [ ] **Post to arXiv — DEFERRED until all experiments/analysis are done (GG).** Package is ready
  (`paper/arxiv/`, instructions in `ARXIV-SUBMISSION.md`); rebuild after the Phase-3 results are
  folded into the manuscript, then upload.

## Phase 3 — New experiments for impact & robustness — Weeks 2–3

- [x] **`llm_speciation` — the cliff at the LLM tier.** *(Run 2026-08-11, 0.5B: DURATION NULL —
  over-trained disjoint specialists merge better not worse (0.84->0.94, above best parent throughout);
  the MLP "no emergent isolation" null generalises. CONFLICT — function-specific hybrid breakdown:
  merged coherence 0.02-0.08 falls below BOTH parents (~0.2) on the conflicted function. Caught a
  design confound (replace mode ties conflict_frac to private-data budget) -> built the de-confounded
  `add` variant (conflict_mode: add; configs/llm/speciation_add.yaml). 7B confirm optional later.)*
  Speciation demonstrated at all three tiers (analytic → MLP → LLM) makes the headline
  unassailable. Structural bonus to state in the paper: LoRA deltas live in the frozen base's
  coordinate system, so there is **no permutation ambiguity by construction** — any LoRA-merge
  failure is *functional* incompatibility, the residual isolated architecturally.
  - Conflict knob: two LoRA children from the same base learn contradictory conventions on a
    shared family (e.g. "sort ascending" vs "sort descending"; answer-format conflicts) on a
    fraction `conflict_frac` of prompts, plus their own disjoint families. Sweep `conflict_frac`,
    soup-merge, evaluate on neutral held-out + both convention sets. Predict a monotone cliff.
  - Emergent knob: take existing disjoint specialists, sweep **training duration**
    (over-specialisation) → merged performance vs steps. Frames the Amazon observation
    (2607.11997: optimal expert duration) as *our theory explaining their data* — a strong PNAS
    move.
  - 0.5B locally first; one 7B CX3 confirm if the sign is clean (`hpc/` PBS, minutes).
- [x] **Multi-seed the LLM arc (0.5B tier done 2026-08-11).** All three claims hold with CIs
  (merge>every specialist; union 0.274±0.026 > fusion 0.174±0.102 hard; directed 0.221±0.026 > soup)
  + NEW finding: fusion is seed-FRAGILE on hard tasks (±0.10) while routing/directed are stable
  (±0.026) — the union/selection operators are the reliable ones. results/llm_*_seeds/ + llm_seeds
  figure. Remaining: 7B CX3 seeds (1-3) when HPC convenient.
  - Thread the seed into specialist cache keys (`spec_<family>[_hard]_s<seed>`); verify nothing
    else assumes the old names.
  - 0.5B: seeds 1–5 × {merge, moe, directed} × {easy, hard}. 7B on CX3: seeds 1–3 × hard
    {merge, moe, directed} (8–25 min walltimes → trivial). Aggregate figures with 95% CI; update
    READMEs; the headroom law now carries error bars.
- [ ] **`epistasis_predicts` — the DECISIVE experiment (from the external review, 2026-08-11; highest
  priority after llm_speciation lands).** The review's exact bar: population-genetic quantities must
  *predict* (not re-describe) — forecast merge success **before merging**, and beat existing
  predictors. Design, reusing the llm_speciation machinery:
  1. Parents with independently controlled interaction structure: sweep `conflict_frac` (ground-truth
     epistasis) *and* compatible/disjoint + duration variants (spread in divergence WITHOUT conflict),
     so functional conflict and divergence are decorrelated by construction.
  2. Pre-merge predictors, none of which touches a merged model: (a) **operational epistasis** =
     functional-disagreement mass between the parents on a shared probe set (the μ(S) estimate — ours);
     (b) **gradient alignment** (the Zhou et al. 2601.22285 predictor); (c) **weight-space geometry**
     (LoRA-delta cosine / norm distance).
  3. Outcome: merged (soup) performance on private families + convention coherence, held-out test,
     multi-seed.
  4. The claim to test: at matched geometric divergence, the epistasis measure predicts merge outcome
     and the geometry measures do not (R² comparison + an operator-choice decision test — merge vs
     route — under matched budgets).
  Pre-registered falsifier: if gradient/geometry predictors match the epistasis measure, the paper's
  "epistasis, not divergence, sets the cliff" claim stays analytic-only and is labelled as such.
- [x] **Manuscript claim-narrowing (external review, 2026-08-11) — done.** Softened identity claims
  (WF exact only in the minimal model + learning-kernel cited against ourselves; ratchet scoped to the
  irreversible arm), removed "nobody has / none imports / theory outrun" (priority-dispute bait),
  added the interpretation/explanation/prediction ladder to §1, stated the merge-don't-average
  operator boundaries (output-mean vs weight-avg vs routing vs max-with-oracle, budgets, oracle,
  capacity), added a "what these experiments do and do not establish" scope block to the speciation
  section (impossibility floor is information-theoretic, not genetic; snowball/epistasis-cliff =
  hypotheses at the neural tier), replaced "control theory" with "framework" (subtitle included —
  GG can veto), fixed the §3/§11 overstatements (frozen core ≠ frozen behaviour; Baldwin = echo not
  identity; archive vs operational irreversibility), added the **claims-at-a-glance table**
  (status/assumptions/evidence/limits) to §13 + table support in md2tex, and matched the calibration
  in the accessible version. Adopted the review's framing sentence as the stated core contribution.
- [ ] **(Optional, SI-grade) ambiguous-families router stress test** — overlapping-skill families
  where the router is no longer trivially perfect; documents the honest limit of union-by-routing.
  Do only if time permits; otherwise keep the existing rider sentence.

## Phase 4 — The PNAS manuscript — Weeks 3–4

- [ ] **Restructure** `paper/the-evolution-of-sex-for-ai.md` → PNAS research article
  (`paper/pnas/`): Significance (~120 w, dual-audience), Abstract (~250 w), Intro (concede the
  diagnosis; thesis: the cure is sex; where this sits), **Results ladder**:
  1. Collapse is drift, grounding is immigration (E1–E3: exact `H_eq`, `g*≈0.048`, tail threshold
     `m·p*≳1`) — concede Riis/First-Extinction, keep the immigration delta.
  2. Merge, don't average — the conservation law (E4 + neural recombination).
  3. Sex: Fisher–Muller offspring exceed every parent; outbreeding depression on rugged
     landscapes; directed sex as the AI advantage (E8–E10).
  4. **Model speciation** (E12 + hardened E13 + `llm_speciation`) — the headline.
  5. The jointly-necessary society (E11) + mating structure (E14, one panel).
  6. Real-weight confirmation tier: neural/MNIST (brief) + multi-seed LLM headroom law.
  Discussion: the borrowed/ours ledger, the design-rules table (average/route/select/don't-merge ×
  landscape), limits (what LLM-scale still lacks: the full grounded society), what biology gets
  back (in-silico tests of sex theory in regimes biology can't reach). Methods: brief + SI.
- [ ] **Manifesto sections → Discussion or drop** (institutions, four timescales, re-minting
  philosophy, fitness-is-not-truth): compress each to ≤1 paragraph or move to SI "extended
  discussion". The accessible companion doc stays as-is for outreach, not submission.
- [ ] **Dual-audience devices**: Table 1 = the population-genetics ↔ machine-learning dictionary;
  every term defined in one clause at first use; keep "the ML statement / the genetics statement"
  paired-paragraph device, compressed.
- [ ] **Figures: consolidate ~25 per-experiment figures into 5 main multi-panel figures**
  (1 concept/dictionary+operator schematic; 2 collapse&grounding incl. the MNIST digit-decay
  montage — the one image both audiences get instantly; 3 sex: Fisher–Muller/outbreeding/directed +
  merge-don't-average; 4 speciation across three tiers; 5 society ablation + headroom law).
  Everything else → SI figures. All regenerated from committed parquet.
- [ ] **SI Appendix**: results-summary.md as the skeleton; full methods, all closed forms +
  tolerances, per-experiment configs/seeds, the E13 floor proposition, confusion matrices,
  reproduce.sh instructions.
- [ ] Word budget: main text ≤ ~6,000 words; check PNAS current LaTeX template + submission
  checklist at writing time.

## Phase 5 — Submission mechanics — Week 5

- [ ] **Code & data availability**: public GitHub snapshot + Zenodo DOI (code + committed results
  artifacts); PNAS data-availability statement; verify `reproduce.sh` end-to-end on a clean clone.
- [ ] **Cover letter**: the fit argument (Evolvable-AI 2026 precedent; geneticist's-lens
  contribution; what biology gains); position vs Riis/Shumailov explicitly.
- [ ] **Editor & reviewer suggestions**: identify the editor who handled "Evolvable AI" (PNAS
  2527700123; N.C. Stenseth per scan — verify); suggest 3–5 reviewers mixing (i) an
  evolution-of-sex theorist, (ii) a model-merging ML researcher, (iii) a model-collapse author.
- [ ] **Policy checks at submission time** (verify, don't assume): PNAS AI-assistance disclosure
  wording; preprint policy; OA/page charges + whether Imperial has a read-publish agreement with
  PNAS; ORCID; competing interests.
- [ ] Sync arXiv v2 with the submitted text.

## Decision items for GG (not blocking Phases 1–3)

- [ ] Title: keep *"The Evolution of Sex for Artificial Intelligence"* vs a more declarative PNAS
  title (e.g. *"A population genetics of model merging: why AI societies should reproduce
  sexually"*). Decide at Phase 4.
- [ ] Authorship & AI-assistance acknowledgement wording (per PNAS policy).
- [ ] Repo public at submission vs at acceptance (Zenodo DOI needed at submission either way).
- [ ] APC/OA budget approval.

## Discovered During Work

*(append here)*