Giorgio Gilestro
2d8f661924
"Model" now means an AI model everywhere; the Wright-Fisher construct is "the
biological model" throughout (19 occurrences): tier header, section title (now
"The biological model, and where trained learners depart from it"), Table 1
support column ("Exact" -> "Closed form"; "Analytic model" -> "Biological
model"), Results, Discussion, Methods ("Biological-model tier"), and all
figure captions. "Exact" survives only in technical noun phrases (exact-match
verifier, exact oracle, exact equilibrium, exact recovery); the abstract's
"exactly Wright-Fisher" is now "literally Wright-Fisher".
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v
218 lines
13 KiB
Python
218 lines
13 KiB
Python
r"""Build the PNAS-draft PDF from main.md (Markdown stays the source of truth).
|
||
|
||
Adapted from paper/arxiv/md2tex.py (same Markdown subset + pipe tables), with one addition: standalone
|
||
`*(FIG:name)*` markers place the publication figures produced by make_figs.py (unified, lettered,
|
||
codename-free panels re-plotted from the committed artifacts). Run make_figs.py before building when
|
||
results change.
|
||
|
||
Usage: python paper/pnas/build.py && (cd paper/pnas && tectonic main.tex)
|
||
"""
|
||
|
||
from __future__ import annotations
|
||
|
||
import re
|
||
import shutil
|
||
from pathlib import Path
|
||
|
||
ROOT = Path(__file__).resolve().parents[2]
|
||
HERE = Path(__file__).resolve().parent
|
||
SRC = HERE / "main.md"
|
||
OUT = HERE / "body.tex"
|
||
|
||
# figure name -> (single publication PDF from make_figs.py, caption)
|
||
FIGURES: dict[str, tuple[list[str], str]] = {
|
||
"fig1": (["paper/pnas/figs/fig1a.pdf", "paper/pnas/figs/fig1b.pdf"],
|
||
"(A) The experimental programme. Each population-genetic abstraction (Table 1) is tested at up "
|
||
"to three tiers, ordered left to right by increasing realism: a biological model (a "
|
||
"Wright--Fisher simulator over knowledge distributions; closed forms, bitwise-reproducible), "
|
||
"trained neural networks measured against exact oracles (recurrent, feedforward, and "
|
||
"variational-autoencoder generators on a synthetic mode universe, and a convolutional VAE on "
|
||
"MNIST), and language models (LoRA specialists on Qwen bases at 0.5B and 7B, scored by an "
|
||
"exact-match verifier). Colour separates the two categories: the biological model in blue, "
|
||
"the two AI-model tiers in oranges. The same abstractions are carried across "
|
||
"all three. Rows are the framework's mechanisms, each defined at the left margin; filled "
|
||
"cells name the experiments run at each tier, and each carries, in its corner, the figure "
|
||
"or table where that result is reported, so this figure doubles as a map of the paper. Each claim is tested at the cheapest tier that "
|
||
"can falsify it, and a costlier tier is entered only where it adds a discriminating test "
|
||
"rather than a replication: grounding at language-model scale is established in prior work "
|
||
"(21, 30) and is not re-run; epistasis and the society skip the middle tier, whose "
|
||
"distinctive value (exact oracles) does not bear on those operator-level questions; and the "
|
||
"society at language-model scale is the integrative experiment this paper specifies but does "
|
||
"not run --- its stated gap. (B) The conceptual basis of the transfer. A population of models "
|
||
"is usually pictured as a society in space: contemporaries exchanging messages. The couplings "
|
||
"this paper studies run instead between generations --- training on model output "
|
||
"(inheritance), weight-space merging (recombination), verified real data entering each "
|
||
"generation (immigration from reality) --- a society in time, the object population genetics "
|
||
"was built to describe. Dots mark capabilities: the rare one (gold) is lost under "
|
||
"single-parent inheritance, reassembled by merging complementary parents, and re-supplied by "
|
||
"grounding."),
|
||
"fig2": (["paper/pnas/figs/fig2.pdf"],
|
||
"Grounding is immigration. (A) Stationary diversity against the grounding fraction in the "
|
||
"biological model: simulation (points, 95\\% CI) matches the exact immigration--drift "
|
||
"equilibrium (dashed). The equilibrium is smooth in $g$; $g \\approx 0.05$ marks the "
|
||
"operational threshold retaining 95\\% of source diversity in this setting (red line, "
|
||
"bootstrap CI shaded); the hollow point at $g=0$ is a finite-time value (the true equilibrium "
|
||
"is zero). (B) The same signs on real images: samples from a convolutional VAE retrained each "
|
||
"generation on its own output (rows: generations 0--15 of an ungrounded lineage) collapse "
|
||
"toward a single blurred mode; 10\\% grounding holds all thirty modes (quantified in SI)."),
|
||
"fig4": (["paper/pnas/figs/fig4.pdf"],
|
||
"Recombination in the biological model: blending inheritance and the Fisher--Muller effect. "
|
||
"(A) Expected rare-capability survival in a child refit from $K$ uncorrelated parents: the "
|
||
"output-mean (blending) stays at the single-parent level --- the first-order cancellation --- "
|
||
"while the union operator (strongest source per item, renormalised, oracle-identified) rises "
|
||
"with parent count. (B) Multi-locus recombination of decorrelated specialists produces "
|
||
"offspring fitter than any parent, approaching the optimum as parents are added; the best "
|
||
"single parent and the blended average plateau below (mean $\\pm$ 95\\% CI)."),
|
||
"fig5": (["paper/pnas/figs/fig5.pdf"],
|
||
"Rugged (epistatic) landscapes: risk, remedy, and population structure. (A) Outbreeding "
|
||
"depression: the mean offspring of blindly recombined specialist parents falls below the best "
|
||
"parent, more steeply the more rugged the landscape (NK ruggedness $K$) and the higher the "
|
||
"recombination rate. (B) Screening candidate offspring against a verifier (directed "
|
||
"recombination) restores the gain at every ruggedness where blind recombination fails. "
|
||
"(C) Mating structure: the best champion arises at wide mate-pool breadth on smooth landscapes "
|
||
"and at intermediate breadth on rugged ones. (D) Wide breadth monotonically erodes population "
|
||
"diversity at every ruggedness (mean $\\pm$ 95\\% CI, 20 replicates)."),
|
||
"fig6": (["paper/pnas/figs/fig6.pdf"],
|
||
"The tested society: grounded evaluation, recombination, and diversity preservation make "
|
||
"complementary contributions. A finite agent population on a rugged NK landscape; selection "
|
||
"weights true fitness against conformity to the population consensus. (A) Best real fitness: "
|
||
"the full system approaches the global optimum; removing grounded evaluation collapses the "
|
||
"population onto a confident, unfit consensus; removing recombination or diversity "
|
||
"preservation strands it lower. (B) Population diversity. (C) The self-consumption signature: "
|
||
"conformity minus true fitness (mean $\\pm$ 95\\% CI, 12 replicates)."),
|
||
"fig7": (["paper/pnas/figs/fig7.pdf"],
|
||
"Model speciation at three tiers. (A) Biological model: hybrid fitness tracks the parents while "
|
||
"lineages are compatible, then falls to inviability; the denser the incompatibilities, the "
|
||
"earlier the fall. (B) The isolation cliff: probability of hybrid inviability against "
|
||
"divergence, by incompatibility density. (C) Trained networks: the merge error barrier between "
|
||
"two MLPs before and after permutation-and-rescaling alignment --- the same-task/different-"
|
||
"start barrier is a coordinate artefact (removed by alignment); the conflicting-task barrier "
|
||
"is left essentially unchanged. (D) Sweeping the fraction of conflicting classes: the residual "
|
||
"barrier rises while merged-model accuracy falls from 0.97 to 0.03. (E) Language models (0.5B "
|
||
"LoRA children of a shared base): on shared ambiguous prompts each parent performs under its "
|
||
"own convention while the merged model falls below both --- function-specific hybrid "
|
||
"breakdown. (F) Divergence without conflict: over-training disjoint specialists from 1 to 12 "
|
||
"epochs produces no isolation; the merged model tracks or exceeds the parents throughout."),
|
||
"fig3": (["paper/pnas/figs/fig3.pdf"],
|
||
"The language-model tier. (A) Seed-replicated merging (0.5B, five seeds, fixed test sets; mean "
|
||
"$\\pm$ 95\\% CI): merged specialists exceed the best single specialist overall, and only "
|
||
"merged models are competent on every task family. (B) Hard, unsaturated tasks at 7B (single "
|
||
"run): the weight-average dilutes a fragile specialist below the best single parent; routing "
|
||
"among intact specialists preserves it. (C) The controlled predictive test (13 conditions "
|
||
"$\\times$ 3 seeds): pre-merge confidence-weighted functional conflict against merge penalty, "
|
||
"coloured by grid axis --- penalty concentrates on the conflict axis. (D) Predictor "
|
||
"comparison, $|$Spearman $\\rho|$ against merge penalty over the full grid: functional "
|
||
"measures carry signal, the tested weight-geometry baselines do not; paired differences "
|
||
"between predictors are not individually significant."),
|
||
}
|
||
|
||
UNICODE = {"—": "---", "–": "--", "→": r"\(\rightarrow\)", "≈": r"\(\approx\)", "≥": r"\(\geq\)",
|
||
"≳": r"\(\gtrsim\)", "×": r"\(\times\)", "·": r"\(\cdot\)", "μ": r"\(\mu\)",
|
||
"ρ": r"\(\rho\)", "≤": r"\(\leq\)", "≪": r"\(\ll\)", "∝": r"\(\propto\)"}
|
||
SPECIALS = {"&": r"\&", "%": r"\%", "#": r"\#", "_": r"\_", "$": r"\$",
|
||
"~": r"\textasciitilde{}", "^": r"\textasciicircum{}"}
|
||
|
||
|
||
def esc(s: str) -> str:
|
||
s = s.replace("\\", r"\textbackslash{}")
|
||
for k, v in SPECIALS.items():
|
||
s = s.replace(k, v)
|
||
for k, v in UNICODE.items():
|
||
s = s.replace(k, v)
|
||
return s
|
||
|
||
|
||
def inline(s: str) -> str:
|
||
parts = re.split(r"(`[^`]*`)", s)
|
||
out = []
|
||
for p in parts:
|
||
if p.startswith("`") and p.endswith("`") and len(p) >= 2:
|
||
out.append(r"\texttt{" + esc(p[1:-1]) + "}")
|
||
else:
|
||
p = esc(p)
|
||
p = re.sub(r"\[([^\]]+)\]\((https?://[^)]+)\)", r"\\href{\2}{\1}", p)
|
||
p = re.sub(r"\*\*([^*]+)\*\*", r"\\textbf{\1}", p)
|
||
p = re.sub(r"\*([^*]+)\*", r"\\emph{\1}", p)
|
||
p = re.sub(r'"([^"]+)"', r"``\1''", p)
|
||
out.append(p)
|
||
return "".join(out)
|
||
|
||
|
||
def figure_env(name: str) -> str:
|
||
pdfs, caption = FIGURES[name]
|
||
incl = "\\\\[6pt]\n".join(f"\\includegraphics[width=\\textwidth]{{figs/{(ROOT / p).name}}}"
|
||
for p in pdfs)
|
||
lines = [f"\\begin{{figure*}}[p]\\centering % {name}",
|
||
incl,
|
||
f"\\caption{{{caption}}}\\label{{{name}}}",
|
||
"\\end{figure*}"]
|
||
return "\n".join(lines)
|
||
|
||
|
||
def convert(text: str) -> str:
|
||
lines = text.split("\n")
|
||
i = 0
|
||
while i < len(lines) and lines[i].strip() != "---":
|
||
i += 1
|
||
i += 1
|
||
|
||
blocks: list[list[str]] = []
|
||
cur: list[str] = []
|
||
for line in lines[i:]:
|
||
if line.strip() == "":
|
||
if cur:
|
||
blocks.append(cur); cur = []
|
||
else:
|
||
cur.append(line)
|
||
if cur:
|
||
blocks.append(cur)
|
||
|
||
def emit_table(block, out):
|
||
rows = [[c.strip() for c in line.strip().strip("|").split("|")] for line in block]
|
||
header, body = rows[0], rows[2:]
|
||
n = len(header)
|
||
widths = " ".join([f"p{{{0.92 / n:.3f}\\textwidth}}"] * n)
|
||
out += ["\\medskip\\noindent\\begin{center}\\footnotesize",
|
||
f"\\begin{{tabular}}{{{widths}}}", "\\hline",
|
||
" & ".join(inline(c) for c in header) + " \\\\ \\hline"]
|
||
for r in body:
|
||
r = (r + [""] * n)[:n]
|
||
out.append(" & ".join(inline(c) for c in r) + " \\\\[3pt]")
|
||
out += ["\\hline\\end{tabular}\\end{center}\\medskip", ""]
|
||
|
||
out: list[str] = []
|
||
for block in blocks:
|
||
first = block[0].strip()
|
||
m = re.match(r"^\*?\(FIG:(\w+)\)\*?$", first)
|
||
if m:
|
||
out.append(figure_env(m.group(1))); out.append("")
|
||
elif first.startswith("|") and len(block) >= 2 and set(block[1].strip()) <= set("|-: "):
|
||
emit_table(block, out)
|
||
elif first == "---" and len(block) == 1:
|
||
out.append("\\medskip\\hrule\\medskip"); out.append("")
|
||
elif first.startswith("## "):
|
||
out.append(f"\\section*{{{inline(first[3:])}}}"); out.append("")
|
||
elif first.startswith("### "):
|
||
out.append(f"\\subsection*{{{inline(first[4:])}}}"); out.append("")
|
||
elif re.match(r"^(- |\d+\. )", first):
|
||
env = "itemize" if first.startswith("- ") else "enumerate"
|
||
out.append(f"\\begin{{{env}}}")
|
||
items: list[str] = []
|
||
for l in block:
|
||
s = l.strip()
|
||
if re.match(r"^(- |\d+\. )", s):
|
||
items.append(re.sub(r"^(- |\d+\. )", "", s))
|
||
else:
|
||
items[-1] += " " + s
|
||
for it in items:
|
||
out.append("\\item " + inline(it.strip()))
|
||
out.append(f"\\end{{{env}}}"); out.append("")
|
||
else:
|
||
joined = re.sub(r"\s{2,}", " ", " ".join(l.strip() for l in block)).strip()
|
||
out.append(inline(joined)); out.append("")
|
||
return "\n".join(out) + "\n"
|
||
|
||
|
||
if __name__ == "__main__":
|
||
OUT.write_text(convert(SRC.read_text()))
|
||
print(f"wrote {OUT}")
|