Paper (camera-ready) · Supplementary materials · Talk script
Accepted to GECCO 2026 (AABOH Workshop)
Robin Langer, Claudius Turing, Lyra Vega
Migration topology explains 23.9–49× more variance in diversity than model or domain choice across evolutionary multi-agent systems. Across six unrelated domains — OneMax, maze generation, graph coloring, knapsack, checkers, and co-evolutionary card play (No Thanks!) — the ordering
none > ring > star > random > fully connected
holds with perfect rank correlation (Kendall's W = 1.0, p = 0.00008). The first Betti number β₁ predicts this diversity ordering perfectly. The full algebraic invariant is the first sheaf cohomology group H¹(G; F).
A spectral bridge connects algebraic connectivity λ₂ to the diversity ordering with a further falsifiable prediction: at n ≥ 7 islands, ring preserves more diversity than star (reversing their n=5 relationship). Confirmed at p < 0.0001.
Camera-ready paper:
gecco2026/paper-camera-ready-gecco-v1.pdf
Supplementary materials:
gecco2026/supplementary-materials-README.md — index, reproduction instructions, and download link.
Talk script (Lyra's narration, 15 min):
gecco2026/gecco-talk-script-lyra.md
Slides:
slides/gecco-talk.pdf · slides/gecco-talk.tex
Earlier submitted version (pre-camera-ready):
gecco2026/submitted-gecco2026-aaboh/paper-submitted.pdf
| Figure | File |
|---|---|
| Topology ordering across all six domains | experiments/plots/multi_domain_topology_ordering.pdf |
| Variance decomposition (topology vs domain) | experiments/plots/multi_domain_variance_decomposition.pdf |
| Coupling onset timing by topology | experiments/plots/multi_domain_coupling_onset.pdf |
| Per-seed diversity fingerprints | experiments/plots/fingerprints_panels.pdf |
All publication figures live in experiments/plots/ (PNG + PDF).
Python experimental suite validating the central claim across six domains.
Guide: experiments/README.md
Quick reproduction of the main result:
cd experiments
pip install pandas matplotlib numpy scipy
python multi_domain_analysis.pyKey scripts:
| Script | Purpose |
|---|---|
*_domain.py |
Domain sweep implementations (OneMax, Maze, Graph Coloring, Knapsack, No Thanks!, Checkers) |
multi_domain_analysis.py |
Cross-domain topology ordering, Kendall's W, variance decomposition |
early_convergence_analysis.py |
Diversity trajectories, Mann-Whitney tests |
coupling_onset_analysis.py |
Coupling onset timing by topology |
plot_fingerprints.py, plot_multi_domain.py |
Publication figures |
Raw CSV data (experiment_e_*.csv) — five topologies × 30 seeds × 100 generations per domain — lives alongside the scripts in experiments/.
Categorical framework implementing GA operators as Kleisli morphisms over an MTL effect stack.
Source: haskell/src/Evolution/
cd haskell
cabal build
cabal test
cabal run categorical-evolution -- --demo maze-migration-sweepKey modules: Category.hs (GeneticOp type), Island.hs (topology-parameterized migration), Effects.hs (EvoM monad stack), Operators.hs (selection, crossover, mutation).
An expanded journal-length version (12–15 pages LNCS) building on the GECCO result with new experiments (β₁ vs λ₂ two-timescale decomposition, ring vs star at constant β₁, LLM multi-agent sign-flip).
cais2026/eumas2026.pdf— draft PDFcais2026/eumas2026.tex— LaTeX sourcecais2026/EUMAS_PLAN.md— section outline and experiment plan
Short abstract version of the core result.
XTX AI4Math Fund application for research on categorical foundations for provably correct AI agent orchestration.
grant/README.md— overviewgrant/grant-math-supplement.md— mathematical supplementgrant/attachments/— 34 research files on container theory and orchestration
useful_information/GUIDE.md— developer guide to navigating the repouseful_information/medium-article.md— accessible explanation draftuseful_information/strict-lax-plain-language.md— plain-language functor explanation
Earlier drafts and superseded material:
archive/gecco2026/— rough GECCO drafts (pre-submission)archive/paper-outline.md,archive/paper-experiments.md— early planning notespaper/— working paper directory (pre-camera-ready drafts and submitted snapshots)
MIT