heights1976/embedded-topology

Exp 3B: Embedded topology in trained recurrent operators

A 14,553-configuration computational sweep of recurrent network architectures trained on dynamical systems. Each configuration's hidden-state activations were measured for topological fidelity to the driving system using persistent homology and Gauss linking integrals. Six post-hoc analyses on saved checkpoints probe the operator properties the embedding theorems describe abstractly.

This dataset is the empirical companion to the manuscript "Topological reconstruction in trained recurrent operators: a 14,553-configuration empirical sweep" on arXiv to follow).

Scope

• 7 architecture families: VanillaRNN, GRU, LSTM, ESN, Mamba, RWKV, Transformer.
• 9 hidden dimensions: 3, 5, 8, 16, 32, 64, 128, 256, 512.
• 3 depths: 1, 2, 4.
• 7 tasks: circle ($S^1$), torus ($T^2$), torus3 ($T^3$), scalar circle, scalar torus, Lorenz, four-dimensional Qi system.
• 11 random seeds per cell.
• Total: 14,553 trained configurations.

Layout

master_results.json          aggregate of all per-config results
master_results.jsonl         streaming form of master_results.json
gpu_co2_report.{md,json}     compute footprint (GPU-hours, kWh, CO2)
batch_summary.json           per-batch aggregated post-hoc metrics
figures/                     20 PNG figures from the analysis pipeline
code/                        analysis pipeline source
configs/<task>/<run_id>/
    results.json             training output (loss, topology metrics)
    post_analysis.json       spectral radius + collision + novel-traj
    dyn_variants.json        altered-dynamics evaluation
    lorenz_ic_sweep.json     Lorenz only: 8-IC robustness
    cross_task.json          cross-task transfer evaluation
    gs_convergence.json      empirical ESP convergence test
    history.json             training curve + per-eval-epoch topology
    epoch_*.pt               final-epoch checkpoint

Hostnames in source data have been mapped to opaque labels (host_A_a2000, host_B_rtx4000, etc.) so the deposit does not leak machine identity.

Reproducibility

Source code for the training and analysis pipeline is under code/. Re-running requires PyTorch, NumPy, scipy, and ripser. See code/scripts/ for individual analyses and code/experiments/exp3b_taxonomy.py for the master training script.

License

CC BY 4.0. Cite the accompanying manuscript when reusing.

Citation