---
license: cc-by-4.0
language: []
pretty_name: "Exp 3B: Embedded topology in trained recurrent operators"
size_categories:
  - 10K<n<100K
tags:
  - dynamical-systems
  - delay-embedding
  - reservoir-computing
  - persistent-homology
  - recurrent-neural-networks
  - topology
viewer: false
---

# 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