Tools for probing the landscape of fractal basins in recurrent reasoning models

Quickstart

Every solver has the same API: pick a model, pass it a puzzle string (such as an 81-char Sudoku puzzle, or a 900-char maze), and optionally inject your own initial latent states:

import torch
from loopscape import get_solver

puzzle = ".....6.....7.3.4..5..8.....9.8.7.3...1.....9...498.7....2....4387....2......2...."

solver = get_solver("eqr")                         # or "fprm"
z = torch.randn(64, 97, 512)                       # 64 initial conditions
r = solver.solve_batch(puzzle, z_H=z, z_L=z * 0,
                       max_steps=24, noise_scale=0.0,   # deterministic map
                       return_intermediates=True)
# r.grids, r.solved, r.intermediates ([steps][64] decoded grids)

FPRM takes initial_latents= instead of z_H/z_L, with residual halting (fp_thresh, max_iters). The latent shapes vary by model and task: Sudoku has shape (97, 512) for both models, while maze has shape (916, 512) for FPRM and shape (916, 128) for EqR.

demos/basins.ipynb producesbasins through a random 2D slice of each model's latent space and plots the resulting basin and settling-time fields for several (model, task) pairs.

Install

uv add "loopscape @ git+https://github.com/williamgilpin/loopscape"
# + matplotlib/jupyter, to run demos/basins.ipynb:
uv add "loopscape[demos] @ git+https://github.com/williamgilpin/loopscape"
# or from a local checkout:
uv add --editable path/to/loopscape

Requires Python ≥ 3.11. On first use each solver downloads its weights. For EqR/Parcae, the upstream model code is pinned to a fixed commit — into a shared cache (downloaded_checkpoints/ at the repo root; override with LOOPSCAPE_CACHE_DIR). On offline clusters, warm the cache first:

uv run python -c "from loopscape import get_solver; get_solver('eqr')"

Weights and upstream code

• FPRM — inference architecture reimplemented in-package; released checkpoints fetched from fixed-point-reasoners/fprm.
• EqR — weights from locuslab/EqR-model; model code from locuslab/EqR pinned to commit e9934826 (override with LOOPSCAPE_EQR_SRC).
• Parcae — model code from sandyresearch/parcae pinned to commit 6e451955 (LOOPSCAPE_PARCAE_SRC overrides). Weights are our own checkpoint, GilpinLab/parcae-countdown-v1 — a 140M Parcae fine-tuned on Countdown with a reduced integration step (dt_scale = 0.3) — used for every Parcae analysis here (never the original SandyResearch releases); see loopscape.parcae.countdown.