mxv456/spatial-wave-search-512m-hero

A 9 M-parameter transformer that runs a path search on its own scratchpad (512 m windows)

Figure. A free-running search by this network on a synthetic house maze (512 m window, 2 m cells). Each frame is one pass: the orange cells are the network's whole output, fed back verbatim as its next input. The state token it emits (SEARCH → BACK → DRAW → DONE) chooses the next pass; nothing outside the network decides anything between passes. Route of 431 m walking, 26 passes. The network was trained only on Amsterdam map layers.

This is the network behind the headline animation of spatial-reasoning-from-scratch, a study of what spatial reasoning a small vision transformer can learn from spatially aligned city map layers with exact targets. It is not a vision-language model: input and output are rasters.

What it does

• Input: a 512 m × 512 m window of Amsterdam drawn as 17 aligned planes at 1 m per pixel (buildings, surface classes, road noise, places, sunshine, …), two markers (start and goal) in a marker plane, and a scratchpad plane holding its own previous output.
• Output: the whole next scratchpad on a 256 × 256 grid of 2 m cells, plus one state token.
• The algorithm it learnt (from a teacher: one clearance-priced wave per route): spread a front 40 m further each pass until the goal is reached, then walk the way back front by front, then draw the path. Run free, it solves 32 % of 500 held-out 512 m routes (91 / 71 / 33 / 18 / 2 % for routes of 2–3 / 4–5 / 6–8 / 9–12 / 13+ fronts) and 40 % of 500 routes on a synthetic house maze it never saw. One pass takes 2.4 ms on an RTX 3060; a route about 60 ms.

Model

4 transformer blocks, width 384, 6 heads, 16 px patches (1,024 tokens at 512 m), learned relative position bias, two condition tokens (state, task), a per-cell 2-class head and a 41-class token head; 8.86 M parameters. Trained from scratch: 48k steps at 256 m, one round of training on its own drawings ("natural noise"), then continued for 16k steps at 512 m (batch 64, lr 1e-4). Run id c5_r5_wave_nat3_tok01_from_ownp50_L4_16k_g256_b64_zc512 in the repository's run ledger.

How to use

The checkpoint is a plain state_dict for the LocalGridViT class of the repository; it needs that code and the data pipeline (or the released evaluation bundle):

git clone https://github.com/Marvel4U/spatial-reasoning-from-scratch
# place this file as runs/checkpoints/c5_r5_wave_nat3_tok01_from_ownp50_L4_16k_g256_b64_zc512.pt
# unpack eval_bundle_v0.2.tar.gz of the GitHub release and copy its data/ and runs/ into the clone (REPRODUCE.md section 8)
cd harness
PYTHONPATH=. python diagnostics/wave_rollout_eval.py c5_r5_wave_nat3_tok01_from_ownp50_L4_16k_g256_b64_zc512 --n 500 --mode free
PYTHONPATH=. python diagnostics/wave_rollout_gif.py   c5_r5_wave_nat3_tok01_from_ownp50_L4_16k_g256_b64_zc512 --route 8 --crops ../data/synthetic/maze_v2_houses/crops/v4ns --store c4_512_val

REPRODUCE.md in the repository lists every command with wall times.

Related models

• mxv456/spatial-wave-search-256m: the 256 m network, the stronger one on its own window (78 % of 500 held-out routes, 60 % on a never-seen district, 51 % on house mazes).
• mxv456/qwen3-vl-2b-lora-map-routes: the Qwen3-VL-2B LoRA fine-tune on the same routes, the vision-language baseline of the repository's PAPER.md (49.6 % under the same rule).

Limitations

One city for training; held-out routes of the training district and one never-seen district of the same city; single seed; the success rule scores the drawing as a set of cells; long routes (13+ fronts) are mostly unsolved at this size.

Citation and licence

Marvin Uhlmann, Spatial reasoning from scratch on real city data, 2026, github.com/Marvel4U/spatial-reasoning-from-scratch. Code and weights MIT; the Amsterdam layers carry their own licences (3DBAG CC BY 4.0, BGT CC0, AHN CC0, OSM ODbL, Overture CDLA-Permissive), listed in the repository's DATA_LICENSES.md.