tiny-cube-solver

A 33.6M-parameter network that guesses how many moves a Rubik's Cube is from solved, plus a search that uses the guess to find the moves. It was trained from nothing: no solver, no example solutions, no human data.

• Solves 95% of fully scrambled cubes (142 of 150, scrambles of 20 to 100 moves)
• Solves every cube scrambled with 10 moves or fewer
• Built as a control for RubiksBench, where language models must write the whole answer in one reply. On the same full scrambles the best of them, GPT-6 Astra, solves 9 of 10 with answers averaging over 100 moves; this model's answers average about 22. It is not the same test: this model gets a search loop, the language models get one reply.

Write-up and replays: https://brianbriscoe.dev/lab/tiny-cube-solver

Try it

pip install torch transformers safetensors huggingface_hub
python solve.py --scramble "R U F' D2 L B'"

or with a cube state in the kociemba layout (faces U R F D L B, nine stickers each):

python solve.py --facelets <54 characters>

Use --beam 1024 for full scrambles, which needs a GPU. The default, 64, is fast enough for a laptop, but it only solves short scrambles.

solve.py has no other dependencies. It downloads config.json and model.safetensors from this repo the first time.

How it works

The network does not write moves. It reads the 54 stickers of one cube and returns one number: its guess of the distance to solved.

solve.py then searches:

1. Apply each of the 18 moves to every position it is keeping.
2. Ask the network to score all the new positions.
3. Keep the best --beam of them, and repeat.
4. Stop when one of them is the solved cube.

Every move is applied by ordinary code, and the answer is checked before it is printed. The network only decides which positions are worth keeping.

Training: the model makes its own answers

The model was trained by approximate value iteration (the method behind DeepCubeA). It starts from one free fact: the solved cube is 0 moves from solved. A cube is then 1 more than its best neighbour. The network learns from its own previous guesses, and the correct answers spread outward from the solved cube, one move further each round. No solver is involved at any point.

An earlier version with the identical network was trained on distances from the Kociemba solver instead. It solved only 16% of full scrambles. Kociemba returns good solutions, not the shortest, and 47% of random cubes got the label "21", so there was nothing to learn from above distance 15. Changing only the labels took full scrambles from 16% to 96%.

Results

Canonical RubiksBench scrambles (the same cubes every language model on the board is tested on), 25 cubes per scramble length:

Scramble length	Solved (beam 1024)	Average answer
3	25/25	3.0 moves
6	25/25	6.0
10	25/25	10.0
15	25/25	20.4
20	24/25	22.0
25	24/25	21.9
30	25/25	21.6
40	23/25	23.0
50	23/25	21.9
100	23/25	21.5
all	242/250 (96.8%)

Measured 2026-09-24 on one RTX A6000. Every cube and answer is replayable at https://brianbriscoe.dev/lab/tiny-cube-solver.

Past about 15 moves, every scramble is fully mixed, so 25, 50 or 100 moves are no harder than 20. A full scramble takes about 80 to 90 seconds on one RTX A6000.

Model

• A Llama-shaped encoder, trained from scratch: 8 layers, width 512, 8 heads. The architecture only; no Llama weights.
• Input: [BOS] + 54 sticker tokens + [SEP]. Output: the mean of the final layer, through one linear layer, to one number.
• 33,577,985 parameters, float32.

Things that give much lower numbers

What you did	What you get at 20 moves
Always take the best-scored move, no search	34% even at 10 moves
Judge the network by its average error	about 1.5 moves, which looks poor; the search only needs the correct ranking of the 18 neighbours

Limits

• It is not fast. The Kociemba two-phase solver solves any cube in milliseconds. This model exists to show that a small network can learn the task at all.
• Solutions are not guaranteed to be shortest. Full scrambles average about 22 moves.
• 3x3x3 only.

License

MIT. See LICENSE.