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How to train a convnet to solve a rubiks cube

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How to train a simple convnet to solve a rubiks cube.

Plenty of efficient algorithms exist to solve a rubik's cube. This is to see if a neural net could learn how to solve a cube in the most "efficient" way, by solving the cube in less than 20 moves, i.e god's number.

This is a very naive solution, to start as a proof of concept. I used a 2 layer neural net: 1 convnet layer and 1 feedforward layer. The input is the state of the cube to be solved. The output is the next predicted move until solved. For the training set, I generated games at random during training of 10 moves or less from solved with the corresponding solutions as label. At each step of the solution, I made the network make a guess for its next move and used SGD for training. I trained this over many epochs until the loss was relatively steady.

Surprisingly, the network works decently well for any position less than 6 moves away from solved. I found that by shuffling up to 6 moves, sometimes more, it is able to correctly solve it. It doesn't always work and can definitely use improvement, but its a good place to start.

I used Keras with tensorflow for training. You will need to install Keras to be able to run the network to make predictions. I provide the weights so you don't have to train from scratch.

I used the pycuber library for writing the code to train, which also needs to be installed. I used the MagicCube library for the cube simulation/visualization. I only found MagicCube after using pycuber, so you need to have both installed for now :

pip install pycuber

For MagicCuber, I provide the .zip of their github repo I used at the time. I suggest using this one to avoid conflicts. I provide the training weights for my ConvNet.

To run and play with the cube/shuffle it yourself, clone this repository :

git clone https://github.com/jerpint/rubiks_cube_convnet/edit/master/README.md cd rubiks_cube_convnet python MagicCube/code/cube_convnet_solver.py

You can shuffle using the keyboard and have it solve your own cube. There is a hard-coded reset if you've gone too far and the network can't solve it. This simply retraces back the steps to the initial solved position.

To train the ConvNet from scratch (final weights are in 'rubiks_model.h5') :

python train_cube.py

There is plenty of exploring to do! Bigger networks might be one solution, fancier networks would likely be more appropriate. I thought of reinforcement learning, but decided to use the simpler supervised-learning approach to begin.

REMEMBER: The search-space for a properly mixed cube is HUGE (something like 4e19 iirc). The original thought was that a ConvNet might be able to solve such a space. I do think that a more sophisticated approach would be necessary to solve for 10+ moves. Maybe an idea would be to 'introduce' the cube to known cube algorithms in the train set and let it learn to optimise based on those, such that it can learn to 'think ahead'. Also a reward system reinforcement approach could be a good idea.