Implement symmetries in training about minigo HOT 6 CLOSED

@amj I have a question for random symmetries on both training and selfplay as current mlperf reference implementation. If random symmetries is added to training, is it really necessary to have random symmetries in MCTS inference as well? I want to understand whether its totally duplication or there are still some subtle difference between do it at training and do it at MCTS selfplay or do both.

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The weights in the network aren't symmetric and contain some biases. Apply random symmetries to self play introduces extra diversity to the games and also mitigates the biases inherent in the network.

To give a clear example: if you disabled random symmetries for the evaluation games every single evaluation game would play the exact same game.

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What does random symmetry in training serves？Double random seems equal to single random at the first glance.

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Random symmetry during training helps prevent the model from overfitting on the selfplay games.

Each 19x19 game will generate about 200 training examples, and every example a game will look very similar to many other examples from the same game. Because the symmetries are applied randomly to the examples, it stops positions from the same game looking similar to each other.

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@delock we scratched our heads about this one as well. Originally, we only had random symmetries in selfplay but not in training. Despite this, the networks without symmetries in training were substantially weaker; v7 and earlier did not have symmetries on in training, and they are far weaker than the later versions.

As for the necessity of having them on in selfplay: the MCTS algorithm benefits strongly from having a large set of inferences to average, because any individual inference is very 'noisy'. Having rotations off during selfplay would almost certainly result in weaker play.

I know it seems redundant, i certainly thought so too! But it appears important to have rotation turned on in both places.

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Thanks for the explanation @tommadams @amj

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