[sushirain]

> just because positions are similar, doesn't mean that best moves in these positions have to be in any way similar too.

To alleviate this, one can add more abstract/heuristic information about the position to the input (indicators for complex relations between several pieces). This kind of high-dimensional vector would be more robust to small changes, and make the objective function more smooth. Perhaps the non-linearities introduced by the three layers cannot do this as effectively.