![]() If we have, this will most of the time be the move that has been scoring best (leading to the position that seems best for the player to move), but sometimes also a move that does not have a terrible score but that we have not looked at very much yet and has a reasonable policy prior (so which could still turn out to be good). If we have not looked at the position before, this will be the one with the highest prior. We will try to find the move that still has odds of being the best (the one with the highest upper confidence bound). Now, we investigate the possible moves in This gives us both an initial evaluation for the position, as well as a list of possible moves with an associated (policy) prior. It works as follows: first, we evaluate the neural network on the root position. The search algorithm used by Leela Zero is Monte Carlo Tree Search (referred to as MCTS). This is, in essence, the evaluation of the position. In the other output, all outputs from the stack are combined to calculate a single value: how likely is it that the player to move wins the game. The network produces a probability for each move that it is the best. There are 2 final layers: in the first one, all outputs from the above "stack" are combined and reworked so they map to the possible moves in the position. Because some processing in the stack (of which we'll not go into detail about) is only done every 2 layers, they are typically thought of as a unit and referred to as a single "residual block". Note that no-one is explaining these features to the program or programming them: it has to discover them all by itself by analyzing millions of chess games. For example now the next layer can compute "is there an opposing pawn one or two ranks up", until it arrives at higher level concepts "is this pawn on an open file", which it can then combine with previously discovered ones, to form features such as "is this pawn isolated on an open file". These allow the network to gradually compute concepts such as "is this pawn isolated" or "is there an opposing pawn one rank up" and combine them. In every layer, every output square is calculated by taking the corresponding square and the surrounding ones (in total a 3x3 square) from all outputs from the previous layer, and applying an image filter to them, to compute a new output. These stacks are typically 20 to 80 layers deep, and typically have 128 to 256 outputs per layer, which then also form the input for the next layer. These inputs are passed through a deep stack of image filters. ![]() Most obviously, this will be the position of the pieces ("is there a pawn belonging to the player to move on this square"), but also some non-visible things, such as "is the player to move still allowed to castle" and "is there an en-passant move" possible? The neural network takes as input a stack of 8 x 8 bitmaps, enough to fully represent the state of a chess game. Understanding how Leela Zero Chess works (2018) How the neural network works, and what it calculates. The article and interview were never published ( despite being announced), but ChessBase would go on to re-publish Leela Chess Zero as "Fat Fritz 1" a year later.Īs I already spent the time writing it, and it might still be interesting to my audience, I'll put it here on my blog, in the hope that someone finds it useful. At that point, most of the easily accessible information was still referring to the Go engine, so I did an attempt to clear up some confusion. During an interview with Albert Silver (an author affiliated with ChessBase, whom the article was supposedly for) about Leela Chess Zero, there were questions about where to find more information, in an easy to understand manner, how the Alpha Zero ideas worked in chess and how they were implemented in Leela. ![]() I wrote the following article in May 2018, now almost 3 years ago. ![]()
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