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Lc0 logo ^[1]

Leela Chess Zero, (LCZero, lc0)
an adaption of Gian-Carlo Pascutto's Leela Zero Go project ^[2] to Chess, initiated and announced by Stockfish co-author Gary Linscott, who was already responsible for the Stockfish Testing Framework called Fishtest. Leela Chess is open source, released under the terms of GPL version 3 or later, and supports UCI. The goal is to build a strong chess playing entity following the same type of deep learning along with Monte-Carlo tree search (MCTS) techniques of AlphaZero as described in DeepMind's 2017 and 2018 papers ^[3] ^[4] ^[5], but using distributed training for the weights of the deep convolutional neural network (CNN, DNN, DCNN).

Lc0

Leela Chess Zero consists of an executable to play or analyze games, initially dubbed LCZero, soon rewritten by a team around Alexander Lyashuk for better performance and then called Lc0 ^[6] ^[7]. This executable, the actual chess engine, performs the MCTS and reads the self-taught CNN, which weights are persistent in a separate file. Lc0 is written in C++ (started with C++14 then upgraded to C++17) and may be compiled for various platforms and backends. Since deep CNN approaches are best suited to run massively in parallel on GPUs to perform all the floating point dot products for thousands of neurons, the preferred target platforms are Nvidia GPUs supporting CUDA and cuDNN libraries ^[8]. Ankan Banerjee wrote the cuDNN backend (also shared by Deus X and Allie ^[9]), and DX12 backend code. There exist different Lc0 backends to be used with different hardware, not all neural network architectures/features are supported on all backends. Different backends and different network architectures with different net size give different nodes per second and Elo. CPUs can be utilized for example via BLAS and DNNL and GPUs via CUDA, cuDNN, OpenCL, DX12, Metal, ONNX, oneDNN backends.

Description

Like AlphaZero, Lc0's evaluates positions using non-linear function approximation based on a deep neural network, rather than the linear function approximation as used in classical chess programs. This neural network takes the board position as input and outputs position evaluation (QValue) and a vector of move probabilities (PValue, policy). Once trained, these network is combined with a Monte-Carlo Tree Search (MCTS) using the policy to narrow down the search to highprobability moves, and using the value in conjunction with a fast rollout policy to evaluate positions in the tree. The MCTS selection is done by a variation of Rosin's UCT improvement dubbed PUCT (Predictor + UCT).

Board Representation

Lc0's color agnostic board is represented by five bitboards (own pieces, opponent pieces, orthogonal sliding pieces, diagonal sliding pieces, and pawns including en passant target information coded as pawns on rank 1 and 8), two king squares, castling rights, and a flag whether the board is color flipped. Getting individual piece bitboards requires some setwise operations such as intersection and set theoretic difference ^[10].

Network

While AlphaGo used two disjoint networks for policy and value, AlphaZero as well as Leela Chess Zero, share a common "body" connected to disjoint policy and value "heads". The “body” consists of spatial 8x8 planes, using B residual blocks with F filters of kernel size 3x3, stride 1. So far, model sizes FxB of 64x6, 128x10, 192x15, and 256x20 were used.

Concerning nodes per second of the MCTS, smaller models are faster to calculate than larger models. They are faster to train and will earlier recognize progress, but they will also saturate earlier so that at some point more training will no longer improve the engine. Larger and deeper network models will improve the receptivity, the amount of knowledge and pattern to extract from the training samples, with potential for a stronger engine. As a further improvement, Leele Chess Zero applies the Squeeze and Excite (SE) extension to the residual block architecture ^[11] ^[12]. The body is connected to both the policy "head" for the move probability distribution, and the value "head" for the evaluation score aka winning probability of the current position and up to seven predecessor positions on the input planes.

Training

Like in AlphaZero, the Zero suffix implies no other initial knowledge than the rules of the game, to build a superhuman player, starting with truly random self-play games to apply reinforcement learning based on the outcome of that games. However, there are derived approaches, such as Albert Silver's Deus X, trying to take a short-cut by initially using supervised learning techniques, such as feeding in high quality games played by other strong chess playing entities, or huge records of positions with a given preferred move. The unsupervised training of the NN is about to minimize the L2-norm of the mean squared error loss of the value output and the policy loss. Further there are experiments to train the value head against not the game outcome, but against the accumulated value for a position after exploring some number of nodes with UCT ^[13].

The distributed training is realized with an sophisticated client-server model. The client, written entirely in the Go programming language, incorporates Lc0 to produce self-play games.Controlled by the server, the client may download the latest network, will start self-playing, and uploading games to the server, who on the other hand will regularly produce and distribute new neural network weights after a certain amount of games available from contributors. The training software consists of Python code, the pipeline requires NumPy and TensorFlow running on Linux ^[14]. The server is written in Go along with Python and shell scripts.

Structure Diagrams

Related to TCEC clone discussions concerning Deus X and Allie aka AllieStein,
Alexander Lyashuk published diagrams with all components of the affected engines,
The above shows the common legend, and the structure of all Leela Chess Zero's components based on current Lc0 engine ^[15]

Same diagram, but initial LCZero engine, which played TCEC Season 12 ^[16]

Tournament Play

First Experience

LCZero gained first tournament experience in April 2018 at TCEC Season 12 and over the board at the WCCC 2018 in Stockholm, July 2018. It won the fourth division of TCEC Season 13 in August 2018, Lc0 finally coming in third in the third division.

Breakthrough

TCEC Season 14 from November 2018 until February 2019 became a breakthrough, Lc0 winning the third, second and first division, to even qualify for the superfinal, losing by the narrow margin of +10 =81 -9, 50½ - 49½ versus Stockfish. Again runner-up at the TCEC Season 15 premier division in April 2019, Lc0 aka LCZero v0.21.1-nT40.T8.610 won the superfinal in May 2019 versus Stockfish with +14 =79 -7, 53½-46½ ^[17]. At the TCEC Season 16 premier division in September 2019, Lc0 became in third behind Stockfish and the supervised trained AllieStein, but Lc0 took revenge by winning the TCEC Season 17 premier division in spring 2020, as LCZero v0.24-sv-t60-3010 fighting down Stockfish in a thrilling superfinal in April 2020 with +17 =71 -12, 52½-47½ ^[18], but tables turned again in TCEC Season 18, when Stockfish won the superfinal.