Winter

Winter in Zurich, ETH Zurich view [1] Winter,

an UCI compliant open source chess engine by Jonathan Rosenthal, written in C++, released on January 08, 2018 under the terms of GPL Version 3. Winter is inspired by machine learning techniques, as applied in move ordering and in particular in evaluation, and heavily relies on C++ templates but not on any library aside from STL as it comes with its own implementations for statistics [2] and linear algebra [3]. Winter started its life in 2016 as a group project at ETH Zurich in a course on parallel computing along with Jonas Kuratli and Jonathan Maurer - the current release with Jonathan Rosenthal as sole author has removed the parallel portion of the code [4]. It started to play on-line at HGM’s Online Engine Blitz Tourneys in April 2017 [5].

Board Representation

BMI2 - PEXT Bitboards

Search

Lazy SMP (Winter 0.3)
Fail-Hard Iterative Deepening
Alpha-Beta Principal Variation Search
Transposition Table
Move Ordering is based on the linear part of a Logistic Regression classifier aka cluster analysis
- The classifier is trained via temporal difference learning to predict whether a move will return beta
- Classifier considers TT move, killers, move type, from square, target square, capture target, SEE, target square of last move, check and changes between forcing and unforcing moves (a capture is more likely after another capture)
- Countermove Heuristic (Winter 0.3)
Selectivity

Evaluation

Non standard approach relied on a mixture model [7], and since Winter 0.3 on Fuzzy C-Means, a more direct generalization of a tapered eval with disjoint phases aka clusters [8] [9]
- Assumes positions encountered in search come from some set of k-means clusters [10]
- Model is trained via EM algorithm [11] [12] either on database games or positions sampled from search
- For each cluster, a separate evaluation function is trained. When the evaluation function is called the relative probability a position stems from each cluster is estimated, the evaluation functions are computed and the final score is returned as the weighted average - a generalization of tapered eval with game phases [13]
Parameter weights are trained via a mixture of reinforcement ( temporal difference) learning and supervised learning
- Minimizing the cross entropy loss of a Logistic Regression model for each phase
- Training converges fast due to linear model at the heart
As of Winter 0.6.2, the evaluation function relies on a neural network with two main parts. The first part is a non-standard convolutional neural network which uses sparsity similarly to NNUE. This convolutional network is used to calculate pawn structure features, so the output can be reused very often as it gets stored in a separate hash table with a high hitrate. The second part is a fully connected network which has as input the output of the convolutional network as well as a set of handcrafted features standard to classical engines, mostly a subset of the features from before neural networks were added to Winter [14]