Editing Evaluation function (section)

===Piece-square tables===
An important technique in evaluation since at least the early 1990s is the use of piece-square tables (also called piece-value tables) for evaluation.<ref>{{citation|title=Learning Piece-Square Values using Temporal Differences|last1=Beal|first1=Don|last2=Smith|first2=Martin C.|publisher=ICCA Journal|volume=22|issue=4}}</ref><ref>{{citation|author1=Jun Nagashima|author2=Masahumi Taketoshi|author3=Yoichiro Kajihara|author4=Tsuyoshi Hashimoto|author5=Hiroyuki Iida|year=2002|title=An Efficient Use of Piece-Square Tables in Computer Shogi|publisher=Information Processing Society of Japan|url=https://ci.nii.ac.jp/naid/110006381103}}</ref>  Each table is a set of 64 values corresponding to the squares of the chessboard. The most basic implementation of piece-square table consists of separate tables for each type of piece per player, which in chess results in 12 piece-square tables in total. More complex variants of piece-square tables are used in computer chess, one of the most prominent being the king-piece-square table, used in [[Stockfish (chess)|Stockfish]], [[Komodo (chess)|Komodo Dragon]], Ethereal, and many other engines, where each table considers the position of every type of piece in relation to the player's king, rather than the position of the every type of piece alone. The values in the tables are bonuses/penalties for the location of each piece on each space, and encode a composite of many subtle factors difficult to quantify analytically. In handcrafted evaluation functions, there are sometimes two sets of tables: one for the opening/middlegame, and one for the endgame; positions of the middle game are interpolated between the two.<ref>{{citation|url=https://hxim.github.io/Stockfish-Evaluation-Guide/|title=Stockfish Evaluation Guide|access-date=12 December 2021}}</ref>

Originally developed in computer [[shogi]] in 2018 by Yu Nasu,<ref name="Nasu">{{cite web|title=Efficiently Updatable Neural-Network-based Evaluation Function for computer Shogi|author=Yu Nasu|url=https://www.apply.computer-shogi.org/wcsc28/appeal/the_end_of_genesis_T.N.K.evolution_turbo_type_D/nnue.pdf|date=April 28, 2018|language=Japanese}}</ref><ref name="Nasu2">{{cite web|title=Efficiently Updatable Neural-Network-based Evaluation Function for computer Shogi (Unofficial English Translation)|author=Yu Nasu|website=[[GitHub]]|url=https://github.com/asdfjkl/nnue/blob/main/nnue_en.pdf|date=April 28, 2018|language=English}}</ref> the most common evaluation function used in computer chess today{{citation needed|date=February 2024}} is the [[efficiently updatable neural network]], or NNUE for short, a sparse and shallow [[Artificial neural network|neural network]] that has only piece-square tables as the inputs into the neural network.<ref>{{cite web | url=https://github.com/glinscott/nnue-pytorch/blob/master/docs/nnue.md | title=NNUE | author=Gary Linscott | website=[[GitHub]] | date=April 30, 2021 | access-date=December 12, 2020}}</ref> In fact, the most basic NNUE architecture is simply the 12 piece-square tables described above, a neural network with only one layer and no [[activation function]]s. An efficiently updatable neural network architecture, using king-piece-square tables as its inputs, was first ported to chess in a Stockfish derivative called Stockfish NNUE, publicly released on May 30, 2020,<ref>{{cite web|url=https://github.com/nodchip/Stockfish/releases/tag/stockfish-nnue-2020-05-30|title=Release stockfish-nnue-2020-05-30|website=Github|last=Noda|first=Hisayori|date=30 May 2020|access-date=12 December 2021}}</ref> and was adopted by many other engines before eventually being incorporated into the official Stockfish engine on August 6, 2020.<ref>{{cite web|title=Introducing NNUE Evaluation|url=https://blog.stockfishchess.org/post/625828091343896577/introducing-nnue-evaluation|date=6 August 2020}}</ref><ref>{{cite web|title= official-stockfish / Stockfish, NNUE merge|url=https://github.com/official-stockfish/Stockfish/issues/2823#issue-665540175|author=Joost VandeVondele|website=[[GitHub]]|date=July 25, 2020}}</ref>