New NNUE architecture and net

Introduces a new NNUE network architecture and associated network parameters

The summary of the changes:

* Position for each perspective mirrored such that the king is on e..h files. Cuts the feature transformer size in half, while preserving enough knowledge to be good. See https://docs.google.com/document/d/1gTlrr02qSNKiXNZ_SuO4-RjK4MXBiFlLE6jvNqqMkAY/edit#heading=h.b40q4rb1w7on.
* The number of neurons after the feature transformer increased two-fold, to 1024x2. This is possibly mostly due to the now very optimized feature transformer update code.
* The number of neurons after the second layer is reduced from 16 to 8, to reduce the speed impact. This, perhaps surprisingly, doesn't harm the strength much. See https://docs.google.com/document/d/1gTlrr02qSNKiXNZ_SuO4-RjK4MXBiFlLE6jvNqqMkAY/edit#heading=h.6qkocr97fezq

The AffineTransform code did not work out-of-the box with the smaller number of neurons after the second layer, so some temporary changes have been made to add a special case for InputDimensions == 8. Also additional 0 padding is added to the output for some archs that cannot process inputs by <=8 (SSE2, NEON). VNNI uses an implementation that can keep all outputs in the registers while reducing the number of loads by 3 for each 16 inputs, thanks to the reduced number of output neurons. However GCC is particularily bad at optimization here (and perhaps why the current way the affine transform is done even passed sprt) (see https://docs.google.com/document/d/1gTlrr02qSNKiXNZ_SuO4-RjK4MXBiFlLE6jvNqqMkAY/edit# for details) and more work will be done on this in the following days. I expect the current VNNI implementation to be improved and extended to other architectures.

The network was trained with a slightly modified version of the pytorch trainer (https://github.com/glinscott/nnue-pytorch); the changes are in https://github.com/glinscott/nnue-pytorch/pull/143

The training utilized 2 datasets.

    dataset A - https://drive.google.com/file/d/1VlhnHL8f-20AXhGkILujnNXHwy9T-MQw/view?usp=sharing
    dataset B - as described in ba01f4b954

The training process was as following:

    train on dataset A for 350 epochs, take the best net in terms of elo at 20k nodes per move (it's fine to take anything from later stages of training).
    convert the .ckpt to .pt
    --resume-from-model from the .pt file, train on dataset B for <600 epochs, take the best net. Lambda=0.8, applied before the loss function.

The first training command:

python3 train.py \
    ../nnue-pytorch-training/data/large_gensfen_multipvdiff_100_d9.binpack \
    ../nnue-pytorch-training/data/large_gensfen_multipvdiff_100_d9.binpack \
    --gpus "$3," \
    --threads 1 \
    --num-workers 1 \
    --batch-size 16384 \
    --progress_bar_refresh_rate 20 \
    --smart-fen-skipping \
    --random-fen-skipping 3 \
    --features=HalfKAv2_hm^ \
    --lambda=1.0 \
    --max_epochs=600 \
    --default_root_dir ../nnue-pytorch-training/experiment_$1/run_$2

The second training command:

python3 serialize.py \
    --features=HalfKAv2_hm^ \
    ../nnue-pytorch-training/experiment_131/run_6/default/version_0/checkpoints/epoch-499.ckpt \
    ../nnue-pytorch-training/experiment_$1/base/base.pt

python3 train.py \
    ../nnue-pytorch-training/data/michael_commit_b94a65.binpack \
    ../nnue-pytorch-training/data/michael_commit_b94a65.binpack \
    --gpus "$3," \
    --threads 1 \
    --num-workers 1 \
    --batch-size 16384 \
    --progress_bar_refresh_rate 20 \
    --smart-fen-skipping \
    --random-fen-skipping 3 \
    --features=HalfKAv2_hm^ \
    --lambda=0.8 \
    --max_epochs=600 \
    --resume-from-model ../nnue-pytorch-training/experiment_$1/base/base.pt \
    --default_root_dir ../nnue-pytorch-training/experiment_$1/run_$2

STC: https://tests.stockfishchess.org/tests/view/611120b32a8a49ac5be798c4

LLR: 2.97 (-2.94,2.94) <-0.50,2.50>
Total: 22480 W: 2434 L: 2251 D: 17795
Ptnml(0-2): 101, 1736, 7410, 1865, 128

LTC: https://tests.stockfishchess.org/tests/view/611152b32a8a49ac5be798ea

LLR: 2.93 (-2.94,2.94) <0.50,3.50>
Total: 9776 W: 442 L: 333 D: 9001
Ptnml(0-2): 5, 295, 4180, 402, 6

closes https://github.com/official-stockfish/Stockfish/pull/3646

bench: 5189338

src/nnue/features/half_ka_v2_hm.cpp

@@ -0,0 +1,85 @@
+/*
+  Stockfish, a UCI chess playing engine derived from Glaurung 2.1
+  Copyright (C) 2004-2021 The Stockfish developers (see AUTHORS file)
+
+  Stockfish is free software: you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+
+  Stockfish is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with this program.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+//Definition of input features HalfKAv2_hm of NNUE evaluation function
+
+#include "half_ka_v2_hm.h"
+
+#include "../../position.h"
+
+namespace Stockfish::Eval::NNUE::Features {
+
+  // Orient a square according to perspective (rotates by 180 for black)
+  inline Square HalfKAv2_hm::orient(Color perspective, Square s, Square ksq) {
+    return Square(int(s) ^ (bool(perspective) * SQ_A8) ^ ((file_of(ksq) < FILE_E) * SQ_H1));
+  }
+
+  // Index of a feature for a given king position and another piece on some square
+  inline IndexType HalfKAv2_hm::make_index(Color perspective, Square s, Piece pc, Square ksq) {
+    Square o_ksq = orient(perspective, ksq, ksq);
+    return IndexType(orient(perspective, s, ksq) + PieceSquareIndex[perspective][pc] + PS_NB * KingBuckets[o_ksq]);
+  }
+
+  // Get a list of indices for active features
+  void HalfKAv2_hm::append_active_indices(
+    const Position& pos,
+    Color perspective,
+    ValueListInserter<IndexType> active
+  ) {
+    Square ksq = pos.square<KING>(perspective);
+    Bitboard bb = pos.pieces();
+    while (bb)
+    {
+      Square s = pop_lsb(bb);
+      active.push_back(make_index(perspective, s, pos.piece_on(s), ksq));
+    }
+  }
+
+
+  // append_changed_indices() : get a list of indices for recently changed features
+
+  void HalfKAv2_hm::append_changed_indices(
+    Square ksq,
+    StateInfo* st,
+    Color perspective,
+    ValueListInserter<IndexType> removed,
+    ValueListInserter<IndexType> added
+  ) {
+    const auto& dp = st->dirtyPiece;
+    for (int i = 0; i < dp.dirty_num; ++i) {
+      Piece pc = dp.piece[i];
+      if (dp.from[i] != SQ_NONE)
+        removed.push_back(make_index(perspective, dp.from[i], pc, ksq));
+      if (dp.to[i] != SQ_NONE)
+        added.push_back(make_index(perspective, dp.to[i], pc, ksq));
+    }
+  }
+
+  int HalfKAv2_hm::update_cost(StateInfo* st) {
+    return st->dirtyPiece.dirty_num;
+  }
+
+  int HalfKAv2_hm::refresh_cost(const Position& pos) {
+    return pos.count<ALL_PIECES>();
+  }
+
+  bool HalfKAv2_hm::requires_refresh(StateInfo* st, Color perspective) {
+    return st->dirtyPiece.piece[0] == make_piece(perspective, KING);
+  }
+
+}  // namespace Stockfish::Eval::NNUE::Features