TD-leaf and another negamax bug

TD-lambda and TD-leaf are separated by the observation that minimax with a parameterised leaf heuristic is differentiable* in the parameters. "All" that had to be done was to extract the "principal variation": which one position survived all of the pruning to become the reported value.

This was a bit fiddly and uncovered a subtle bug (again) in negamax.c: we were not being complete in our overriding of the TT entry and by omitting key it was possible that later searches would find incorrect values.

The more interesting question to me was: how do we introduce enough variety while not corrupting the PV chain? I settled on having selfplay have one of the players be epsilon-random but the other greedy (minimax) and simply report only the greedy portion PV chain. This appears to work well enough in practice and doesn't introduce nonsense training data for the net (we don't force its actions to be nonsensical). I also deciced, perhaps in a departure from tradition, that we had good supervised labels for PVs that happened to be winning states, so the training overrides the targets in that case. Finally rolled back some of the ambition in nn_train.py default arguments.

*almost always

1 files changed, 122 insertions, 0 deletions

diff --git a/include/nn.c b/include/nn.c
new file mode 100644
index 0000000..705f258
--- /dev/null
+++ b/include/nn.c
@@ -0,0 +1,122 @@
+/*
+  This file is part of ctak.
+
+  This program 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.
+
+  This program 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 ctak. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+#include "nn.h"
+
+#include "weights_5.h"
+#include "weights_6.h"
+
+// ===================================================================
+// Helpers
+// ===================================================================
+
+#define RELU(x) ((x) = ((x) < 0) ? 0 : (x))
+
+static float fast_tanh(const float x) {
+  // tanh via a degree-11 odd polynomial, least-squares fit of tanh on [-3, 3]
+  //  (max absolute error ~4e-3), saturating to +-1 outside that interval.
+  if (x > 3.0f)
+    return 1.0f;
+  if (x < -3.0f)
+    return -1.0f;
+  const float x2 = x * x;
+  return x * (0.997136032f + x2 * (-0.305215124f + x2 *
+                                   (0.0832466371f + x2 *
+                                    (-0.0139947924f + x2 *
+                                     (0.00123106314f + x2 * -4.29748644e-05f)))));
+}
+// ===================================================================
+// Input encoding
+// ===================================================================
+
+inline uint8_t cell_idx_at(const tak_state_p state, const uint8_t loc) {
+  const uint8_t d = state->celldat[loc];
+  if ((d & NUM_MASK) == 0)
+    return 0; // empty
+  return (uint8_t)(1u + 3u * (state->colours[loc] & 1u) + (d & STONE_MASK));
+}
+
+inline void nn_cell_idxs(uint8_t *out, tak_state_p state) {
+  const unsigned int n_cells = state->board_size * state->board_size;
+  for (unsigned int loc = 0; loc < n_cells; loc++)
+    out[loc] = cell_idx_at(state, loc);
+}
+
+inline void nn_prepare_head(float out_head[3], tak_state_p state) {
+  const float inv_max_flats =
+    (state->board_size == 6) ? (1.0f / 30.0f) : (1.0f / 21.0f);
+  out_head[0] = (state->ply & 1) ? 1 : -1;
+  out_head[1] = (float)(state->white_count & 127) * inv_max_flats;
+  out_head[2] = (float)(state->black_count & 127) * inv_max_flats;
+}
+
+void nn_prepare_input(float *cur_board, tak_state_p state,
+                      const float embedding[NN_N_EMB]) {
+  const unsigned int n_cells = state->board_size * state->board_size;
+  nn_prepare_head(cur_board, state);
+  uint8_t idxs[36];
+  nn_cell_idxs(idxs, state);
+  for (unsigned int loc = 0; loc < n_cells; loc++)
+    cur_board[3 + loc] = embedding[idxs[loc]];
+}
+
+// ===================================================================
+// Implementation of small neural networks
+// ===================================================================
+
+float eval_net(const float *board, const unsigned int n_inp,
+               const float *w, const float *biases,
+               const float *logit_w, const float logit_b,
+               const unsigned int n_dense) {
+  float dense1[FIVE_DENSE_NUM]; // FIVE_DENSE_NUM == SIX_DENSE_NUM
+  float z = logit_b;
+
+  for (unsigned int d1 = 0; d1 < n_dense; d1++) {
+    float h = biases[d1];
+    const float *wd = w + d1 * n_inp;
+    for (unsigned int fl = 0; fl < n_inp; fl++)
+      h += board[fl] * wd[fl];
+    RELU(h);
+    dense1[d1] = h;
+  }
+  for (unsigned int d1 = 0; d1 < n_dense; d1++)
+    z += dense1[d1] * logit_w[d1];
+
+  return fast_tanh(z);
+}
+
+// ===================================================================
+// Interfaces to the two built-in evaluators
+// ===================================================================
+
+float five_nn_fn(tak_state_p state) {
+  static float cur_board[FIVE_INP_NUM] NN_ALIGNED;
+
+  nn_prepare_input(cur_board, state, five_embedding);
+  return eval_net(cur_board, FIVE_INP_NUM, &five_dense_weights[0][0],
+                  five_dense_biases, five_logit_weights, five_logit_bias,
+                  FIVE_DENSE_NUM);
+}
+
+float six_nn_fn(tak_state_p state) {
+  static float cur_board[SIX_INP_NUM] NN_ALIGNED;
+
+  nn_prepare_input(cur_board, state, six_embedding);
+  return eval_net(cur_board, SIX_INP_NUM, &six_dense_weights[0][0],
+                  six_dense_biases, six_logit_weights, six_logit_bias,
+                  SIX_DENSE_NUM);
+}