The Linear engines evaluate an inconclusive rollout position with 64 player-relative floating-point features:
linear_score = dot(features, weights)
player_score = tanh(linear_score)
white_score = player_to_move == White ? player_score : -player_score
The bounded result is compatible with the [-1, 1] terminal scores used by
MCTS.
| Indices | Count | Features |
|---|---|---|
| 0 | 1 | Bias |
| 1–8 | 8 | Mandatory-timeline material sums |
| 9–16 | 8 | Mandatory-timeline material differences |
| 17–24 | 8 | Optional-timeline material sums |
| 25–32 | 8 | Optional-timeline material differences |
| 33–40 | 8 | Unplayable-timeline material sums |
| 41–48 | 8 | Unplayable-timeline material differences |
| 49–61 | 13 | Timeline statistics |
| 62–63 | 2 | Logarithmic move-space volumes |
Material components are ordered as pawn/brawn, knight, rook movement, bishop movement, unicorn movement, dragon movement, non-royal queen bonus, and royal membership. Sliding-piece components overlap, so compound pieces receive the sum of their movement-component weights.
Indices 49–61 follow timeline_data declaration order. Index 58 is timeline
advantage (hostile_created - friendly_created), so a positive value means
the player to move has more active-timeline allowance.
The move-space values are logarithms of hypercuboid candidate volumes, not exact legal-action counts. Index 62 includes new-timeline axes; index 63 fixes those axes at their null coordinate. Summing logarithms avoids overflow for large multiverses.
5dchess linear uses hand-written weights. Mandatory material-difference
weights are 0.05, 0.15, 0.25, 0.15, 0.08, 0.05, 0.45, 0.30; optional and
unplayable differences use 50% and 15% of those values. Timeline advantage is
weighted 0.25, and both move-space values are weighted 0.04. Other
hand-written weights are zero.
5dchess linear-trained uses a frozen experimental vector embedded in
linear.cpp. It is the first 64 coefficients of the final r=40 checkpoint;
royal-safety coefficients from that experiment are intentionally excluded.
Consequently this projected profile is not identical to the engine evaluated
in the original matches. See Frozen Linear profile.
Both engines retain the normal rollout option, for example:
5dchess linear -r 40
5dchess linear-trained -r 40