Matilda: Engine-Agnostic Search with Human Policy Guidance

Chess engines have evolved from search-based systems optimized solely for strength to neural policies capable of modeling human decisions across much of the rating spectrum.

Maia-3, the strongest human-like move policy for chess, models the typical moves of a given rating but does not model high Elo strength well (2500+ Lichess Elo) nor has an extensible architecture for modeling individual play style.

On the other hand, search-based engines like Stockfish are far stronger than any known human but struggle to model human-like play.

To solve these problems, we present Matilda, a permutation-invariant set transformer that re-ranks the full legal-move distribution produced by a frozen Maia-3 and improves it along both dimensions with one 1.7M-parameter model.

Matilda uses Maia-3 to provide both global context and search candidates.

Context is encoded from Maia-3's hidden representation, time control, and an optional 32-dimensional player-style vector, while the top-16 candidate moves are optionally rescored by Stockfish.

A zero-initialized head scatters per-candidate adjustments back into the policy logits, so the untrained model is exactly Maia-3 and every gain is value-added under full-vocabulary NLL.

On a 2500+ Elo benchmark from Lichess, Matilda improves on Maia-3 by +0.5-0.6% below 2800 but +4.3%, +11.9%, and +21.9% at 2800-2900, 2900-3000, and 3000+, respectively, and an additional +0.41% overall from player-style embeddings.

Ablations show that the improvements are primarily driven by the engine-derived features, the mechanism is not engine-specific, and the gains survive memorization, sibling, and account audits while preserving Maia-3 at 1000-2500 Elo.

Because search supervision is modular, Matilda naturally supports interchangeable search engines, demonstrated by replacing Stockfish with an AlphaZero-family engine.