Concepts

Information states

A player's information state is the public position plus its own private setup plus the history of moves. The engine's observation carries the first two exactly: its own pieces by type, the opponent's revealed pieces by type, the hidden opponent pieces with a flag saying whether each has moved (a moved piece is not a Bomb and not the Flag), the counts of lost pieces on both sides, the move and battleless-move counters and the last move. The network never sees a hidden type, and the arbiter never leaks the random seed.

The paper's planes

Ataraxos feeds its transformer 488 channels of ten by ten floating-point planes. Twelve planes mark the player's own pieces by type. Twenty-four planes give, for each square, the probability that it holds an opponent piece of each type under the assumption that the setup and moves were chosen uniformly at random, once from the player's view and once from the opponent's. Occupancy, movement and the fraction of the two draw limits used fill the next seven. Then come the history features, defined over the piece standing on each square:

77ThreatA move that ends adjacent to an opponent piece.The opponent piece is now threatened.Faded tile: where the piece was before the move.
A threat ends a quiet move adjacent to an opponent piece.
7EvadeThe piece threatened on the previous turnmoves to a square not adjacent to the threatener.Faded tile: where the piece was before the move.
An evade moves a piece that was threatened last turn away from the threatening piece.
422Active adjacencyA piece could have attacked a neighbourand chose not to. That silence is informative.Faded tile: where the piece was before the move.
A piece is actively adjacent when its owner could have attacked the neighbour and did not.
7ProtectionAfter A threatens B, C moves next to B.If A attacks, C can attack A in return.Faded tile: where the piece was before the move.
A protection move brings a third piece next to a threatened piece so that the attacker can be answered.

Each of these is recorded per revealed opponent type (ten planes) plus one for hidden opponents, from both points of view, giving planes 43 to 108. Planes 109 to 130 mark the starting squares of captured pieces by type; 131 to 250 mark where pieces died and which of six causes killed them (attacked a stronger revealed piece, attacked an equal one, attacked a hidden one and lost, was attacked while revealed and weaker, was attacked while revealed and equal, was attacked while hidden); 251 to 354 encode the protection relations; 355 to 455 one-hot the starting location of every piece; and the last 32 planes record the most recent 32 moves with a minus one on the source and a plus one on the destination.

The paper notes that access to history through features rather than recurrence is a choice made for speed, and that interleaving temporal attention gave much stronger belief models per unit of compute but did not pay off for reinforcement learning under their budget.

The compact encoding used here

The training bindings expose 58 planes: own pieces by type, revealed opponent pieces by type, hidden-unmoved and hidden-moved masks, empty and lake masks, the twelve belief planes from the counting prior, own moved and revealed masks, the two counters as broadcast planes, the last move, and the remaining counts of each own type as broadcast planes. The threat, evade, protection and death-cause history is left out at first. That is a deliberate ablation: the first question for the RL rung is how much strength the history features carry, and the plane list is one table in the bindings so it can grow without touching the learner.

Every observation is rotated into the acting player's frame, so a network always sees its own home rows at the bottom and never needs to learn the same pattern twice. Blue's moves are un-rotated before they reach the engine.

Beliefs from counting

The belief planes come from the same counting the paper uses: the number of unknown pieces of each type is the army count minus those revealed on the board minus those lost. A hidden piece that has moved is drawn from the movable types in proportion to their unknown counts; an unmoved hidden piece takes its share of the Bombs and the Flag as well. This prior ignores everything about how the opponent actually plays; the belief network is what replaces it.