  How do sequence models represent their decision-making process? Prior work
suggests that Othello-playing neural network learned nonlinear models of the
board state (Li et al., 2023). In this work, we provide evidence of a closely
related linear representation of the board. In particular, we show that probing
for "my colour" vs. "opponent's colour" may be a simple yet powerful way to
interpret the model's internal state. This precise understanding of the
internal representations allows us to control the model's behaviour with simple
vector arithmetic. Linear representations enable significant interpretability
progress, which we demonstrate with further exploration of how the world model
is computed.
