Iterative Inference in a Chess-Playing Neural Network

Abstract: Do neural networks build their representations through smooth, gradual refinement, or via more complex computational processes? We investigate this by extending the logit lens to analyze the policy network of Leela Chess Zero, a superhuman chess engine. We find strong monotonic trends in playing strength and puzzle-solving ability across layers, yet policy distributions frequently follow non-smooth trajectories. Evidence for this includes correct puzzle solutions that are discovered early but subsequently discarded, move rankings that remain poorly correlated with final outputs, and high policy divergence until late in the network. These findings contrast with the smooth distributional convergence typically observed in LLMs.