AlphaZero in Sparsely Rewarded Games: Limits and Auxiliary Supervision

AlphaZero has demonstrated that a neural-guided Monte Carlo Tree Search can achieve superhuman performance, but strong play does not necessarily imply perfect play. We study this gap in two oracle-evaluable domains with contrasting structure: Connect Four, a solved partisan game with exact game-theoretic values, and Chomp, an impartial game whose optimal play is governed by Grundy-number structure. Under a unified self-play $+$ MCTS pipeline, we compare vanilla AlphaZero, a multi-frame variant (limited to Chomp), and an AlphaZero Auxiliary Loss (AZAL) that adds oracle-derived policy supervision. We find that vanilla AlphaZero achieves strong play across both domains but cannot preserve the exact trajectories required for optimal play: in Connect Four, it fails to maintain the optimal line of play, while in Chomp, it fails to consistently restore the $g=0$ invariant. On rectangular Chomp boards, multi-frame inputs alone do not remove this gap. Nevertheless, AZAL substantially improves oracle consistency across multi-seeded full-game traces and sampled-state evaluations. On Chomp, AZAL reaches perfect full-game oracle consistency on 10x11 and high but not complete consistency on 9x10; on Connect Four, AZAL improves oracle-match rate and delays the first oracle mistake, but does not reach perfect play.

Right Makes Might: Aligning Verified Hidden States Empowers RL Reasoning

Reinforcement Learning from Verifiable Rewards (RLVR) has become the dominant approach for improving mathematical reasoning in large language models, yet current methods reduce each correct rollout to a single reward bit, ignoring the geometric structure shared among their hidden states. Investigating this structure, we find that at the anchor token (the position immediately before the answer marker), correct rollouts converge naturally because they must produce the same answer (cosine similarity ~0.84), yet each retains residual variance from its unique reasoning path. Encouraging full alignment at this point pushes the model to extract a unified "correct decision" representation, reducing sensitivity to which reasoning path was taken. Based on this observation, we propose Hidden-Align, an auxiliary loss function that aligns the last-layer hidden states of correct rollouts at the anchor token during RL training, with zero overhead in both training and inference. On eight mathematical reasoning benchmarks, Hidden-Align improves average pass@1 over the DAPO baseline by 3.8, 6.2, and 5.4 percentage points on Qwen3-1.7B, 4B, and 14B respectively, with consistent pass@k gains across all three scales, supported by ablations on loss type, anchor position, layer depth, and loss weight.