研究大模型如何追踪状态变化，发现其能力随状态增多而急剧下降。
Scaling Laws for State Dynamics in Large Language Models
- 通过三类有限状态系统测试模型状态预测能力
- 状态数超5或10时准确率降至30%以下
- 关键注意力头可传递状态信息但难融合动作
大型语言模型在需要内部状态追踪的任务中应用日益广泛，但其对状态转移动态的建模能力仍不清晰。本文在盒追踪、抽象有限自动机序列和复杂文本游戏三个领域评估了模型对确定性状态动态的捕捉能力，这些任务均可形式化为有限状态系统。结果显示，随着状态空间增大和转移稀疏，下一状态预测准确率下降。GPT-2 XL在低复杂度场景下准确率约70%，但当盒子数或状态数超过5或10时，准确率低于30%。在有限自动机任务中，Pythia-1B在状态数>10且转移数<30时准确率无法突破50%。通过激活拼接分析，识别出负责传播状态信息的关键注意力头：GPT-2 XL Layer 22 Head 20，以及Pythia-1B在第10、11、12、14层的多个头。尽管这些头能有效传递状态特征，但动作信息未被可靠传至最终标记，表明联合状态-动作推理能力弱。结果表明，大模型的状态追踪来自多头下一词预测的分布式交互，而非显式符号计算。
原文摘要 · Abstract (English)
Large Language Models (LLMs) are increasingly used in tasks requiring internal state tracking, yet their ability to model state transition dynamics remains poorly understood. We evaluate how well LLMs capture deterministic state dynamics across 3 domains: Box Tracking, Abstract DFA Sequences, and Complex Text Games, each formalizable as a finite-state system. Across tasks, we find that next-state prediction accuracy degrades with increasing state-space size and sparse transitions. GPT-2 XL reaches about 70% accuracy in low-complexity settings but drops below 30% when the number of boxes or states exceeds 5 or 10, respectively. In DFA tasks, Pythia-1B fails to exceed 50% accuracy when the number of states is > 10 and transitions are < 30. Through activation patching, we identify attention heads responsible for propagating state information: GPT-2 XL Layer 22 Head 20, and Pythia-1B Heads at Layers 10, 11, 12, and 14. While these heads successfully move relevant state features, action information is not reliably routed to the final token, indicating weak joint state-action reasoning. Our results suggest that state tracking in LLMs emerges from distributed interactions of next-token heads rather than explicit symbolic computation.
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