用能量函数指导推理路径选择，让递归模型更高效准确
Energy-guided Recursive Model
- 基于霍普菲尔德能量设计路径选择机制
- 在数独等任务上达98.97%准确率
- 适合需要严谨推理的结构化问题求解
递归推理模型通过反复更新小神经网络的潜在状态来解决结构化问题。然而，其测试时扩展缺乏合理的推理机制：增加深度或随机广度会产生更多轨迹，但缺乏明确的选择标准，现有方法多依赖额外q头或启发式投票。本文提出能量引导的递归模型（ERM），引入基于显式霍普菲尔德能量的内在选择原则。ERM利用霍普菲尔德型记忆存储有效局部或全局结构，以定义候选轨迹的选择器。由此产生的能量可无缝集成能量基技术（如并行退火）以提升采样效率和排序能力。在D=64次递归步骤、K=128个候选路径条件下，ERM在数独（98.97%）、铅笔谜题基准（PPBench，88.04%）和迷宫（99.30%）任务中达到最优解，优于近期概率性微型递归模型和平衡推理器。结果表明，在递归推理中引入显式能量函数为更有效的推理提供了合理路径。
原文摘要 · Abstract (English)
Recursive reasoning models address structured problems by repeatedly updating latent states of small neural networks. However, their test-time scaling lacks a principled inference mechanism: increasing depth or stochastic breadth generates more trajectories without a clear criterion for selection, and existing methods predominantly rely on additional q-heads or heuristic voting. Here, we develop the Energy-guided Recursive Model (ERM), which introduces an intrinsic selection principle based on explicit Hopfield energies. ERM leverages Hopfield-type memories of valid local or global structures to define the selector over candidate trajectories. The resulting energy seamlessly integrates with energy-based techniques such as parallel tempering to enhance sampling efficiency and ranking. With $D=64$ recurrent steps and $K=128$ candidates, ERM reaches optimal solutions on Sudoku ($98.97\%$), Pencil Puzzle Bench (PPBench, $88.04\%$) and Maze ($99.30\%$), improving upon recent Probabilistic Tiny Recursive Model and Equilibrium Reasoners. These results suggest that incorporating explicit energy functions into recursive reasoning offers a principled path toward more effective inference.
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