Energy-guided Recursive Model

Recursive models show promise on reasoning and language tasks, yet their test-time scaling lacks a principled criterion for selecting trajectories or determining recurrent depth. We introduce Energy-guided Recursive Model (ERM), which uses Hopfield-type memories of valid local and global structures to assign intrinsic energies to candidate trajectories. These energies guide candidate selection and suggest an effective range of recurrent depths, implying that deeper recurrence does not necessarily improve reasoning accuracy. They also enable sampling methods such as parallel tempering to improve exploration. For reasoning tasks, ERM achieves optimal solutions on Sudoku ($98.97$), Pencil Puzzle Bench (PPBench, $88.04$) and Maze ($99.30$), reaching the best accuracy in recursive modeling. On language modeling, ERM reduces RedPajama-V2 perplexity by $1.74\%$ with marginal inference overhead. The results support energy guidance as a practical framework for improving test-time scaling in recursive models.