Energy-guided Recursive Model
Abstract
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 \textbf{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.
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BibTeX
@misc{zhao2026energyguided,
title = {{Energy-guided Recursive Model}},
author = {Yifei Zhao and Ying Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.10128},
eprint = {2607.10128},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10128},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Energy-guided Recursive Model
AU - Yifei Zhao
AU - Ying Tang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2607.10128
UR - https://arxiv.org/abs/2607.10128
AB - 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 \textbf{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.
ER -