{"ID":6536340,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-14T05:36:24.914033594Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10128","arxiv_id":"2607.10128","title":"Energy-guided Recursive Model","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2607.10128","url_pdf":"https://arxiv.org/pdf/2607.10128v1","authors":"[\"Yifei Zhao\",\"Ying Tang\"]","published":"2026-07-11T05:39:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}