# Energy-guided Recursive Model

arXiv: https://arxiv.org/abs/2607.10128 · HTML: https://mlsanity.com/paper/2607.10128/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 33 of its 41 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 33)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Energy Transformer](https://mlsanity.com/paper/2302.07253/) (2023)
- [Learning Iterative Reasoning through Energy Minimization](https://mlsanity.com/paper/2206.15448/) (2022)
- [Energy-Based Transformers are Scalable Learners and Thinkers](https://mlsanity.com/paper/2507.02092/) (2025)
- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)
- [Implicit Language Models are RNNs: Balancing Parallelization and Expressivity](https://mlsanity.com/paper/2502.07827/) (2025)
- [Probabilistic Tiny Recursive Model](https://mlsanity.com/paper/2605.19943/) (2026)
- [Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning](https://mlsanity.com/paper/2605.21488/) (2026)
- [Solve the Loop: Attractor Models for Language and Reasoning](https://mlsanity.com/paper/2605.12466/) (2026)

## Built on by (most cited first, 2 of 2)

- [Recursive Vision Language Models for General Symbolic Reasoning](https://mlsanity.com/paper/2608.01534/) (2026)
- [Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning](https://mlsanity.com/paper/2610.16427/) (2026)

## Abstract (arXiv)

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.