mlsanityData to 14 Oct 2026

Energy-guided Recursive Model

arXiv 2607.10128 ↗First posted 11 Jul 2026cs.LG stat.MLcited by 2

On the map: LLM reasoning → Test-time compute and efficient thinking

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.

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.

Builds on

33 of 41 references.

Closest ancestors · 10

Same direction, newest first

  1. 2026Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning20 May
  2. 2026Solve the Loop: Attractor Models for Language and Reasoning12 May
  3. 2025Scaling Latent Reasoning via Looped Language Models29 Oct
  4. 2025Energy-Based Transformers are Scalable Learners and Thinkers2 Jul
  5. 2025Hierarchical Reasoning Model26 Jun
  6. 2025Reasoning with Latent Thoughts: On the Power of Looped Transformers24 Feb
  7. 2025Implicit Language Models are RNNs: Balancing Parallelization and Expressivity10 Feb
  8. 2025Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach7 Feb
  9. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  10. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May

Other references · 23

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  4. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  5. 2023Let's Verify Step by Stepcited by 3,789
  6. 2018Universal Transformerscited by 647
  7. 2019Deep Equilibrium Modelscited by 615
  8. 2016Adaptive Computation Time for Recurrent Neural Networkscited by 506
  9. 2020Hopfield Networks is All You Needcited by 475
  10. 2023Looped Transformers as Programmable Computerscited by 237
  11. 2016Dense Associative Memory for Pattern Recognitioncited by 236
  12. 2024RedPajama: an Open Dataset for Training Large Language Modelscited by 182
11 more
  1. 2023Looped Transformers are Better at Learning Learning Algorithmscited by 149
  2. 2025Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computationcited by 133
  3. 2015Neural GPUs Learn Algorithmscited by 121
  4. 2021On Training Implicit Modelscited by 75
  5. 2023Energy Transformercited by 71
  6. 2022Learning Iterative Reasoning through Energy Minimizationcited by 32
  7. 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformerscited by 28
  8. 2026Probabilistic Tiny Recursive Modelcited by 19
  9. 2026Are Your Reasoning Models Reasoning or Guessing? A Mechanistic Analysis of Hierarchical Reasoning Modelscited by 10
  10. 2026Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasonerscited by 6
  11. 2026Pencil Puzzle Bench: A Benchmark for Multi-Step Verifiable Reasoningcited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Recursive Vision Language Models for General Symbolic Reasoningcited by 0
  2. 2026Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Boosting Inference with Guided Reasoning: Stochastic Exploration for Recursive Models
  2. 2026What Limits Recursive Reasoning Models: Optimization, Architecture and Test-Time Scaling
  3. 2026Form Follows Function: Recursive Stem Model
  4. 2026Quantizing Recursive Reasoning Models
  5. 2026Recurrent Reasoning on Symbolic Puzzles with Sequence Models
  6. 2026Steering Recurrent Reasoners at Inference Time with Readout Feedback
  7. 2025Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scaling
  8. 2026Recursive Models for Long-Horizon Reasoning