mlsanityData to 14 Oct 2026

Symbol-Equivariant Recurrent Reasoning Models

arXiv 2603.02193 ↗First posted 2 Mar 2026cs.LG cs.AI stat.MLcited by 4

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

Reasoning problems such as Sudoku and ARC-AGI remain challenging for neural networks. The structured problem solving architecture family of Recurrent Reasoning Models (RRMs), including Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM), offer a compact alternative to large language models, but currently handle symbol symmetries only implicitly via costly data augmentation. We introduce Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), which enforce permutation equivariance at the architectural level through symbol-equivariant layers, guaranteeing identical solutions under symbol or color permutations. SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize from just training on 9x9 to smaller 4x4 and larger 16x16 and 25x25 instances, to which existing RRMs cannot extrapolate. On ARC-AGI-1 and ARC-AGI-2, SE-RRMs achieve competitive performance with substantially less data augmentation and only 2 million parameters, demonstrating that explicitly encoding symmetry improves the robustness and scalability of neural reasoning. Code is available at https://github.com/ml-jku/SE-RRM.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 43 of its 62 references that are in the map. First posted on arXiv 2 Mar 2026.

Builds on

43 of 62 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Sudoku-Bench: Evaluating creative reasoning with Sudoku variants22 May
  2. 2024Can Large Language Models Reason? A Characterization via 3-SAT13 Aug

Other references · 41

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  4. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  5. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  6. 2021RoFormer: Enhanced Transformer with Rotary Position Embeddingcited by 4,703
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  11. 2020GLU Variants Improve Transformercited by 1,804
  12. 2019Root Mean Square Layer Normalizationcited by 1,480
29 more
  1. 2021MLP-Mixer: An all-MLP Architecture for Visioncited by 1,446
  2. 2017Deep Setscited by 1,421
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2018Attention-based Deep Multiple Instance Learningcited by 1,095
  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
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  13. 2022Exploring Length Generalization in Large Language Modelscited by 206
  14. 2023Large Language Models as General Pattern Machinescited by 197
  15. 2025ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systemscited by 190
  16. 2024The Illusion of State in State-Space Modelscited by 187
  17. 2025Hierarchical Reasoning Modelcited by 177
  18. 2020DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learningcited by 161
  19. 2021End-to-End Constrained Optimization Learning: A Surveycited by 157
  20. 2023The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domaincited by 101
  21. 2024Combining Induction and Transduction for Abstract Reasoningcited by 53
  22. 2025UGPhysics: A Comprehensive Benchmark for Undergraduate Physics Reasoning with Large Language Modelscited by 48
  23. 2022A Survey for Solving Mixed Integer Programming via Machine Learningcited by 44
  24. 2025Self-Improving Language Models for Evolutionary Program Synthesis: A Case Study on ARC-AGIcited by 36
  25. 2025Limitations of Large Language Models in Clinical Problem-Solving Arising from Inflexible Reasoningcited by 31
  26. 2025Frontier LLMs Still Struggle with Simple Reasoning Taskscited by 21
  27. 2026MolecularIQ: Characterizing Chemical Reasoning Capabilities Through Symbolic Verification on Molecular Graphscited by 8
  28. 2025Don't throw the baby out with the bathwater: How and why deep learning for ARCcited by 7
  29. 2026Tab-TRM: Tiny Recursive Model for Insurance Pricing on Tabular Datacited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026SCORE: Replacing Layer Stacking with Contractive Recurrent Depthcited by 2
  2. 2026G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Modelscited by 0
  3. 2026Recursive Vision Language Models for General Symbolic Reasoningcited by 0
  4. 2026Tiny Recursive Message Passingcited by 0

Similar, not cited

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  1. 2026MaxSAT-Based Feedback for Guiding Vision-Language Models in Sudoku
  2. 2023Bridging Logic and Learning: A Neural-Symbolic Approach for Enhanced Reasoning in Neural Models (ASPER)
  3. 2026Quantizing Recursive Reasoning Models
  4. 2024Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles
  5. 2026Recurrent Reasoning on Symbolic Puzzles with Sequence Models
  6. 2025Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error
  7. 2023Assessing SATNet's Ability to Solve the Symbol Grounding Problem
  8. 2026Neuro-symbolic PRM: Enhancing Scientific Reasoning via Structured Traces and Symbolic Verification