Algorithmic Reasoning

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Algorithmic reasoning asks whether AI systems can apply step-by-step procedures to problems such as graph algorithms, symbolic puzzles, mathematics, and code—not merely recognize familiar patterns. Approaches include graph neural networks aligned with known algorithms, recurrent and recursive models that iterate over internal states, neuro-symbolic architectures, and language models that use code execution, search, or external tools. Researchers evaluate these systems on tasks such as CLRS graph problems, Sudoku and maze puzzles, ARC-style visual reasoning, and programming benchmarks, including tests of longer inputs and unfamiliar variants. A central challenge is achieving reliable multi-step execution and generalization beyond training examples: extra recurrence, search, or tools can help, but may increase cost and do not always prevent errors from accumulating.

Latest papers

108 papers11 papers in the last four weeks, level with the four weeks before. 0.1% of all new papers.

Symbol-Equivariant Recurrent Reasoning Models
Mar 2, 2026Richard Freinschlag, Timo Bertram, Erich Kobler +2Permutation-Equivariant Neural Networks Sudoku Solving
ELLIS Unit Linz, LIT AI Lab & Institute for Machine Learning, Johannes Kepler University Linz, Austria · Clinical Research Institute for Medical AI, Johannes Kepler University Linz, Austria
Recursive Models for Long-Horizon Reasoning
Mar 2, 2026Chenxiao Yang, Nathan Srebro, Zhiyuan LiRecursive Language Models Language Modeling
Toyota Technological Institute at Chicago
Intrinsic Task Symmetry Drives Generalization in Algorithmic Tasks
Mar 2, 2026Hyeonbin Hwang, Yeachan ParkNeural Network Generalization Grokking
KAIST · Sejong University
Algorithmic Blindness in Large Language Models: A Calibration Study of Performance Prediction
Feb 25, 2026Sohan Venkatesh, Ashish Mahendran Kurapath, Tejas MelkoteAlgorithmic Reasoning LLM Evaluation
Manipal Institute of Technology Bengaluru
Tool Use Reduces Depth-Induced Collapse in OOD Reasoning
Feb 24, 2026David Koplow, Tomer Galanti, Tomaso PoggioOOD Generalization LLM Tool Use
Massachusetts Institute of Technology · Texas A&M University
GraphSkill: Documentation-Guided Hierarchical Retrieval-Augmented Coding for Complex Graph Reasoning
Feb 20, 2026Fali Wang, Chenglin Weng, Xianren Zhang +3LLM Reasoning with Graphs Graph Reasoning
The Pennsylvania State University, University Park, Pennsylvania, USA · Michigan State University, East Lansing, Michigan, USA
FloydNet: A Learning Paradigm for Global Relational Reasoning
Jan 27, 2026Jingcheng Yu, Mingliang Zeng, Qiwei YeGraph Neural Networks Relational Reasoning
Beijing Academy of Artificial Intelligence
Efficiently Learning Branching Networks for Multitask Algorithmic Reasoning
Nov 30, 2025Dongyue Li, Zhenshuo Zhang, Minxuan Duan +2Neural Algorithmic Reasoning Multi-Task Learning
†Northeastern University, Boston, Massachusetts · ‡University of Pennsylvania, Philadelphia, Pennsylvania
A Quantitative Study of Sustained Focus in Large Language Models via Repetitive Deterministic Prediction Tasks
Nov 2, 2025Wanda Hou, Leon Zhou, Hong-Ye Hu +3LLM Evaluation LLM Reliability
EdenCode Inc. · Stevenson School · Harvard University +2
Higher Embedding Dimension Creates a Stronger World Model for a Simple Sorting Task
Oct 21, 2025Brady Bhalla, Honglu Fan, Nancy Chen +1Transformer Interpretability Representation Learning
California Institute of Technology · Pasadena, CA 91125 · Google DeepMind +3
Learning How to Use Tools, Not Just When: Pattern-Aware Tool-Integrated Reasoning
Sep 27, 2025Ningning Xu, Yuxuan Jiang, Shubhashis Roy Dipta +1Tool-Integrated Reasoning LLM Tool Use
University of Georgia · University of Maryland, Baltimore County · 3The University of Hong Kong
Tackling GNARLy Problems: Graph Neural Algorithmic Reasoning Reimagined through Reinforcement Learning
Sep 23, 2025Alex Schutz, Victor-Alexandru Darvariu, Efimia Panagiotaki +2Graph Neural Networks Reinforcement Learning
Oxford Robotics Institute, University of Oxford · Stateful Robotics
PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains
Aug 29, 2025Joshua Ong Jun Leang, Zheng Zhao, Aryo Pradipta Gema +7Confidence Estimation in Language Models Best-of-N Sampling
Imperial College London · University of Edinburgh · UCL
PuzzleJAX: A Benchmark for Reasoning and Learning
Aug 22, 2025Sam Earle, Graham Todd, Yuchen Li +5RL Benchmarks Game-Playing Agents
New York University · University of Malta · University of the Witwatersrand +1
Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning
Aug 13, 2025Xiaojun Wu, Xiaoguang Jiang, Huiyang Li +11CoT Distillation Language Model Distillation
1Zhongxing Telecom Equipment(ZTE), China · 2China Mobile Communications Group Co Ltd
Hierarchical Reasoning Model
Jun 26, 2025Guan Wang, Jin Li, Yuhao Sun +6Recurrent Neural Networks Algorithmic Reasoning
Sapient Intelligence, Singapore · Tsinghua University
BigO(Bench): Can LLMs Generate Code with Controlled Time and Space Complexity?
Mar 19, 2025Pierre Chambon, Baptiste Roziere, Benoit Sagot +1Benchmark Design Code Generation
FAIR at Meta · Inria · Work done at Meta, now working at Mistral AI
Scaling Online Complex Event Detection with Synthetic Supervision and Mamba-Based Neural Algorithmic Reasoning
Feb 11, 2025Liying Han, Gaofeng Dong, Xiaomin Ouyang +4Neural Algorithmic Reasoning Algorithmic Reasoning
Department of Electrical and Computer Engineering University of California, Los Angeles · Department of Computer Science and Engineering Hong Kong University of Science and Technology · U.S. Army DEVCOM Army Research Laboratory +1

Mar 2, 2026J/K move · Enter open · S save

Symbol-Equivariant Recurrent Reasoning Models

Richard Freinschlag, Timo Bertram, Erich Kobler, Andreas Mayr+1

ELLIS Unit Linz, LIT AI Lab & Institute for Machine Learning, Johannes Kepler University Linz, Austria · Clinical Research Institute for Medical AI, Johannes Kepler University Linz, Austria

Permutation-Equivariant Neural Networks Sudoku Solving Neural Algorithmic Reasoning Algorithmic Reasoning Recurrent Neural Networks Equivariant Neural Networks+1

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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.