Neural algorithmic reasoning
Open accessAbstract
We present neural algorithmic reasoning-the art of building neural networks that are able to execute algorithmic computation-and provide our opinion on its transformative potential for running classical algorithms on inputs previously considered inaccessible to them.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Python function tools are a more generic form of Chain-of-Thought, enhancing the overall utility and flexibility of the LLMs, as they can be used to solve questions that involve algorithmic reasoning ability.
“Furthermore, the Python function tools are a more generic form of Chain-of-Thought, enhancing the overall utility and flexibility of the LLMs, as they can be used to solve questions that involve algorithmic reasoning ability (Veličković and Blundell, 2021).”
From Large language models as tool makers (2023) · cites this paper as Veličković and Blundell, 2021
The Main text and the blueprint of neural algorithmic reasoning discuss neural networks learning to execute algorithms, not Python function tools or LLMs. Searches for Chain-of-Thought, Python function tools, and LLM tool use found no passage addressing the claimed relationship or improvement in utility and flexibility. (LLM, conf=0.76)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
A note on two problems in connexion with graphs
Dijkstra, E. (1959) · Numerische Mathematik · doi:10.1007/bf01386390 · Cited by 24,351 · see citing works
Graves, A., Wayne, G., & Danihelka, I. (2014) · arXiv · doi:10.48550/arxiv.1410.5401 · Cited by 1,058 · see citing works
Combinatorial Optimization and Reasoning with Graph Neural Networks
Cappart, Q., Chételat, D., Khalil, E. B., Lodi, A., Morris, C., & Veličković, P. (2021) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2021/595 · Cited by 226 · see citing works
Self-citationNeural GPUs Learn AlgorithmsPreprint
Kaiser, Ł., & Sutskever, I. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.08228 · Cited by 224 · see citing works
TreeQN and ATreeC: Differentiable Tree-Structured Models for Deep Reinforcement LearningPreprint
Farquhar, G., Rocktäschel, T., Igl, M., & Whiteson, S. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1710.11417 · Cited by 36 · see citing works
Strong Generalization and Efficiency in Neural ProgramsPreprint
Li, Y., Gimeno, F., Kohli, P., & Vinyals, O. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.03629 · Cited by 20 · see citing works
Neural Random-Access MachinesPreprint
Kurach, K., Andrychowicz, M., & Sutskever, I. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.06392 · Cited by 14 · see citing works
XLVIN: eXecuted Latent Value Iteration NetsPreprint
Deac, A., Veličković, P., Milinković, O., Bacon, P., Tang, J., & Nikolić, M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.13146 · Cited by 11 · see citing works
Self-citationNeural Programmer-Interpreters
Reed, S., & de Freitas, N. (2015) · arXiv · doi:10.48550/arxiv.1511.06279
Flagged first, then by citations
Research works printed but not linked: 3
- [1]Cormen T.H. Leiserson C.E. Rivest R.L. Stein C. Introduction to Algorithms 2009 MIT press
- [7]Veličković P. Buesing L. Matthew C Overlan, Razvan Pascanu, Oriol Vinyals, and Charles Blundell. Pointer Graph Networks arXiv 2020 arXiv:2006.06380 · arXiv
- [8]Veličković P. Ying R. Padovano M. Hadsell R. Blundell C. Neural execution of graph algorithms arXiv 2019 arXiv:1910.10593 · arXiv
Cited by
Sorted by citations
A neural network boosting regression model based on XGBoost
Dong, J., Chen, Y., Yao, B., Zhang, X. L., & Zeng, N. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109067 · Cited by 219 · see citing works
Faith and Fate: Limits of Transformers on Compositionality
Dziri, N., Lu, X., Sclar, M., Li, X. (., Jiang, L., Lin, B. Y., Welleck, S., West, P., Bhagavatula, C., Bras, R. L., et al. (2023) · Advances in Neural Information Processing Systems 36 · doi:10.52202/075280-3081 · Cited by 124 · see citing works
“However, these models have also been shown to struggle across multiple domains [32], including algorithmic reasoning [78], commonsense reasoning [62, 40], theory of mind [65], planning [76], logical reasoning [70], and ethical reasoning [36].”
BackgroundCurrent and future directions in network biology
Žitnik, M., Li, M. M., Wells, A., Glass, K., Gysi, D. M., Krishnan, A., Murali, T. M., Predrag Radivojac, A., Roy, S., Baudot, A., et al. (2024) · Bioinformatics Advances · doi:10.1093/bioadv/vbae099 · Cited by 118 · see citing works
Learning the travelling salesperson problem requires rethinking generalization
Joshi, C. K., Cappart, Q., Rousseau, L.-M., & Laurent, T. (2022) · Constraints · doi:10.1007/s10601-022-09327-y · Cited by 161 · see citing works
Generalization potential of large language models
Budnikov, M., Bykova, A., & Yamshchikov, I. P. (2024) · Neural Computing and Applications · doi:10.1007/s00521-024-10827-6 · Cited by 36 · see citing works
NERO: NEural algorithmic reasoning for zeRO-day attack detection in the IoT: A hybrid approach
Moreno, J. F. C., Rizzardi, A., Sicari, S., & Coen‐Porisini, A. (2024) · Computers & Security · doi:10.1016/j.cose.2024.103898 · Cited by 30 · see citing works
Large language models as tool makers
Cai, T., Wang, X., Ma, T., Chen, X., & Zhou, D. (2023) · arXiv · doi:10.48550/arxiv.2305.17126 · Cited by 28 · see citing works
Zhang, Z., & Fink, O. (2025) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2025.111494 · Cited by 26 · see citing works
Giusti, L., Battiloro, C., Testa, L., Lorenzo, P. D., Sardellitti, S., & Barbarossa, S. (2023) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn54540.2023.10191530 · Cited by 22 · see citing works
Show Your Work: Scratchpads for Intermediate Computation with Language Models
Nye, M., Andreassen, A. J., Gur-Ari, G., Michalewski, H., Austin, J., Bieber, D., Dohan, D., Lewkowycz, A., Bosma, M., Luan, D., et al. (2021) · arXiv · doi:10.48550/arxiv.2112.00114 · Cited by 144 · see citing works
HERO: From High-dimensional network traffic to zERO-Day attack detection
Moreno, J. F. C., Rizzardi, A., Sicari, S., & Coen‐Porisini, A. (2025) · Computer Networks · doi:10.1016/j.comnet.2025.111264 · Cited by 15 · see citing works
Visually-guided motion planning for autonomous driving from interactive demonstrations
Pérez‐Dattari, R., Brito, B., de Groot, O., Kober, J., & Alonso–Mora, J. (2022) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2022.105277 · Cited by 15 · see citing works
What Algorithms can Transformers Learn? A Study in Length Generalization
Zhou, H., Bradley, A., Littwin, E., Razin, N., Saremi, O., Susskind, J., Bengio, S., & Nakkiran, P. (2023) · arXiv · doi:10.48550/arxiv.2310.16028 · Cited by 10 · see citing works
“In the previous section, we noted two aspects of a naive addition algorithm that pose problems for RASP-L: index-arithmetic (to query the sum-mand digits for the current output digit), and non-causality (for the carry).”
BackgroundFink, O., Sharma, V., Nejjar, I., Krannichfeldt, L. V., Garmaev, S., Zhang, Z., Wei, A., Frusque, G., Forest, F., Zhao, M., et al. (2026) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2026.112213 · Cited by 10 · see citing works
Fabre, R., Azeroual, O., Schöpfel, J., Bellot, P., & Egret, D. (2023) · Future Internet · doi:10.3390/fi15040147 · Cited by 10 · see citing works
SmartVille: A Framework for Realistic Deep Learning-Based Online Network Intrusion Detection
Moreno, J. F. C., Rizzardi, A., Sicari, S., & Coen‐Porisini, A. (2026) · Journal of Network and Systems Management · doi:10.1007/s10922-026-10097-8 · Cited by 3 · see citing works
Graph neural network based time estimator for SAT solver
Liu, J., Xiao, W., Cheng, H., & Shi, C. (2024) · International Journal of Machine Learning and Cybernetics · doi:10.1007/s13042-024-02327-9 · Cited by 3 · see citing works
Hierarchical layered multigraph network with scale importance estimation for image classification
Batisteli, J. P. O., Passat, N., Guimarães, S. J. F., & Patrocínio, Z. K. G. (2025) · Applied Soft Computing · doi:10.1016/j.asoc.2025.113877 · Cited by 3 · see citing works
An Overview of the State-of-the-Art Machine Learning Methods for Traveling Salesman Problem
Požgaj, S., Kurdija, A. S., Šilić, M., Delač, G., & Vladimir, K. (2024) · International Convention on Information and Communication Technology, Electronics and Microelectronics · doi:10.1109/mipro60963.2024.10569360 · Cited by 3 · see citing works
Finding Hamiltonian Cycles with Graph Neural Networks
Bosnić, F., & Šikić, M. (2023) · International symposium on image and signal processing and analysis/ISPA ... · doi:10.1109/ispa58351.2023.10278690 · Cited by 2 · see citing works
Accelerated Discovery of Set Cover Solutions via Graph Neural Networks
Shafi, Z., Miller, B. A., Eliassi‐Rad, T., & Caceres, R. S. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-95976-9_12 · Cited by 2 · see citing works
Monocular 3D-trajectory reconstruction using models-driven weakly supervised learning
Chen, Z., Xu, J., Wan, M., & Tian, J. (2023) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2023.107798 · Cited by 2 · see citing works
Scalable pragmatic communication via self-supervisionPreprint
Hu, J., Lévy, R., & Zaslavsky, N. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.05799 · Cited by 2 · see citing works
Topological Message Passing for Higher - Order and Long - Range Interactions
Giusti, L., Reu, T., Ceccarelli, F., Bodnar, C., & Lió, P. (2024) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn60899.2024.10650343 · Cited by 1 · see citing works
Andreev, A., Kochemazov, S., & Semenov, A. (2025) · PLoS ONE · doi:10.1371/journal.pone.0331109 · Cited by 1 · see citing works
Carbó‐Dorca, R., & Chakraborty, T. (2023) · Elsevier eBooks · doi:10.1016/b978-0-32-390257-1.00025-5 · Cited by 1 · see citing works
Neural Algorithmic Reasoners informed Large Language Model for Multi-Agent Path Finding
Feng, P., Wang, S., Cao, Y., Liang, J., Shi, R., & Wu, W. (2025) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn64981.2025.11227551 · Cited by 1 · see citing works
Solving Visual Analogies Using Neural Algorithmic Reasoning (Student Abstract)
Sonwane, A., Shroff, G. M., Vig, L., Srinivasan, A., & Dash, T. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i11.21664 · Cited by 1 · see citing works
Reasoning-Modulated RepresentationsPreprint
Veličković, P., Bošnjak, M., Kipf, T., Lerchner, A., Hadsell, R. T., Pascanu, R., & Blundell, C. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.08881 · Cited by 1 · see citing works
Self-citationSolving Visual Analogies Using Neural Algorithmic ReasoningPreprint
Sonwane, A., Shroff, G. M., Vig, L., Srinivasan, A., & Dash, T. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.10361
Spatio-Temporal Activity Recognition for Evolutionary Search Behavior Prediction
Friess, S., Peter Tiňo, B., Menzel, S., Zhao, X., Sendhoff, B., & Yao, X. (2022) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn55064.2022.9892483
Bridging the Gaps between Graph Neural Networks and Data-Flow Analysis: The Closer, the Better
Yu, Q., Liu, X., Zhou, Q., & Wu, C. (2025) · Proceedings of the ACM on software engineering. · doi:10.1145/3728906
GraphVeri: A NAR-based control plane verification framework for routing protocols
Li, S., Luo, L., Qiu, C., Ren, B., Zhou, Y. F., Guo, D., & Ma, R. T. B. (2025) · Computer Networks · doi:10.1016/j.comnet.2025.111635
A feature-based generalizable prediction model for both perceptual and abstract reasoning
Do, Q. H., Morin, T., Stern, C. E., & Hasselmo, M. E. (2025) · Cognitive Neuroscience · doi:10.1080/17588928.2025.2599784
Ang, A. W. L., Chen, J., & Stouffs, R. M. F. A. (2025) · Digital innovations in architecture, engineering and construction · doi:10.1007/978-3-032-02782-5_19
Mono Multi-model kinetic fingerprinting of Arundo donax pyrolysis
Dias, A. P. S., Casquilho, M., Fonseca, F. G., Pereira, M. F., & Rijo, B. (2026) · Energy · doi:10.1016/j.energy.2026.141073
Short Paper: Towards Algorithmically Grounded Embedded AI Models
Wang, Z., Uddin, M. Y. S., & Nirjon, S. (2026) · Proceedings of the 2026 ACM/IEEE International Conference on Embedded Artificial Intelligence and Sensing Systems · doi:10.1145/3774906.3800495
A Logical View of GNN-Style Computation and the Role of Activation Functions
Barceló, P., Geerts, F., Lanzinger, M., Pakhomenko, K., & den Bussche, J. V. (2026) · Proceedings of the ACM on Management of Data · doi:10.1145/3801914
Shi, F., & Zhang, D. (2026) · International Conference on Artificial Intelligence and Industrial Technology Applications (AIITA) · doi:10.1109/aiita69518.2026.11567367
Interactive Visualizer for Neural Algorithmic Reasoners
Brajko, T., Požgaj, S., Kurdija, A. S., Vladimir, K., Delač, G., & Šilić, M. (2026) · International Convention on Information and Communication Technology, Electronics and Microelectronics · doi:10.1109/mipro70003.2026.11591554
Harish, K. (2026) · International Conference on Advanced Computational Intelligence (ICACI) · doi:10.1109/icaci69731.2026.11677908
Critical Challenges in Bookless Libraries
Rajkumar, N., Viji, C., Nachiappan, B., Mohanraj, A., & Nagarajan, G. (2026) · IGI Global eBooks · doi:10.4018/979-8-3373-6521-3.ch005
Flexible Prefrontal Control over Hippocampal Episodic Memory for Goal-Directed Generalization
Zheng, Y., Wolf, N., Ranganath, C., O'Reilly, R. C., & McKee, K. L. (2025) · Proceedings of Cognitive Computational Neuroscience 2025 · doi:10.32470/jnqbpro
- Authors
- Veličković, P., & Blundell, C.
- Affiliations
- Google DeepMind (United Kingdom) (GB)
- Corresponding author
- Veličković, Petar
- ORCID
- Blundell, Charles
- Venue
- Patterns
- Publisher
- Elsevier BV
- Published
- 2021-07
- Volume
- 2
- Issue
- 7
- Pages
- 100273
- ISSN
- 2666-3899 (ISSN-L)
- PMC
- PMC8276006
- OpenAlex
- W3158330599
- Cited by
- 39
- References
- 9
- Citations by year
- 2026: 9 · 2025: 10 · 2024: 6 · 2023: 5 · 2022: 5 · 2021: 4
- FWCI
- 1.77
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Patterns (publishedVersion, cc-by-nc-nd)
- PubMed Central (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Artificial Intelligence Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Keywords
- artificial neural networks, algorithmic computation, classical algorithms, intractable problems, computational complexity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review