The DOI matches its Crossref record; 149 of the 152 references it cites were found in a registry or an index, and 1 are not checked yet.
Computational Mechanics: Pattern and Prediction, Structure and Simplicity
Open accessOverview
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
Verification
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 cited source says what the claim attributes to it.
In the citing paper
“These can be abstract (e.g. Turing machines (Delahaye and Zenil, 2007, 2012), ϵ -machines (Shalizi and Crutchfield, 2001; G¨ ornerup and Crutchfield, 2008)), biological (ecosystems, organisms), economic, social or technological (Helbing, 2011).”
From Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis (2013) · cites this paper as Shalizi and Crutchfield, 2001
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
A Mathematical Theory of Communication
Shannon, C. E. (1948) · The MIT Press eBooks · doi:10.1002/j.1538-7305.1948.tb00917.x · Cited by 50,201
The Nature of Statistical Learning Theory
Vapnik, V. (2000) · Statistics for Engineering and Information Science · doi:10.1007/978-1-4757-3264-1 · Cited by 46,387
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 37,139
Causality: Models, Reasoning, and Inference
Pearl, J. (2009) · doi:10.1017/cbo9780511803161 · Cited by 11,653
Introduction to automata theory, languages and computation
(1981) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(81)90068-9 · Cited by 10,781
Detecting strange attractors in turbulence
Takens, F. (1981) · Lecture Notes in Mathematics · doi:10.1007/bfb0091924 · Cited by 10,459
The Mathematical Theory of Communication
Shannon, C. E., Weaver, W., & Wiener, N. (1950) · Physics Today · doi:10.1063/1.3067010 · Cited by 9,882
Doob, J. L., & Doob, J. L. (1953) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,053
Research works printed but not linked: 11
- J. P. Crutchfield and K. Young, Computation at the onset of chaos, In Zurek et al.,(137) pages 223–269.
- J. P. Crutchfield, Semantics and thermodynamics, In Nonlinear Modeling and Forecasting, M. Casdagli and S. Eubank, eds., volume 12 of Santa Fe Institute Studies in the Sciences of Complexity, pages 317–359 (Addison-Wesley, Reading, Massachusetts, 1992).
- A. N. Whitehead and B. Russell, Principia Mathematica, 2nd ed. (Cambridge University Press, Cambridge, England), pp. 1925–27.
- J. Rhodes, Applications of Automata Theory and Algebra via the Mathematical Theory of Complexity to Biology, Physics, Psychology, Philosophy, Games, and Codes (University of California, Berkeley, California, 1971).
- C. H. Bennett, How to define complexity in physics, and why, In Zurek et al.,(137) pages 137–148.
- M. Koppel, Complexity, depth, and sophistication, Complex Systems 1:1087–1091 (1987).
- M. Bunge, Causality: The Place of the Causal Princple in Modern Science (Harvard University Press, Cambridge, Massachusetts, 1959). Reprinted as Causality and Modern Science, NY: Dover Books, 1979.
- Anonymous, Kuan Yin Tzu, T'ang Dynasty, Written in China during the T'ang dynasty. Partial translation in Joseph Needham, Science and Civilisation in China, vol. II (Cambridge University Press, 1956), p. 73.
- H. R. Lewis and C. H. Papadimitriou, Elements of the Theory of Computation, 2nd ed. (Prentice-Hall, Upper Saddle River, New Jersey, 1998).
- I. M. Gel'fand and A. M. Yaglom, Calculation of the amount of information about a random function contained in another such function, Uspekhi Matematicheski Nauk 12:3–52 (1956). Trans. in American Mathematical Society Translations 12(2):199û246 (1959).
- A. N. Kolmogorov, Interpolation und extrapolation von stationären zufälligen folgen, Bull. Acad. Sci. U.S.S.R., Math. 3:3–14 (1941). In Russian with German summary.
Cited by
Sorted by citations
Items 201–300 of 514
Robust inference of memory structure for efficient quantum modeling of stochastic processes
Ho, M., Gu, M., & Elliott, T. J. (2020) · Physical Review A · doi:10.1103/physreva.101.032327 · Cited by 14
Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems
Rupe, A., Vesselinov, V. V., & Crutchfield, J. P. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac95b7 · Cited by 14
Self-citationMendes, R. V. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405012715 · Cited by 14
Using the uncertainty principle to design simple interactions for targeted self-assembly
Edlund, E., Lindgren, O., & Jacobi, M. N. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4812727 · Cited by 14
Reductions of Hidden Information Sources
Ay, N., & Crutchfield, J. P. (2005) · Journal of Statistical Physics · doi:10.1007/s10955-005-6797-4 · Cited by 14
Self-citationPattern recognition for command and control data systems
Brooks, R. R., & Schwier, J. M. (2009) · TigerPrints (Clemson University) · Cited by 14
Caractérisation et modélisation de la co-évolution des réseaux de transport et des territoires.
Raimbault, J. (2018) · theses.fr (ABES) · doi:10.70675/127ceebaz182az46e1z95d6zbd11088acb20 · Cited by 14
The Origins of Computational Mechanics: A Brief Intellectual History and Several ClarificationsPreprint
Crutchfield, J. P. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1710.06832 · Cited by 14
Self-citationContextual emergence of mental states.
Atmanspacher, H. (2015) · Cognitive Processing · doi:10.1007/s10339-015-0658-0 · Cited by 13
Nature computes: Information processing in quantum dynamical systems
Wiesner, K. (2010) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3491238 · Cited by 13
Unifying complexity science and machine learning
Krakauer, D. C. (2023) · Frontiers in Complex Systems · doi:10.3389/fcpxs.2023.1235202 · Cited by 13
Graph-based predictable deep transfer network for soft sensing of dynamic industrial processes
Zhang, Z., Xu, Y., Huang, J. L., & Shardt, Y. A. W. (2025) · Knowledge-Based Systems · doi:10.1016/j.knosys.2025.113495 · Cited by 13
Non-sufficient Memories That Are Sufficient for Prediction
Löhr, W., & Ay, N. (2009) · Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering · doi:10.1007/978-3-642-02466-5_25 · Cited by 13
The observer's observer's paradox
Dale, R. A. C., & Vinson, D. W. (2013) · Journal of Experimental & Theoretical Artificial Intelligence · doi:10.1080/0952813x.2013.782987 · Cited by 13
Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?
Ruebeck, J. B., James, R. G., Mahoney, J. R., & Crutchfield, J. P. (2018) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5003041 · Cited by 13
Self-citationError-tolerant witnessing of divergences in classical and quantum statistical complexity
Ghafari, F., Gu, M., Ho, J., Thompson, J. E., Suen, W. Y., Wiseman, H. M., & Pryde, G. J. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/addfff · Cited by 13
Feldman, D. P., & Crutchfield, J. P. (2022) · Entropy · doi:10.3390/e24091282 · Cited by 13
Self-citationSummarizing Complexity in High Dimensions
Young, K., Chen, Y., Kornak, J., Matson, G. B., & Schuff, N. W. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.098701 · Cited by 13
On Hidden Markov Processes with Infinite Excess Entropy
Dębowski, Ł. (2012) · Journal of Theoretical Probability · doi:10.1007/s10959-012-0468-6 · Cited by 12
Reflections on the asymmetry of causation
Ismael, J. (2023) · Interface Focus · doi:10.1098/rsfs.2022.0081 · Cited by 12
Melchert, O., & Hartmann, A. K. (2013) · Physical Review E · doi:10.1103/physreve.87.022107 · Cited by 12
Analysing Emergent Dynamics of Evolving Computation in 2D Cellular Automata
McCaskill, J. S., & Packard, N. H. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-34500-6_1 · Cited by 12
Central limit theorem for chemical kinetics in complex systems
Bandstra, J. Z., & Tratnyek, P. G. (2005) · Journal of Mathematical Chemistry · doi:10.1007/s10910-004-1107-y · Cited by 12
On $g$-functions for subshifts
Krieger, W. (2006) · Lecture notes-monograph series · doi:10.1214/lnms/1196285831 · Cited by 11
An investigation of spatial behavior in agile guidance tasks
Kong, Z., & Mettler, B. (2011) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/icsmc.2011.6084049 · Cited by 11
Predictive models and generative complexity
Löhr, W. (2012) · Journal of Systems Science and Complexity · doi:10.1007/s11424-012-9173-x · Cited by 11
Summarizing Simulation Results Using Causally-Relevant States
Parikh, N., MARATHE, M. V., & Swarup, S. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-46840-2_6 · Cited by 11
Quantum Coarse Graining for Extreme Dimension Reduction in Modeling Stochastic Temporal Dynamics
Elliott, T. J. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.020342 · Cited by 11
Complexity and Emergence in Engineering Systems
Chen, C., Nagl, S., & Clack, C. D. (2008) · Studies in computational intelligence · doi:10.1007/978-3-540-88075-2_5 · Cited by 11
Quantifying the complexity of random Boolean networks
Gong, X., & Socolar, J. E. S. (2012) · Physical Review E · doi:10.1103/physreve.85.066107 · Cited by 11
Quantitative measures of organization for multiagent systems
Krivov, S., Ulanowicz, R. E., & Dahiya, A. (2003) · Biosystems · doi:10.1016/s0303-2647(03)00003-0 · Cited by 11
A Multidisciplinary Approach to Complex Systems Design
Ryan, A. (2007) · Adelaide Research & Scholarship (AR&S) (University of Adelaide) · Cited by 11
Hierarchical Model of Human Guidance Performance Based on Interaction Patterns in BehaviorPreprint
Mettler, B., & Kong, Z. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.3672 · Cited by 11
Models and people: An alternative view of the emergent properties of computational models
Boschetti, F. (2015) · Complexity · doi:10.1002/cplx.21680 · Cited by 10
A METHOD FOR FINDING AGGREGATED REPRESENTATIONS OF LINEAR DYNAMICAL SYSTEMS
Görnerup, O., & Jacobi, M. N. (2010) · Advances in Complex Systems · doi:10.1142/s0219525910002542 · Cited by 10
Reconstructing non-Markovian open quantum evolution from multiple time measurements
Guo, C. (2022) · Physical Review A · doi:10.1103/physreva.106.022411 · Cited by 10
Provably superior accuracy in quantum stochastic modeling
Yang, C., Garner, A. J. P., Liu, F., Tischler, N., Thompson, J. E., Yung, M., Gu, M., & Dahlsten, O. (2023) · Physical Review A · doi:10.1103/physreva.108.022411 · Cited by 10
Measures of distinguishability between stochastic processes
Yang, C., Binder, F. C., Gu, M., & Elliott, T. J. (2020) · Physical review. E · doi:10.1103/physreve.101.062137 · Cited by 10
Algorithmic Information Theory for Physicists and Natural Scientists
Devine, S. D. (2020) · Institute of Physics eBooks · doi:10.1088/978-0-7503-2640-7 · Cited by 10
Pattern Discovery and Computational MechanicsPreprint
Shalizi, C. R., & Crutchfield, J. P. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.cs/0001027 · Cited by 10
Self-citationDarmon, D. M., Sylvester, J., Girvan, M., & Rand, W. M. (2013) · SSRN Electronic Journal · doi:10.2139/ssrn.2285537 · Cited by 10
Energetic Advantages for Quantum Agents in Online Execution of Complex Strategies
Thompson, J., Riechers, P. M., Garner, A. J. P., Elliott, T. J., & Gu, M. (2025) · Physical Review Letters · doi:10.1103/dryx-l5rt · Cited by 9
Varn, D. P., Canright, G., & Crutchfield, J. P. (2013) · Acta Crystallographica Section A Foundations of Crystallography · doi:10.1107/s0108767313008738 · Cited by 9
Self-citationState Aggregations in Markov Chains and Block Models of Networks
Faccin, M., Schaub, M. T., & Delvenne, J. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.078301 · Cited by 9
Steady visualization of the dynamics in fluids using -machines
Jänicke, H., & Scheuermann, G. (2009) · Computers & Graphics · doi:10.1016/j.cag.2009.06.003 · Cited by 9
Quantification of complexity of power electronics based systems
El-Mezyani, T., Wilson, R., Sattler, M., Srivastava, S., Edrington, C. S., & Cartes, D. A. (2012) · IET Electrical Systems in Transportation · doi:10.1049/iet-est.2011.0019 · Cited by 9
Large-Scale Communication is More Complex and Unpredictable with Automated Bots
Hilbert, M., & Darmon, D. M. (2020) · Journal of Communication · doi:10.1093/joc/jqaa021 · Cited by 9
Minimum Entropy Rate Simplification of Stochastic Processes
Henter, G. E., & Kleijn, W. B. (2016) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2533382 · Cited by 9
How does a choice of Markov partition affect the resultant symbolic dynamics?
Teramoto, H., & Komatsuzaki, T. (2010) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3491097 · Cited by 9
Cenek, M., & Dahl, S. K. (2016) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4965982 · Cited by 9
Electric power synchrophasor network cyber security vulnerabilities
Beasley, C. (2014) · TigerPrints (Clemson University) · Cited by 9
Capturing the emergent dynamical structure in biophysical neural models
Milinkovic, B., Barnett, L., Carter, O. L., Seth, A. K., & Andrillon, T. (2025) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1012572 · Cited by 8
Complex event types for agent-based simulation
Chen, C. (2009) · Cited by 8
Rasetti, M., & Merelli, E. (2015) · Journal of Physics Conference Series · doi:10.1088/1742-6596/626/1/012005 · Cited by 8
Crutchfield, J. P., & Machta, J. L. (2011) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3643065 · Cited by 8
Self-citationOn Quitting: Performance and Practice in Online Game Play
Agarwal, T., Burghardt, K., & Lerman, K. (2017) · Proceedings of the International AAAI Conference on Web and Social Media · doi:10.1609/icwsm.v11i1.14939 · Cited by 8
Choi, J., Hiraoka, T., & Jo, H.-H. (2021) · Physical review. E · doi:10.1103/physreve.104.014312 · Cited by 8
Accuracy vs memory advantage in the quantum simulation of stochastic processes
Banchi, L. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad444a · Cited by 8
Increasing complexity with quantum physics
Anders, J., & Wiesner, K. (2011) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3640753 · Cited by 8
Formalising the role of behaviour in neuroscience
Piantadosi, S. T., & Gallistel, C. R. (2024) · European Journal of Neuroscience · doi:10.1111/ejn.16372 · Cited by 7
Bulat, B., & Hilbert, M. (2025) · Entropy · doi:10.3390/e27060573 · Cited by 7
Predictive Information in a Nonequilibrium Critical Model
Tchernookov, M., & Nemenman, I. M. (2013) · Journal of Statistical Physics · doi:10.1007/s10955-013-0833-6 · Cited by 7
Sultana, T., Takagi, H., Morimatsu, M., Teramoto, H., Li, C., Sako, Y., & Komatsuzaki, T. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4848719 · Cited by 7
Minimum memory for generating rare events
Aghamohammadi, C., & Crutchfield, J. P. (2017) · Physical review. E · doi:10.1103/physreve.95.032101 · Cited by 7
Self-citationMettler, B., Verma, A., & Feit, A. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.09.001 · Cited by 7
Albanna, B. F., Hillar, C. J., Sohl‐Dickstein, J., & DeWeese, M. R. (2017) · Entropy · doi:10.3390/e19080427 · Cited by 7
Dynamic Knowledge—A Century of Evolution
Weber, G. F. (2013) · Sociology Mind · doi:10.4236/sm.2013.34036 · Cited by 7
Surveying Structural Complexity in Quantum Many-Body Systems
Suen, W. Y., Elliott, T. J., Thompson, J. E., Garner, A. J. P., Mahoney, J. R., Vedral, V., & Gu, M. (2022) · Journal of Statistical Physics · doi:10.1007/s10955-022-02895-6 · Cited by 7
Predicting two-dimensional turbulence
Cerbus, R., & Goldburg, W. I. (2015) · Physical Review E · doi:10.1103/physreve.91.043003 · Cited by 7
Can Classical Epistemic States Be Entangled?
Harald Atmanspacher, A., Graben, P. B., & Thomas Filk, A. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-24971-6_11 · Cited by 7
Foundations of Stochastic Thermodynamics
Altaner, B. (2015) · eDiss (Georg-August-Universität Göttingen) · doi:10.53846/goediss-4985 · Cited by 7
Network Traffic Analysis Using Stochastic Grammars
Lü, C. (2012) · TigerPrints (Clemson University) · Cited by 7
Kong, Z., & Mettler, B. (2011) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2011.6094903 · Cited by 6
Simulation Analytics for Social and Behavioral Modeling
Swarup, S., Marathe, A., MARATHE, M. V., & Barrett, C. L. (2019) · Wiley eBooks · doi:10.1002/9781119485001.ch26 · Cited by 6
Engines for predictive work extraction from memoryful quantum stochastic processes
Huang, R. C., Riechers, P. M., Gu, M., & Narasimhachar, V. (2023) · Quantum · doi:10.22331/q-2023-12-11-1203 · Cited by 6
Determining a purely symbolic transfer function from symbol streams: Theory and algorithms
Griffin, C. H., Brooks, R. R., & Schwier, J. M. (2008) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2008.4587129 · Cited by 6
Roli, A., Ligot, A., & Birattari, M. (2019) · Frontiers in Robotics and AI · doi:10.3389/frobt.2019.00130 · Cited by 6
Algebraic Theory of Patterns as Generalized Symmetries
Rupe, A., & Crutchfield, J. P. (2022) · Symmetry · doi:10.3390/sym14081636 · Cited by 6
Self-citationInference, Prediction, & Entropy-Rate Estimation of Continuous-Time, Discrete-Event Processes
Marzen, S., & Crutchfield, J. P. (2022) · Entropy · doi:10.3390/e24111675 · Cited by 6
Self-citationThe application of algorithmic information theory to noisy patterned strings
Devine, S. (2006) · Complexity · doi:10.1002/cplx.20152 · Cited by 6
Learning zero-cost portfolio selection with pattern matching
Loonat, F., & Gebbie, T. (2018) · PLoS ONE · doi:10.1371/journal.pone.0202788 · Cited by 6
Computation in Complex Systems
Lizier, J. T. (2012) · Springer theses · doi:10.1007/978-3-642-32952-4_2 · Cited by 6
Anomaly Detection in Complex Systems †
Surana, A., Ray, A., & Chin, S. (2003) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)36643-0 · Cited by 6
A Unified Paradigm of Organized Complexity and Semantic Information TheoryPreprint
Okamoto, T. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1608.00941 · Cited by 6
Discovering Functional Communities in Dynamical NetworksPreprint
Shalizi, C. R., Camperi, M., & Klinkner, K. L. (2006) · arXiv (Cornell University) · doi:10.1184/r1/6586568 · Cited by 6
Self-citationTowards Unsupervised Segmentation of Extreme Weather EventsPreprint
Rupe, A., Kashinath, K., Kumar, N., Lee, V., Prabhat, & Crutchfield, J. P. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.07520 · Cited by 6
Self-citationTraffic analysis of anonymity systems
Craven, R. M. (2010) · TigerPrints (Clemson University) · Cited by 6
Dimension reduction in quantum sampling of stochastic processes
Yang, C., Florido-Llinas, M., Gu, M., & Elliott, T. J. (2025) · npj Quantum Information · doi:10.1038/s41534-025-00978-2 · Cited by 5
Exact but Too Late: Non-Identical Restitution and the Genealogy of Physical State
BORTOLAMEOTTI, D. (2026) · PhilPapers (PhilPapers Foundation) · doi:10.5281/zenodo.21670916 · Cited by 5
Disentangled representations for causal cognition
Torresan, F., & Baltieri, M. (2024) · Physics of Life Reviews · doi:10.1016/j.plrev.2024.10.003 · Cited by 5
Structural Drift: The Population Dynamics of Sequential Learning
Crutchfield, J. P., & Whalen, S. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002510 · Cited by 5
Self-citationJames, R. G., Mahoney, J. R., & Crutchfield, J. P. (2017) · Physical review. E · doi:10.1103/physreve.95.060102 · Cited by 5
Self-citationThermodynamically-efficient local computation and the inefficiency of quantum memory compression
Loomis, S. P., & Crutchfield, J. P. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023039 · Cited by 5
Self-citationVarn, D. P. (2001) · Cited by 5
Marzen, S., Riechers, P. M., & Crutchfield, J. P. (2024) · Scientific Reports · doi:10.1038/s41598-024-58814-0 · Cited by 5
Self-citationDarmon, D. M., & Girvan, M. (2014) · Entropy · doi:10.3390/e17010001 · Cited by 5
Prediction of Elevated Activity in Online Social Media Using Aggregated and Individualized Models
Harada, J., Darmon, D. M., Girvan, M., & Rand, W. M. (2017) · Lecture notes in social networks · doi:10.1007/978-3-319-53420-6_7 · Cited by 5
The fundamental thermodynamic bounds on finite models
Garner, A. J. P. (2021) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0044741 · Cited by 5
Time-Series Information and Unsupervised Learning of Representations
Ryabko, D. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2961814 · Cited by 5
Quantifying the Autonomy of Structurally Diverse Automata: A Comparison of Candidate Measures
Albantakis, L. (2021) · Entropy · doi:10.3390/e23111415 · Cited by 5
Metadata
- Authors
- Shalizi, C. R., & Crutchfield, J. P.
- Affiliations
- Santa Fe Institute (US)
- Venue
- Journal of Statistical Physics
- Published
- 2001-08
- Volume
- 104
- Issue
- 3-4
- Pages
- 817-879
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W1551871633
- Cited by
- 471
- References
- 152
- Citations by year
- 2026: 31 · 2025: 22 · 2024: 28 · 2023: 15 · 2022: 20 · 2021: 16 · 2020: 23 · 2019: 23 · 2018: 25 · 2017: 29 · 2016: 24 · 2015: 24 · 2014: 20 · 2013: 26 · 2012: 20
- FWCI
- 11.27
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Journal of Statistical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9970158)
- Santa Fe Institute
- Science Foundation Ireland
- Defense Advanced Research Projects Agency
- Office of Naval Research (N00014-95-1-0975)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- computational mechanics, causal states, structural complexity, prediction, minimal representation, randomness measures, ergodic theory, information theory
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