The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Weak pairwise correlations imply strongly correlated network states in a neural population
Open accessAbstract
Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.
Overview
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.
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
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
Cluster analysis and display of genome-wide expression patterns
Eisen, M. B., Spellman, P. T., Brown, P. O., & Botstein, D. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.25.14863 · Cited by 16,184
Information theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931
Network biology: understanding the cell's functional organization
Barabási, A.-L., & Oltvai, Z. N. (2004) · Nature Reviews Genetics · doi:10.1038/nrg1272 · Cited by 7,903
Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications
Mezard, M., Parisi, G., & Virasoro, M. (1986) · World Scientific Lecture Notes in Physics · doi:10.1142/0271 · Cited by 3,653
Correlated neuronal discharge rate and its implications for psychophysical performance
Zohary, E., Shadlen, M. N., & Newsome, W. T. (1994) · Nature · doi:10.1038/370140a0 · Cited by 1,237
Synfire Chains and Cortical Songs: Temporal Modules of Cortical Activity
Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D., & Yuste, R. (2004) · Science · doi:10.1126/science.1093173 · Cited by 838
Dynamic predictive coding by the retina
Hosoya, T., Baccus, S. A., & Meister, M. (2005) · Nature · doi:10.1038/nature03689 · Cited by 468
Cited by
Complex brain networks: graph theoretical analysis of structural and functional systems
Bullmore, E., & Sporns, O. (2009) · Nature Reviews Neuroscience · doi:10.1038/nrn2575 · Cited by 11,820
Neurophysiological and Computational Principles of Cortical Rhythms in Cognition
Wang, X.-J. (2010) · Physiological Reviews · doi:10.1152/physrev.00035.2008 · Cited by 1,939
Whole-brain functional imaging at cellular resolution using light-sheet microscopy
Ahrens, M. B., Orger, M. B., Robson, D. N., Li, J. M., & Keller, P. J. (2013) · Nature Methods · doi:10.1038/nmeth.2434 · Cited by 1,392
Spatio-temporal correlations and visual signalling in a complete neuronal population
Pillow, J. W., Shlens, J., Paninski, L., Sher, A., Litke, A. M., Chichilnisky, E. J., & Simoncelli, E. P. (2008) · Nature · doi:10.1038/nature07140 · Cited by 1,311
Dimensionality reduction for large-scale neural recordings
Cunningham, J. P., & Yu, B. M. (2014) · Nature Neuroscience · doi:10.1038/nn.3776 · Cited by 1,219
Metadata
- Authors
- Schneidman, E., Berry, M. J., Segev, R., & Bialek, W.
- Venue
- Nature
- Published
- 2006-04-01
- Volume
- 440
- Issue
- 7087
- Pages
- 1007-1012
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2147238273
- Cited by
- 1,760
- References
- 8
- FWCI
- 28.10
- Type
- journal article
- Language
- en
- Open access
- green
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Weak pairwise correlations imply strongly correlated network states in a neural population. https://app.cochat.ai/papers/10.1038/nature04701
- The paper
- Schneidman, E., Berry, M. J., Segev, R., & Bialek, W. (2006). Weak pairwise correlations imply strongly correlated network states in a neural population. Nature. https://doi.org/10.1038/nature04701
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
