Wilson, M. A. & McNaughton, B. L. Dynamics of the hippocampal ensemble code for space. Science 261, 1055–1058 (1993).

CAS  PubMed  Article  Google Scholar 

Rigotti, M. et al. The importance of mixed selectivity in complex cognitive tasks. Nature 497, 585–590 (2013).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Bernardi, S. et al. The geometry of abstraction in the hippocampus and prefrontal cortex. Cell 183, 954–967.e21 (2020).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Koren, V., Andrei, A. R., Hu, M., Dragoi, V. & Obermayer, K. Pairwise synchrony and correlations depend on the structure of the population code in visual cortex. Cell Rep. https://doi.org/10.1016/j.celrep.2020.108367 (2020).

Article  PubMed  Google Scholar 

Battiston, F. et al. The physics of higher-order interactions in complex systems. Nat. Phys. 17, 1093–1098 (2021).

CAS  Article  Google Scholar 

Barlow, H. B. Possible principles underlying the transformation of sensory messages. Sens. Commun. 1, 217–234 (1961).

Google Scholar 

Attneave, F. Some informational aspects of visual perception. Psychol. Rev. 61, 183–193 (1954).

CAS  PubMed  Article  Google Scholar 

Olshausen, B. A. & Field, D. J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607–609 (1996).

CAS  PubMed  Article  Google Scholar 

Mlynarski, W. F. & Hermundstad, A. M. Efficient and adaptive sensory codes. Nat. Neurosci. 24, 998–1009 (2021).

CAS  PubMed  Article  Google Scholar 

Vyas, S., Golub, M. D., Sussillo, D. & Shenoy, K. V. Computation through neural population dynamics. Annu. Rev. Neurosci. 43, 249–275 (2020).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Panzeri, S., Schultz, S. R., Treves, A. & Rolls, E. T. Correlations and the encoding of information in the nervous system. Proc. Biol. Sci. 266, 1001–1012 (1999).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Pola, G., Thiele, A., Hoffmann, K. P. & Panzeri, S. An exact method to quantify the information transmitted by different mechanisms of correlational coding. Network 14, 35–60 (2003).

CAS  PubMed  Article  Google Scholar 

Averbeck, B. B., Latham, P. E. & Pouget, A. Neural correlations, population coding and computation. Nat. Rev. Neurosci. 7, 358–366 (2006).

CAS  PubMed  Article  Google Scholar 

Abbott, L. F. & Dayan, P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11, 91–101 (1999).

CAS  PubMed  Article  Google Scholar 

Gawne, T. J. & Richmond, B. J. How independent are the messages carried by adjacent inferior temporal cortical neurons? J. Neurosci. 13, 2758–2771 (1993).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Cohen, M. R. & Kohn, A. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14, 811–819 (2011).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Averbeck, B. B. & Lee, D. Effects of noise correlations on information encoding and decoding. J. Neurophysiol. 95, 3633–3644 (2006).

PubMed  Article  Google Scholar 

Nogueira, R. et al. The effects of population tuning and trial-by-trial variability on information encoding and behavior. J. Neurosci. 40, 1066–1083 (2020).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Zohary, E., Shadlen, M. N. & Newsome, W. T. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370, 140–143 (1994).

CAS  PubMed  Article  Google Scholar 

Ecker, A. S., Berens, P., Tolias, A. S. & Bethge, M. The effect of noise correlations in populations of diversely tuned neurons. J. Neurosci. 31, 14272–14283 (2011).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Shamir, M. & Sompolinsky, H. Nonlinear population codes. Neural Comput. 16, 1105–1136 (2004).

PubMed  Article  Google Scholar 

Josic, K., Shea-Brown, E., Doiron, B. & de la Rocha, J. Stimulus-dependent correlations and population codes. Neural Comput. 21, 2774–2804 (2009).

PubMed  Article  Google Scholar 

Azeredo da Silveira, R. & Rieke, F. The geometry of information coding in correlated neural populations. Annu. Rev. Neurosci. 44, 403–424 (2021).

CAS  PubMed  Article  Google Scholar 

Gray, C. M., Konig, P., Engel, A. K. & Singer, W. Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338, 334–337 (1989).

CAS  PubMed  Article  Google Scholar 

deCharms, R. C. & Merzenich, M. M. Primary cortical representation of sounds by the coordination of action-potential timing. Nature 381, 610–613 (1996).

CAS  PubMed  Article  Google Scholar 

Franke, F. et al. Structures of neural correlation and how they favor coding. Neuron 89, 409–422 (2016).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Dan, Y., Alonso, J. M., Usrey, W. M. & Reid, R. C. Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus. Nat. Neurosci. 1, 501–507 (1998).

CAS  PubMed  Article  Google Scholar 

Zylberberg, J., Cafaro, J., Turner, M. H., Shea-Brown, E. & Rieke, F. Direction-selective circuits shape noise to ensure a precise population code. Neuron 89, 369–383 (2016).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Kohn, A. & Smith, M. A. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25, 3661–3673 (2005).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Romo, R., Hernandez, A., Zainos, A. & Salinas, E. Correlated neuronal discharges that increase coding efficiency during perceptual discrimination. Neuron 38, 649–657 (2003).

CAS  PubMed  Article  Google Scholar 

Reich, D. S., Mechler, F. & Victor, J. D. Independent and redundant information in nearby cortical neurons. Science 294, 2566–2568 (2001).

CAS  PubMed  Article  Google Scholar 

Pillow, J. W. et al. Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454, 995–999 (2008).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Graf, A. B., Kohn, A., Jazayeri, M. & Movshon, J. A. Decoding the activity of neuronal populations in macaque primary visual cortex. Nat. Neurosci. 14, 239–245 (2011).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Rupasinghe, A. et al. Direct extraction of signal and noise correlations from two-photon calcium imaging of ensemble neuronal activity. eLife https://doi.org/10.7554/eLife.68046 (2021).

Article  PubMed  PubMed Central  Google Scholar 

Rothschild, G., Nelken, I. & Mizrahi, A. Functional organization and population dynamics in the mouse primary auditory cortex. Nat. Neurosci. 13, 353–360 (2010).

CAS  PubMed  Article  Google Scholar 

Kwon, S. E., Tsytsarev, V., Erzurumlu, R. S. & O’Connor, D. H. Organization of orientation-specific whisker deflection responses in layer 2/3 of mouse somatosensory cortex. Neuroscience 368, 46–56 (2018).

CAS  PubMed  Article  Google Scholar 

Bartolo, R., Saunders, R. C., Mitz, A. R. & Averbeck, B. B. Information-limiting correlations in large neural populations. J. Neurosci. 40, 1668–1678 (2020).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Kafashan, M. et al. Scaling of sensory information in large neural populations shows signatures of information-limiting correlations. Nat. Commun. 12, 473 (2021).

CAS  PubMed  PubMed Central  Article  Google Scholar 

Petersen, R. S., Panzeri, S. & Diamond, M. E. Population coding of stimulus location in rat somatosensory cortex. Neuron 32, 503–514 (2001).

CAS  PubMed  Article