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Neural correlations, population coding and computation

Nature Reviews Neuroscience volume 7, pages 358–366 (2006)Cite this article

Key Points

  • Correlations among neurons can affect both the amount of information encoded in a population and strategies for decoding the population. These two issues — encoding and decoding — lead to complementary perspectives about the role of correlations.

  • In the encoding perspective, the information encoded in a population of correlated neurons is compared with the information that would be encoded if the population were uncorrelated.

  • In the decoding perspective, the amount of information lost if correlations are ignored when decoding is measured. Note that the decoding perspective is much more subtle than the encoding perspective — it asks whether a potentially suboptimal strategy, ignoring correlations, really is suboptimal, and, if so, just how bad it is.

  • If we knew only that neural responses were correlated, we would not know whether or not those correlations affected information encoding, nor would we know whether or not they affected decoding strategies. Furthermore, correlations can increase, decrease or not affect the amount of information encoded, just as they can affect or not affect the amount of information extracted using a decoder that ignores correlations.

  • As a corollary to the previous point, the information present in neural responses, as well as the change in information due to attentional or learning-related factors, cannot be estimated by single neuron recordings.

  • At the level of pairs of neurons, the measured effects of correlations on encoding and decoding have been small (in all but one study less than ∼10%) across many brain areas and species.

  • Correlations can have a large effect at the population level even when they have a small effect at the level of pairs. Consequently, results obtained for pairs of neurons cannot be directly extrapolated to populations, a fact that is true for both encoding and decoding.

Abstract

How the brain encodes information in population activity, and how it combines and manipulates that activity as it carries out computations, are questions that lie at the heart of systems neuroscience. During the past decade, with the advent of multi-electrode recording and improved theoretical models, these questions have begun to yield answers. However, a complete understanding of neuronal variability, and, in particular, how it affects population codes, is missing. This is because variability in the brain is typically correlated, and although the exact effects of these correlations are not known, it is known that they can be large. Here, we review studies that address the interaction between neuronal noise and population codes, and discuss their implications for population coding in general.

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Figure 1: Effects of correlations on information encoding.
Figure 2: Information, I, and ΔI shuffled versus population size.
Figure 3: Effects of correlations on information decoding.
Figure 4: ΔI diag/I versus population size.

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References

  1. Lee, C., Rohrer, W. H. & Sparks, D. L. Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332, 357–360 (1988).

    Article  CAS  Google Scholar 

  2. Sparks, D. L., Holland, R. & Guthrie, B. L. Size and distribution of movement fields in the monkey superior colliculus. Brain Res. 113, 21–34 (1976).

    Article  CAS  Google Scholar 

  3. Georgopoulos, A. P., Schwartz, A. B. & Kettner, R. E. Neuronal population coding of movement direction. Science 233, 1416–1419 (1986).

    Article  CAS  Google Scholar 

  4. Paradiso, M. A. A theory for the use of visual orientation information which exploits the columnar structure of striate cortex. Biol. Cybern. 58, 35–49 (1988).

    Article  CAS  Google Scholar 

  5. Pouget, A., Dayan, P. & Zemel, R. Information processing with population codes. Nature Rev. Neurosci. 1, 125–132 (2000).

    Article  CAS  Google Scholar 

  6. Seung, H. S. & Sompolinsky, H. Simple models for reading neuronal population codes. Proc. Natl Acad. Sci. USA 90, 10749–10753 (1993).

    Article  CAS  Google Scholar 

  7. Salinas, E. & Abbott, L. F. Vector reconstruction from firing rates. J. Comput. Neurosci. 1, 89–107 (1994).

    Article  CAS  Google Scholar 

  8. Deneve, S., Latham, P. E. & Pouget, A. Reading population codes: a neural implementation of ideal observers. Nature Neurosci. 2, 740–745 (1999).

    Article  CAS  Google Scholar 

  9. McAdams, C. J. & Maunsell, J. H. Effects of attention on the reliability of individual neurons in monkey visual cortex. Neuron 23, 765–773 (1999).

    Article  CAS  Google Scholar 

  10. Schoups, A., Vogels, R., Qian, N. & Orban, G. Practising orientation identification improves orientation coding in V1 neurons. Nature 412, 549–553 (2001).

    Article  CAS  Google Scholar 

  11. Yang, T. & Maunsell, J. H. The effect of perceptual learning on neuronal responses in monkey visual area V4. J. Neurosci. 24, 1617–1626 (2004).

    Article  Google Scholar 

  12. Ghose, G. M., Yang, T. & Maunsell, J. H. Physiological correlates of perceptual learning in monkey V1 and V2. J. Neurophysiol. 87, 1867–1888 (2002).

    Article  Google Scholar 

  13. Averbeck, B. B. & Lee, D. Effects of noise correlations on information encoding and decoding. J. Neurophysiol. (in the press). Combines a theoretical and empirical examination of the way in which studies of information encoding and decoding are related, as well as investigating the role of stimulus-modulated correlations.

  14. Hung, C. P., Kreiman, G., Poggio, T. & DiCarlo, J. J. Fast readout of object identity from macaque inferior temporal cortex. Science 310, 863–866 (2005).

    Article  CAS  Google Scholar 

  15. Rolls, E. T., Treves, A. & Tovee, M. J. The representational capacity of the distributed encoding of information provided by populations of neurons in primate temporal visual cortex. Exp. Brain Res. 114, 149–162 (1997).

    Article  CAS  Google Scholar 

  16. Gochin, P. M., Colombo, M., Dorfman, G. A., Gerstein, G. L. & Gross, C. G. Neural ensemble coding in inferior temporal cortex. J. Neurophysiol. 71, 2325–2337 (1994).

    Article  CAS  Google Scholar 

  17. Georgopoulos, A. P. & Massey, J. T. Cognitive spatial-motor processes. 2. Information transmitted by the direction of two-dimensional arm movements and by neuronal populations in primate motor cortex and area 5. Exp. Brain Res. 69, 315–326 (1988).

    Article  CAS  Google Scholar 

  18. Oram, M. W., Foldiak, P., Perrett, D. I. & Sengpiel, F. The 'Ideal Homunculus': decoding neural population signals. Trends Neurosci. 21, 259–265 (1998).

    Article  CAS  Google Scholar 

  19. Johnson, K. O. Sensory discrimination: decision process. J. Neurophysiol. 43, 1771–1792 (1980).

    Article  CAS  Google Scholar 

  20. Panzeri, S., Schultz, S. R., Treves, A. & Rolls, E. T. Correlations and the encoding of information in the nervous system. Proc. R. Soc. Lond. B 266, 1001–1012 (1999). Although somewhat technical, this was one of the first studies to clearly define a set of measures that can be used to assess the role of correlations in information coding. The basic approach presented in this manuscript was further elaborated in reference 22.

    Article  CAS  Google Scholar 

  21. Engel, A. K., Konig, P. & Singer, W. Direct physiological evidence for scene segmentation by temporal coding. Proc. Natl Acad. Sci. USA 88, 9136–9140 (1991).

    Article  CAS  Google Scholar 

  22. 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).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  25. Golledge, H. D. et al. Correlations, feature-binding and population coding in primary visual cortex. Neuroreport 14, 1045–1050 (2003).

    Article  Google Scholar 

  26. Panzeri, S., Golledge, H. D., Zheng, F., Tové e, M. J. & Young, M. P. Objective assessment of the functional role of spike train correlations using information measures. Vis. Cogn. 8, 531–547 (2001).

    Article  Google Scholar 

  27. Averbeck, B. B., Crowe, D. A., Chafee, M. V. & Georgopoulos, A. P. Neural activity in prefrontal cortex during copying geometrical shapes. II. Decoding shape segments from neural ensembles. Exp. Brain Res. 150, 142–153 (2003).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  29. Averbeck, B. B. & Lee, D. Coding and transmission of information by neural ensembles. Trends Neurosci. 27, 225–230 (2004).

    Article  CAS  Google Scholar 

  30. Milner, P. M. A model for visual shape recognition. Psychol. Rev. 81, 521–535 (1974).

    Article  CAS  Google Scholar 

  31. von der Malsburg, C. The correlation theory of brain function. Internal Report, Dept Neurobiology, MPI for Biophysical Chemistry (1981).

  32. Singer, W. & Gray, C. M. Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci. 18, 555–586 (1995).

    Article  CAS  Google Scholar 

  33. Schnitzer, M. J. & Meister, M. Multineuronal firing patterns in the signal from eye to brain. Neuron 37, 499–511 (2003).

    Article  CAS  Google Scholar 

  34. Vaadia, E. et al. Dynamics of neuronal interactions in monkey cortex in relation to behavioural events. Nature 373, 515–518 (1995).

    Article  CAS  Google Scholar 

  35. Roskies, A. L. The binding problem. Neuron 24, 7–9 (1999).

    Article  CAS  Google Scholar 

  36. Zohary, E., Shadlen, M. N. & Newsome, W. T. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370, 140–143 (1994). The first study to show, in the context of neural coding, that small correlations between neurons can have a large effect on the ability of a population of neurons to encode information. The main conclusion of this manuscript was that the correlations in MT cause information to saturate as the population reaches ∼100 neurons. Whether or not this is correct remains an open experimental question (see also references 45 and 46).

    Article  CAS  Google Scholar 

  37. 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).

    Article  CAS  Google Scholar 

  38. Simoncelli, E. P. & Olshausen, B. A. Natural image statistics and neural representation. Annu. Rev. Neurosci. 24, 1193–1216 (2001).

    Article  CAS  Google Scholar 

  39. Hyvarinen, A. & Hoyer, P. O. A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images. Vision Res. 41, 2413–2423 (2001).

    Article  CAS  Google Scholar 

  40. Hyvarinen, A., Karhunen, J. & Oja, E. Independent Component Analysis (John Wiley and Sons, New York, 2001).

    Book  Google Scholar 

  41. Bell, A. J. & Sejnowski, T. J. An information-maximization approach to blind separation and blind deconvolution. Neural Comput. 7, 1129–1159 (1995).

    Article  CAS  Google Scholar 

  42. Nadal, J. P. & Parga, N. Nonlinear neurons in the low-noise limit: a factorial code maximizes information transfer. Network 5, 565–581 (1994).

    Article  Google Scholar 

  43. Gold, J. I. & Shadlen, M. N. Neural computations that underlie decisions about sensory stimuli. Trends Cogn. Sci. 5, 10–16 (2001).

    Article  Google Scholar 

  44. Lee, D. K., Itti, L., Koch, C. & Braun, J. Attention activates winner-take-all competition among visual filters. Nature Neurosci. 2, 375–381 (1999).

    Article  CAS  Google Scholar 

  45. Sompolinsky, H., Yoon, H., Kang, K. & Shamir, M. Population coding in neuronal systems with correlated noise. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 051904 (2001).

  46. Abbott, L. F. & Dayan, P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11, 91–101 (1999). One of the most influential theoretical studies of the effect of noise correlations on information encoding.

    Article  CAS  Google Scholar 

  47. Wilke, S. D. & Eurich, C. W. Representational accuracy of stochastic neural populations. Neural Comput. 14, 155–189 (2002).

    Article  Google Scholar 

  48. Hubel, D. H. & Wiesel, T. N. Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J. Physiol. (Lond.) 160, 106–154 (1962).

    Article  CAS  Google Scholar 

  49. Seriès, P., Latham, P. E. & Pouget, A. Tuning curve sharpening for orientation selectivity: coding efficiency and the impact of correlations. Nature Neurosci. 7, 1129–1135 (2004). One of the first papers to show that manipulations that increase the information in single cells (through, for example, sharpening tuning curves) can, because the manipulation modifies correlations, reduce the information in the population.

    Article  Google Scholar 

  50. Casella, G. & Berger, R. L. Statistical Inference (Duxbury Press, Belmont, California, 1990).

    Google Scholar 

  51. Nirenberg, S., Carcieri, S. M., Jacobs, A. L. & Latham, P. E. Retinal ganglion cells act largely as independent encoders. Nature 411, 698–701 (2001).

    Article  CAS  Google Scholar 

  52. Latham, P. E. & Nirenberg, S. Synergy, redundancy, and independence in population codes, revisited. J. Neurosci. 25, 5195–5206 (2005).

    Article  CAS  Google Scholar 

  53. Shannon, C. E. & Weaver, W. The Mathematical Theory of Communication (Univ. Illinois Press, Urbana Champagne, Illinois, 1949).

    Google Scholar 

  54. Nirenberg, S. & Latham, P. E. Decoding neuronal spike trains: how important are correlations? Proc. Natl Acad. Sci. USA 100, 7348–7353 (2003).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  56. Averbeck, B. B. & Lee, D. Neural noise and movement-related codes in the macaque supplementary motor area. J. Neurosci. 23, 7630–7641 (2003).

    Article  CAS  Google Scholar 

  57. Oram, M. W., Hatsopoulos, N. G., Richmond, B. J. & Donoghue, J. P. Excess synchrony in motor cortical neurons provides redundant direction information with that from coarse temporal measures. J. Neurophysiol. 86, 1700–1716 (2001).

    Article  CAS  Google Scholar 

  58. Wu, S., Nakahara, H. & Amari, S. Population coding with correlation and an unfaithful model. Neural Comput. 13, 775–797 (2001). The first study to theoretically investigate the effects of ignoring correlations when decoding a large population of neurons. As such it is the decoding complement to reference 46.

    Article  CAS  Google Scholar 

  59. Strong, S. P., Koberle, R., de Ruyter van Steveninck, R. R. & Bialek, W. Entropy and information in neural spike trains. Phys. Rev. Lett. 80, 197–200 (1998).

    Article  CAS  Google Scholar 

  60. Treves, A. & Panzeri, S. The upward bias in measures of information derived from limited data samples. Neural Comput. 7, 399–407 (1995).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  62. Schneidman, E., Bialek, W. & Berry, M. J. Synergy, redundancy, and independence in population codes. J. Neurosci. 23, 11539–11553 (2003).

    Article  CAS  Google Scholar 

  63. Narayanan, N. S., Kimchi, E. Y. & Laubach, M. Redundancy and synergy of neuronal ensembles in motor cortex. J. Neurosci. 25, 4207–4216 (2005).

    Article  CAS  Google Scholar 

  64. Gawne, T. J., Kjaer, T. W., Hertz, J. A. & Richmond, B. J. Adjacent visual cortical complex cells share about 20% of their stimulus-related information. Cereb. Cortex 6, 482–489 (1996).

    Article  CAS  Google Scholar 

  65. Puchalla, J. L., Schneidman, E., Harris, R. A. & Berry, M. J. Redundancy in the population code of the retina. Neuron 46, 493–504 (2005).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  67. Barlow, H. B. in Current Problems in Animal Behaviour (eds Thorpe, W. H. & Zangwill, O. L.) 331–360 (Cambridge Univ. Press, Cambridge, 1961).

    Google Scholar 

  68. Srinivasan, M. V., Laughlin, S. B. & Dubs, A. Predictive coding: a fresh view of inhibition in the retina. Proc. R. Soc. Lond. B 216, 427–459 (1982).

    Article  CAS  Google Scholar 

  69. Barlow, H. Redundancy reduction revisited. Network 12, 241–253 (2001).

    Article  CAS  Google Scholar 

  70. Atick, J. J. & Redlich, A. N. Towards a theory of early visual processing. Neural Comput. 2, 308–320 (1990).

    Article  Google Scholar 

  71. Braitenberg, V. & Schüz, A. Anatomy of the Cortex (Springer, Berlin, 1991).

    Book  Google Scholar 

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Acknowledgements

P.E.L. was supported by the Gatsby Charitable Foundation, London, UK, and a grant from the National Institute of Mental Health, National Institutes of Health, USA. A.P. was supported by grants from the National Science Foundation. B.B.A. was supported by a grant from the National Institutes of Health.

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Authors and Affiliations

  1. Department of Brain and Cognitive Sciences and Center for Visual Science, University of Rochester, Rochester, 14627, New York, USA

    Bruno B. Averbeck & Alexandre Pouget

  2. Gatsby Computational Neuroscience Unit, University College London, 17 Queen Square, London, WC1N 3AR, UK

    Peter E. Latham

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Glossary

No-sharpening model

A model in which the orientation tuning curves of cortical cells are solely the result of the converging afferents from the LGN, without further sharpening in the cortex.

Sharpening model

A model in which the LGN afferents provide broad tuning curves to orientation that are sharpened in the cortex through lateral interactions.

Fisher information

Measures the variance of an optimal estimator.

Shannon information

Measures how much one's uncertainty about the stimuli decreases after receiving responses.

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Averbeck, B., Latham, P. & Pouget, A. Neural correlations, population coding and computation. Nat Rev Neurosci 7, 358–366 (2006). https://doi.org/10.1038/nrn1888

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