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Neural correlations, population coding and computation

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.


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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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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Correspondence to Alexandre Pouget.

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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).

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