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The structures and functions of correlations in neural population codes

Abstract

The collective activity of a population of neurons, beyond the properties of individual cells, is crucial for many brain functions. A fundamental question is how activity correlations between neurons affect how neural populations process information. Over the past 30 years, major progress has been made on how the levels and structures of correlations shape the encoding of information in population codes. Correlations influence population coding through the organization of pairwise-activity correlations with respect to the similarity of tuning of individual neurons, by their stimulus modulation and by the presence of higher-order correlations. Recent work has shown that correlations also profoundly shape other important functions performed by neural populations, including generating codes across multiple timescales and facilitating information transmission to, and readout by, downstream brain areas to guide behaviour. Here, we review this recent work and discuss how the structures of correlations can have opposite effects on the different functions of neural populations, thus creating trade-offs and constraints for the structure–function relationships of population codes. Further, we present ideas on how to combine large-scale simultaneous recordings of neural populations, computational models, analyses of behaviour, optogenetics and anatomy to unravel how the structures of correlations might be optimized to serve multiple functions.

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Fig. 1: Different types of population codes and the functions they can perform.
Fig. 2: Noise correlations and information encoding.
Fig. 3: Across-time noise correlations can generate long information consistency timescales.
Fig. 4: Noise correlations for information transmission and behavioural readout.

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Acknowledgements

The authors thank members of their laboratories for helpful discussions, and B. Babadi, C. Becchio, G. Bondanelli, J. Drugowitsch, M. Histed, G. Iurilli, S. Lemke, J. Maunsell and E. Piasini for feedback. This work was supported by the US National Institutes of Health (NIH) grants DP1 MH125776 (C.D.H.); the US National Institute of Neurological Disorders and Stroke (NINDS) R01 NS089521 (C.D.H.); the Brain Research Through Advancing Innovative Neurotechnologies (BRAIN) Initiative R01 NS108410 (C.D.H. and S.P.), U19 NS107464 (S.P.), R01 NS109961 (S.P.); and the Fondation Bertarelli (S.P.).

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Glossary

Population code

The features and patterns of activity of neural populations that are used to perform key information-processing computations, such as encoding information and/or transmitting information.

Space of neural population activity

A space where each dimension represents the activity of a neuron and each point is a population vector.

Functional interactions

The statistical relationships between the activity of different neurons, often quantified as correlations between the activity of different neurons.

Pseudo-population

Collections of activity of non-simultaneously measured neurons, either because they were recorded at a different time or from different experiments, or because they were created by trial shuffling.

Efficient coding theories

Theories that postulate that the properties of neurons in sensory areas are designed to maximize the information that these neurons carry about sensory stimuli with naturalistic features.

Signal correlations

The correlations of the trial-averaged neural responses across different stimuli.

Noise correlations

The correlated trial-to-trial variability of the activity of different neurons or of different neural populations over repeated presentations of the same stimulus.

Signal–noise angle

The angle between the noise axis and the signal axis.

Signal axis

The axis in neural population activity space of the largest stimulus-related variations, which in linear cases is measured as the axis that connects the trial-averaged population responses to the different stimuli.

Noise axis

The axis of largest variation in neural population activity for a fixed stimulus.

Trial shuffling

An analytical procedure to remove the effect of noise correlations by combining responses of neurons taken from different trials to a given stimulus.

Redundant neuron pairs

Pairs of neurons that together carry less information than the sum of the information carried by the two neurons in each pair, owing to the information-limiting effect of noise and signal correlations.

Synergistic neuron pairs

Pairs of neurons that together carry more information than the sum of the information carried by the two neurons in each pair, owing to the information-enhancing effect of noise correlations.

Redundant hubs

Neurons with high probability of having redundant interactions with other neurons.

Synergistic hubs

Neurons with high probability of having synergistic interactions with other neurons.

Population-wise correlations

Correlated variability of an entire population of neurons, usually measured applying dimensionality-reduction techniques to the population covariance matrix.

Across-neuron noise correlations

The noise correlation between the time-averaged activity of two different neurons or two different neural populations, quantifying the similarity of the time-averaged neural or population responses across trials with the same stimulus.

Across-time noise correlations

The noise correlation between the population activity vector of the same population at different times, quantifying the similarity of the population responses at different times across trials with the same stimulus.

Persistent activity

The activity of individual cells whose firing rate remains sustained over an entire task period, for example, during working memory or decision-making tasks.

Ramping activity

The activity of individual cells whose firing rate decreases or increases constantly over time during a task, for example, to reflect the accumulation of evidence to make a decision.

Attractor states

Set of values of population vectors towards which the activity of a neuronal network is attracted during its temporal evolution.

Posterior parietal cortex

(PPC). A region of cortex considered to be at the interface of sensation and action and to participate in evidence accumulation for decision-making, movement planning, spatial navigation and other processes.

Population vector

Vector in the space of neural population activity whose components represent the activity of individual neurons in the population.

Information consistency timescale

The correlation across time of the instantaneous stimulus or choice signal (for example, the posterior probability of stimulus or choice given the observation of a population vector at a specific time).

Optimal stimulus-discrimination boundary

The plane (or surface) in the high-dimensional space of population activity that optimally separates responses elicited by different sensory stimuli, and that thus serves as an indication of how to extract sensory information from neural activity optimally.

Coincidence detection

Spike-generation mechanism that, because of the neuron’s short integration time constant, requires the near-simultaneous occurrence of several input action potentials to generate an output action potential.

Consistent information encoding

When different elements of a population code (for example, the activity of different pools of neurons) all signal the presence of the same stimulus.

Across-time encoding consistency

When population activity at a given time signals the same stimulus as the population activity at another time.

Across-neuron encoding consistency

When the activity of separate neuronal pools in the same time window signals the same stimulus.

Feature amplification motifs

Motifs of cells with similar tuning that functionally excite one another to increase the signal contained in the neural population as revealed by anatomical connections or influence mapping.

Two-photon patterned optogenetics

The use of light-sculpting, such as with a spatial light modulator, and two-photon excitation to create arbitrary spatial and temporal patterns of light to photostimulate neurons with approximately single-cell resolution.

Influence mapping

The process of measuring how spikes added by two-photon-patterned optogenetic perturbation to one or a few neurons causally affect the spiking of neighbouring neurons.

Multi-objective optimization

An optimization procedure that minimizes multiple cost functions simultaneously.

Retrograde labelling

Methods based on dyes or viruses that are taken up by axons and transported back to a neuron’s cell body.

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Panzeri, S., Moroni, M., Safaai, H. et al. The structures and functions of correlations in neural population codes. Nat Rev Neurosci (2022). https://doi.org/10.1038/s41583-022-00606-4

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