Neural population coding: combining insights from microscopic and mass signals
Authors: Stefano Panzeri, Jakob H. Macke, Joachim Gross, Christoph Kayser
Journal: Trends in Cognitive Sciences (2015)

•Neural population codes are organized at multiple spatial scales.•Microscopic organization of neural codes reveals a key role of neural heterogeneity.•Microscopic and population dynamics interact to make processing state-dependent.•Additional computational analyses of neural activity across resolutions are needed. Behavior relies on the distributed and coordinated activity of neural populations. Population activity can be measured using multi-neuron recordings and neuroimaging. Neural recordings reveal how the heterogeneity, sparseness, timing, and correlation of population activity shape information processing in local networks, whereas neuroimaging shows how long-range coupling and brain states impact on local activity and perception. To obtain an integrated perspective on neural information processing we need to combine knowledge from both levels of investigation. We review recent progress of how neural recordings, neuroimaging, and computational approaches begin to elucidate how interactions between local neural population activity and large-scale dynamics shape the structure and coding capacity of local information representations, make them state-dependent, and control distributed populations that collectively shape behavior. Behavior relies on the distributed and coordinated activity of neural populations. Population activity can be measured using multi-neuron recordings and neuroimaging. Neural recordings reveal how the heterogeneity, sparseness, timing, and correlation of population activity shape information processing in local networks, whereas neuroimaging shows how long-range coupling and brain states impact on local activity and perception. To obtain an integrated perspective on neural information processing we need to combine knowledge from both levels of investigation. We review recent progress of how neural recordings, neuroimaging, and computational approaches begin to elucidate how interactions between local neural population activity and large-scale dynamics shape the structure and coding capacity of local information representations, make them state-dependent, and control distributed populations that collectively shape behavior. In complex animals, information about behaviorally important variables such as sensory signals or motor actions is carried by the activity of populations of neurons [1Averbeck B.B. et al.Neural correlations, population coding and computation.Nat. Rev. Neurosci. 2006; 7: 358-366Crossref PubMed Scopus (415) Google Scholar, 2Stanley G.B. Reading and writing the neural code.Nat. Neurosci. 2013; 16: 259-263Crossref PubMed Scopus (12) Google Scholar, 3Hebb D.O. The Organization of Behaviour. A Neuropsychological Theory. Wiley, 1949Google Scholar, 4Jacobs A.L. et al.Ruling out and ruling in neural codes.Proc. Natl. Acad. Sci. U.S.A. 2009; 106: 5936-5941Crossref PubMed Scopus (64) Google Scholar]. Our understanding of neural information processing is founded on the conceptual assumption that, if two or more sensory stimuli can be discriminated, or two or more behavioral responses are different, their associated patterns of neural activity must be readily discriminable. Several key ingredients shape the capacity of a neural population code (see Glossary) to form such discriminable representations: the diversity of neural response properties, their spatial and temporal response profiles, the cross-neural correlations, and the state-dependence of cortical activity (Box 1).Box 1Neural response features contributing to a population codeUnderstanding a population code requires investigating its statistical properties along all relevant dimensions and linking them to the external events that are encoded (for example, sensory inputs). Informative response features can spread across the dimension of time (temporal variations in the responses of individual neurons or of the population), space (stimulus tuning differences in the firing of different neurons), or along non-separable combinations of both dimensions.Current experimental methods emphasize different dimensions. Multi-neuron recordings resolving individual neurons at high temporal resolution provide information about both spatial and temporal dimensions and their non-separable intersection [6Berenyi A. et al.Large-scale, high-density (up to 512 channels) recording of local circuits in behaving animals.J. Neurophysiol. 2014; 111: 1132-1149Crossref PubMed Scopus (11) Google Scholar]. Imaging techniques such as two-photon imaging resolve individual neurons in space but often lack the fine temporal resolution to inform about spike timing [107Kerr J.N. Denk W. Imaging in vivo: watching the brain in action.Nat. Rev. Neurosci. 2008; 9: 195-205Crossref PubMed Scopus (116) Google Scholar]. Measures of mass activity at high temporal resolution (LFP, ECoG, EEG, MEG) cannot resolve individual neurons (and sometimes even brain regions), but capture temporal activity patterns that are coordinated across multiple neurons [108Lopes da Silva F. EEG and MEG: relevance to neuroscience.Neuron. 2013; 80: 1112-1128Abstract Full Text Full Text PDF PubMed Scopus (27) Google Scholar].Diversity of single-neuron firing rates. Neurons with heterogeneous stimulus preferences can each add complementary stimulus information as they each differ in terms of stimulus preference or tuning width. In the example, neuron A has narrow tuning (it responds only to the diamond), whereas neurons B and C prefer other stimuli and have a wider tuning than neuron A. Neuron D is uninformative and responds equally to all stimuli.Relative timing. In a population, informative response patterns can include the relative timing between neurons. For example, the star and square can be distinguished by the relative timing between neurons B and C (emphasized by the dashed line connecting their spikes), while both neurons elicit the same number of spikes for these stimuli.Network state modulation. Neural responses depend not only on sensory inputs but also on large-scale brain states that vary on timescales slower than the transient responses to individual stimuli. In the example, these are represented by a slow wave of a mass signal (e.g., an LFP filtered into a low-frequency component; the bottom row). In this cartoon, firing rates during one state (reflected by the peak of the cycle) are stronger than during another state (around the trough of the cycle), but the individual stimulus preferences or relative timing are preserved. Such state variables likely play a key – though not yet fully understood – role in population coding [60Panzeri S. et al.Sensory neural codes using multiplexed temporal scales.Trends Neurosci. 2010; 33: 111-120Abstract Full Text Full Text PDF PubMed Scopus (140) Google Scholar, 78Curto C. et al.A simple model of cortical dynamics explains variability and state dependence of sensory responses in urethane-anesthetized auditory cortex.J. Neurosci. 2009; 29: 10600-10612Crossref PubMed Scopus (42) Google Scholar, 79Macke, J.H. et al. (2011) Empirical models of spiking in neural populations. In In Advances in neural information processing systems, pp. 1350–1358Google Scholar, 81Marder E. Neuromodulation of neuronal circuits: back to the future.Neuron. 2012; 76: 1-11Abstract Full Text Full Text PDF PubMed Scopus (68) Google Scholar].Periods of silence. Neural populations also encode information by the silence (i.e., absence of firing) of some neurons [109Schneidman E. et al.Synergy from silence in a combinatorial neural code.J. Neurosci. 2011; 31: 15732-15741Crossref PubMed Scopus (14) Google Scholar]. In the schematic of Figure I, when neuron A is silent, it is reporting information about the absence of the diamond. Understanding a population code requires investigating its statistical properties along all relevant dimensions and linking them to the external events that are encoded (for example, sensory inputs). Informative response features can spread across the dimension of time (temporal variations in the responses of individual neurons or of the population), space (stimulus tuning differences in the firing of different neurons), or along non-separable combinations of both dimensions. Current experimental methods emphasize different dimensions. Multi-neuron recordings resolving individual neurons at high temporal resolution provide information about both spatial and temporal dimensions and their non-separable intersection [6Berenyi A. et al.Large-scale, high-density (up to 512 channels) recording of local circuits in behaving animals.J. Neurophysiol. 2014; 111: 1132-1149Crossref PubMed Scopus (11) Google Scholar]. Imaging techniques such as two-photon imaging resolve individual neurons in space but often lack the fine temporal resolution to inform about spike timing [107Kerr J.N. Denk W. Imaging in vivo: watching the brain in action.Nat. Rev. Neurosci. 2008; 9: 195-205Crossref PubMed Scopus (116) Google Scholar]. Measures of mass activity at high temporal resolution (LFP, ECoG, EEG, MEG) cannot resolve individual neurons (and sometimes even brain regions), but capture temporal activity patterns that are coordinated across multiple neurons [108Lopes da Silva F. EEG and MEG: relevance to neuroscience.Neuron. 2013; 80: 1112-1128Abstract Full Text Full Text PDF PubMed Scopus (27) Google Scholar]. Diversity of single-neuron firing rates. Neurons with heterogeneous stimulus preferences can each add complementary stimulus information as they each differ in terms of stimulus preference or tuning width. In the example, neuron A has narrow tuning (it responds only to the diamond), whereas neurons B and C prefer other stimuli and have a wider tuning than neuron A. Neuron D is uninformative and responds equally to all stimuli. Relative timing. In a population, informative response patterns can include the relative timing between neurons. For example, the star and square can be distinguished by the relative timing between neurons B and C (emphasized by the dashed line connecting their spikes), while both neurons elicit the same number of spikes for these stimuli. Network state modulation. Neural responses depend not only on sensory inputs but also on large-scale brain states that vary on timescales slower than the transient responses to individual stimuli. In the example, these are represented by a slow wave of a mass signal (e.g., an LFP filtered into a low-frequency component; the bottom row). In this cartoon, firing rates during one state (reflected by the peak of the cycle) are stronger than during another state (around the trough of the cycle), but the individual stimulus preferences or relative timing are preserved. Such state variables likely play a key – though not yet fully understood – role in population coding [60Panzeri S. et al.Sensory neural codes using multiplexed temporal scales.Trends Neurosci. 2010; 33: 111-120Abstract Full Text Full Text PDF PubMed Scopus (140) Google Scholar, 78Curto C. et al.A simple model of cortical dynamics explains variability and state dependence of sensory responses in urethane-anesthetized auditory cortex.J. Neurosci. 2009; 29: 10600-10612Crossref PubMed Scopus (42) Google Scholar, 79Macke, J.H. et al. (2011) Empirical models of spiking in neural populations. In In Advances in neural information processing systems, pp. 1350–1358Google Scholar, 81Marder E. Neuromodulation of neuronal circuits: back to the future.Neuron. 2012; 76: 1-11Abstract Full Text Full Text PDF PubMed Scopus (68) Google Scholar]. Periods of silence. Neural populations also encode information by the silence (i.e., absence of firing) of some neurons [109Schneidman E. et al.Synergy from silence in a combinatorial neural code.J. Neurosci. 2011; 31: 15732-15741Crossref PubMed Scopus (14) Google Scholar]. In the schematic of Figure I, when neuron A is silent, it is reporting information about the absence of the diamond. Recent progress in understanding the contribution and the interplay of each of these key ingredients arises from both technical and conceptual developments. Experimental methods now allow measuring and manipulating up to hundreds of neurons simultaneously in behaving animals and permit a direct link between population codes and behavior [5Stark E. et al.Diode probes for spatiotemporal optical control of multiple neurons in freely moving animals.J. Neurophysiol. 2012; 108: 349-363Crossref PubMed Scopus (38) Google Scholar, 6Berenyi A. et al.Large-scale, high-density (up to 512 channels) recording of local circuits in behaving animals.J. Neurophysiol. 2014; 111: 1132-1149Crossref PubMed Scopus (11) Google Scholar, 7Harvey C.D. et al.Choice-specific sequences in parietal cortex during a virtual-navigation decision task.Nature. 2012; 484: 62-68Crossref PubMed Scopus (99) Google Scholar, 8Scott B.B. et al.Cellular resolution functional imaging in behaving rats using voluntary head restraint.Neuron. 2013; 80: 371-384Abstract Full Text Full Text PDF PubMed Scopus (9) Google Scholar]. 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Dimensionality reduction for large-scale neural recordings.Nat. Neurosci. 2014; 15: 1752-1758Google Scholar, 13Churchland M.M. et al.Techniques for extracting single-trial activity patterns from large-scale neural recordings.Curr. Opin. Neurobiol. 2007; 17: 609-618Crossref PubMed Scopus (61) Google Scholar, 14Haxby J.V. et al.Decoding neural representational spaces using multivariate pattern analysis.Annu. Rev. Neurosci. 2014; 37: 435-456Crossref PubMed Scopus (3) Google Scholar]. We review here how these developments facilitate the convergence of knowledge gained from invasive multi-neuron recordings, neuroimaging data, and mathematical modeling, and begin to reveal the organization and computations of neural population codes at multiple scales of organization. For simplicity, we mostly focus on the encoding of sensory variables, but the concepts are relevant for the generic encoding of any variable (for example, motor variables). The computational properties of population codes are usually quantified using measures of the information they carry about sensory stimuli [15Quian Quiroga R. Panzeri S. Extracting information from neuronal populations: information theory and decoding approaches.Nat. Rev. Neurosci. 2009; 10: 173-185Crossref PubMed Scopus (209) Google Scholar]. The most widely used quantifications of neural information are based upon Shannon information (quantifying the accuracy of discrimination among different stimuli in a set) or Fisher information (quantifying discrimination of small stimulus changes, or the accuracy of decoding an individual stimulus). Because most concepts reviewed here apply to both types of information, we only distinguish between them when necessary. How a neural population represents information is partly determined by the diverse selectivity of individual neurons [16Shamir M. Emerging principles of population coding: in search for the neural code.Curr. Opin. 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Neurosci. 2013; 33: 7325-7344Crossref PubMed Scopus (6) Google Scholar]. For example, different neurons may have different stimulus tuning curves exhibiting a preference for different stimulus features or exhibiting different stimulus tuning widths. The heterogeneity of stimulus tuning generally implies that individual neurons may carry complementary information to that provided by others. As a result, the ability of a heterogeneous population to discriminate among stimuli in a set should, under most conditions, increase with population size. If individual neurons in a population each prefer well-separated stimulus features (such that their tuning curves do not overlap), the range of stimulus features encoded by that population would increase with population size. If, instead, neurons in a population have diverse but partly overlapping tuning curves, the complementary information carried by different neurons would lead to a better discrimination of stimulus features in the regions where the tuning curves overlap. The scaling of information with population size depends on the structure of tuning preferences and of trial-to-trial response correlations, and its investigation can provide important insights. It can indicate how many neurons would be sufficient to achieve a desired level of sensory accuracy (assuming that the decoding mechanisms or later processing stages do not discard any of this information). Its extrapolation to infinite population size sets an upper bound on the information that can be achieved by a population with the considered response properties. The scaling of information with population size is often studied by averaging information over subpopulations that are randomly sampled from the recorded neurons. This approach typically reveals a steady increase of information with population size (Figure 1A) , and led to the hypothesis that increasing population size allows the encoding of arbitrarily high amounts of information [20Quiroga R.Q. et al.Decoding visual inputs from multiple neurons in the human temporal lobe.J. Neurophysiol. 2007; 98: 1997-2007Crossref PubMed Scopus (48) Google Scholar, 21Rolls E.T. et al.The representational capacity of the distributed encoding of information provided by populations of neurons in primate temporal visual cortex.Exp. Brain Res. 1997; 114: 149-162Crossref PubMed Scopus (130) Google Scholar]. However, recent work [22Ince R.A. et al.Neural codes formed by small and temporally precise populations in auditory cortex.J. Neurosci. 2013; 33: 18277-18287Crossref PubMed Scopus (1) Google Scholar] has shown that this steady increase may actually be an artifact resulting from random subsampling. This artifact arises because of an often neglected aspect of neural heterogeneity [22Ince R.A. et al.Neural codes formed by small and temporally precise populations in auditory cortex.J. Neurosci. 2013; 33: 18277-18287Crossref PubMed Scopus (1) Google Scholar]: only a small fraction of neurons in a given population carry significant sensory information in a specific context (Figure 1B). As a result of this heterogeneity in single-neuron properties, a small but highly informative subset of neurons is sufficient to carry essentially all the information present in the entire observed population (Figure 1A) [22Ince R.A. et al.Neural codes formed by small and temporally precise populations in auditory cortex.J. Neurosci. 2013; 33: 18277-18287Crossref PubMed Scopus (1) Google Scholar]. The above results are part of an emerging picture that a small-dimensional subspace of the experimentally measured activity suffices to explain the population dynamics underling sensory processing [23Bathellier B. et al.Discrete neocortical dynamics predict behavioral categorization of sounds.Neuron. 2012; 76: 435-449Abstract Full Text Full Text PDF PubMed Scopus (31) Google Scholar] and motor behavior [24Shenoy K.V. et al.Cortical control of arm movements: a dynamical systems perspective.Annu. Rev. Neurosci. 2013; 36: 337-359Crossref PubMed Scopus (32) Google Scholar]. This picture is consistent with the observed sparseness of cortical activity [25Barth A.L. Poulet J.F. 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Importantly, the information carried by these precise spike patterns cannot be replaced by the information in the coarse-scale firing rates of other neurons in the population (Figure 1C), because information in spike patterns is complementary to that in firing rates and because the fraction of neurons carrying information by rates is limited [22Ince R.A. et al.Neural codes formed by small and temporally precise populations in auditory cortex.J. Neurosci. 2013; 33: 18277-18287Crossref PubMed Scopus (1) Google Scholar]. This implies that spike timing remains crucial even for population codes [22Ince R.A. et al.Neural codes formed by small and temporally precise populations in auditory cortex.J. Neurosci. 2013; 33: 18277-18287Crossref PubMed Scopus (1) Google Scholar, 29Garcia-Lazaro J.A. et al.Independent population coding of speech with sub-millisecond precision.J. 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Thus, both the spatial and temporal dimensions are important for understanding neural population codes, raising questions as to how such precise timing or population sparseness can be assessed using neuroimaging. In higher association regions the heterogeneity of cortical neurons expresses itself as patterns of selectivity to multiple sensory and task-related variables, which can be mixed in complex, sometimes nonlinear ways [34Eskandar E.N. Assad J.A. Dissociation of visual, motor and predictive signals in parietal cortex during visual guidance.Nat. Neurosci. 1999; 2: 88-93Crossref PubMed Scopus (101) Google Scholar, 35Rigotti M. et al.The importance of mixed selectivity in complex cognitive tasks.Nature. 2013; 497: 585-590Crossref PubMed Scopus (62) Google Scholar]. A pioneering study unveiled the advantages of nonlinear mixed selectivity [35Rigotti M. et al.The importance of mixed selectivity in complex cognitive tasks.Nature. 2013; 497: 585-590Crossref PubMed Scopus (62) Google Scholar]. If responses were selective only to individual task or stimulus aspects, or to their linear combinations (linear mixed selectivity; Figure 1D), the dimensionality of the neural representation would be lower than the number of neurons in the population. In the example in Figure 1D–F, the neural representation of a set of stimuli of two linearly mixed neurons lies on a line. This implies that complex nonlinear operations are required for decoding the information content (Figure 1F). By contrast, a heterogeneous nonlinear mixed representation (Figure 1E) leads to a richer population representation that has higher dimensionality than its linear counterpart and that can be more easily decoded by downstream areas using linear combinations of neural activity [36Rigotti M. et al.Internal representation of task rules by recurrent dynamics: the importance of the diversity of neural responses.Front. Comput. Neurosci. 2010; 4: 24Crossref PubMed Scopus (42) Google Scholar] (Figure 1F). In sum, heterogeneous nonlinear mixtures of selectivity increase the effective dimensionality of a population code and help to extract diverse information using simple linear decoding. This high-dimensional population representation by mixed selectivity may seem at odds with reports of small subpopulations effectively encoding primary sensory information. However, sparseness and high dimensionality of mixed nonlinear selectivity can coexist and may even combine optimally under appropriate conditions [37Barak O. et al.The sparseness of mixed selectivity neurons controls the generalization-discrimination trade-off.J. Neurosci. 2013; 33: 3844-3856Crossref PubMed Scopus (8) Google Scholar]. In fact, when nonlinearly mixed neural representations are also sparse, they naturally achieve an optimal trade-off between the need to maximize the diversity of responses to different stimuli (increasing the stimulus discrimination properties of population responses), and the need to maintain high response reliability (i.e., achieving consistent responses for noisy variations of the input) [37Barak O. et al.The sparseness of mixed selectivity neurons controls the generalization-discrimination trade-off.J. Neurosci. 2013; 33: 3844-3856Crossref PubMed Scopus (8) Google Scholar]. 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