1932

Abstract

Brain function involves the activity of neuronal populations. Much recent effort has been devoted to measuring the activity of neuronal populations in different parts of the brain under various experimental conditions. Population activity patterns contain rich structure, yet many studies have focused on measuring pairwise relationships between members of a larger population—termed noise correlations. Here we review recent progress in understanding how these correlations affect population information, how information should be quantified, and what mechanisms may give rise to correlations. As population coding theory has improved, it has made clear that some forms of correlation are more important for information than others. We argue that this is a critical lesson for those interested in neuronal population responses more generally: Descriptions of population responses should be motivated by and linked to well-specified function. Within this context, we offer suggestions of where current theoretical frameworks fall short.

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2016-07-08
2024-06-17
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Literature Cited

  1. Abbott LF, Dayan P. 1999. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11:91–101 [Google Scholar]
  2. Adibi M, McDonald JS, Clifford CWG, Arabzadeh E. 2013. Adaptation improves neural coding efficiency despite increasing correlations in variability. J. Neurosci. 33:2108–20 [Google Scholar]
  3. Adibi M, McDonald JS, Clifford CWG, Arabzadeh E. 2014. Population decoding in rat barrel cortex: optimizing the linear readout of correlated population responses. PLOS Comput. Biol. 10:1e1003415 [Google Scholar]
  4. Arandia-Romero I, Tanabe S, Drugowitsch J, Kohn A, Moreno-Bote R. 2016. Multiplicative and additive modulation of neuronal tuning with population activity affects encoded information. Neuron 89:61305–16 [Google Scholar]
  5. Arieli A, Sterkin A, Grinvald A, Aertsen A. 1996. Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science 273:1868–71 [Google Scholar]
  6. Atick J, Redlich A. 1990. Towards a theory of early visual processing. Neural Comput. 2:308–20 [Google Scholar]
  7. Averbeck BB, Latham PE, Pouget A. 2006. Neural correlations, population coding and computation. Nat. Rev. Neurosci. 7:358–66 [Google Scholar]
  8. Babadi B, Sompolinsky H. 2014. Sparseness and expansion in sensory representations. Neuron 83:1213–26 [Google Scholar]
  9. Bair W1, Zohary E, Newsome WT. 2001. Correlated firing in macaque visual area MT: time scales and relationship to behavior. J. Neurosci. 21:1676–97 [Google Scholar]
  10. Baker PM, Bair W. 2012. Inter-neuronal correlation distinguishes mechanisms of direction selectivity in cortical circuit models. J. Neurosci. 32:8800–16 [Google Scholar]
  11. Barlow H. 2001. Redundancy reduction revisited. Network 12:241–53 [Google Scholar]
  12. Beck JM, Bejjanki VR, Pouget A. 2011. Insights from a simple expression for linear Fisher information in a recurrently connected population of spiking neurons. Neural Comput. 23:1484–502 [Google Scholar]
  13. Beck JM, Heller K, Pouget A. 2012a. Complex inference in neural circuits with probabilistic population codes and topic models. Advances in Neural Information Processing Systems 4 P Bartlett 3068–76 Cambridge, MA: MIT Press [Google Scholar]
  14. Beck JM, Ma WJ, Pitkow X, Latham PE, Pouget A. 2012b. Not noisy, just wrong: the role of suboptimal inference in behavioral variability. Neuron 74:30–39 [Google Scholar]
  15. Bejjanki VR, Beck JM, Lu ZL, Pouget A. 2011. Perceptual learning as improved probabilistic inference in early sensory areas. Nat. Neurosci. 14:642–48 [Google Scholar]
  16. Berens P, Ecker AS, Cotton RJ, Ma WJ, Bethge M, Tolias AS. 2012. A fast and simple population code for orientation in primate V1. J. Neurosci. 32:10618–26 [Google Scholar]
  17. Berkes P, Orbán G, Lengyel M, Fiser J. 2011. Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment. Science 331:83–87 [Google Scholar]
  18. Bosking WH, Zhang Y, Schofield B, Fitzpatrick D. 1997. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17:2112–27 [Google Scholar]
  19. Bujan AF, Aertsen A, Kumar A. 2015. Role of input correlations in shaping the variability and noise correlations of evoked activity in the neocortex. J. Neurosci. 35:8611–25 [Google Scholar]
  20. Butts DA, Goldman MS. 2006. Tuning curves, neuronal variability, and sensory coding. PLOS Biol. 4:4e92 [Google Scholar]
  21. Buzsaki G. 2006. Rhythms of the Brain New York: Oxford Univ. Press [Google Scholar]
  22. Calabrese A, Woolley SM. 2015. Coding principles of the canonical cortical microcircuit in the avian brain. PNAS 112:3517–22 [Google Scholar]
  23. Cohen MR, Kohn A. 2011. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14:811–19 [Google Scholar]
  24. Cohen MR, Maunsell JH. 2009. Attention improves performance primarily by reducing interneuronal correlations. Nat. Neurosci. 12:1594–600 [Google Scholar]
  25. Cohen MR, Newsome WT. 2008. Context-dependent changes in functional circuitry in visual area MT. Neuron 60:162–73 [Google Scholar]
  26. Cortes C, Vapnik V. 1995. Support-vector networks. Mach. Learn. 20:273–97 [Google Scholar]
  27. Cossell L, Iacaruso MF, Muir DR, Houlton R, Sader EN. et al. 2015. Functional organization of excitatory synaptic strength in primary visual cortex. Nature 518:399–403 [Google Scholar]
  28. da Silveira RA, Berry MJ II. 2014. High-fidelity coding with correlated neurons. PLOS Comput. Biol. 10:11e1003970 [Google Scholar]
  29. Dayan P, Abbott LF. 2001. Theoretical Neuroscience Cambridge, MA: MIT Press [Google Scholar]
  30. Deneve S, Latham PE, Pouget A. 1999. Reading population codes: a neural implementation of ideal observers. Nat. Neurosci. 2:740–45 [Google Scholar]
  31. Denman DJ, Contreras D. 2014. The structure of pairwise correlation in mouse primary visual cortex reveals functional organization in the absence of an orientation map. Cereb. Cortex 24:2707–20 [Google Scholar]
  32. DiCarlo JJ, Zoccolan D, Rust NC. 2012. How does the brain solve visual object recognition?. Neuron 73:415–34 [Google Scholar]
  33. Doiron B, Litwin-Kumar A, Rosenbaum R, Ocker GK, Josić K. 2016. The mechanics of state-dependent neural correlations. Nat. Neurosci. 19:3383–93 [Google Scholar]
  34. Ecker AS, Berens P, Cotton RJ, Subramaniyan M, Denfield GH. et al. 2014. State dependence of noise correlations in macaque primary visual cortex. Neuron 82:235–48 [Google Scholar]
  35. Ecker AS, Berens P, Keliris GA, Bethge M, Logothetis NK, Tolias AS. 2010. Decorrelated neuronal firing in cortical microcircuits. Science 327:584–87 [Google Scholar]
  36. Ecker AS, Berens P, Tolias AS, Bethge M. 2011. The effect of noise correlations in populations of diversely tuned neurons. J. Neurosci. 31:14272–83 [Google Scholar]
  37. Ecker AS, Denfield GH, Bethge M, Tolias AS. 2015. On the structure of population activity under fluctuations in attentional state. bioRxiv018226
  38. Fetsch CR, Pouget A, DeAngelis GC, Angelaki DE. 2011. Neural correlates of reliability-based cue weighting during multisensory integration. Nat. Neurosci. 15:146–54 [Google Scholar]
  39. Fiser J, Berkes P, Orbán G, Lengyel M. 2010. Statistically optimal perception and learning: from behavior to neural representations. Trends Cogn. Sci. 14:119–30 [Google Scholar]
  40. Foldiak P. 1993. The ‘ideal homunculus’: statistical inference from neural population responses. Computation and Neural Systems F Eeckman, J Bower 55–60 Norwell, MA: Kluwer Acad. [Google Scholar]
  41. Friedrich RW. 2013. Neuronal computations in the olfactory system of zebrafish. Annu. Rev. Neurosci. 36:383–402 [Google Scholar]
  42. Friedrich RW, Laurent G. 2001. Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science 291:889–94 [Google Scholar]
  43. Ganguli D, Simoncelli EP. 2014. Efficient sensory encoding and Bayesian inference with heterogeneous neural populations. Neural Comput. 26:2103–34 [Google Scholar]
  44. Gerhard F, Kispersky T, Gutierrez GJ, Marder E, Kramer M, Eden U. 2013. Successful reconstruction of a physiological circuit with known connectivity from spiking activity alone. PLOS Comput. Biol. 9:7e1003138 [Google Scholar]
  45. Gerwinn S, Macke JH, Bethge M. 2010. Bayesian inference for generalized linear models for spiking neurons. Front. Comput. Neurosci. 4:12 [Google Scholar]
  46. Ginzburg II, Sompolinsky H. 1994. Theory of correlations in stochastic neural networks. Phys. Rev. E. 50:3171–91 [Google Scholar]
  47. Goris RL, Movshon JA, Simoncelli EP. 2014. Partitioning neuronal variability. Nat. Neurosci. 17:858–65 [Google Scholar]
  48. Grabska-Barwińska A, Beck J, Pouget A, Latham P. 2014. Demixing odors—fast inference in olfaction. Advances in Neural Information Processing Systems 24 P Bartlett 1968–76 Cambridge, MA: MIT Press [Google Scholar]
  49. Graf AB, Kohn A, Jazayeri M, Movshon JA. 2011. Decoding the activity of neuronal populations in macaque primary visual cortex. Nat. Neurosci. 14:239–45 [Google Scholar]
  50. Graupner M, Reyes AD. 2013. Synaptic input correlations leading to membrane potential decorrelation of spontaneous activity in cortex. J. Neurosci. 33:15075–85 [Google Scholar]
  51. Gu Y, Liu S, Fetsch CR, Yang Y, Fok S. et al. 2011. Perceptual learning reduces interneuronal correlations in macaque visual cortex. Neuron 71:750–61 [Google Scholar]
  52. Gutnisky DA, Dragoi V. 2008. Adaptive coding of visual information in neural populations. Nature 452:220–24 [Google Scholar]
  53. Haefner RM, Berkes P, Fiser J. 2014. Perceptual decision-making as probabilistic inference by neural sampling. arXiv:1409.0257 [q-bio.NC]
  54. Haefner RM, Gerwinn S, Macke JH, Bethge M. 2013. Inferring decoding strategies from choice probabilities in the presence of correlated variability. Nat. Neurosci. 16:235–42 [Google Scholar]
  55. Hansen BJ, Chelaru MI, Dragoi V. 2012. Correlated variability in laminar cortical circuits. Neuron 76:590–602 [Google Scholar]
  56. Harris KD, Thiele A. 2011. Cortical state and attention. Nat. Rev. Neurosci. 12:509–23 [Google Scholar]
  57. Hennequin G, Aitchison L, Lengyel M. 2014. Fast sampling-based inference in balanced neuronal networks. Advances in Neural Information Processing Systems 27 P Bartlett 2240–48 Cambridge, MA: MIT Press [Google Scholar]
  58. Herrero JL, Gieselmann MA, Sanayei M, Thiele A. 2013. Attention-induced variance and noise correlation reduction in macaque V1 is mediated by NMDA receptors. Neuron 78:729–39 [Google Scholar]
  59. Hirabayashi T, Takeuchi D, Tamura T, Miyashita Y. 2013. Microcircuits for hierarchical elaboration of object coding across primate temporal areas. Science 341:191–95 [Google Scholar]
  60. Huang X, Lisberger SG. 2009. Noise correlations in cortical area MT and their potential impact on trial-by-trial variation in the direction and speed of smooth-pursuit eye movements. J. Neurophysiol. 101:3012–30 [Google Scholar]
  61. Jazayeri M, Movshon JA. 2006. Optimal representation of sensory information by neural populations. Nat. Neurosci. 9:690–96 [Google Scholar]
  62. Jeanne JM, Sharpee TO, Gentner TQ. 2013. Associative learning enhances population coding by inverting interneuronal correlation patterns. Neuron 78:352–63 [Google Scholar]
  63. Jorgenson LA, Newsome WT, Anderson DJ, Bargmann CI, Brown EN. et al. 2015. The BRAIN Initiative: developing technology to catalyse neuroscience discovery. Philos. Trans. R. Soc. B 370:20140164 [Google Scholar]
  64. Kanitscheider I, Coen-Cagli R, Kohn A, Pouget A. 2015a. Measuring Fisher information accurately in correlated neural populations. PLOS Comput. Bio. 11:6e1004218 [Google Scholar]
  65. Kanitscheider I, Coen-Cagli R, Pouget A. 2015b. The origin of information-limiting correlations. PNAS. 112:E6973–82 [Google Scholar]
  66. Kohn A, Smith MA. 2005. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25:3661–73 [Google Scholar]
  67. Kohn A, Zandvakili A, Smith MA. 2009. Correlations and brain states: from electrophysiology to functional imaging. Curr. Opin. Neurobiol. 19:434–38 [Google Scholar]
  68. Komiyama T, Sato TR, O'Connor DH, Zhang YX, Huber D. et al. 2010. Learning-related fine-scale specificity imaged in motor cortex circuits of behaving mice. Nature 464:1182–86 [Google Scholar]
  69. Kumar A, Rotter S, Aertsen A. 2010. Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding. Nat. Rev. Neurosci. 11:615–27 [Google Scholar]
  70. Lin IC, Okun M, Carandini M, Harris KD. 2015. The nature of shared cortical variability. Neuron 87:644–56 [Google Scholar]
  71. Litvak V, Sompolinsky H, Segev I, Abeles M. 2003. On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance. J. Neurosci. 23:3006–15 [Google Scholar]
  72. Litwin-Kumar A, Doiron B. 2012. Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat. Neurosci. 15:1498–1505 [Google Scholar]
  73. Ma WJ, Beck JM, Latham PE, Pouget A. 2006. Bayesian inference with probabilistic population codes. Nat. Neurosci. 9:1432–38 [Google Scholar]
  74. Martin KA, Schroder S. 2013. Functional heterogeneity in neighboring neurons of cat primary visual cortex in response to both artificial and natural stimuli. J. Neurosci. 33:7325–44 [Google Scholar]
  75. Masud MS, Borisyuk R. 2011. Statistical technique for analysing functional connectivity of multiple spike trains. J. Neurosci. Methods 196:201–19 [Google Scholar]
  76. McDonald JS, Clifford CW, Solomon SS, Chen SC, Solomon SG. 2014. Integration and segregation of multiple motion signals by neurons in area MT of primate. J. Neurophysiol. 111:369–78 [Google Scholar]
  77. Mitchell JF, Sundberg KA, Reynolds JH. 2009. Spatial attention decorrelates intrinsic activity fluctuations in macaque area V4. Neuron 63:879–88 [Google Scholar]
  78. Moore GP, Segundo JP, Perkel DH, Levitan H. 1970. Statistical signs of synaptic interactions in neurons. Biophys. J. 10:876–900 [Google Scholar]
  79. Moreno-Bote R, Beck J, Kanitscheider I, Pitkow X, Latham P, Pouget A. 2014. Information-limiting correlations. Nat. Neurosci. 17:1410–17 [Google Scholar]
  80. Nienborg H, Cohen MR, Cumming BG. 2012. Decision-related activity in sensory neurons: correlations among neurons and with behavior. Annu. Rev. Neurosci. 35:463–83 [Google Scholar]
  81. Ohiorhenuan IE, Mechler F, Purpura KP, Schmid AM, Hu Q, Victor JD. 2010. Sparse coding and high-order correlations in fine-scale cortical networks. Nature 466:617–21 [Google Scholar]
  82. Okatan M, Wilson MA, Brown EN. 2005. Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Comput. 17:1927–61 [Google Scholar]
  83. Okun M, Steinmetz NA, Cossell L, Iacaruso MF, Ko H. et al. 2015. Diverse coupling of neurons to populations in sensory cortex. Nature 521:511–15 [Google Scholar]
  84. Ostojic S. 2014. Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons. Nat. Neurosci. 17:594–600 [Google Scholar]
  85. Ostojic S, Brunel N, Hakim V. 2009. How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J. Neurosci. 29:10234–53 [Google Scholar]
  86. Pachitariu M, Lyamzin DR, Sahani M, Lesica NA. 2015. State-dependent population coding in primary auditory cortex. J. Neurosci. 35:2058–73 [Google Scholar]
  87. Paradiso MA. 1988. A theory for the use of visual orientation information which exploits the columnar structure of striate cortex. Biol. Cybern. 58:35–49 [Google Scholar]
  88. Pillow JW, Shlens J, Paninski L, Sher A, Litke AM. et al. 2008. Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454:995–99 [Google Scholar]
  89. Pitkow X, Liu S, Angelaki DE, DeAngelis GC, Pouget A. 2015. How can single sensory neurons predict behavior?. Neuron 87:411–23 [Google Scholar]
  90. Pouget A, Beck JM, Ma WJ, Latham PE. 2013. Probabilistic brains: knowns and unknowns. Nat. Neurosci. 16:1170–78 [Google Scholar]
  91. Pouget A, Dayan P, Zemel R. 2000. Information processing with population codes. Nat. Rev. Neurosci. 1:125–32 [Google Scholar]
  92. Pouget A, Thorpe S. 1991. Connectionist model of orientation identification. Connect. Sci. 3:127–42 [Google Scholar]
  93. Poulet JF, Petersen CC. 2008. Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice. Nature 454:881–85 [Google Scholar]
  94. Rabinowitz NC, Goris RL, Cohen M, Simoncelli EP. 2015. Attention stabilizes the shared gain of V4 populations. eLife 2:4e08998 [Google Scholar]
  95. Ramalingam N, McManus JNJ, Li W, Gilbert CD. 2013. Top-down modulation of lateral interactions in visual cortex. J. Neurosci. 33:1773–89 [Google Scholar]
  96. Rasch MJ, Schuch K, Logothetis NK, Maass W. 2011. Statistical comparison of spike responses to natural stimuli in monkey area V1 with simulated responses of a detailed laminar network model for a patch of V1. J. Neurophysiol. 105:757–78 [Google Scholar]
  97. Reid RC, Alonso JM. 1995. Specificity of monosynaptic connections from thalamus to visual cortex. Nature 378:281–84 [Google Scholar]
  98. Renart A, de la Rocha J, Bartho P, Hollender L, Parga N. et al. 2010. The asynchronous state in cortical circuits. Science 327:587–90 [Google Scholar]
  99. Renart A, van Rossum MC. 2012. Transmission of population-coded information. Neural Comput. 24:391–407 [Google Scholar]
  100. Rescorla RA, Wagner AR. 1972. A theory of Pavlovian conditioning: the effectiveness of reinforcement and non-reinforcement. Classical Conditioning II: Current Research and Theory AH Black, WF Prokasy 64–69 New York: Appleton-Century-Crofts [Google Scholar]
  101. Roelfsema PR, Lamme VA, Spekreijse H. 2004. Synchrony and covariation of firing rates in the primary visual cortex during contour grouping. Nat. Neurosci. 7:982–91 [Google Scholar]
  102. Ruff DA, Cohen MR. 2014. Attention can either increase or decrease spike count correlations in visual cortex. Nat. Neurosci. 17:1591–97 [Google Scholar]
  103. Salinas E, Abbott LF. 1994. Vector reconstruction from firing rates. J. Comput. Neurosci. 1:89–107 [Google Scholar]
  104. Salinas E, Sejnowski TJ. 2000. Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. J. Neurosci. 20:6193–6209 [Google Scholar]
  105. Sanger T. 1996. Probability density estimation for the interpretation of neural population codes. J. Neurophys. 76:2790–2793 [Google Scholar]
  106. Sato TK, Nauhaus I, Carandini M. 2012. Traveling waves in visual cortex. Neuron 75:218–29 [Google Scholar]
  107. Schneidman E, Berry MJ II, Segev R, Bialek W. 2006. Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440:1007–12 [Google Scholar]
  108. Schölvinck ML, Saleem AB, Benucci A, Harris KD, Carandini M. 2015. Cortical state determines global variability and correlations in visual cortex. J. Neurosci. 35:170–78 [Google Scholar]
  109. Seriès P, Latham PE, Pouget A. 2004. Tuning curve sharpening for orientation selectivity: coding efficiency and the impact of correlations. Nat. Neurosci. 7:1129–35 [Google Scholar]
  110. Seung HS, Sompolinsky H. 1993. Simple models for reading neuronal population codes. PNAS 90:10749–53 [Google Scholar]
  111. Shadlen MN, Newsome WT. 1998. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18:3870–96 [Google Scholar]
  112. Shamir M, Sompolinsky H. 2004. Nonlinear population codes. Neural Comput. 16:1105–36 [Google Scholar]
  113. Shamir M, Sompolinsky H. 2006. Implications of neuronal diversity on population coding. Neural Comput. 18:1951–86 [Google Scholar]
  114. Simoncelli EP, Olshausen BA. 2001. Natural image statistics and neural representation. Annu. Rev. Neurosci. 24:1193–1216 [Google Scholar]
  115. Smith MA, Jia X, Zandvakili A, Kohn A. 2013. Laminar dependence of neuronal correlations in visual cortex. J. Neurophysiol. 109:940–47 [Google Scholar]
  116. Smith MA, Kohn A. 2008. Spatial and temporal scales of neuronal correlation in primary visual cortex. J. Neurosci. 28:12591–603 [Google Scholar]
  117. Smith MA, Sommer MA. 2013. Spatial and temporal scales of neuronal correlation in visual area V4. J. Neurosci. 33:5422–32 [Google Scholar]
  118. Solomon SS, Chen SC, Morley JW, Solomon SG. 2014. Local and global correlations between neurons in the middle temporal area of primate visual cortex. Cereb. Cortex 25:3182–96 [Google Scholar]
  119. Sompolinsky H, Yoon H, Kang K, Shamir M. 2001. Population coding in neuronal systems with correlated noise. Phys. Rev. E. 64:051904 [Google Scholar]
  120. Song S, Sjöström PJ, Reigl M, Nelson S, Chklovskii DB. 2005. Highly nonrandom features of synaptic connectivity in local cortical circuits. PLOS Biol. 3:3e68 [Google Scholar]
  121. Stevenson IH, Rebesco JM, Miller LE, Körding KP. 2008. Inferring functional connections between neurons. Curr. Opin. Neurobiol. 18:582–88 [Google Scholar]
  122. Tan AY, Chen Y, Scholl B, Seidemann E, Priebe NJ. 2014. Sensory stimulation shifts visual cortex from synchronous to asynchronous states. Nature 509:226–29 [Google Scholar]
  123. Tolhurst DJ, Movshon JA, Dean AF. 1983. The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vis. Res. 23:775–85 [Google Scholar]
  124. van Vreeswijk C, Sompolinsky H. 1996. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274:1724–26 [Google Scholar]
  125. Vogels TP, Abbott LF. 2005. Signal propagation and logic gating in networks of integrate-and-fire neurons. J. Neurosci. 25:10786–95 [Google Scholar]
  126. Vogels TP, Rajan K, Abbott LF. 2005. Neural network dynamics. Annu. Rev. Neurosci. 28:357–76 [Google Scholar]
  127. Widrow B, Hoff ME Jr. 1960. Adaptive switching circuits. IRE WESCON Conv. Rec. 4:96–104 [Google Scholar]
  128. Wilke SD, Eurich CW. 2002. Representational accuracy of stochastic neural populations. Neural Comput. 14:155–89 [Google Scholar]
  129. Wimmer K, Compte A, Roxin A, Peixoto D, Renart A, de la Rocha J. 2015. Sensory integration dynamics in a hierarchical network explains choice probabilities in cortical area MT. Nat. Commun. 6:6177 [Google Scholar]
  130. Wu S, Nakahara H, Amari S. 2001. Population coding with correlation and an unfaithful model. Neural Comput. 13:775–97 [Google Scholar]
  131. Yoshimura Y, Dantzker JLM, Callaway EM. 2005. Excitatory cortical neurons form fine-scale functional networks. Nature 433:868–73 [Google Scholar]
  132. Yu BM, Kohn A, Smith MA. 2011. Estimating shared firing rate fluctuations in neural populations Program No. 483.18/NN1. Presented at Soc. Neurosci., Nov. 14, Washington DC. [Google Scholar]
  133. Yu J, Ferster D. 2013. Functional coupling from simple to complex cells in the visually driven cortical circuit. J. Neurosci. 33:18855–66 [Google Scholar]
  134. Zandvakili A, Kohn A. 2015. Coordinated neuronal activity enhances corticocortical communication. Neuron 87:827–39 [Google Scholar]
  135. Zohary E, Shadlen MN, Newsome WT. 1994. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370:140–43 [Google Scholar]
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