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Normalization as a canonical neural computation

An Erratum to this article was published on 18 January 2013

This article has been updated

Key Points

  • Normalization computes a ratio between the response of an individual neuron and the summed activity of a pool of neurons.

  • The normalization model was developed to explain responses in the primary visual cortex (V1), and has been seen to operate in a variety of other regions of the visual system: light adaptation in the retina, contrast normalization in the retina and lateral geniculate nucleus, and visual processing in higher visual cortical areas beyond V1.

  • Normalization has also been proposed to be at the root of the modulatory effects of visual attention on neural responses in the visual cortex.

  • Normalization is seen in multiple species and brain regions. These include olfactory processing and representation in the fruitfly antennal lobe, the encoding of value in the posterior parietal cortex, multisensory integration of visual motion and vestibular signals, and auditory processing in the primary auditory cortex.

  • Different (feedforward and feedback) neural circuits and mechanisms might perform normalization, including presynaptic inhibition, shunting inhibition, synaptic depression, changes in the amplitude of ongoing activity and balanced amplification.

  • The effects of normalization can be measured behaviourally.

  • The computational benefits of normalization include maximizing sensitivity, providing invariance with respect to some stimulus dimensions at the expense of others, facilitating the decoding of a distributed neural representation, facilitating the discrimination among representations of different stimuli, providing max-pooling (winner-take-all competition) and reducing redundancy.

  • Understanding canonical neural computations such as normalization may shed light on psychiatric, neurological and developmental disorders.

Abstract

There is increasing evidence that the brain relies on a set of canonical neural computations, repeating them across brain regions and modalities to apply similar operations to different problems. A promising candidate for such a computation is normalization, in which the responses of neurons are divided by a common factor that typically includes the summed activity of a pool of neurons. Normalization was developed to explain responses in the primary visual cortex and is now thought to operate throughout the visual system, and in many other sensory modalities and brain regions. Normalization may underlie operations such as the representation of odours, the modulatory effects of visual attention, the encoding of value and the integration of multisensory information. Its presence in such a diversity of neural systems in multiple species, from invertebrates to mammals, suggests that it serves as a canonical neural computation.

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Figure 1: Normalization in the olfactory system of the fruitfly.
Figure 2: Normalization in the retina.
Figure 3: Normalization in the primary visual cortex.
Figure 4: Attentional modulation of responses in the visual cortex and predictions of the normalization model of attention.
Figure 5: Some networks and mechanisms that have been proposed for normalization.

Change history

  • 18 January 2013

    On page 52 of this article, in the legend for figure 1, the text "lower concentrations are shown by darker colours" should have read "lower concentrations are shown by darker colours". This has been corrected in the online version.

References

  1. Douglas, R. J., Martin, K. A. C. & Whitteridge, D. A functional microcircuit for cat visual cortex. J. Physiol. 440, 735–769 (1991).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Douglas, R. J., Koch, C., Mahowald, M., Martin, K. A. C. & Suarez, H. H. Recurrent excitation in neocortical circuits. Science 269, 981–985 (1995).

    Article  CAS  PubMed  Google Scholar 

  3. Wang, X. J. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36, 955–968 (2002).

    Article  CAS  PubMed  Google Scholar 

  4. Hanes, D. P. & Schall, J. D. Neural control of voluntary movement initiation. Science 274, 427–430 (1996).

    Article  CAS  PubMed  Google Scholar 

  5. Lo, C. C. & Wang, X. J. Cortico-basal ganglia circuit mechanism for a decision threshold in reaction time tasks. Nature Neurosci. 9, 956–963 (2006).

    Article  CAS  PubMed  Google Scholar 

  6. Cisek, P. Integrated neural processes for defining potential actions and deciding between them: a computational model. J. Neurosci. 26, 9761–9770 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Priebe, N. J. & Ferster, D. Inhibition, spike threshold, and stimulus selectivity in primary visual cortex. Neuron 57, 482–497 (2008).

    Article  CAS  PubMed  Google Scholar 

  8. Wiechert, M. T., Judkewitz, B., Riecke, H. & Friedrich, R. W. Mechanisms of pattern decorrelation by recurrent neuronal circuits. Nature Neurosci. 13, 1003–1010 (2010).

    Article  CAS  PubMed  Google Scholar 

  9. Smith, P. L. & Ratcliff, R. Psychology and neurobiology of simple decisions. Trends Neurosci. 27, 161–168 (2004).

    Article  CAS  PubMed  Google Scholar 

  10. Stanford, T. R., Shankar, S., Massoglia, D. P., Costello, M. G. & Salinas, E. Perceptual decision making in less than 30 milliseconds. Nature Neurosci. 13, 379–385 (2010).

    Article  CAS  PubMed  Google Scholar 

  11. Carandini, M. et al. Do we know what the early visual system does? J. Neurosci. 25, 10577–10597 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Depireux, D. A., Simon, J. Z., Klein, D. J. & Shamma, S. A. Spectro-temporal response field characterization with dynamic ripples in ferret primary auditory cortex. J. Neurophysiol. 85, 1220–1234 (2001).

    Article  CAS  PubMed  Google Scholar 

  13. DiCarlo, J. J. & Johnson, K. O. Receptive field structure in cortical area 3b of the alert monkey. Behav. Brain Res. 135, 167–178 (2002).

    Article  PubMed  Google Scholar 

  14. Graham, N. V. S. Visual Pattern Analyzers. (Oxford Univ. Press, New York, 1989).

    Book  Google Scholar 

  15. Pouget, A. & Snyder, L. H. Computational approaches to sensorimotor transformations. Nature Neurosci. 3, 1192–1198 (2000).

    Article  CAS  PubMed  Google Scholar 

  16. Bizzi, E., Giszter, S. F., Loeb, E., Mussa-Ivaldi, F. A. & Saltiel, P. Modular organization of motor behavior in the frog's spinal cord. Trends Neurosci. 18, 442–446 (1995).

    Article  CAS  PubMed  Google Scholar 

  17. Heeger, D. J. in Computational Models of Visual Processing (eds Landy, M. & Movshon, J. A.) 119–133 (MIT Press, Cambridge, Massachusetts,1991).

    Google Scholar 

  18. Albrecht, D. G. & Geisler, W. S. Motion sensitivity and the contrast-response function of simple cells in the visual cortex. Vis. Neurosci. 7, 531–546 (1991).

    Article  CAS  PubMed  Google Scholar 

  19. Heeger, D. J. Normalization of cell responses in cat striate cortex. Vis. Neurosci. 9, 181–197 (1992). This study introduced the normalization model and showed through simulations that it could explain numerous properties of neurons in primary visual cortex.

    Article  CAS  PubMed  Google Scholar 

  20. Grossberg, S. Nonlinear neural networks: principles, mechanisms and architectures. Neural Netw. 1, 17–61 (1988).

    Article  Google Scholar 

  21. Naka, K. I. & Rushton, W. A. S-potentials from luminosity units in the retina of fish (Cyprinidae). J. Physiol. 185, 587–599 (1966).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Baylor, D. A. & Fuortes, M. G. F. Electrical responses of single cones in the retina of the turtle. J. Physiol. 297, 77–92 (1970).

    Article  Google Scholar 

  23. Boynton, R. M. & Whitten, D. N. Visual adaptation in monkey cones: recordings of late receptor potentials. Science 170, 1423–1426 (1970).

    Article  CAS  PubMed  Google Scholar 

  24. Normann, R. A. & Perlman, I. The effects of background illumination on the photoresponses of red and green cones. J. Physiol. 286, 491–507 (1979).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Reichardt, W., Poggio, T. & Hausen, K. Figure-ground discrimination by relative movement in the visual system of the fly. Part II. Towards the neural circuitry. Biol. Cybern. 46, 1–30 (1983).

    Article  Google Scholar 

  26. McNaughton, B. L. & Morris, R. G. M. Hippocampal synaptic enhancement and information storage within a distributed memory system. Trends Neurosci. 10, 408–415 (1987).

    Article  Google Scholar 

  27. Olsen, S. R., Bhandawat, V. & Wilson, R. I. Divisive normalization in olfactory population codes. Neuron 66, 287–299 (2010). This study demonstrated normalization in the fly olfactory system, and showed how it may benefit the population code for odours (see also REF. 127).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Rodieck, R. W. The First Steps in Seeing. (Sinauer, Sunderland, Massachusetts, 1998).

    Google Scholar 

  29. Rieke, F. & Rudd, M. E. The challenges natural images pose for visual adaptation. Neuron 64, 605–616 (2009).

    Article  CAS  PubMed  Google Scholar 

  30. Mante, V., Frazor, R. A., Bonin, V., Geisler, W. S. & Carandini, M. Independence of luminance and contrast in natural scenes and in the early visual system. Nature Neurosci. 8, 1690–1697 (2005).

    Article  CAS  PubMed  Google Scholar 

  31. Burkhardt, D. A. Light adaptation and photopigment bleaching in cone photoreceptors in situ in the retina of the turtle. J. Neurosci. 14, 1091–1105 (1994).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Schneeweis, D. M. & Schnapf, J. L. The photovoltage of macaque cone photoreceptors: adaptation, noise, and kinetics. J. Neurosci. 19, 1203–1216 (1999).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Shapley, R. M. & Enroth-Cugell, C. in Progress in Retinal Research Vol. 3 (eds Osborne, N. & Chader, G.) 263–346 (Pergamon, Oxford, UK, 1984).

    Google Scholar 

  34. Laughlin, S. A simple coding procedure enhances a neuron's information capacity. Z. Naturforsch. C 36, 910–912 (1981).

    Article  CAS  PubMed  Google Scholar 

  35. Mante, V., Bonin, V. & Carandini, M. Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli. Neuron 58, 625–638 (2008).

    Article  CAS  PubMed  Google Scholar 

  36. Shapley, R. M. & Victor, J. D. The effect of contrast on the transfer properties of cat retinal ganglion cells. J. Physiol. 285, 275–298 (1978).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Shapley, R. M. & Victor, J. How the contrast gain modifies the frequency responses of cat retinal ganglion cells. J. Physiol. 318, 161–179 (1981).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Baccus, S. A. & Meister, M. Fast and slow contrast adaptation in retinal circuitry. Neuron 36, 909–919 (2002).

    Article  CAS  PubMed  Google Scholar 

  39. Demb, J. B. Multiple mechanisms for contrast adaptation in the retina. Neuron 36, 781–783 (2002).

    Article  CAS  PubMed  Google Scholar 

  40. Bonin, V., Mante, V. & Carandini, M. The suppressive field of neurons in lateral geniculate nucleus. J. Neurosci. 25, 10844–10856 (2005). This study extended the normalization model to the responses of subcortical neurons, and demonstrated its similarity with earlier models of retinal contrast gain control.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Beaudoin, D. L., Borghuis, B. G. & Demb, J. B. Cellular basis for contrast gain control over the receptive field center of mammalian retinal ganglion cells. J. Neurosci. 27, 2636–2645 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Bonin, V., Mante, V. & Carandini, M. The statistical computation underlying contrast gain control. J. Neurosci. 26, 6346–6353 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Carandini, M., Heeger, D. J. & Movshon, J. A. Linearity and normalization in simple cells of the macaque primary visual cortex. J. Neurosci. 17, 8621–8644 (1997). This study measured responses of neurons in primary visual cortex of primates using stimuli expressly designed to test the normalization model, and found that the model provided good quantitative fits. This study also formalized the resistor–capacitor model of normalization (see Ref. 45).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Heeger, D. J. Modeling simple cell direction selectivity with normalized, half-squared, linear operators. J. Neurophysiol. 70, 1885–1897 (1993).

    Article  CAS  PubMed  Google Scholar 

  45. Carandini, M. & Heeger, D. J. Summation and division by neurons in primate visual cortex. Science 264, 1333–1336 (1994).

    Article  CAS  PubMed  Google Scholar 

  46. Reynolds, J. H. & Heeger, D. J. The normalization model of attention. Neuron 61, 168–185 (2009). This study showed how the normalization model can be extended to account for the modulatory effects of visual attention.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Sit, Y. F., Chen, Y., Geisler, W. S., Miikkulainen, R. & Seidemann, E. Complex dynamics of V1 population responses explained by a simple gain-control model. Neuron 64, 943–946 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Busse, L., Wade, A. R. & Carandini, M. Representation of concurrent stimuli by population activity in visual cortex. Neuron 64, 931–942 (2009). This study showed that the normalization model can quantitatively describe the combined activity of large populations of neurons in V1, and that the responses (and the model) can exhibit winner-take-all behaviour. It also demonstrated normalization in responses from human area V1.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Albrecht, D. G. & Hamilton, D. B. Striate cortex of monkey and cat: contrast response function. J. Neurophysiol. 48, 217–237 (1982).

    Article  CAS  PubMed  Google Scholar 

  50. Sclar, G., Maunsell, J. H. R. & Lennie, P. Coding of image contrast in central visual pathways of the macaque monkey. Vision Res. 30, 1–10 (1990).

    Article  CAS  PubMed  Google Scholar 

  51. Finn, I. M., Priebe, N. J. & Ferster, D. The emergence of contrast-invariant orientation tuning in simple cells of cat visual cortex. Neuron 54, 137–152 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Sclar, G. & Freeman, R. D. Orientation selectivity in the cat's striate cortex is invariant with stimulus contrast. Exp. Brain Res. 46, 457–461 (1982).

    Article  CAS  PubMed  Google Scholar 

  53. Bauman, L. A. & Bonds, A. B. Inhibitory refinement of spatial frequency selectivity in single cells of the cat striate cortex. Vision Res. 31, 933–944 (1991).

    Article  CAS  PubMed  Google Scholar 

  54. Bonds, A. B. Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex. Vis. Neurosci. 2, 41–55 (1989).

    Article  CAS  PubMed  Google Scholar 

  55. Morrone, M. C., Burr, D. C. & Maffei, L. Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence. Proc. R. Soc. Lond. Sci. 216, 335–354 (1982).

    CAS  Google Scholar 

  56. Freeman, T. C., Durand, S., Kiper, D. C. & Carandini, M. Suppression without inhibition in visual cortex. Neuron 35, 759–771 (2002).

    Article  CAS  PubMed  Google Scholar 

  57. Ohshiro, T., Angelaki, D. E. & Deangelis, G. C. A normalization model of multisensory integration. Nature Neurosci. 14, 775–782 (2011). This study summarized decades of research in multisensory integration and showed that numerous aspects of the responses of multisensory neurons could be described by the normalization model.

    Article  CAS  PubMed  Google Scholar 

  58. Cavanaugh, J. R., Bair, W. & Movshon, J. A. Selectivity and spatial distribution of signals from the receptive field surround in macaque V1 neurons. J. Neurophysiol. 88, 2547–2556 (2002).

    Article  PubMed  Google Scholar 

  59. Cavanaugh, J. R., Bair, W. & Movshon, J. A. Nature and interaction of signals from the receptive field center and surround in macaque V1 neurons. J. Neurophysiol. 88, 2530–2546 (2002).

    Article  PubMed  Google Scholar 

  60. Kapadia, M. K., Westheimer, G. & Gilbert, C. D. Dynamics of spatial summation in primary visual cortex of alert monkeys. Proc. Natl Acad. Sci. USA 96, 12073–12078 (1999).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Sceniak, M. P., Ringach, D. L., Hawken, M. J. & Shapley, R. Contrast's effect on spatial summation by macaque V1 neurons. Nature Neurosci. 2, 733–739 (1999).

    Article  CAS  PubMed  Google Scholar 

  62. Heeger, D. J., Simoncelli, E. P. & Movshon, J. A. Computational models of cortical visual processing. Proc. Natl Acad. Sci. USA 93, 623–627 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Simoncelli, E. P. & Heeger, D. J. A model of neuronal responses in visual area MT. Vision Res. 38, 743–761 (1998).

    Article  CAS  PubMed  Google Scholar 

  64. Rust, N. C., Mante, V., Simoncelli, E. P. & Movshon, J. A. How MT cells analyze the motion of visual patterns. Nature Neurosci. 9, 1421–1431 (2006).

    Article  CAS  PubMed  Google Scholar 

  65. Britten, K. H. & Heuer, H. W. Spatial summation in the receptive fields of MT neurons. J. Neurosci. 19, 5074–5084 (1999).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Zoccolan, D., Kouh, M., Poggio, T. & DiCarlo, J. J. Trade-off between object selectivity and tolerance in monkey inferotemporal cortex. J. Neurosci. 27, 12292–12307 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. Riesenhuber, M. & Poggio, T. Hierarchical models of object recognition in cortex. Nature Neurosci. 2, 1019–1025 (1999).

    Article  CAS  PubMed  Google Scholar 

  68. Kouh, M. & Poggio, T. A canonical neural circuit for cortical nonlinear operations. Neural Comput. 20, 1427–1451 (2008).

    Article  PubMed  Google Scholar 

  69. Reynolds, J. H. & Desimone, R. Interacting roles of attention and visual salience in V4. Neuron 37, 853–863 (2003).

    Article  CAS  PubMed  Google Scholar 

  70. Zoccolan, D., Cox, D. D. & DiCarlo, J. J. Multiple object response normalization in monkey inferotemporal cortex. J. Neurosci. 25, 8150–8164 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Jarrett, K., Kavukcuoglu, K., Ranzato, M. A. & LeCun, Y. What is the best multi-stage architecture for object recognition? Proc. IEEE Int. Conf. Comput. Vis. (2009).

  72. David, S. V., Mesgarani, N., Fritz, J. B. & Shamma, S. A. Rapid synaptic depression explains nonlinear modulation of spectro-temporal tuning in primary auditory cortex by natural stimuli. J. Neurosci. 29, 3374–3386 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Ahrens, M. B., Linden, J. F. & Sahani, M. Nonlinearities and contextual influences in auditory cortical responses modeled with multilinear spectrotemporal methods. J. Neurosci. 28, 1929–1942 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  74. Rabinowitz, N. C., Willmore, B. D., Schnupp, J. W. & King, A. J. Contrast gain control in auditory cortex. Neuron 70, 1178–1191 (2011). This study demonstrated that the responses of neurons in the auditory cortex share many similarities with those in the visual cortex and that these can be described by the normalization equation.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Blake, D. T. & Merzenich, M. M. Changes of AI receptive fields with sound density. J. Neurophysiol. 88, 3409–3420 (2002).

    Article  PubMed  Google Scholar 

  76. Phillips, D. P. Neural representation of sound amplitude in the auditory cortex: effects of noise masking. Behav. Brain Res. 37, 197–214 (1990).

    Article  CAS  PubMed  Google Scholar 

  77. Asadollahi, A., Mysore, S. P. & Knudsen, E. I. Rules of competitive stimulus selection in a cholinergic isthmic nucleus of the owl midbrain. J. Neurosci. 31, 6088–6097 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Morgan, M. L., Deangelis, G. C. & Angelaki, D. E. Multisensory integration in macaque visual cortex depends on cue reliability. Neuron 59, 662–673 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Glimcher, P. Foundations of Neuroeconomic Analysis. (Oxford Univ. Press, New York, 2010).

    Book  Google Scholar 

  80. Louie, K., Grattan, L. E. & Glimcher, P. W. Reward value-based gain control: divisive normalization in parietal cortex. J. Neurosci. 31, 10627–10639 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  81. Herrmann, K., Montaser-Kouhsari, L., Carrasco, M. & Heeger, D. J. When size matters: attention affects performance by contrast or response gain. Nature Neurosci. 13, 1544–1559 (2010).

    Article  CAS  Google Scholar 

  82. Katzner, S., Busse, L. & Carandini, M. GABAa inhibition controls response gain in visual cortex. J. Neurosci. 31, 5931–5941 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Olsen, S. R. & Wilson, R. I. Lateral presynaptic inhibition mediates gain control in an olfactory circuit. Nature 452, 956–960 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Carandini, M., Heeger, D. J. & Senn, W. A synaptic explanation of suppression in visual cortex. J. Neurosci. 22, 10053–10065 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  85. Angelucci, A., Levitt, J. B. & Lund, J. S. Anatomical origins of the classical receptive field and modulatory surround field of single neurons in macaque visual cortical area V1. Prog. Brain Res. 136, 373–388 (2002).

    Article  PubMed  Google Scholar 

  86. Smith, M. A., Bair, W. & Movshon, J. A. Dynamics of suppression in macaque primary visual cortex. J. Neurosci. 26, 4826–4834 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Durand, S., Freeman, T. C. & Carandini, M. Temporal properties of surround suppression in cat primary visual cortex. Vis. Neurosci. 24, 679–690 (2007).

    Article  PubMed  Google Scholar 

  88. Bair, W., Cavanaugh, J. R. & Movshon, J. A. Time course and time-distance relationships for surround suppression in macaque V1 neurons. J. Neurosci. 23, 7690–7701 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Holt, G. R. & Koch, C. Shunting inhibition does not have a divisive effect on firing rates. Neural Comput. 9, 1001–1013 (1997).

    Article  CAS  PubMed  Google Scholar 

  90. Silver, R. A. Neuronal arithmetic. Nature Rev. Neurosci. 11, 474–489 (2010).

    Article  CAS  Google Scholar 

  91. Chance, F. S., Abbott, L. F. & Reyes, A. D. Gain modulation from background synaptic input. Neuron 35, 773–782 (2002).

    Article  CAS  PubMed  Google Scholar 

  92. Sperling, G. & Sondhi, M. M. Model for visual luminance discrimination and flicker detection. J. Opt. Soc. Am. A 58, 1133–1145 (1968).

    Article  CAS  Google Scholar 

  93. Anderson, J., Carandini, M. & Ferster, D. Orientation tuning of input conductance, excitation and inhibition in cat primary visual cortex. J. Neurophysiol. 84, 909–931 (2000).

    Article  CAS  PubMed  Google Scholar 

  94. Monier, C., Chavane, F., Baudot, P., Graham, L. J. & Fregnac, Y. Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning. Neuron 37, 663–680 (2003).

    Article  CAS  PubMed  Google Scholar 

  95. Haider, B. et al. Synaptic and network mechanisms of sparse and reliable visual cortical activity during nonclassical receptive field stimulation. Neuron 65, 107–121 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  96. Ozeki, H., Finn, I. M., Schaffer, E. S., Miller, K. D. & Ferster, D. Inhibitory stabilization of the cortical network underlies visual surround suppression. Neuron 62, 578–592 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Priebe, N. J. & Ferster, D. Mechanisms underlying cross-orientation suppression in cat visual cortex. Nature Neurosci. 9, 552–561 (2006).

    Article  CAS  PubMed  Google Scholar 

  98. Abbott, L. F., Varela, J. A., Sen, K. & Nelson, S. B. Synaptic depression and cortical gain control. Science 275, 220–224 (1997).

    Article  CAS  PubMed  Google Scholar 

  99. Ringach, D. L. Spontaneous and driven cortical activity: implications for computation. Curr. Opin. Neurobiol. 19, 439–444 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  100. Carandini, M. Amplification of trial-to-trial response variability by neurons in visual cortex. PLoS Biol. 2, e264 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Ringach, D. L. & Malone, B. J. The operating point of the cortex: neurons as large deviation detectors. J. Neurosci. 27, 7673–7683 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. Murphy, B. K. & Miller, K. D. Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61, 635–648 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Chubb, C., Sperling, G. & Solomon, J. A. Texture interactions determine perceived contrast. Proc. Natl Acad. Sci. USA 86, 9631–9635 (1989).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. Xing, J. & Heeger, D. J. Measurement and modeling of center-surround suppression and enhancement. Vision Res. 41, 571–583 (2001).

    Article  CAS  PubMed  Google Scholar 

  105. Solomon, J. A., Sperling, G. & Chubb, C. The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation. Vision Res. 33, 2671–2683 (1993).

    Article  CAS  PubMed  Google Scholar 

  106. Petrov, Y., Carandini, M. & McKee, S. Two distinct mechanisms of suppression in human vision. J. Neurosci. 25, 8704–8707 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Foley, J. M. Human luminance pattern-vision mechanisms: masking experiments require a new model. J. Opt. Soc. Am. A 11, 1710–1719 (1994).

    Article  CAS  Google Scholar 

  108. Polat, U., Sagi, D. & Norcia, A. M. Abnormal long-range spatial interactions in amblyopia. Vision Res. 37, 737–744 (1997).

    Article  CAS  PubMed  Google Scholar 

  109. Ellemberg, D., Hess, R. F. & Arsenault, A. S. Lateral interactions in amblyopia. Vision Res. 42, 2471–2478 (2002).

    Article  PubMed  Google Scholar 

  110. Heimel, J. A., Saiepour, M. H., Chakravarthy, S., Hermans, J. M. & Levelt, C. N. Contrast gain control and cortical TrkB signaling shape visual acuity. Nature Neurosci. 13, 642–648 (2010).

    Article  CAS  PubMed  Google Scholar 

  111. Porciatti, V., Bonanni, P., Fiorentini, A. & Guerrini, R. Lack of cortical contrast gain control in human photosensitive epilepsy. Nature Neurosci. 3, 259–263 (2000).

    Article  CAS  PubMed  Google Scholar 

  112. Tsai, J. J., Norcia, A. M. & Wade, A. in American Epilepsy Society 63rd Annual Meeting.

  113. Bubl, E., Tebartz Van Elst, L., Gondan, M., Ebert, D. & Greenlee, M. W. Vision in depressive disorder. World J. Biol. Psychiatry 10, 377–384 (2009).

    Article  PubMed  Google Scholar 

  114. Golomb, J. D. et al. Enhanced visual motion perception in major depressive disorder. J. Neurosci. 29, 9072–9077 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  115. Must, A., Janka, Z., Benedek, G. & Keri, S. Reduced facilitation effect of collinear flankers on contrast detection reveals impaired lateral connectivity in the visual cortex of schizophrenia patients. Neurosci. Lett. 357, 131–134 (2004).

    Article  CAS  PubMed  Google Scholar 

  116. Yoon, J. H. et al. Diminished orientation-specific surround suppression of visual processing in schizophrenia. Schizophr. Bull. 35, 1078–1084 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  117. Yoon, J. H. et al. GABA concentration is reduced in visual cortex in schizophrenia and correlates with orientation-specific surround suppression. J. Neurosci. 30, 3777–3781 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  118. Butler, P. D. et al. Early-stage visual processing and cortical amplification deficits in schizophrenia. Arch. Gen. Psychiatry 62, 495–504 (2005).

    Article  PubMed  PubMed Central  Google Scholar 

  119. Dakin, S., Carlin, P. & Hemsley, D. Weak suppression of visual context in chronic schizophrenia. Curr. Biol. 15, R822–R824 (2005).

    Article  CAS  PubMed  Google Scholar 

  120. Tadin, D. et al. Weakened center-surround interactions in visual motion processing in schizophrenia. J. Neurosci. 26, 11403–11412 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  121. Butler, P. D., Silverstein, S. M. & Dakin, S. C. Visual perception and its impairment in schizophrenia. Biol. Psychiatry 64, 40–47 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  122. Salinas, E. & Thier, P. Gain modulation: a major computational principle of the central nervous system. Neuron 27, 15–21 (2000).

    Article  CAS  PubMed  Google Scholar 

  123. Andersen, R. A., Snyder, L. H., Bradley, D. C. & Xing, J. Multimodal representation of space in the posterior parietal cortex and its use in planning movements. Annu. Rev. Neurosci. 20, 303–330 (1997).

    Article  CAS  PubMed  Google Scholar 

  124. Deneve, S. & Pouget, A. Basis functions for object-centered representations. Neuron 37, 347–359 (2003).

    Article  CAS  PubMed  Google Scholar 

  125. Salinas, E. Fast remapping of sensory stimuli onto motor actions on the basis of contextual modulation. J. Neurosci. 24, 1113–1118 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. Kepecs, A. & Raghavachari, S. Gating information by two-state membrane potential fluctuations. J. Neurophysiol. 97, 3015–3023 (2007).

    Article  CAS  PubMed  Google Scholar 

  127. Luo, S. X., Axel, R. & Abbott, L. F. Generating sparse and selective third-order responses in the olfactory system of the fly. Proc. Natl Acad. Sci. USA 107, 10713–10718, doi:10.1073/pnas.1005635107 (2010). This study explored the benefits of normalization in the fly olfactory system (see also REF. 27) in terms of coding for different odours

    Article  PubMed  PubMed Central  Google Scholar 

  128. Troy, J. B. & Enroth-Cugell, C. X and Y ganglion cells inform the cat's brain about contrast in the retinal image. Exp. Brain Res. 93, 383–390 (1993).

    Article  CAS  PubMed  Google Scholar 

  129. Ringach, D. L. Population coding under normalization. Vision Res. 50, 2223–2232 (2010).

    Article  PubMed  Google Scholar 

  130. DiCarlo, J. J. & Cox, D. D. Untangling invariant object recognition. Trends Cogn. Sci. 11, 333–341 (2007).

    Article  PubMed  Google Scholar 

  131. Shaw, M. L. in Attention and Performance VIII (ed. Nickerson, R. S.) 277–296 (Erlbaum, Hillsdale, New Jersey, 1980).

    Google Scholar 

  132. Palmer, J. Attention in visual search: Distinguishing four causes of a set-size effect. Curr. Dir. Psychol. Sci. 4, 118–123 (1995).

    Article  Google Scholar 

  133. Palmer, J., Verghese, P. & Pavel, M. The psychophysics of visual search. Vision Res. 40, 1227–1268 (2000).

    Article  CAS  PubMed  Google Scholar 

  134. Verghese, P. Visual search and attention: a signal detection theory approach. Neuron 31, 523–535 (2001).

    Article  CAS  PubMed  Google Scholar 

  135. Baldassi, S., Megna, N. & Burr, D. C. Visual clutter causes high-magnitude errors. PLoS Biol. 4, e56 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  136. Desimone, R. & Duncan, J. Neural mechanisms of selective visual attention. Annu. Rev. Neurosci. 18, 193–222 (1995).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  138. Barlow, H. B. in Sensory communication (ed. Rosenblith, W. A.) 217–234 (MIT Press, Cambridge, Massachusetts, 1961).

    Google Scholar 

  139. Geisler, W. S. Visual perception and the statistical properties of natural scenes. Annu. Rev. Psychol. 59, 167–192 (2008).

    Article  PubMed  Google Scholar 

  140. Lyu, S. & Simoncelli, E. P. Nonlinear extraction of independent components of natural images using radial gaussianization. Neural Comput. 21, 1485–1519 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  141. Schwartz, O. & Simoncelli, E. P. Natural signal statistics and sensory gain control. Nature Neurosci. 4, 819–825 (2001). This study showed how normalization can reduce redundancy in a population. Without normalization, responses of pairs of neurons in the primary visual cortex to natural images would not be independent. Normalization makes them more independent.

    Article  CAS  PubMed  Google Scholar 

  142. Carandini, M. in The Cognitive Neurosciences (ed. Gazzaniga, M. S.) 313–326 (MIT Press, Cambridge, Massachusetts, 2004).

    Google Scholar 

  143. Carandini, M. Melting the iceberg: contrast invariance in visual cortex. Neuron 54, 11–13 (2007).

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

We thank K. Harris, E. Simoncelli, J. Linden, R. Wilson and F. Rieke for helpful comments on the manuscript. his work was supported by awards from the Medical Research Council and by an Advanced Investigator award from the European Research Council (to M.C.) and by US National Institutes of Health grants R01-EY016752 and R01-EY019693 (to D.J.H.). M.C. holds the GlaxoSmithKline/Fight for Sight Chair in Visual Neuroscience.

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Glossary

Attention

The cognitive process of selecting one of many possible stimuli or events. In this Review, we focus on visuospatial attention. Rigorous methods have been developed for quantifying the effects of attention on performance.

Local contrast

(Also known as Weber contrast). An image that is obtained by subtracting the intensity at each location by the mean intensity averaged over a nearby region and dividing the result by that mean intensity.

Summation field

A region of sensory space that provides drive to a neuron. In many sensory systems, neurons derive their stimulus selectivity from a weighted sum of sensory inputs. The summation field comprises the weights in this sum.

Suppressive field

A region of sensory space providing suppression. In the normalization model, responses are suppressed by a weighted sum of activity of a population of neurons. The suppressive field comprises the weights in this weighted sum.

Grating contrast

(Also known as Michelson contrast). The contrast of a grating is given by twice the mean intensity minus the lowest intensity divided by the highest intensity. This is often expressed as a percentage. A 100% contrast grating is one in which the black bars have zero intensity.

Response saturation

Neural responses that increase with the strength of the input but progressively level off with very strong inputs. Normalization controls the strength at which responses saturate.

Normalization factor

A weighed sum of activity of a population of neurons, as determined by the suppressive field.

Winner-take-all

A neural computation in which the response depends on the maximum of the inputs.

MT

(Middle temporal area). Primate cortical area in which most neurons are selective for speed and direction of visual motion.

V4

Primate visual cortical area in which neurons respond selectively to combinations of visual features. The modulatory effects of attention on neural activity have been extensively studied in V4.

IT

(Inferotemporal cortex). A region of primate cortex in which neurons respond selectively to pictures of objects, faces and complex combinations of visual features.

Spectrotemporal receptive field

The receptive field of auditory neurons, which is typically defined in terms of sound frequency and time.

MST

(medial superior temporal area). Primate cortical area in which neurons combine information about visual motion, head movements and eye movements.

Heading

Trajectory of movement through the environment.

Lateral intraparietal area

Primate cortical area in which neural activity depends on visual input, eye movements, attention to visual input, intention to make an eye movement and factors that affect when and where to move the eyes (including the expected probability and magnitude of a reward).

Rational choice theory

Economic model of decision making.

Attentional gain factors

A key component of the normalization model of attention. Each attentional gain factor corresponds to a particular spatial location and sensory feature, and has a value that is larger than one when that location and/or feature is attended.

Gain control

Change in gain that multiplies or divides the amplitude of the response to an input.

Ongoing activity

Fluctuations in neural activity in the absence of any change in sensory inputs or task demands.

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Carandini, M., Heeger, D. Normalization as a canonical neural computation. Nat Rev Neurosci 13, 51–62 (2012). https://doi.org/10.1038/nrn3136

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