Normalization as a canonical neural computation

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

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

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

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

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).

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

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

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

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

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).

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

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).

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

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

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

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).

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

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).

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.

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

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

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

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

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

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).

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

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).

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

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

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).

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).

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

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

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

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

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).

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

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

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

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.

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).

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

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).

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

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

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.

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).

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.

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

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).

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).

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).

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).

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).

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).

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

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.

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).

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).

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).

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).

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

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

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).

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

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).

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

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

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

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

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).

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).

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).

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.

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

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

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).

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

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

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

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).

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

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

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

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).

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

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

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).

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

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

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

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

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).

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).

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).

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).

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

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

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

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

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

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

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

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

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).

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

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

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

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

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).

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

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

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).

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

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).

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

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).

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

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

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

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

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

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).

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

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

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

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

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).

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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