Abstract
Sub-additivity and variability are ubiquitous response motifs in the primary visual cortex (V1). Response sub-additivity enables the construction of useful interpretations of the visual environment, whereas response variability indicates the factors that limit the precision with which the brain can do this. There is increasing evidence that experimental manipulations that elicit response sub-additivity often also quench response variability. Here, we provide an overview of these phenomena and suggest that they may have common origins. We discuss empirical findings and recent model-based insights into the functional operations, computational objectives and circuit mechanisms underlying V1 activity. These different modelling approaches all predict that response sub-additivity and variability quenching often co-occur. The phenomenology of these two response motifs, as well as many of the insights obtained about them in V1, generalize to other cortical areas. Thus, the connection between response sub-additivity and variability quenching may be a canonical motif across the cortex.
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References
Born, R. T. & Tootell, R. B. Single-unit and 2-deoxyglucose studies of side inhibition in macaque striate cortex. Proc. Natl Acad. Sci. USA 88, 7071–7075 (1991).
Sceniak, M. P., Hawken, M. J. & Shapley, R. Visual spatial characterization of macaque v1 neurons. J. Neurophysiol. 85, 1873–1887 (2001).
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).
Coen-Cagli, R., Kohn, A. & Schwartz, O. Flexible gating of contextual influences in natural vision. Nat. Neurosci. 18, 1648 (2015).
Albrecht, D. G. & Hamilton, D. B. Striate cortex of monkey and cat: contrast response function. J. Neurophysiol. 48, 217–237 (1982).
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. B Biol. Sci. 216, 335–354 (1982).
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).
DeAngelis, G. C., Robson, J. G., Ohzawa, I. & Freeman, R. D. Organization of suppression in receptive fields of neurons in cat visual cortex. J. Neurophysiol. 68, 144–163 (1992).
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).
Tolhurst, D. & Heeger, D. Comparison of contrast-normalization and threshold models of the responses of simple cells in cat striate cortex. Vis. Neurosci. 14, 293–309 (1997).
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).
Azouz, R. & Gray, C. M. Cellular mechanisms contributing to response variability of cortical neurons in vivo. J. Neurosci. 19, 2209–2223 (1999).
Sadagopan, S. & Ferster, D. Feedforward origins of response variability underlying contrast invariant orientation tuning in cat visual cortex. Neuron 74, 911–923 (2012).
Andoni, S., Tan, A. & Priebe, N. J. in The New Visual Neurosciences 367–380 (MIT Press, 2013).
Tomko, G. J. & Crapper, D. R. Neuronal variability: non-stationary responses to identical visual stimuli. Brain Res. 79, 405–418 (1974).
Heggelund, P. & Albus, K. Response variability and orientation discrimination of single cells in striate cortex of cat. Exp. Brain Res. 32, 197–211 (1978).
Vogels, R., Spileers, W. & Orban, G. A. The response variability of striate cortical neurons in the behaving monkey. Exp. Brain Res. 77, 432–436 (1989).
Shadlen, M. & Newsome, W. T. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18, 3870–3896 (1998).
Talluri, B. C. et al. Activity in primate visual cortex is minimally driven by spontaneous movements. Nat. Neurosci. 26, 1953–1959 (2023).
Tolhurst, D. J., Movshon, J. A. & Thompson, I. D. The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast. Exp. Brain Res. 41, 414–419 (1981).
Orbán, G., Berkes, P., Fiser, J. & Lengyel, M. Neural variability and sampling-based probabilistic representations in the visual cortex. Neuron 92, 530–543 (2016).
Churchland, M. M. et al. Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat. Neurosci. 13, 369–378 (2010).
Arandia-Romero, I., Tanabe, S., Drugowitsch, J., Kohn, A. & Moreno-Bote, R. Multiplicative and additive modulation of neuronal tuning with population activity affects encoded information. Neuron 89, 1305–1316 (2016).
Rosenbaum, R., Smith, M., Kohn, A., Rubin, J. & Doiron, B. The spatial structure of correlated neuronal variability. Nat. Neurosci. 20, 107–114 (2017).
Davis, Z. W., Muller, L., Martinez-Trujillo, J., Sejnowski, T. & Reynolds, J. H. Spontaneous travelling cortical waves gate perception in behaving primates. Nature 587, 432–436 (2020).
Kenet, T., Bibitchkov, D., Tsodyks, M., Grinvald, A. & Arieli, A. Spontaneously emerging cortical representations of visual attributes. Nature 425, 954–956 (2003).
Berkes, P., Orbán, G., Lengyel, M. & Fiser, J. Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment. Science 331, 83–87 (2011).
Goris, R. L. T., Movshon, J. A. & Simoncelli, E. P. Partitioning neuronal variability. Nat. Neurosci. 17, 858–865 (2014).
Ecker, A. S. et al. State dependence of noise correlations in macaque primary visual cortex. Neuron 82, 235–248 (2014).
Rabinowitz, N. C., Goris, R. L., Cohen, M. & Simoncelli, E. P. Attention stabilizes the shared gain of V4 populations. eLife 4, e08998 (2015).
Goris, R. L., Ziemba, C. M., Movshon, J. A. & Simoncelli, E. P. Slow gain fluctuations limit benefits of temporal integration in visual cortex. J. Vis. 18, 8 (2018).
Coen-Cagli, R. & Solomon, S. S. Relating divisive normalization to neuronal response variability. J. Neurosci. 39, 7344–7356 (2019).
Hénaff, O. J., Boundy-Singer, Z. M., Meding, K., Ziemba, C. M. & Goris, R. L. T. Representation of visual uncertainty through neural gain variability. Nat. Commun. 11, 2513 (2020).
DiCarlo, J. J., Zoccolan, D. & Rust, N. C. How does the brain solve visual object recognition? Neuron 73, 415–434 (2012).
Pitkow, X. & Angelaki, D. E. Inference in the brain: statistics flowing in redundant population codes. Neuron 94, 943–953 (2017).
Moreno-Bote, R. et al. Information-limiting correlations. Nat. Neurosci. 17, 1410 (2014).
Beck, J. M., Ma, W. J., Pitkow, X., Latham, P. E. & Pouget, A. Not noisy, just wrong: the role of suboptimal inference in behavioral variability. Neuron 74, 30–39 (2012).
Snyder, A. C., Morais, M. J., Kohn, A. & Smith, M. A. Correlations in v1 are reduced by stimulation outside the receptive field. J. Neurosci. 34, 11222–11227 (2014).
Festa, D., Aschner, A., Davila, A., Kohn, A. & Coen-Cagli, R. Neuronal variability reflects probabilistic inference tuned to natural image statistics. Nat. Commun. 12, 3635 (2021).
Henry, C. A. & Kohn, A. Feature representation under crowding in macaque v1 and v4 neuronal populations. Curr. Biol. 32, 5126–5137 (2022).
Nassi, J. J., Avery, M. C., Cetin, A. H., Roe, A. W. & Reynolds, J. H. Optogenetic activation of normalization in alert macaque visual cortex. Neuron 86, 1504–1517 (2015).
Isaacson, J. & Scanziani, M. How inhibition shapes cortical activity. Neuron 72, 231–243 (2011).
Adesnik, H., Bruns, W., Taniguchi, H., Huang, Z. J. & Scanziani, M. A neural circuit for spatial summation in visual cortex. Nature 490, 226–231 (2012).
Atallah, B. V., Bruns, W., Carandini, M. & Scanziani, M. Parvalbumin-expressing interneurons linearly transform cortical responses to visual stimuli. Neuron 73, 159–170 (2012).
Sanzeni, A. et al. Inhibition stabilization is a widespread property of cortical networks. eLife 9, e54875 (2020).
Keller, A. J. et al. A disinhibitory circuit for contextual modulation in primary visual cortex. Neuron 108, 1181–1193 (2020).
Millman, D. J. et al. VIP interneurons in mouse primary visual cortex selectively enhance responses to weak but specific stimuli. eLife 9, e55130 (2020).
Veit, J., Handy, G., Mossing, D. P., Doiron, B. & Adesnik, H. Cortical VIP neurons locally control the gain but globally control the coherence of gamma band rhythms. Neuron 111, 405–417 (2023).
Stringer, C. et al. Spontaneous behaviors drive multidimensional, brainwide activity. Science 364, eaav7893 (2019).
Stringer, C., Michaelos, M., Tsyboulski, D., Lindo, S. E. & Pachitariu, M. High-precision coding in visual cortex. Cell 184, 2767–2778 (2021).
Weiss, O., Bounds, H. A., Adesnik, H. & Coen-Cagli, R. Modeling the diverse effects of divisive normalization on noise correlations. PloS Comput. Biol. 19, e1011667 (2023).
Hubel, D. H. & Wiesel, T. N. Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160, 106-54 (1962).
Barlow, H. B., Blakemore, C. & Pettigrew, J. D. The neural mechanism of binocular depth discrimination. J. Physiol. 193, 327–342 (1967).
Priebe, N. J. & Ferster, D. A. Inhibition, spike threshold, and stimulus selectivity in primary visual cortex. Neuron 57, 482–497 (2008).
Priebe, N. J. & Ferster, D. Mechanisms underlying cross-orientation suppression in cat visual cortex. Nat. Neurosci. 9, 552–561 (2006).
Freeman, T. C., Durand, S., Kiper, D. C. & Carandini, M. Suppression without inhibition in visual cortex. Neuron 35, 759–771 (2002).
Angelucci, A. et al. Circuits and mechanisms for surround modulation in visual cortex. Annu. Rev. Neurosci. 40, 425–451 (2017).
Nurminen, L. & Angelucci, A. Multiple components of surround modulation in primary visual cortex: multiple neural circuits with multiple functions? Vis. Res. 104, 47–56 (2014).
Sillito, A. M., Grieve, K. L., Jones, H. E., Cudeiro, J. & Davis, J. Visual cortical mechanisms detecting focal orientation discontinuities. Nature 378, 492–496 (1995).
Walker, G. A., Ohzawa, I. & Freeman, R. D. Asymmetric suppression outside the classical receptive field of the visual cortex. J. Neurosci. 19, 10536–10553 (1999).
Albrecht, D. G., Geisler, W. S., Frazor, R. A. & Crane, A. M. Visual cortex neurons of monkeys and cats: temporal dynamics of the contrast response function. J. Neurophysiol. 88, 888–913 (2002).
Geisler, W. S. & Albrecht, D. G. Cortical neurons: isolation of contrast gain control. Vis. Res. 32, 1409–1410 (1992).
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).
Webb, B. S., Dhruv, N. T., Solomon, S. G., Tailby, C. & Lennie, P. Early and late mechanisms of surround suppression in striate cortex of macaque. J. Neurosci. 25, 11666–11675 (2005).
Henry, C. A., Joshi, S., Xing, D., Shapley, R. M. & Hawken, M. J. Functional characterization of the extraclassical receptive field in macaque v1: contrast, orientation, and temporal dynamics. J. Neurosci. 33, 6230–6242 (2013).
Walker, G. A., Ohzawa, I. & Freeman, R. D. Binocular cross-orientation suppression in the cat’s striate cortex. J. Neurophysiol. 79, 227–239 (1998).
Sengpiel, F. & Vorobyov, V. Intracortical origins of interocular suppression in the visual cortex. J. Neurosci. 25, 6394–6400 (2005).
Chen, S. C.-Y. et al. Similar neural and perceptual masking effects of low-power optogenetic stimulation in primate v1. eLife 11, e68393 (2022).
Werner, G. & Mountcastle, V. B. The variability of central neural activity in a sensory system, and its implications for the central reflection of sensory events. J. Neurophysiol. 26, 958–977 (1963).
Parker, A. J. & Newsome, W. T. Sense and the single neuron: probing the physiology of perception. Annu. Rev. Neurosci. 21, 227–277 (1998).
Vogels, R. & Orban, G. A. How well do response changes of striate neurons signal differences in orientation: a study in the discriminating monkey. J. Neurosci. 10, 3543–3558 (1990).
Goris, R. L., Ziemba, C. M., Stine, G. M., Simoncelli, E. P. & Movshon, J. A. Dissociation of choice formation and choice-correlated activity in macaque visual cortex. J. Neurosci. 37, 5195–5203 (2017).
Jasper, A. I., Tanabe, S. & Kohn, A. Predicting perceptual decisions using visual cortical population responses and choice history. J. Neurosci. 39, 6714–6727 (2019).
Britten, K. H., Shadlen, M. N., Newsome, W. T. & Movshon, J. A. The analysis of visual motion: a comparison of neuronal and psychophysical performance. J. Neurosci. 12, 4745–4765 (1992).
Dayan, P. & Abbott, L. F. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, 2005).
Tolhurst, D. J., Movshon, J. A. & Dean, A. F. The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vis. Res. 23, 775–785 (1983).
Charles, A. S., Park, M., Weller, J. P., Horwitz, G. D. & Pillow, J. W. Dethroning the Fano factor: a flexible, model-based approach to partitioning neural variability. Neural Comput. 30, 1012–1045 (2018).
Nurminen, L., Bijanzadeh, M. & Angelucci, A. Size tuning of neural response variability in laminar circuits of macaque primary visual cortex. Preprint at bioRxiv https://doi.org/10.1101/2023.01.17.524397 (2023).
Troyer, T. W., Krukowski, A. E., Priebe, N. J. & Miller, K. D. Contrast-invariant orientation tuning in cat visual cortex: feedforward tuning and correlation-based intracortical connectivity. J. Neurosci. 18, 5908–5927 (1998).
McLaughlin, D., Shapley, R., Shelley, M. & Wielaard, D. J. A neuronal network model of macaque primary visual cortex (v1): orientation selectivity and dynamics in the input layer 4cα. Proc. Natl Acad. Sci. USA 97, 8087–8092 (2000).
Rubin, D. B., Van Hooser, S. D. & Miller, K. D. The stabilized supralinear network: a unifying circuit motif underlying multi-input integration in sensory cortex. Neuron 85, 402–417 (2015).
Heeger, D. J. & Zemlianova, K. O. A recurrent circuit implements normalization, simulating the dynamics of v1 activity. Proc. Natl Acad. Sci. USA 117, 22494–22505 (2020).
Olshausen, B. A. & Field, D. J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607–609 (1996).
Bell, A. J. & Sejnowski, T. J. The ‘independent components’ of natural scenes are edge filters. Vis. Res. 37, 3327–3338 (1997).
Rao, R. P. N. & Ballard, D. H. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nat. Neurosci. 2, 79–87 (1999).
Schwartz, O. & Simoncelli, E. P. Natural signal statistics and sensory gain control. Nat. Neurosci. 4, 819–825 (2001).
Wiskott, L. & Sejnowski, T. J. Slow feature analysis: unsupervised learning of invariances. Neural Comput. 14, 715–770 (2002).
Coen-Cagli, R., Dayan, P. & Schwartz, O. Statistical models of linear and nonlinear contextual interactions in early visual processing. In Advances in Neural Information Processing Systems 22 (eds Bengio, Y. et al.) https://proceedings.neurips.cc/paper_files/paper/2009/file/be3159ad04564bfb90db9e32851ebf9c-Paper.pdf (Curran Associates, 2009).
Movshon, J. A., Thompson, I. D. & Tolhurst, D. J. Receptive field organization of complex cells in the cat’s striate cortex. J. Physiol. 283, 79–99 (1978).
Heeger, D. J. Normalization of cell responses in cat striate cortex. Vis. Neurosci. 9, 181–197 (1992).
Rust, N. C., Schwartz, O., Movshon, J. A. & Simoncelli, E. P. Spatiotemporal elements of macaque V1 receptive fields. Neuron 46, 945–956 (2005).
Vintch, B., Movshon, J. A. & Simoncelli, E. P. A convolutional subunit model for neuronal responses in macaque v1. J. Neurosci. 35, 14829–14841 (2015).
Goris, R. L., Simoncelli, E. P. & Movshon, J. A. Origin and function of tuning diversity in macaque visual cortex. Neuron 88, 819–831 (2015).
Freeman, J. & Simoncelli, E. P. Metamers of the ventral stream. Nat. Neurosci. 14, 1195–1201 (2011).
Rust, N. C., Mante, V., Simoncelli, E. P. & Movshon, J. A. How MT cells analyze the motion of visual patterns. Nat. Neurosci. 9, 1421–1431 (2006).
Goris, R. L., Putzeys, T., Wagemans, J. & Wichmann, F. A. A neural population model for visual pattern detection. Psychol. Rev. 120, 472 (2013).
Hénaff, O. J., Goris, R. L. & Simoncelli, E. P. Perceptual straightening of natural videos. Nat. Neurosci. 22, 984–991 (2019).
Carandini, M. & Heeger, D. J. Normalization as a canonical neural computation. Nat. Rev. Neurosci. 13, 51–62 (2012).
Cadena, S. A. et al. Deep convolutional models improve predictions of macaque v1 responses to natural images. PloS Comput. Biol. 15, e1006897 (2019).
Albrecht, D. G. & Geisler, W. S. Motion selectivity and the contrast-response function of simple cells in the visual cortex. Vis. Neurosci. 7, 531–546 (1991).
Geisler, W. S. Visual perception and the statistical properties of natural scenes. Annu. Rev. Psychol. 59, 167–192 (2008).
Yamins, D. L. K. & DiCarlo, J. J. Using goal-driven deep learning models to understand sensory cortex. Nat. Neurosci. 19, 356–365 (2016).
Barlow, H. Possible principles underlying the transformations of sensory messages. Sens. Commun. 1, 217–234 (1961).
Simoncelli, E. P. & Olshausen, B. A. Natural image statistics and neural representation. Annu. Rev. Psychol. 24, 1193–1216 (2001).
van Hateren, J. H. & Ruderman, D. L. Independent component analysis of natural image sequences yields spatio-temporal filters similar to simple cells in primary visual cortex. Proc. R. Soc. Lond. B Biol. Sci. 265, 2315–2320 (1998).
Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27 379–423 (1948).
Ernst, M. O. & Banks, M. S. Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415, 429–433 (2002).
Knill, D. C. & Pouget, A. The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci. 27, 712–719 (2004).
Boundy-Singer, Z. M., Ziemba, C. M. & Goris, R. L. T. Confidence reflects a noisy decision reliability estimate. Nat. Hum. Behav. 7, 142–154 (2023).
Ma, W. J., Beck, J. M., Latham, P. E. & Pouget, A. Bayesian inference with probabilistic population codes. Nat. Neurosci. 9, 1432–1438 (2006).
Jazayeri, M. & Movshon, J. A. Optimal representation of sensory information by neural populations. Nat. Neurosci. 9, 690–696 (2006).
Buesing, L., Bill, J., Nessler, B. & Maass, W. Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons. PloS Comput. Biol. 7, e1002211 (2011).
Lochmann, T. & Deneve, S. Neural processing as causal inference. Curr. Opin. Neurobiol. 21, 774–781 (2011).
Pouget, A., Beck, J. M., Ma, W. J. & Latham, P. E. Probabilistic brains: knowns and unknowns. Nat. Neurosci. 16, 1170–1178 (2013).
Meyniel, F., Sigman, M. & Mainen, Z. F. Confidence as Bayesian probability: from neural origins to behavior. Neuron 88, 78–92 (2015).
Pouget, A., Drugowitsch, J. & Kepecs, A. Confidence and certainty: distinct probabilistic quantities for different goals. Nat. Neurosci. 19, 366–374 (2016).
Lange, R. D. & Haefner, R. M. Task-induced neural covariability as a signature of approximate Bayesian learning and inference. PloS Comput. Biol. 18, e21009557 (2022).
Fiser, J., Berkes, P., Orbán, G. & Lengyel, M. Statistically optimal perception and learning: from behavior to neural representations. Trends Cogn. Sci. 14, 119–130 (2010).
Hoyer, P. & Hyvarinen, A. Interpreting neural response variability as Monte Carlo sampling of the posterior. Advances in Neural Information Processing Systems 15 (2002).
Mareschal, I. & Shapley, R. M. Effects of contrast and size on orientation discrimination. Vis. Res. 44, 57–67 (2004).
Echeveste, R., Aitchison, L., Hennequin, G. & Lengyel, M. Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference. Nat. Neurosci. 23, 1138–1149 (2020).
Coen-Cagli, R., Dayan, P. & Schwartz, O. Cortical surround interactions and perceptual salience via natural scene statistics. PloS Comput. Biol. 8, e1002405 (2012).
Barbera, D., Priebe, N. J. & Glickfeld, L. L. Feedforward mechanisms of cross-orientation interactions in mouse v1. Neuron 110, 297–311 (2022).
Lauritzen, T. Z., Krukowski, A. E. & Miller, K. D. Local correlation-based circuitry can account for responses to multi-grating stimuli in a model of cat V1. J. Neurophysiol. 86, 1803–1815 (2001).
Kayser, A. S., Priebe, N. J. & Miller, K. D. Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning. J. Neurophysiol. 85, 2130–2149 (2001).
Carandini, M., Heeger, D. J. & Senn, W. A synaptic explanation of suppression in visual cortex. J. Neurosci. 22, 10053–10065 (2002).
Kara, P., Reinagel, P. & Reid, R. C. Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron 27, 635–646 (2000).
Henry, C. A., Jazayeri, M., Shapley, R. M. & Hawken, M. J. Distinct spatiotemporal mechanisms underlie extra-classical receptive field modulation in macaque V1 microcircuits. eLife 9, e54264 (2020).
Litwin-Kumar, A. & Doiron, B. Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat. Neurosci. 15, 1498–1505 (2012).
Ahmadian, Y., Rubin, D. B. & Miller, K. D. Analysis of the stabilized supralinear network. Neural Comput. 25, 1994–2037 (2013).
Hennequin, G., Ahmadian, Y., Rubin, D. B., Lengyel, M. & Miller, K. D. The dynamical regime of sensory cortex: stable dynamics around a single stimulus-tuned attractor account for patterns of noise variability. Neuron 98, 846–860 (2018).
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).
Douglas, R. J., Koch, C., Mahowald, M., Martin, K. A. & Suarez, H. H. Recurrent excitation in neocortical circuits. Science 269, 981–985 (1995).
Bosking, W. H., Zhang, Y., Schofield, B. & Fitzpatrick, D. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17, 2112–2127 (1997).
Borg-Graham, L. J., Monier, C. & Frégnac, Y. Visual input evokes transient and strong shunting inhibition in visual cortical neurons. Nature 393, 369–373 (1998).
Gilbert, C. D. & Wiesel, T. N. Morphology and intracortical projections of functionally characterised neurones in the cat visual cortex. Nature 280, 120–125 (1979).
Softky, W. R. & Koch, C. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334–350 (1993).
Mainen, Z. F. & Sejnowski, T. J. Reliability of spike timing in neocortical neurons. Science 268, 1503–1506 (1995).
Schneidman, E., Freedman, B. & Segev, I. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 10, 1679–1703 (1998).
O’Donnell, C. & van Rossum, M. C. Systematic analysis of the contributions of stochastic voltage gated channels to neuronal noise. Front. Comput. Neurosci. 8, 105 (2014).
Stevens, C. F. & Zador, A. M. Input synchrony and the irregular firing of cortical neurons. Nat. Neurosci. 1, 210–217 (1998).
DeWeese, M. R. & Zador, A. M. Non-Gaussian membrane potential dynamics imply sparse, synchronous activity in auditory cortex. J. Neurosci. 26, 12206–12218 (2006).
Tsodyks, M. V. & Sejnowski, T. Rapid state switching in balanced cortical network models. Network 6, 111–124 (1995).
Van Vreeswijk, C. & Sompolinsky, H. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724–1726 (1996).
Troyer, T. W. & Miller, K. D. Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Comput. 9, 971–983 (1997).
Amit, D. & Brunel, N. Dynamics of a recurrent network of spiking neurons before and following learning. Netw. Comput. Neural Syst. 8, 373–404 (1997).
Ahmadian, Y. & Miller, K. D. What is the dynamical regime of cerebral cortex? Neuron 109, 3373–3391 (2021).
Kadmon, J. & Sompolinsky, H. Transition to chaos in random neuronal networks. Phys. Rev. X 5, 041030 (2015).
Deco, G. & Hugues, E. Neural network mechanisms underlying stimulus driven variability reduction. PloS Comput. Biol. 8, e1002395 (2012).
Smith, G. B., Hein, B., Whitney, D. E., Fitzpatrick, D. & Kaschube, M. Distributed network interactions and their emergence in developing neocortex. Nat. Neurosci. 21, 1600–1608 (2018).
Trägenap, S., Whitney, D. E., Fitzpatrick, D. & Kaschube, M. Visual experience drives the development of novel and reliable visual representations from endogenously structured networks. J. Vis. 23, 5225–5225 (2023).
Ponce-Alvarez, A., Thiele, A., Albright, T. D., Stoner, G. R. & Deco, G. Stimulus-dependent variability and noise correlations in cortical MT neurons. Proc. Natl Acad. Sci. USA 110, 13162–13167 (2013).
Bressloff, P. C. Stochastic neural field model of stimulus-dependent variability in cortical neurons. PloS Comput. Biol. 15, e1006755 (2019).
Rajan, K., Abbott, L. & Sompolinsky, H. Stimulus-dependent suppression of chaos in recurrent neural networks. Phys. Rev. E 82, 011903 (2010).
Mossing, D. P., Veit, J., Palmigiano, A., Miller, K. D. & Adesnik, H. Antagonistic inhibitory subnetworks control cooperation and competition across cortical space. Preprint at bioRxiv https://doi.org/10.1101/2021.03.31.437953 (2021).
Di Santo, S. et al. Unifying model for three forms of contextual modulation including feedback input from higher visual areas. Preprint at bioRxiv https://doi.org/10.1101/2022.05.27.493753 (2022).
Tsodyks, M. V., Skaggs, W. E., Sejnowski, T. J. & McNaughton, B. L. Paradoxical effects of external modulation of inhibitory interneurons. J. Neurosci. 17, 4382–4388 (1997).
Ekelmans, P., Kraynyukova, N. & Tchumatchenko, T. Targeting operational regimes of interest in recurrent neural networks. PloS Comput. Biol. 19, e1011097 (2023).
Murphy, B. K. & Miller, K. D. Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61, 635–648 (2009).
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).
Holt, C. J., Miller, K. D. & Ahmadian, Y. The stabilized supralinear network accounts for the contrast dependence of visual cortical gamma oscillations. Preprint at bioRxiv https://doi.org/10.1101/2023.05.11.540442 (2023).
Spoerer, C. J., Kietzmann, T. C., Mehrer, J., Charest, I. & Kriegeskorte, N. Recurrent neural networks can explain flexible trading of speed and accuracy in biological vision. PloS Comput. Biol. 16, e1008215 (2020).
Kar, K., Kubilius, J., Schmidt, K., Issa, E. B. & DiCarlo, J. J. Evidence that recurrent circuits are critical to the ventral stream’s execution of core object recognition behavior. Nat. Neurosci. 22, 974–983 (2019).
Nayebi, A. et al. Task-driven convolutional recurrent models of the visual system. Advances in Neural Information Processing Systems 31 (2018).
Miller, M., Chung, S. & Miller, K. D. Divisive feature normalization improves image recognition performance in AlexNet. In International Conference on Learning Representations (Vienna, 2021).
Maheswaranathan, N. et al. Interpreting the retinal neural code for natural scenes: from computations to neurons. Neuron 111, 2742–2755 (2023).
Burg, M. F. et al. Learning divisive normalization in primary visual cortex. PloS Comput. Biol. 17, e1009028 (2021).
Pan, X., DeForge, A. & Schwartz, O. Generalizing biological surround suppression based on center surround similarity via deep neural network models. PloS Comput. Biol. 19, e1011486 (2023).
Zoccolan, D., Cox, D. D. & DiCarlo, J. J. Multiple object response normalization in monkey inferotemporal cortex. J. Neurosci. 25, 8150–8164 (2005).
Olsen, S. R., Bhandawat, V. & Wilson, R. I. Divisive normalization in olfactory population codes. Neuron 66, 287–299 (2010).
Rabinowitz, N. C., Willmore, B. D., Schnupp, J. W. & King, A. J. Contrast gain control in auditory cortex. Neuron 70, 1178–1191 (2011).
Ohshiro, T., Angelaki, D. E. & DeAngelis, G. C. A neural signature of divisive normalization at the level of multisensory integration in primate cortex. Neuron 95, 399–411 (2017).
Louie, K., Grattan, L. E. & Glimcher, P. W. Reward value-based gain control: divisive normalization in parietal cortex. J. Neurosci. 31, 10627–10639 (2011).
Churchland, A. K., Kiani, R. & Shadlen, M. N. Decision-making with multiple alternatives. Nat. Neurosci. 11, 693–702 (2008).
Fenno, L., Yizhar, O. & Deisseroth, K. The development and application of optogenetics. Annu. Rev. Neurosci. 34, 389–412 (2011).
Cohen, M. R. & Kohn, A. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14, 811 (2011).
Chung, S. & Abbott, L. Neural population geometry: an approach for understanding biological and artificial neural networks. Curr. Opin. Neurobiol. 70, 137–144 (2021).
Kriegeskorte, N. & Wei, X.-X. Neural tuning and representational geometry. Nat. Rev. Neurosci. 22, 703–718 (2021).
Kohn, A. & Smith, M. A. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25, 3661–3673 (2005).
Cohen, M. R. & Maunsell, J. H. Attention improves performance primarily by reducing interneuronal correlations. Nat. Neurosci. 12, 1594–1600 (2009).
Mitchell, J. F., Sundberg, K. A. & Reynolds, J. H. Spatial attention decorrelates intrinsic activity fluctuations in macaque area v4. Neuron 63, 879–888 (2009).
Ruff, D. A. & Cohen, M. R. Global cognitive factors modulate correlated response variability between v4 neurons. J. Neurosci. 34, 16408–16416 (2014).
Verhoef, B.-E. & Maunsell, J. H. Attention-related changes in correlated neuronal activity arise from normalization mechanisms. Nat. Neurosci. 20, 969–977 (2017).
Hennequin, G. & Lengyel, M. Characterizing variability in nonlinear recurrent neuronal networks. Preprint at https://doi.org/10.48550/arXiv.1610.03110 (2016).
Geisler, W. S. & Albrecht, D. Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty. Vis. Res. 35, 2723–2730 (1995).
Wainwright, M. J. & Simoncelli, E. P. in Adv. Neural Information Processing Systems (NIPS*99) Vol. 12 (eds Solla, S. A. et al.) 855–861 (MIT Press, 2000).
Churchland, A. K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818–831 (2011).
Acknowledgements
We thank D. Heeger, S. Martiniani and Y. Ahmadian for the helpful discussions. This work was supported by the US National Institutes of Health grants EY032999 (R.L.T.G.), EY030578 and DA056400 (R.C.-C.), EY025102, EY024071 and NS120562 (N.J.P), and U01NS108683 and U19NS107613 (K.D.M.), by CAREER award #2146369 (R.L.T.G.), by award DBI-1707398 (K.D.M.) from the National Science Foundation, by a Wellcome Trust Investigator Award in Science 212262/Z/18/Z (M.L.), and by Simons Foundation award 543017 and the Gatsby Charitable Foundation (K.D.M.).
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Goris, R.L.T., Coen-Cagli, R., Miller, K.D. et al. Response sub-additivity and variability quenching in visual cortex. Nat. Rev. Neurosci. 25, 237–252 (2024). https://doi.org/10.1038/s41583-024-00795-0
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DOI: https://doi.org/10.1038/s41583-024-00795-0
