Summation and Division by Neurons in Primate Visual Cortex

“In particular, they have implications for contrast gain control (Carandini & Heeger, 1994; Foley, doi: 10 .1167 /7 .4 .7 Received July 17, 2006; published March 22, 2007 ISSN 1534-7362 * ARVO Downloaded From: https://jov.arvojournals.org/pdfaccess.ashx?url=/data/journals/jov/933521/ on…”

“Inhibition that acts divisively, rather than subtractively, has been implemented in feedforward models of primary visual cortex to account for a number of response features (Heeger 1992, 1993, Carandini and Heeger 1994).”

“The properties of the QR or EME1 decoder can be used to find biophysical correlates of neural decoding such as previously proposed for short term plasticity [71,72], non-linear dendrites [73] or lateral inhibition [74].”

“of cortical neurons [3,4], while several other studies have”

“One candidate mechanism underlying the stimulus-driven drop in FF is shunting inhibition, which can modulate firing rates of neighboring neurons through lateral connections (Mitchell and Silver, 2003) and has been proposed as a general cortical mechanism for response normalization (Carandini and Heeger, 1994; Reynolds…”

“Although simple, the tuning and form of this relationship is critical for processing of stimuli and network dynamics (Carandini and Heeger, 1994; Treue and Martínez Trujillo, 1999; Priebe and Ferster, 2008).”

“Renewed interest in contrast gain control sparked a new class of models (Foley & Chen, 1997; Watson & Solomon, 1997), which normalize the linear response of each unit by a measure of stimulus energy from a large pool of neurons (Carandini & Heeger, 1994; Geisler & Albrecht, 1992; Heeger, 1992).”

“Second, the two main operations deployed by the model (see below) can be implemented by biologically plausible neural microcircuits (Carandini & Heeger, 1994; Kouh & Poggio, 2008; Yu, Giese, & Poggio, 2002); evidence suggests that these operations are used in the visual cortex (Gawne & Martin,…”

“On the other hand, within the RC-circuit model class, Carandini and Heeger 1994 [10], Mikaelian and Simoncelli 2001 [12], and Mante et al 2008 [13] all included a gain control computation.”

“Divisive normalization is a ubiquitous neural computation wherein the output of each neuron is divided by the summed activity of a normalization pool (Carandini & Heeger 1994, 2011).”

“Shunting inhibition has long been considered as a mechanism for changing neuronal gain (Carandini & Heeger, 1994; Nelson, 2008).”

“Normalization models explain the nonlinear way that neurons sum their responses to individual stimuli when those stimuli appear together (Bonds 1989; Carandini et al. 1997; Carandini and Heeger 1994; Heeger et al. 1996; Morrone et al. 1982).”

“Although the population response at the binocular level was modeled as a linear combination of the monocular population responses, we observed qualitatively similar behavior when multiplicative interactions were implemented [37, 38].”

“It is known that non–linear computations on synaptic inputs are performed as early as from LGN and primary visual cortex on [52–54], and it is possible that these non–linearities provide the substrate required to compute the AND-like operations necessary for implementing Bayesian inference.”

“1b) is often assumed in rate-based models of neurons (Carandini and Heeger 1994; Chance and Abbott 2000), and is a central feature in both visual and motor control (Salinas and Thier 2000).”

“…lag psychophysical experiment, is not readily comparable to previous physiological studies in V1 that examined luminance or contrast effect on latency using different stimulus configurations (Carandini and Heeger 1994; Gawne et al. 1996; Maunsell and Gibson 1992; Oram 2010; Reich et al. 2001).”

“Typically, invariance was suggested to occur via a contrast gain control mechanism that normalized the response of a filter (receptive field) by the pooled responses of surrounding filters (Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997).”

“Consistent with models for the mediation of contrast gain control (Shapley and Victor, 1981; Carandini and Heeger, 1994), attention increased VEP amplitudes and reduced the phase-advance with contrast.”

“Here, we propose a variation of the biophysical normalization model of Carandini and Heeger (Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1999), in which r1/2 is a locally pooled activity that is orientation selective.”

“DN is believed to be implementable with the cortical neurons (Carandini & Heeger, 1994; Carandini, Heeger, & Senn, 2002), though the specific neural mechanism for such an implementation is still under debate (see Holt & Koch, 1997).”

“However, only a few of them have examined both features together, either unsuccessfully [42] or using parameter regimes that may not be relevant to the in vivo situation (membrane time constants: [49,50]; synaptic depressions: [52,53]).”

“…framework for this idea in terms of a divisive normalisationmechanism that derives from earliermodels of striate gain control (e.g. Bonds, 1989, 1991; Heeger, 1992; Geisler and Albrecht, 1992; Wilson and Humanski, 1993; Carandini and Heeger, 1994; Carandini et al., 1997; Wainwright et al., 2001).”

“In the above-mentioned studies on pursuit eye movements, vector averaging was assumed to result when all of the active neurons in the population make a contribution (summation) and there is a divisive normalization ( Carandini & Heeger, 1994; Heeger, Simoncelli, & Movshon, 1996; Simoncelli & Heeger, 1998), whereas win…”

“This is a much simpler and effective technique for robust purpose and has been widely used in saliency detection, such as in [21], [23], and [70]–[72].”

“If we consider divisive contrast gain control mechanisms that integrate stimuli across a broad range of spatial frequencies ( Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997; Heeger, 1992; Schwartz & Simoncelli, 2001), the dipper is predicted to be less pronounced in the broadbandnoise condition than with…”

“These elementary mathematical computations constitute building blocks for both the CNS (Carandini and Heeger, 1994; Peña and Konishi, 2001) and optimal encoding of stimuli in early sensory processing across modalities and species (Barlow and Levick, 1965, Laughlin, 1994; Carandini and Heeger, 1994; Harris et al., 200…”

“This could explain how V1 cells maintain orientation (and direction) selecSelected Readingtivity notably unchanged over a wide range of stimulus intensities and contrasts (Carandini and Heeger, 1994).”

“Each model area consists of a three-stage processing cascade of initial filtering, application of modulatory feedback effects and center-surround interactions leading to an activity normalization (Carandini and Heeger, 1994; Carandini et al., 1999; Kouh and Poggio, 2008; Carandini and Heeger, 2012).”

“A simple version is the so-called normalization model, which proposes a rescaling mechanism consisting of a feedback-driven inhibitory shunt whose strength is proportional to the average activity of a pool of excitatory neurons [9,10].”

“This result is in good accordance with the literature on single Type-I neurons, pointing out a subtractive and divisive effect of inhibition (Carandini and Heeger 1994; Doiron et al. 2001).”

“In the mammalian cortex, it been observed in sensory areas, including primary visual (V1) (Carandini et al. 1997; Carandini and Heeger 1994; Heeger 1992; Heeger et al. 1996) and auditory (A1) (Rabinowitz et al. 2011) and somatosensory cortex (S1) (Garcia-Lazaro et al. 2007), as well as in higher…”

“In the language of control theory, centering is a form of additive gain control while scaling is divisive (or multiplicative) in nature, and may be nonlinear (Carandini and Heeger, 1994).”

“(Other local contrast response models (Albrecht and Geisler, 1991; Carandini and Heeger, 1994) could be used.”

“Implementing local contrast normalization, as done by Robinson et al. (2007) in their LODOG version of the ODOG model, and which is characteristic of visual neurons (Carandini & Heeger, 1994; Cope et al, 2013; 2014), allows it to account for the zig-zag White stimulus.”

“This kind of pooling scheme can account for numerous nonlinear neural computations ( Britten and Heuer 1999 ; Car - andini and Heeger 1994 ; Carandini et al .”

“For example, it is well established that there is mutual suppression between spatiotemporally tuned channels in primary visual cortex (Bonds, 1989; Carandini & Heeger, 1994; Heeger, 1992; Morrone, Burr, & Maffei, 1982).”

“Population based models, such as the shunting inhibition model (Carandini and Heeger, 1994), use pooling of the responses from many neurones with varying stimulus preferences (orientation, spatial frequency, phase, etc.).”

“…the existence of cross-orientation inhibition has led to the suggestion that inhibition from cells tuned to dissimilar orientations plays an important role in setting the gain of cortical responses (Carandini and Heeger 1994; Carandini et al. 1997, 1999; Heeger 1992; Heeger et al. 1996).”

“Many neurons are thought to perform scaling operations on their input over a variety of time scales (Koch, 1999; Carandini and Heeger, 1994; Nelson, 1994; Salinas and Thier, 2000).”

“Normalization mechanisms (also commonly referred to as gain control) in this case, can be achieved by a feedforward (or recurrent) shunting inhibition (Torre and Poggio, 1978; Reichardt et al., 1983; Carandini and Heeger, 1994).”

“…& Tolhurst, 1978), saturation (Dean, 1981; Maffei & Fiorentini, 1973), expansion (Albrecht & Hamilton, 1982; Sclar & Freeman, 1982), phase advance (Carandini & Heeger, 1994; Dean & Tolhurst, 1986), and cross-orientation inhibition (Bonds, 1989; Morrone, Burr, & Maffei, 1982), to mention a few.”

“…by saturation (Robson, 1975) is largely prevented by a contrast gain control in striate cortex, which preserves the CRF shape for nonoptimal stimuli (Albrecht & Hamilton, 1982; Skottun et al., 1987; Albrecht & Geisler, 1991; Bonds, 1991; Geisler & Albrecht, 1992; Carandini & Heeger, 1994).”

“This can be related to the model of local gain control in primary visual cortex simple cells discussed in [5].”

“In the present paper, we study the dynamics of such a contrast gain control, by measuring detection thresholds for tests that are presented shortly after an onset of the background flicker (Wolfson & Graham, 2000; Snowden, 2001), and also after the offset of the background flicker ( Foley & Boynton, 1993 ).”

“As contrast rises, the cell’s excitatory response is increasingly inhibited by a ‘normalisation pool’ of neighbouring neurones (2,3).”

“Neurons that perform multiplicative (Salinas and Sejnowski, 2001; Salinas and Thier, 2000), and divisive (Carandini and Heeger, 1994; Heeger, 1992), operations are common throughout the brain.”

“…sodium and calcium conductances in the dendrites, which may also serve to amplify the synaptic inputs to different parts of the dendritic tree (Shepherd et ø1., 7985; Huguenard et aL, 7989; Pockberger, 1991; Bernander et ø1., 1994; Hirsch et ø1., 7995; Markram & Sakmann, 7994; Yuste et ø1., 7994 ).”

“The first phase was an early and rapid increase, starting 40 ms after the stimulus onset, reflecting an increase in neural population activity.”

“Without dendritic compartmentalization, recurrent inhibition itself possesses the ability to implement input normalization, as proposed in the models of sensory processing circuits (Carandini and Heeger, 1994; Hahnloser et al., 2000).”

“Shunting inhibition has been proposed as a possible mechanism for divisive interactions in a number of studies (Borg-Graham et al., 1998; Carandini and Heeger, 1994).”

“As the contrast increases, the reaction time for the V1 network dynamics will be accelerated (Discussion) similar to what was observed in single neuron studies (19, 20).”

“The nature of this conversion causes the output of an averaging scheme to become dependent on whether its computation occurs before or after the exponential transformation.”

“This form of cortical normalization was primarily introduced by Carandini and Heeger (1994), Heeger (1992a, 1992b, 1993), and gained support from subtly different models proposed by Carandini, Heeger, and Movshon (1997, 1999), Simoncelli and Schwartz (1999), Wilson and Kim (1998),Wilson, Loffler,…”

“Various studies have pointed out the importance of divisive normalization for explaining the tuning properties of cortical visual neurons (Carandini and Heeger, 1994; Rust et al., 2006), the processing of natural images (Schwartz and Simoncelli, 2001), and olfactory signals (Borst, 1983; Olsen et al.”

“This is puzzling because many previous studies of interactions between Fourier components report nonlinear interactions (Britten & Heuer, 1999; Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997; Heuer & Britten, 2002; Kumbhani et al., 2008; Liu & Sperling, 2006; Miura et al., 2014b;…”

“tuning therefore constitutes a strong constraint for understanding mechanisms underlying generation of orientation selectivity and has been the cornerstone in numerous modeling studies attempting to explain generation of orientation tuning [9,13–25].”

“Such a stage of divisive inhibition has been previously proposed to account for nonlinear effects in contrast and motion responses of V1 cells [20,21,22].”

“…curve, spatial frequency tuning, temporal frequency tuning, response phase, direction selectivity and speed tuning (Dean & Tolhurst, 1986; Carandini & Heeger, 1994; Levitt & Lund, 1997; Kapadia et al., 1999; Sceniak et al., 1999, 2002; Alitto & Usrey, 2004; Guo et al., 2005; Peterson et…”

“This filter effects the shape of the contrast tuning curve and also works in a divisive way (Heeger 1992; Carandini and Heeger 1994; Carandini et al. 1997).”

“However, contrast normalization is a well-established phenomenon in V1 (Carandini and Heeger, 1994, 2012; Carandini et al., 1997; Tolhurst and Heeger, 1997; Albrecht et al., 2002), and if cholinergic mechanisms were a main driver thereof we should have been able to uncover these with our models.”

“To compute the neural responses, the excitatory drive of each neuron was multiplied by its attentional gain factor [12] and then divided by its suppressive drive [5,6,12,32].”

“…cross-channel response is divisive normalization, which is a form of gain control that has been proposed as a canonical computational feature of neural responses in the visual cortex (Carandini & Heeger, 1994, 2012) but is yet to be demonstrated for gaze processing or social vision more broadly.”

“Positive evidence for pools of neurons doing precisely such a divisive normalisation is summarised in Carandini and Heeger (1994). Furthermore there needs to be a competitive process among the output neurons to finally select one according to Qy as the winning neuron.”

“…control effectively modulates synaptic weights and is considered a canonical neural computation [56] in that it has been described across primary [55] and extrastriate [57] visual cortex, auditory cortex [58], the superior colliculus [59], and the antenna lobe of fruit fl ies [60], among others.”

“Rather, we postulate an active process like the divisive normalization often described in visual-motionsensitive neurons in the cortex and generally attributed to some global inhibitory process (Heeger, 1992; Carandini and Heeger, 1994; Carandini et al., 1997; Simoncelli and Heeger, 1998; Britten and Heuer, 1999; Heue…”

“Simoncelli and Heeger [50] proposed a model of detecting motion energy in areas V1 and MT using linear spatiotemporal filters.”

“Given the similarity in name, it is important to point out that a gain change in the perceptual template model is qualitatively different from contrast gain control—a mechanism whose role is well established in visual processing (Heeger, 1992; Carandini and Heeger, 1994; Carandini et al., 1997).”

“…of the nonlinearity is a distinct feature of the masking effect (Foley, 1994; Watson and Solomon, 1997), and more importantly, it is a distinct feature of real neurons (Carandini and Heeger, 1994, 2012) with regard to the simplified neurons used in deep learning (Goodfellow et al., 2016).”