Summation and Division by Neurons in Primate Visual Cortex

“…a given broad feature dimension, however, strong local interactions between filters sensitive to different properties of that feature (for example, between different orientations within the broad orientation feature) have been precisely characterized, both in physiology 60 and psy-chophysics 45 .”

“Although the transformation from stimulus to neural activity is not known exactly, reasonable quantitative models do exist, especially for V1 (Heeger, 1992, 1993; Carandini and Heeger, 1994).”

“Indeed, the normalization model was first developed to account for the physiological responses of neurons in the primary visual cortex (V1”

“Inhibitory networks become powerful and organized so that they suppress alternative patterns of excitation (Galarreta & Hestrin, 2001; Zheng & Knudsen, 2001; Hensch et al., 1998; Carandini & Heeger, 1994).”

“…visual cortex offer a classical example of gain modulation, where two independent properties of a visual stimulus, contrast, and orientation, interact in a multiplicative manner in generating spike output (Anderson et al., 2000; Carandini and Heeger, 1994; Miller, 2003; Sclar and Freeman, 1982).”

“This saves having to replicate the training set over all possible values of image contrast, and is a very simpli ed model of the contrast normalization which may take place in the mammalian visual system (Carandini and Heeger, 1994).”

“…in the early 1990s to explain a variety of such suppressive phenomena evident in the response properties of V1 neurons (Albrecht and Geisler, 1991; Carandini and Heeger, 1994; Carandini et al., 1997; Heeger, 1991, 1992a, 1992b, 1993; Nestares and Heeger, 1997; Robson, 1988; Tolhurst and Heeger,…”

“The normalization scales the activations of a map to the squared difference between its global maximum and the average of the remaining (local) maxima in the map (such a normalization has been used successfully to explain single-cell behavior in primary visual cortex; Carandini & Heeger, 1994).”

“Although mechanisms that would produce multiplicative scaling have been described (Albrecht and Geisler, 1991; Carandini and Heeger, 1994), it is not known why such separability of response sensitivities may be important for cortical processing.”

“…neurophysiology, and they have driven the development of increasingly detailed models of the underlying cortical circuit (Albrecht & Geisler 1991, Carandini & Heeger 1994, Carandini et al. 1997, Grossberg 1973, Heeger 1992, McLaughlin et al. 2000, Murphy & Miller 2003, Somers et al. 1995,…”

“One is response saturation (Maffei and Fiorentini, 1973; Dean, 1981a; Albrecht and Hamilton, 1982; Ohzawa et al., 1982; Li and Creutzfeldt, 1984; Sclar et al., 1990; Bonds, 1991; Carandini and Heeger, 1994).”

“Instead, it causes an increase in membrane conductance, which divides the excitatory synaptic current (Carandini and Heeger, 1994).”

“Many of these behaviors can be accounted for by incorporating response normalization (Robson, 1988; Bonds, 1989; Albrecht and Geisler, 1991; Heeger 1991, 1992a,b, 1993; DeAngelis et al., 1992; Carandini and Heeger, 1994; Carandini et al., 1997; Tolhurst and Heeger, 1997a,b; Nestares and Heeger, 1997).”

“This shunt would lower the membrane time constant of the cell, thereby lowering its integration time, with the resulting effect of advancing the phase of responses to sinusoidal gratings and enhancing responses to higher temporal frequencies (Carandini & Heeger 1994, Carandini et al 1997).”

“The effect of contrast on cortical receptive-field size is also relevant to our understanding of cortical contrast gain contro”

“Elaborations of the contrast-normalization model (Carandini and Heeger, 1994; Carandini et al., 1997) have embraced additional nonlinear behaviors (previously unaccounted), such as “phase advance” at high contrasts (Dean and Tolhurst, 1986).”

“Although network architectures that can accomplish normalization have been proposed (Carandini & Heeger 1994, Groh 2001), there is still no substantial anatomical evidence in the oculomotor system to support this structure.”

“Generally an exponent >1 is required to fit the data (Albrecht and Hamilton, 1982; Heeger, 1992; Carandini and Heeger, 1994; Reynolds and Heeger, 2009), although the mechanisms underlying this are uncertain.”

“Such normalization of feature values is supported by neurobiological evidence of the non-linear single-cell behavior in the primary visual cortex [70].”

“, specifically, the normalization of individual filter responses relative to the total response of the local filter population ('divisive inhibition”

“Copyright © 1998 Society for Neuroscience 0270-6474/98/185908-20$05.00/0 Geisler, 1991; Heeger, 1992; Carandini and Heeger, 1994; Carandini et al., 1997, 1998).”

“The main assumption of the computation of local feature contrast has found empirical support from V1 physiology (reviewed in Carandini et al., 2005) and computational support in models of V1 (Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997).”

“discussed by Heeger (1992) and Carandini and Heeger (1994).”

“The particular form of the contrast‐response function (Eq. (1)) was chosen because it has been used successfully both to fit psychophysical TvC data (Foley, 1994; Foley & Boynton, 1994; Teo & Heeger, 1994, 1995) and to fit electrophysiological contrast‐response data (Bonds, 1989; Albrecht & Geisler, 1991; Heeger, 1991…”

“, 1982), it serves as a low bound because the contribution of “shunting” inhibition does not cause appreciable hyperpolarization (Carandini and Heeger, 1994).”

“Mechanistic models of normalization processes in cortex (Heeger, 1992; Carandini and Heeger, 1994; Carandini et al., 1997) such as the contrast gain control (Sclar and Freeman, 1982; Ohzawa et al., 1982) call for large, visually evoked changes in the membrane conductance, which, our results suggest…”

“Normalization characterizes stimulus interaction within the V1 RF (Carandini and Heeger, 1994; Carandini et al., 1997), as well as interactions between the RF center and nonclassical suppressive surround (Cavanaugh et al.”

“…adaptation aftereffects, if resulting from GABAA receptor-mediated inhibition, should be associated with substantial decreases of input resistance (Carandini and Heeger, 1994; Borg-Graham et al., 1998), which have not been detected (Ahmed et al., 1997; Carandini and Ferster, 1997; present study).”

“A quantitative evaluation of re-neurons (Albrecht et al. 1984; Carandini and Heeger 1994; Heeger 1992a,b; Ohzawa et al. 1982, 1985), such mecha- sponses in the frequency domain shows that cells are not sensitive to motion-in-depth (Cynader and Regan 1978,nisms must clearly be incorporated.”

“Thus, changes in the barrages of synaptic activity may underlie diverse changes in neuronal responsiveness, owing to the combined influences of changes in membrane potential, conductance, and membrane potential variance (Matsumura et al., 1988; Bernander et al., 1991; Carandini and Heeger, 1994; Borg-Graham et al., 19…”

“…much faster form of contrast gain control in the primary visual cortex (Albrecht & Geisler, 1991; Albrecht et al., 2002; Albrecht & Hamilton, 1982; Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997; Frazor, Albrecht, Geisler, & Crane, 2004; Geisler & Albrecht, 1992, 1997; Heeger, 1991,…”

“The Simoncelli‐Heeger model posits a particular kind of divisive suppression in V1 in which the response of each individual V1 neuron is divided by a quantity proportional to the summed activity of a large pool of neighboring neurons (Robson, 1988; Bonds, 1989; Albrecht and Geisler, 1991; DeAngelis et al., 1992; Heege…”

“…Heeger, 1992a for review) To explain non-speciic suppression and response saturation, a new model of simple cell responses , known as the the normalization model, has recently been proposed (Robson et al., 1991; Albrecht and Geisler, 1991; Heeger, 1991, 1992a, 1993; Carandini and Heeger, 1994).”

“Changes in gain amplify or reduce neuronal responsiveness with minimal effects on stimulus selectivity or receptive field structure (Sclar and Freeman, 1982; Carandini and Heeger, 1994).”

“49 Example of relevant evidence are provided by Carandini and Heeger (1994) and Geisler and Albrecht”

“…inputs, were presented monocularly to the dominant eye at a frequency of either excitatory or inhibitory, accounts for this invari- 1 Hz or less. ance, as proposed in several models of cortical function (Carandini and Heeger, 1994; Somers et al., 1995; Troyer Electrical Stimulation et al., 1998).”

“Neurons usually increase their firing rate with increasing stimulus size and somewhat reduce their firing rate when stimuli start to encroach into the suppressive surround (Carandini & Heeger, 1994; Sceniak et al., 1999; Cavanaugh et al., 2002; Levitt & Lund, 2002; Roberts et al., 2005).”

“simple cells, such as the sigmoidal shape of their contrast response functions (CRFs) and the inhibitory effect of adding a second stimulus to the receptive field at a non-preferred orientation [4–7].”

“In the language of control theory, centring is a form of additive (subtractive) gain control while scaling is divisive (multiplicative) in nature (Carandini & Heeger 1994).”

“An important concept in models based on divisive normalization is that of the normalization pool, the pool of neurons whose summed activations provide the denominator of the divisive operation (Carandini and Heeger, 1994, 2012).”

“This normalization is also consistent with models of contrast adaptation later in the visual system (e.g., Bonin et al., 2005; Carandini and Heeger, 1994).”

“Indeed, early conclusions (Carandini and Heeger, 1994; Carandini et al., 1997; drawn from similar experiments (Sillito, 1975) have later Heeger, 1992; Schwartz and Simoncelli, 2001). been challenged (Nelson et al., 1994).”

“They have been ascribed to GABA inhibition from other cortical neurons (Morrone et al., 1982; Bonds, 1989; Carandini and Heeger, 1994; Carandini et al., 1997; Somers et al., 1998).”

“The equation itself is agnostic regarding the mechanism underlying contrast-dependent normalization; the normalization computation fits simple cell behavior well regardless of the origin of the contrast-dependent normalization signal (Carandini and Heeger, 1994).”

“Several models of cortical function rely on the so-called “divisive” effect provided by the neuronal input conductance (invoked, for instance, to explain the saturation of simple cell spike response amplitude with increasing contrast) ( Carandini and Heeger, 1994 ).”

“While this chloride-mediated shunt inhibition may often be insufficiently hyperpolarizing to evoke clearly visible ipsps, it is highly effective at blocking spike initiation by multiplicatively decrementing the cumulative effect of excitatory sensory input (Figure 4Avi–vii;[61,65]; see also [66]).”

“…explain diverse effects such as: (i) the ability of sensory context (i.e. far field stimuli) to modulate the response to discrete sensory stimuli (Carandini and Heeger, 1994; Angelucci et al., 2002; Stettler et al., 2002); (ii) the transformation of sensory to motor maps of external space…”

“Other Models Contrast saturation effects have been achieved by other network models (e.g. Grossberg, 1973; Heeger, 1992, 1993; Carandini and Heeger, 1994); however, these models oversimplify cortical circuitry, effectively yoking together excitatory and inhibitory responses.”

“Since contrast of stimuli affects temporal responses (Shapley and Victor, 1981; Sclar 1987; Carandini and Heeger, 1994), it may be argued that the changes in latencies are due to changes in the stimulus energy (or effective contrast) contained in stimuli of different durations.”

“The quest to find circuit motifs that mediate gain control has driven a large body of research in various sensory systems, including olfaction (Carandini and Heeger, 1994, 2012; Nikolaev et al., 2013; Ohshiro et al., 2011; Olsen et al., 2010; Robinson and McAlpine, 2009).”

“More specifically, the response to the value of the saccade in the receptive field is divided by the weighted response of the saccadic values of all options presented in the choice set, similarly to what has been proposed for sensory neurons [55,56].”

“However, the change in the orientation sensitivity obtained with broad-spectrum stimuli cannot be expected from standard models of contrast gain control (e.g., Bonds, 1989; Heeger, 1992; Geisler & Albrecht 1992; Wilson & Humanski , 1993, Carandini & Heeger, 1994; Carandini et al., 1997).”

“It proposes that inhibition scales down the membrane potential tuning by reducing responses in a divisive manner (Carandini and Heeger, 1994; Murphy and Miller, 2003; Wehr and Zador, 2003; Katzner et al., 2011).”

“…recurrent excitation between local units in the population followed by mutual inhibition to normalize the responses (Hadeler, 1974; Feldman and Ballard, 1982; Carandini and Heeger, 1994) but other circuits can also perform the task that are faster and more reliable (Yuille and Grzywacz, 1989).”

“, 2002), which extended earlier normalization models (Sperling and Sondhi, 1968; Albrecht and Geisler, 1991; Heeger, 1992; Carandini and Heeger, 1994; Simoncelli and Heeger, 1998) to include a broad divisive surround component.”

“The energy model and many divisive normalization models (Adelson & Bergen, 1985; Carandini & Heeger, 1994; Rust et al., 2005) have used (half) squaring operations only.”

“Gain modulation is seen in early visual processing (Weyland and Malpeli, 1993; Pouget and Sejnowski, 1994, 1997; Trotter and Celebrini, 1999), and it has been proposed as a mechanism for generating a variety of non-classical receptive field effects for neurons in primary visual cortex (Heeger, 1992, 1993; Carandini an…”

“Further, the trends appear to be consistent with the behavior of the contrast-normalization model proposed by Carandini and Heeger (1994).”

“In the 1960s, higher-order units were very common in pattern recognition, where they appear in the form of polynomial discriminant functions (Cover, 1965; Nilsson, 1965; Duda & Hart, 1973). There is an obvious reason for this popularity: higher-order units are computationally more powerful than single neurons since th…”

“Conclusions From the early days of Hubel and Wiesel (1962) until today (e.g., Carandini and Heeger, 1994), it has always been assumed that geniculate input provides the dominant excitatory drive to striate cortex.”

“or the average activity of a large population of surrounding cell”

“Typically, inhibitory circuits are responsible for control neuronal gain (Morrone et al., 1982; Heeger, 1992; Carandini and Heeger, 1994).”

“Another extension is some form of contrast gain control ( Carandini & Heeger, 1994 ).”

“Indeed, a large number of observations suggest the presence of broadly tuned inhibition acting as a gain control mechanism in ~ahe visual cortex, both in cat and in monkey (Heeger, 1992; Carandini & Heeger, 1994; Carandinl, 1996 ).”

“A number of investigators proposed to extend the LN model by adding a gain control mechanism (Albrecht & Geisler, 1991; Bonds, 1991; Heeger, 1992; Carandini & Heeger, 1994; Tolhurst & Heeger, 1997; Carandini et al. 1997).”

“It is also possible that differences in integration properties at low compared to high contrasts are related to the well-known stimulusdependent level of saturation of V1 neurons that was suggested to arise from a contrast normalization mechanism (Carandini and Heeger 1994; Heeger 1992).”