Summation and Division by Neurons in Primate Visual Cortex

“Two models have recently been proposed for the mediation of contrast gain control: one by Shapley and Victor (1981), the other by Carandini and Heeger (1994) and Carandini et al. (1997).”

“For example, (Carandini & Heeger, 1994) show that the process of contrast gain could be implement through a process of shunting inhibition (but see (Holt & Koch, 1997).”

“…contrast influences the relative sensitivity to low and high TFs in retinal ganglion cells (Shapley and Victor, 1981), and it affects the phase of cortical simple-cell responses to drifting gratings (Dean and Tolhurst, 1986; Carandini and Heeger, 1994; Albrecht, 1995; Carandini et al., 1997).”

“Interestingly, Carandini and Heeger (1994) proposed a somewhat similar mechanism to account for the response properties of orientation selective cells in primate visual cortex.”

“Inhibition may also contribute to selectivity by acting as a gain control mechanism (Heeger, 1992; Carandini and Heeger, 1994; Borg-Graham et al., 1998) or by controlling response timing (Wehr and Zador, 2003; Higley and Contreras, 2006).”

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

“The biophysical mechanism for such effects remains elusive, although there are several candidates (Carandini and Heeger, 1994; Chance et al., 2002).”

“gif"/> changes nonlinearly (Albrecht, Geisler, & Crane, 2003 ; Carandini & Heeger, 1994 ; Geisler & Albrecht, 1995; Heeger et al, 2000 ; Li, Miller, & Desimone, 1993 ; Meeter, Myers, & Gluck, 2005 ; Sawamura, Organ, & Vogels, 2006).”

“Division or multiplication of firing rate by synaptic input, originally suggested by Reichardt (1961), has since become a key component of many models of neural processing (Salinas and Sejnowski, 2001) and is required in models characterizing the response of cells in the visual cortex (Carandini and Heeger, 1994) and…”

“…by the sum of the unnormalized quantities, reminiscent of the divisive normalization that is commonly supposed to occur during visual processing (e.g., Carandini & Heeger, 1994; Yu, 2005b) and in neural computations more generally (e.g., O'Reilly & Munakata, 2000; Schwartz & Simoncelli, 2001).”

“and uncertainty about how past experiences can inform future decisions (Britten and Heuer, 1999; Carandini and Heeger, 1994; Carandini et al., 1997; Koch et al., 2004; Kouh and Poggio, 2008; Law and Gold, 2009a; Miller and Troyer, 2002; Nassar et al., 2010; Petrov et al., 2005; Purushothaman and Bradley, 2005; Rust et…”

“Biophysically plausible implementations of this equation have been described elsewhere [19,31].”

“An influential divisive normalization model hypothesizes that the response of a neuron is reduced in proportion to the pooled activity of other neurons in the neighborhood (Heeger, 1992; Carandini and Heeger, 1994; Carandini et al., 1997).”

“Thus, the suppressive tuning in Figure 5a is likely to reflect known mechanisms of contrast normalization (Heeger, 1992; Carandini and Heeger, 1994; Zipser et al., 1996; Rossi et al., 2001) and cross-orientation suppression (DeAngelis et al.”

“Cortical gain control and contrast adaptation may be affected by the size of a stimulus (Ohzawa et al., 1985; Carandini and Heeger, 1994; Sceniak et al., 1999).”

“Gain modulation is thought to be an important step in the processing of sensory inputs (see, e.g., Carandini & Heeger, 1994; Ohzawa et al., 1982, 1985) and here it is modeled as a normalization of the strengths of the competing inputs (Equation 5, Methods section).”

“, 1992 ; Carandini and Heeger , 1994 ; Albrecht , 1995 ; Kremers et al .”

“…between filters, for example, the inhibitory interactions between filters at the same visual location suggested by Heeger and others (Heeger, 1993; Carandini & Heeger, 1994), or the competitive interactions between filters at distant visual locations postulated by Koch, Desimone and others (Koch…”

“Such network interactions have been been previously proposed to account for response of V1 neurons receiving afferent LGN inputs and lateral cortical inputs (Carandini & Heeger, 1994).”

“After (Carandini and Heeger, 1994).”

“An operator of removing these dependences is divisive normalization [60], [65], which represents each coefficient by a weighted combination of its rectified neighbors.”

“Multiplicative modulation of tuning is also evident with manipulations of stimulus contrast (Carandini and Heeger, 1994; Finn et al., 2007; Priebe and Ferster, 2012).”

“Normalization operates in multiple sensory levels and modalities, explaining features of both early stimulus coding (Heeger, 1992; Carandini and Heeger, 1994; Britten and Heuer, 1999; Bonin et al., 2005; Rabinowitz et al., 2011) and higher-order processing such as object identification, visual…”

“We then analyzed the type of inhibition that is conveyed by L1 NDNF INs onto excitatory neurons (i.e., subtractive or divisive; Carandini and Heeger, 1994; Isaacson and Scanziani, 2011; Wilson et al., 2012) by comparing the effects of optogenetic L1 NDNF IN activation on excitatory neuron”

“…the following sense: If we assume that the brain uses divisive normalization (Weber, 1846; Fechner, 1860; Craik, 1938; Geisler and Albrecht, 1992; Carandini and Heeger, 1994), the key change in sensory information, following an increase in contrast, is an increase in signal to noise; in other…”

“To account for the observed properties in both time and space, we propose a simple feedforward population gain-control (PGC) model that generalizes earlier normalization models for single V1 neurons (Albrecht and Geisler, 1991; Heeger, 1991, 1992; Carandini and Heeger, 1994; Carandini et al., 1997).”

“…of the response as a code for spatial frequency We have known for many decades that the latency of the response of visual cortex neurons decreases as the contrast increases (e.g., Albrecht 1978, 1995; Carandini and Heeger 1994; Carandini et al. 1997; Dean and Tolhurst 1986; Reid et al. 1992).”

“In the striate cortex, a decrease in contrast from 100% to 5–10% generally induces a latency increase of 30–50 ms (Carandini & Heeger, 1994; Albrecht, 1995; Gawne et al., 1996; Reich et al., 2001).”

“An alternative view interprets cross-orientation inhibition as a means of response normalization with respect to local image contrast (Heeger, 1992; Carandini and Heeger, 1994; Carandini et al., 1997).”

“3) As supported by the biological studies [36], [37]”

“Alternatively, deficits in nonlinear mechanisms present in cortex, such as shunting inhibition which are important in producing responses at higher harmonics or temporal frequencies (Carandini and Heeger, 1994) would also result in greater attenuation of higher harmonic responses in patients than controls.”

“This manipulation was based onWeber's law (Weber, 1846) and evidence that the brain uses divisive normalisation (Brady and Field, 2000; Carandini and Heeger, 1994), meaning that higher contrast stimuli have a higher signal-to-noise ratio and therefore higher precision.”

“Such models were motivated e.g., by experimentally observed properties of sensory processing like divisive normalization (Heeger, 1992; Carandini and Heeger, 1994) or synaptic depression (Carandini et al., 2002; Goldman et al., 2002).”

“Two-dimensional Gabor function [94] Gain control operation [95] “Winner is king” model [96,97] Gaussian response model [98] Macro models Neocognitron model [99] HMAX model [100,101] Three stages model [102] Models based on attention mechanism [103–105] Models based on multiple mechanisms…”

“It may be noted that that the original divisive inhibition-based gain-control models (Albrecht & Geisler, 1991; Carandini & Heeger, 1994; Foley, 1994; Heeger, 1992; Ross & Speed, 1991), which were designed to account for the interaction among mechanisms, are incompatible with many aspects of the…”

“Intracortical inhibitory connections included in other models (Albrecht and Geisler 1991; Ben-Yishai et al. 1995; Carandini and Heeger 1994; Carandini and Ringach 1997; Heeger 1992; McLaughlin et al. 2000, 2003; Shelley and McLaughlin 2002; Shelley et al. 2002; Wielaard et al. 2001) are not…”

“Dynamic normalization models have been developed to account for the time courses of neuronal responses 5, 10, 23–27 and dynamic sensory processes like adaptation 2, 28–32 .”

“We incorporate subtractive and divisive mechanisms of inhibition into a model based on the “normalization model” (Carandini and Heeger 1994; Carandini et al. 1997; Heeger 1992, 1993; Tolhurst and Heeger 1997) and examine whether they can reproduce realistic gain modulation effects on model neuron…”

“Because it produces a nonlinear change in excitatory synaptic inputs, shunting inhibition has been proposed as a mechanism for division (Carandini and Heeger, 1994), but the effect of having a threshold for spiking acts to offset this nonlinearity and make the input/output function for spiking activity very nearly lin…”

“A more detailed model of membrane conductances, such as shunting inhibition (Carandini and Heeger, 1994; Carandini et al., 1997; Sit et al., 2009) may be a way to augment the model.”

“Furthermore, for monocularly viewed stimuli, a change in contrast can result in an advance in response phase (Dean and Tolhurst, 1986; Carandini and Heeger, 1994) and a change in contrast gain (Albrecht and Hamilton, 1982).”

“, increasing conductance by a balanced increase in excitation and inhibition without changing the total synaptic current (6, 94).”

“The variation of the latency of the response with contrast is in line with measurements from single cells (Dean and Tolhurst, 1986; Carandini and Heeger, 1994; Albrecht, 1995).”

“…such consistency is somewhat remarkable because the divisive mechanism was originally derived from empirical observations (Wilson & Humanski, 1993; Carandini & Heeger, 1994; Carandini et al., 1997; Simoncelli & Heeger, 1998; Wilson, 1998; Schwartz & Simoncelli, 2001) and its biophysical…”

“Simple cells in area V1 tend to saturate their activation as a consequence of increasing stimulus contrast and surround activities (Heeger, 1992; Carandini & Heeger, 1994; Carandini et al., 1999; Carandini, Heeger, & Movshon, 1997; see Smith, 2006, for a summary).”

“2 ), a property that is distinct from the typical effects of divisive normalization of neural activit”

“The simplest prevailing hypothesis concerning the relationship between V1 and MT responses is that the activity of MT neurons reflect summed inputs from V1 that have been passed through a divisive nonlinearity (Carandini and Heeger, 1994; Rust et al., 2006).”

“To illustrate this point, Chirimuuta (2014) offers the example of Heeger’s contrast normalisation model of the primary visual cortex (Heeger 1992; Carandini and Heeger 1994, 2012).”

“1) In the biased competition framework (Desimone and Duncan 1995), competition takes the form of normalization: two simultaneously presented images elicit levels of activation intermediate between those elicited by the images in isolation (Carandini and Heeger 1994; Reynolds et al. 1999).”

“We developed a graph-based model by which PV interneurons exerting inhibition onto striosomal neurons could improve discrimination through shifting excitation-inhibition balance (van Vreeswijk and Sompolinsky, 1996; Vogels and Abbott, 2009) due to modulating SNR alongside gain (Atallah et al., 2012; Carandini and Heeg…”

“The precise form of normalization across filter units is similar to that proposed by Heeger (1993; Carandini and Heeger, 1994 ), although this choice has no significant influence on the present model performance.”

“Divisive gain control mechanisms is often assumed as a key operation for neural computations (Carandini and Heeger, 1994; Chance and Abbott, 2000), but biophysical mechanisms for such a modulation have been hard to identify, regardless of being network-based mechanisms (Holt and Koch, 1997; Doiron…”

“inhibitory circuits are capable of producing averaging responses (Carandini and Heeger, 1994; Carandini et al., 1997).”

“Another minimal adaptation hypothesis is to consider a gain control process before the nonlinear filtering stage (pre-NL), that rescales the gain of the afferent subunits with regard to the increase in the stimulus powe”

“Several hypotheses for the recurrent circuits underlying normalization have been proposed (50, 51, 96, 106 – 108), but most of them are inconsistent with experimental observations suggesting that normalization is implemented via recurrent amplification (109 – 114).”

“…of these two opposing effects in different parameter regions explains many of the the differing results on gain modulation reported by a number of authors (Nelson, 1994; Carandini & Heeger, 1994; Holt & Koch, 1997; Tiesinga et al., 2000; Capaday, 2002; Longtin et al., 2002; Chance et al., 2002).”

“After applying our estimation method for the Poissonian firing intensity to all of the data, we report an exponential increase of the firing intensity with depolarizing membrane potential, which is comparable with the quadratic shape reported in previous studies (Anderson et al. 2000; Carandini and Heeger 1994; Gabbia…”

“…gain-control mechanism must arise from local cortical interactions, e.g., from a divisive inhibitory mechanism (Rose, 1977; Morrone et al., 1982; Worgotter and Koch, 1991; Carandini and Heeger, 1994; Ben-Yishai et al., 1995; Sompolinsky and Shapley, 1997; Troyer et al., 1998; Teich and Qian, 2006).”