linear unit function, or Re LU for short. By constraining the network activity to levels below 60 spikes/sec, we ignore the effects of neuronal saturation commonly implemented in modelsofg(h)(Ben-Yishai et al., 1995 ;Ermentrout, 1998 ). Here, Tis the threshold potential of a neuron, below which the synaptic input has no effect on the mean firing rate of the network. Interestingly, as a processing feature, this thresholding nonlinearity has been speculated toaccount for the chromatic responses of individual neurons in V1 ( Hanazawa et al., 2000 ). The amplification of these responses, and thus the mean network response, is modulated by β, the neural gain measured in spikes · sec-1/m V. We assume that βis determined by far-ranging internal and external influences, from attentional mechanisms to hallucinogenicinput ( Ferguson & Cardin, 2020 ;Michaiel, Parker, & Niell, 2019 ). Feedforward Input To parameterize the input, prior work has relied on the direct relationship between cortical feature preferences and properties of the visual stimulus ( Ben-Yishai et al., 1995 ;Bressloff & Cowan, 2003b ). Cells in the cortex labeled, for instance, by their spatial frequency preferences can be mapped directly onto a visual space parameterized by the same variable. Thus, theactivity of each neuronal population is no longer labeled purely by its position on the corticalsheet, but also by its preferred stimulus in an analogous feature space. The corresponding network topology may be modeled on the cortical histology, such as the orientation map of Bosking, Zhang, Schofield, and Fitzpatrick (1997) or spatial frequency maps addressed in Bressloff and Cowan (2002),Bressloff and Cowan (2003a), and Bressloff and Cowan (2003b). Conversely, it may be based entirely on functional considerations, as, for instance, in the orientation tuning model of Sompolinksy et al. ( Ben-Yishai et al., 1995 ; Hansel & Sompolinksy, 1998 ), also known as the “ring model, ”which posits a topology based on the experimentally motivated assumption that populations with similar orientation prefer-ences are maximally connected ( Ben-Yishai et al., 1995 ) and on the argument that the impor-tant features of such a connectivity are captured by its first-order Fourier components ( Hansel & Sompolinksy, 1998 ). Our model deviates in this regard by emphasizing that the stimulus 's chromatic information is first discretized along the two cone-opponent pathways. We incorporate this aspect of early processing by projecting the stimulus 's DKL space position θ/C22onto the two cardinal axes: l¼cosθ/C22 s¼sinθ/C22:(4) The magnitudes of landsare thus taken to represent the normalized strengths of the L-M and S-(L+M) cone-opponent signals respectively. The feedforward input is then given by h lgn¼clcosθþssinθ ð Þ ; (5) where cis the signal strength, or contrast, expressed as the mean postsynaptic coarse mem-brane potential (in units of m V) of the target hue population generated by the presynaptic LGN neurons ( Carandini & Ferster, 2000 ). Formulated in this way, the input captures the colocali-zation of cone-opponency and hue selectivity in the activity of V1 cells as observed in Li et al. (2022) and Xiao et al. (2007). The hue tuning networks, parameterized by θ, are not only responsive to the individual cone-opponent stimulus signals, land s, but also implement the combinatorial mechanisms by which they are first mixed ( De Valois et al., 2000 ). Substitut-ing the expressions for land sinto Equation 5, we obtain hlgn¼ccosθ-θ/C22ð Þ : (6) Network Neuroscience 683Pattern forming mechanisms of color vision Downloaded from http://direct. mit. edu/netn/article-pdf/7/2/679/2118501/netn_a_00294. pdf by guest on 09 August 2024 