However, no biological neuron is completely linear. Whether we consider simple thresholds, saturating nonlinearities, gain control, or a variety of nonclassical responses, the response of a neuron to complex stimuli like natural scenes can rarely be determined solely from a two-dimensional receptive field (e.g., David & Gallant,
2005; Mante, Frazor, Bonin, Geisler, & Carandini,
2005; Murray,
2011; Olshausen & Field,
2005; Prenger, Wu, David, & Gallant,
2004). A wide variety of attempts have been made to model these nonlinearities, with various degrees of success (e.g., Mély & Serre,
2016; Prenger et al.,
2004; Schwartz & Simoncelli,
2001; Tolhurst & Heeger,
1997). In this article, we are not attempting to provide a model that produces a better fit to all the experiments in the literature (see Mély & Serre,
2016). Rather, we have two goals here. First, along the lines of Zetzsche (e.g., Zetzsche et al.,
1999; Zetzsche & Nuding,
2005) and Golden et al. (
2016), we wish to emphasize that many of these nonlinearities can be described in terms of simple curvature of the response surfaces. Second, we argue that this curvature is responsible for a number of interesting behaviors that we believe provide deeper insights into the function of these nonlinearities.