"Normalization is a widespread computation in the brain; it can be found in the retina (Benardete, Kaplan, & Knight, 1992; Shapley & Victor, 1979a, 1979b, 1981; Solomon, Lee, & Sun, 2006), the lateral geniculate nucleus (Bonin, Mante, & Carandini, 2005, 2006), primary visual cortex (Carandini et al., 1997; Heeger, 1992; Ringach & Malone, 2007; Rust, Schwartz, Movshon, & Simoncelli, 2005), area MT (Simoncelli & Heeger, 1998), and area IT (Zoccolan, Cox, & DiCarlo, 2005). Furthermore, normalization models appear to account well for the modulatory effects of attention (Reynolds, Chelazzi, & Desimone, 1999; Reynolds & Heeger, 2009)."
"These findings demonstrate that normalization imposes important constraints on the coding of information and, giving its incidence in cortical circuits, it should be incorporated as an integral
component in formal models of population coding."
Normalization model of simple cells in V1: Carandini et al. 1997, Heeger, 1992.
normalization in orientation tuning: Benyishai, Baror & Sompolinsky, 1995; Salinas & Abbott, 1994; Seung & Sompolinsky, 1993).
Only a small number of neurons is needed to efficiently encode an orientation.
They then relate the problem of normalized population coding with fitting a necklace on a hypersphere, having each node of necklace spaced out as far as possible. This is like a maximum entropy arrangement, leading to most information.
Not always beneficial to sharpen tuning curves (information in population code): Zhang & Sejnowski, 1999.
Normalization and correlated noise: Abbott & Dayan, 1999; Averback, Latham & Pouget, 2006; Sompolinsky et al. 2001.
their geometrical approach as related to the probabilistic view of encoding: Beck, Ma, Latham & Pouget, 2007; Beck et al., 2008; Pouget, Dayan & Zemel, 2000, 2003; Schwartz & Simoncelli, 2001; Simoncelli & Olshausen, 2001; Zemel, Dayan, & Pouget, 1998.
Spiking neurons: Jazayeri & Movshon, 2006; Ma, Beck, Latham, & Pouget, 2006.
