Population coding under normalization

By Dario L. Ringach. 2009

44 citations recorded by the source corpus.

Divisive normalization of neuronal responses by a pooled signal of the activity of cells within its neighborhood is a common computation in visual cortex. From a geometrical point of view, normalization constraints the population response to high-contrast stimuli to lie on the surface of a high-dimensional sphere. Here we study the implications this constraint on the representation of a circular variable, such as the orientation of a visual stimulus. New results are derived for the infinite dimensional case of a homogeneous populations of neurons with identical tuning curves but different orientation preferences. An important finding is that the ability of the population to discriminate between any two orientations depends exclusively on the Fourier amplitude spectrum of the orientation tuning curve. We also study the problem of encoding by a finite set of neurons. A central result is that, under normalization, optimal encoding can be achieved by a finite number of neurons with heterogeneous tuning curves. In other words, increasing the number of neurons in the population does not always allow for an improved population code. These results are used to estimate the number of neurons involved in the coding of orientation at one position in the visual field. If the cortex were to code orientation optimally, we find that a small number (~5) of neurons should suffice.

Subfields: Biophysics, Cognitive Neuroscience

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biophysics

1. Richard S. Zemel
2. Renjie Liao
3. Raquel Urtasun
4. Fabian H Sinz

In Cognitive Neuroscience

1. Richard S. Zemel
2. Renjie Liao
3. Raquel Urtasun
4. Mengye Ren
5. Fabian H Sinz

Citations in the corpus

• Normalizing the Normalizers: Comparing and Extending Network Normalization Schemes (2016, background): “…(Ball ´ e et al., 2016), image compression (Malo et al., 2006), distributed neural representations (Simoncelli & Heeger, 1998), stimulus decoding (Ringach, 2009; Froudarakis et al., 2014), winner-take-all mechanisms (Busse et al., 2009), attention (Reynolds & Heeger, 2009), redundancy…”
• Generating sparse and selective third-order responses in the olfactory system of the fly (2010, unknown): “It has been recently noted that normalization affects the population coding of orientation in the visual system in ways related to what we have found here for olfaction (37).”