Normalization model explained

The normalization model^[1] is an influential model of responses of neurons in primary visual cortex. David Heeger developed the model in the early 1990s,^[2] and later refined it together with Matteo Carandini and J. Anthony Movshon.^[3] The model involves a divisive stage. In the numerator is the output of the classical receptive field. In the denominator, a constant plus a measure of local stimulus contrast. Although the normalization model was initially developed to explain responses in the primary visual cortex, normalization is now thought to operate throughout the visual system, and in many other sensory modalities and brain regions, including the representation of odors in the olfactory bulb,^[4] the modulatory effects of visual attention, the encoding of value, and the integration of multisensory information. It has also been observed at subthreshold potentials in the hippocampus.^[5] Its presence in such a diversity of neural systems in multiple species, from invertebrates to mammals, suggests that normalization serves as a canonical neural computation. Divisive normalization reduces the redundancy in natural stimulus statistics^[6] and is sometimes viewed as an implementation of the efficient coding principle. Formally, divisive normalization is an information-maximizing code for stimuli following a multivariate Pareto distribution.^[7]

Notes and References

1. Carandini . M. . Heeger . D. J. . 10.1038/nrn3136 . Normalization as a canonical neural computation . Nature Reviews Neuroscience . 13 . 1 . 51–62 . 2011 . 22108672 . 3273486 .
2. 10.1017/S0952523800009640 . Heeger . D. J. . Normalization of cell responses in cat striate cortex . Visual Neuroscience . 9 . 2 . 181–197 . 1992 . 1504027. 22804285 .
3. Carandini . M . Heeger . DJ . Movshon . JA . Linearity and normalization in simple cells of the macaque primary visual cortex . Journal of Neuroscience . 17 . 21 . 8621–44 . 1997 . 9334433 . 10.1523/JNEUROSCI.17-21-08621.1997. 6573724 . free .
4. Divisive normalization in olfactory population codes . Olsen SR, Bhandawat V, Wilson R. Neuron . 2011 . 66 . 2. 287–299 . 10.1016/j.neuron.2010.04.009 . 20435004 . 2866644.
5. Precise excitation-inhibition balance controls gain and timing in the hippocampus . Bhatia A, Moza S, Bhalla US. eLife . 2019 . 8 . 10.7554/eLife.43415 . 31021319 . 6517031. free.
6. Schwartz . O . Simoncelli . EP . Natural signal statistics and sensory gain control. . Nature Neuroscience . 2001 . 4 . 8 . 819–25 . 10.1038/90526 . 11477428. free .
7. Bucher . SF . Brandenburger . AM . Divisive normalization is an efficient code for multivariate Pareto-distributed environments. . Proceedings of the National Academy of Sciences of the United States of America . 2022 . 119 . 40 . e2120581119 . 10.1073/pnas.2120581119 . 36161961. 9546555 . 2022PNAS..11920581B . free.