What is the limit of redundancy reduction with divisive normalization?

Area of Science:

• Neuroscience
• Computational Neuroscience
• Information Theory

Background:

• Divisive normalization is a key neural computation for sensory processing, acting as a nonlinear mechanism to reduce redundancy by capturing contrast correlations.
• The radial rescaling of population responses is the fundamental operation of divisive normalization.
• Saturation in divisive normalization prevents achieving a completely independent neural representation of stimuli.

Purpose of the Study:

• To derive a theoretical upper bound on the residual redundancy inherent in saturating divisive normalization.
• To quantify the limitations imposed by saturation on the information processing capacity of neural populations.

Main Methods:

• Analytical derivation of an upper bound for residual redundancy.
• Mathematical modeling of saturating radial rescaling mechanisms.

Main Results:

• An analytical upper bound on the inevitable residual redundancy was derived.
• The study demonstrates that saturation fundamentally limits the degree of redundancy reduction achievable.

Conclusions:

• Saturating radial rescaling mechanisms, like divisive normalization, inherently retain a level of redundancy.
• Understanding these bounds is crucial for comprehending neural information processing and designing efficient artificial systems.