Saliency Thresholds in Neural Code and its Relation to the Power-Law, Gaussian, and Lambert W Function
Alex Alvarez*, Jin Hyun Park*, and Yoonsuck Choe
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How many pixels are needed to make out what I'm looking at? I perceive the saliency threshold conceptually as the point where marginal information gain per pixel begins to diminish sharply.
We explore a theoretical juncture where the power law, Gaussian, and Lambert W converge to compute saliency thresholds in neural code. The Lambert W function emerges naturally in instances where exponential processes (like the Gaussian's exponentially decaying tails) and polynomial processes (like the power law's polynomially decaying tails) meet. Our results point to a biologically plausible invariant property in neural thresholding that could greatly simplify downstream processing in visual systems and potentially generalizes across different sensory modalities and processing levels.