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Non-Euclidean Universal Approximation
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Learn about the developments of Non-Euclidean Universal Approximation, and how it allows estimation of approximation bounds given a density of your neural network.
Potential Use Cases
Test how estimation changes with different NN densities.
Who is This For ?
Advanced audience looking to mathematically deduce estimation capabilities of NN given specified densities
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1. Intro to Universal Approximation Theorem
What even is the universal approximation theorem and why should I care about it?
2. Approximation by Superpositions of a Sigmoidal Function
Can we estimate the approximation capabilities of a feed forward network with sigmoidal activation functions and one single hidden internal layer?
3. Universal Approximation with Deep Narrow Networks
Does there exist a universal approximation theorem for neural networks on bounded width and arbitrary depth that acts on Euclidean spaces?
4. Quantitative Rates and Fundamental Obstructions to Non-Euclidean Universal Approximation with Deep Narrow Feed-Forward Networks
Can we specify estimates of a deep and narrow network with general activation functions, irregardless if the spaces it acts on are Euclidean?