Covers: theory of Non-Eucliden Universal Approximation of Deep Feed-Forward Neural Network
Estimated time needed to finish: 30 minutes
Questions this item addresses:
  • Can we specify estimates of a deep and narrow network with general activation functions, irregardless if the spaces it acts on are Euclidean?
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Author(s) / creator(s) / reference(s)
Anastasis Kratsios, Leonie Papon
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Non-euclidean Universal Approximation

Contributors
Total time needed: ~2 hours
Objectives
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 ?
ADVANCEDAdvanced audience looking to mathematically deduce estimation capabilities of NN given specified densities
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Resources4/4
VIDEO 1. Intro to Universal Approximation Theorem
  • What even is the universal approximation theorem and why should I care about it?
10 minutes
PAPER 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?
30 minutes
PAPER 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?
30 minutes
PAPER 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?
30 minutes

Concepts Covered

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