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Updated: Jul 25, 2025

Deep Neural Networks for Image-Based Dietary Assessment
Published on: March 13, 2021
Approximation of classifiers by deep perceptron networks
Věra Kůrková1, Marcello Sanguineti2
1Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 18207 Prague, Czech Republic.
Abstract:
We employ properties of high-dimensional geometry to obtain some insights into capabilities of deep perceptron networks to classify large data sets. We derive conditions on network depths, types of activation functions, and numbers of parameters that imply that approximation errors behave almost deterministically. We illustrate general results by concrete cases of popular activation functions: Heaviside, ramp sigmoid, rectified linear, and rectified power. Our probabilistic bounds on approximation errors are derived using concentration of measure type inequalities (method of bounded differences) and concepts from statistical learning theory.
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