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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.
Summary
Deep perceptron networks can classify large datasets effectively. High-dimensional geometry reveals conditions for deterministic approximation errors in deep learning models, using statistical learning theory.
Area of Science:
- Computational mathematics
- Machine learning theory
- High-dimensional geometry
Background:
- Deep perceptron networks are crucial for large dataset classification.
- Understanding their approximation error behavior is key to improving performance.
Purpose of the Study:
- To derive conditions for deterministic approximation errors in deep perceptron networks.
- To provide insights into network depth, activation functions, and parameter impact on classification accuracy.
Main Methods:
- Employing high-dimensional geometry principles.
- Utilizing concentration of measure inequalities (method of bounded differences).
- Applying concepts from statistical learning theory.
Main Results:
- Derived conditions on network architecture and activation functions (Heaviside, ramp sigmoid, rectified linear, rectified power) for deterministic error behavior.
- Established probabilistic bounds on approximation errors.
Conclusions:
- Network properties significantly influence classification accuracy and error predictability.
- Theoretical insights can guide the design of more effective deep learning models for large-scale data.
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