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Some numerical aspects of the training problem for feed-forward neural nets
Gary Hall1, Fabio Stella, John J McKeown
1The Queen's University of Belfast, Belfast, UK
Summary
This study examines the numerical conditioning of feed-forward training problems. Understanding ill-conditioning is crucial for selecting effective training algorithms and achieving high-quality solutions in machine learning.
Area of Science:
- Numerical analysis
- Machine learning
Background:
- The feed-forward training problem is known to be frequently ill-conditioned.
- Ill-conditioning negatively impacts training algorithm behavior, selection, and solution quality.
Purpose of the Study:
- To analyze the feed-forward training problem from a numerical conditioning perspective.
- To explore the geometric interpretation of ill-conditioning in this context.
Main Methods:
- Numerical analysis of the feed-forward training problem.
- Geometric interpretation of ill-conditioning.
- Detailed analysis of a function approximation example.
Main Results:
- The paper investigates the numerical conditioning of feed-forward training.
- A geometric interpretation of ill-conditioning is presented.
- An example of function approximation is analyzed to illustrate the concepts.
Conclusions:
- The numerical conditioning of feed-forward training problems significantly influences algorithm performance and solution quality.
- Understanding and addressing ill-conditioning is essential for effective machine learning model training.