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Training a perceptron in a discrete weight space
1Minerva Center and the Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
Summary
This study analyzes learning in perceptrons with discrete weights. We introduce new parameters to describe learning and find generalization errors depend on activation functions and synaptic depth.
Area of Science:
- Computational Neuroscience
- Machine Learning Theory
Background:
- Perceptrons are fundamental models in machine learning.
- Understanding learning dynamics in discrete weight spaces is crucial for efficient algorithms.
Purpose of the Study:
- To analytically and numerically examine learning in perceptrons with discrete weight spaces.
- To investigate the impact of discrete versus continuous transfer functions on generalization error.
Main Methods:
- Development of novel order parameters to describe learning dynamics.
- Analysis of on-line learning scenarios with both discrete and continuous transfer functions.
- Numerical simulations to validate analytical findings.
Main Results:
- Generalization error for clipped weights follows distinct asymptotic decay patterns based on activation functions.
- Perfect agreement between discrete and teacher models achieved for specific parameter regimes (alpha~Lsqrt[ln(NL)]).
- A crossover to continuous weight-like generalization error observed for large synaptic depths (L>O(sqrt[N])).
Conclusions:
- Discrete weight perceptrons exhibit unique learning behaviors distinct from their continuous counterparts.
- Synaptic depth and activation function type significantly influence generalization performance.
- The findings provide insights into designing more efficient learning algorithms for discrete systems.