Low-Discrepancy Points for Deterministic Assignment of Hidden Weights in Extreme Learning Machines

Area of Science:

• Machine Learning
• Computational Mathematics

Background:

• Traditional extreme learning machines (ELMs) utilize random hidden weight assignment.
• Analytical methods determine output layer linear coefficients in ELMs.
• Random assignment can lead to inefficiencies in covering multidimensional spaces.

Purpose of the Study:

• To investigate replacing random weight generation in ELMs with low-discrepancy sequences (LDSs).
• To analyze the geometric properties of sampling points for ELM weight assignment.
• To demonstrate the theoretical and practical benefits of using LDSs in ELMs.

Main Methods:

• Analysis of geometric properties of sampling points.
• Replacement of random weight generation with low-discrepancy sequences (LDSs).
• Theoretical proof of universal approximation property with LDSs.

Main Results:

• Universal approximation property of ELMs is guaranteed when using LDSs.
• Efficient covering by LDSs positively impacts ELM convergence.
• Deterministic nature of LDSs removes probabilistic outcomes.
• Simulation results validate theoretical findings.

Conclusions:

• Low-discrepancy sequences offer a deterministic and efficient alternative to random assignment in ELMs.
• The use of LDSs enhances ELM performance and theoretical guarantees.
• This approach provides a more robust and predictable machine learning model.