Conventional modeling of the multilayer perceptron using polynomial basis functions.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Neural Networks

Background:

• Multilayer perceptron (MLP) neural networks are widely used in machine learning.
• Modeling MLP networks can be complex, limiting their interpretability and application in certain domains.

Purpose of the Study:

• To introduce a new technique for modeling MLP neural networks.
• To represent MLP units using polynomial basis functions (PBFs).
• To establish the isomorphism between MLPs and polynomial discriminant classifiers or Volterra filters.

Main Methods:

• Representing input and hidden units of MLP networks with polynomial basis functions (PBFs).
• Expressing the MLP output as a linear combination of PBFs, resulting in a polynomial function of the inputs.
• Applying the modeling technique to pre-trained MLP networks.

Main Results:

• The proposed technique successfully models trained MLP networks.
• The MLP output is shown to be a polynomial function of its inputs.
• The MLP is demonstrated to be isomorphic to polynomial discriminant classifiers and Volterra filters.

Conclusions:

• The presented modeling technique offers a new perspective on MLP network architecture.
• This approach establishes a clear mathematical equivalence between MLPs and polynomial models.
• The technique has been validated through successful application to trained MLP networks.