NN2Poly: A Polynomial Representation for Deep Feed-Forward Artificial Neural Networks.

Area of Science:

• Artificial Intelligence
• Machine Learning Theory

Background:

• Neural network (NN) interpretability remains a challenge despite deep learning's success.
• Existing methods for NN interpretability are often limited in scope.

Purpose of the Study:

• To propose NN2Poly, a theoretical approach for creating explicit polynomial models of trained feed-forward neural networks.
• To extend NN interpretability to arbitrarily deep multilayer perceptrons (MLPs) for both classification and regression.

Main Methods:

• Utilizes Taylor expansion of activation functions at each layer.
• Applies combinatorial properties to derive polynomial coefficients.
• Addresses computational challenges by introducing training constraints.

Main Results:

• NN2Poly accurately represents trained MLPs as explicit polynomial models.
• The method is effective for deep networks and various tasks.
• Demonstrated through simulations and real-world tabular datasets.

Conclusions:

• NN2Poly offers a novel theoretical framework for understanding complex neural networks.
• The approach enhances the interpretability of deep learning models.
• Practical implementation is feasible with strategic training modifications.