Estimating Multiplicative Relations in Neural Networks
This addresses a specific bottleneck in neural network function approximation for tasks involving multiplicative relations, but appears incremental as it builds on known logarithmic transformations.
The paper tackles the problem of neural networks overfitting when learning multiplicative functions by proposing a pair of activation functions based on logarithmic properties to translate products into linear expressions, and tests accuracy on disjoint distributions.
Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation functions perform very well when the output is a linear combination of input data. When trying to learn a function which involves product of input data, the neural networks tend to overfit the data to approximate the function. In this paper we will use properties of logarithmic functions to propose a pair of activation functions which can translate products into linear expression and learn using backpropagation. We will try to generalize this approach for some complex arithmetic functions and test the accuracy on a disjoint distribution with the training set.