A Novel Explanation Against Linear Neural Networks
This addresses a foundational issue in machine learning theory for researchers, but it is incremental as it builds on known limitations of LNNs.
The paper tackles the problem of why linear neural networks (LNNs) without activation functions are impractical, showing that they reduce both training and testing performance compared to linear regression due to optimization difficulties, requiring more iterations to converge.
Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for these activation functions is that without them, neural networks only can model a line. However, a novel explanation we propose in this paper for the impracticality of neural networks without activation functions, or linear neural networks, is that they actually reduce both training and testing performance. Having more parameters makes LNNs harder to optimize, and thus they require more training iterations than linear regression to even potentially converge to the optimal solution. We prove this hypothesis through an analysis of the optimization of an LNN and rigorous testing comparing the performance between both LNNs and linear regression on synthethic, noisy datasets.