Fixing one of the components of w to any non-zero constant and allowing the others to vary, the new linear model retains the same modeling power, but the (D − 1) free parameters are no longer scale invariant, i.e., scaling the (D − 1)-dimensional vector now has an effect on linear model predictions.
other non-convex problems in machine learning, such as deep neural networks (DNN) and word alignment models, commonly require such initializers in order to obtain decent performance.