For logistic regression, this loss function is conveniently convex. A convex funcconvex tion has just one minimum; there are no local minima to get stuck in, so gradient descent starting from any point is guaranteed to find the minimum. (By contrast, the loss for multi-layer neural networks is non-convex, and gradient descent may get stuck in local minima for neural network training and never find the global optimum.) Although the algorithm (and the concept of gradient) are designed for direction vectors, let's first consider a visualization of the case where the parameter of our system is just a single scalar w, shown in Fig. 5 .3.