Before revision:  Since this choice involves infinite degrees of freedom, the predictive power of models that are based on this principle can be called into question . Despite its great success in machine learning, especially in training deep neural networks, arguments about brain function that rely on gradient-based optimization have to be closely examined .
After revision:  Since this choice involves infinite degrees of freedom, the predictive power of models that are based on this principle can be called into question , unless there are strong constraints on the choice of the metric. Here we provide a didactic review of the mathematics of gradient descent, illustrate common pitfalls of using gradient descent as a principle of brain function with examples from the literature and propose ways forward to constrain the metric .