For example, the partial derivative, whereas the full derivative. In the calculations above, note the difference between partial and full derivatives. Using the chain rule (1) twice, we can compute the derivative as follows:īackpropagation computes the derivative via a different route: The neural network describes as a function of in the following way: It has been discussed in many blog posts that backpropagation is not just the chain rule, but we want to focus on a simple and basic difference here.Ĭonsider the “neural network” above: it consists of an input variable, an output variable, and two intermediate variables and. While this is in a sense true, we wish to point out in this blog post that this belief is over-simplifying and can lead to incorrect implementations of the backpropagation algorithm. This leads to a common belief that “backpropagation is just applying the chain rule repeatedly”. This blog post by Boaz Barak is a beautiful tutorial on the chain rule and the backpropagation algorithm.Īs in Barak’s post, the backpropagation algorithm is usually taught as an application of the chain rule in machine learning classes. Roughly speaking, it states that if a variable is a differentiable function of intermediate variables, and each intermediate variable is itself a differentiable function of, then we can compute the derivative as follows:īesides being a handy tool for computing derivatives in calculus homework, the chain rule is closely related to the backpropagation algorithm that is widely-used for computing derivatives (gradients) in neural network training. (in billions of dollars) t years after the year 2000 can be modeled by $G(t)=9743.77 = 2(1) = 2$įind the equation of the line tangent to the graph of f at the indicated value of x.The chain rule is a fundamental result in calculus. The Gross Domestic Product (GDP) of the U.S. 2.P Exponential and Logarithmic Equations Homework
0 kommentar(er)
