Calculus chain rule help update#

A positive slope represents a condition where an increase in the value of x will increase the value of f(x).The sign of this derivative at a certain point conveys critical information about the curve at that point.

So, at x=5, the derivative of f(x) = x² will be 2*5 = 10, a positive value. From the derivative theory, differentiating x² with respect to x will produce 2*x. For example, the image below shows the derivate of f(x) = x², at x = 5.

A Quick Recap on Derivative of any Mathematical Functionĭerivates of a function at any point describe the slope of that function at that point. But before this discussion, we should know why we calculate the derivative or partial derivative of the cost function. The chain rule helps in finding the partial derivative of the cost function with respect to the learnable parameters.

Common mistakes while applying the chain rule.

Use of chain rule while performing backpropagation in ANNs.

Why is derivative calculation considered difficult for ANNs compared to traditional ML algorithms?.

Why do we calculate derivatives or partial derivates in Neural Networks?.

Key takeaways from this blogĪfter going through this article, we will be able to understand the following things:

Calculus chain rule help update#

In this article, we will use the Gradient Descent algorithm to find how gradients help backpropagation or update the parameters when training ML models. All these optimization algorithms use gradients to sense the direction of the update. ML algorithms use optimization algorithms, like Gradient Descent, Stochastic Gradient Descent, or Adam, to find this direction. To find these optimum values, machines start with random values (as initialization) for these learnable parameters and then slowly update these parameters by sensing the direction (increase or decrease) in which the update should happen. In Machine Learning, our primary goal is to find the most optimum values for the learnable parameters such that the value of the cost function becomes minimum.