Mathematics in AI and ML- Five Days FDP of Emerging Trends in M

What does a derivative represent in the context of AI and ML?

• The total change over an interval

• The rate of change of a function at a given point

• The maximum value of a function

• The area under a curve

What is the integral used for in AI and ML?

• Finding the rate of change

• Accumulating quantities over a range

• Minimizing a function

• Maximizing a function

In gradient descent, what is the role of the learning rate (η)?

• It determines the size of the steps taken towards the minimum

• It identifies the global minimum

• It maximizes the loss function

• It eliminates the need for backpropagation

What is the primary goal of the gradient descent algorithm?

• To find the maximum value of a function

• To find the minimum value of the cost function

• To increase the number of parameters

• To compute integrals

Which of the following is a characteristic of convex optimization problems?

• Multiple local minima

• Only one local minimum which is also the global minimum

• Non-linear constraints

• Difficult to solve

Which type of gradient descent updates parameters using a small batch of training examples?

• Batch Gradient Descent

• Stochastic Gradient Descent

• Mini-Batch Gradient Descent

• Recursive Gradient Descent

Why is Lagrange multipliers used in optimization problems?

• To convert non-convex problems to convex ones

• To handle constraints in optimization problems

• To simplify linear problems

• To find the maximum value of a function

What does the Lagrangian function combine?

• Objective function and constraints

• Variables and constants

• Gradient and Hessian

• Cost function and learning rate

What is the purpose of backpropagation in neural networks?

• To initialize weights

• To update weights using the gradient of the loss function

• To compute the cost function

• To perform data preprocessing

In gradient descent, what happens if the learning rate is too high?

• Convergence is too slow

• The algorithm may overshoot the minimum

• The gradient will vanish

• The cost function will become convex