Assignment 03 (Due date: Oct. 20, 2024)
Neural Networks
Assignment 03
Due date: Oct. 20, 2024
Performance Surface and and performance Optimization
 
Consider the following performance surface:

graphic
 
Assuming an initial point
 graphic 
And given a direction
 graphic
  • Find the value of the function and gradient and Hessian at graphic 
  • Find the Taylor series of this function up to the second derivatives aroundgraphic
  • Write the Taylor series expansion of the previous step as quadratic function in matrix form.
  • Perform two steps of gradient descent using minimization along a line (calculate graphic ) and show the graphic and  graphic positions and the value of the of the function after each step.
  • Perform two steps of gradient descent using graphic and show the graphic and  graphic positions and the value of the of the function after each step.
  • Perform one step of minimization in the direction of graphic and show the value graphic and the value of the function after the step.
Submission guidelibnes:
 
It is necessary to display your calculations and provide explanations for each step and show which equation you are planning to use. Simply presenting the final values without detailing the process will not be sufficient to receive credit.
 
For example, when trying to find the Taylor series, you should articulate it as follows:
 
To find Taylor series of the function up to the second derivative, I will use the following equation:
graphic
 
 
You must submit your assignment as a MSWord or a pdf document.
  • The first four lines of any submitted file must follow the following format according to the assignment submission guidelines.
# Your name (last name, first name)
# Your student ID (100x_xxx_xxx)
# Date of submission (yyyy_mm_dd)
# Assignment_nn_kk
 
  • Change the name of the file according to the submission guidelines.
  • Create a directory and name it according to the submission guidelines and include your file in that directory.
  • Zip the directory and upload it  to Canvas according to the submission guidelines.
 
 
 
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