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Due Wednesday December 4, in class

• Section 10.1
  • Read Section 10.1.
  • Worked example (group work): Solve the following problem (not from the text).
    • 1. Use DESMOS to determine the relevant \(r_i, b_0\) and \(w_i\) so that \[z=b_0+\Sigma w_ir_i\] is equal to the piecewise linear function \[f(x) = \left\{\matrix{ -6x-4&-1\lt x \lt -0.5\cr -x-1.5 & -0.5\lt x\lt 0.5\cr 4x-4 & 0.5\lt x\lt 1 }\right. \] on the interval \(-1\leq x \leq 1\).
  • Homework: 1* (below)
  • Hand In: 1* (below) :
    • 1*. Use DESMOS to determine the relevant \(r_i, b_0\) and \(w_i\) so that \[z=b_0+\Sigma w_ir_i\] is equal to the piecewise linear function \[f(x) = \left\{\matrix{2x+1&-1\lt x\lt -0.5\cr -4x-2 & -0.5\lt x\lt 0\cr 8x-2 & 0\lt x\lt 0.5\cr -2x+3 & 0.5\lt x\lt 1}\right.\] on the interval \(-1\leq x \leq 1\).
• Section 10.2
  • Read Section 10.2.
  • Neural net playground
  • Neural network worksheet
  • Machine learning playground - including several methods
  • Worked example (group work): 3.
  • Homework: 1, 3, 4
  • Hand In: 1*:
    • 1*. Follow the instructions for Problem 1, but this time run the training with \(N=3\) neurons (one layer and the two original inputs). Repeat the training 20 times and report the numbers of sides of the resulting white polygon in a frequency table (how many times did you get \(n\) sides for \(n = 1, 2, 3, 4, 5, 6, ...\)). Stop the training after no more than 1000 epochs (sooner if the training stabilizes quickly) for each trial. Make sure you reset the training between trainings. Did you have any trainings when the test and/or training loss was more than 0.2? When?
  • Link to the article Strang refers to on Page 384 about solving and generating university-level math problems: A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level