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hw5-solutions - University of Texas, Dallas CS 6320

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CS 6320.002: Natural Language Processing Fall 2020 Homework 5 — 45 points Issued 11 Nov. 2020 Due 11:59 pm 25 Nov. 2020 Deliverables: Answers can be typed directly into Gradescope. LaTeX can be... handtyped or generated using Mathpix Snip. See the assignment guide for more details. What does it mean to show your work? Write out the math step-by-step; we should be able to clearly follow your reasoning from one step to another. (You can combine obvious steps like simplifying fractions or doing basic arithmetic.) The point of showing your work is twofold: to get partial credit if your answer is incorrect, and to show us that you worked the problem yourself and understand it. We will deduct points if steps are missing. 1 Recurrent Neural Networks — 30 points The questions in this section are based on material covered in Week 13. W = (n × m), U = (n × n), and b = (n × 1). V = (3 × n). 1.1 Backpropagation Through Time Suppose we have the following small recurrent neural network: h (t) = RELU(w1x (t) 1 + w2x (t) 2 + uh(t−1) + bh) y (t) = σ(vh(t) + by) (The superscript notation (t) is used to avoid confusion when we also want to use subscripts for our parameters; h (t) means the same thing as ht in the slides.) Suppose we have the following loss function: L(y) = −ln(y) (For the problems in this section, it is not required to submit a picture of the computation graph, but it is highly recommended to draw one for yourself to aid in answering the questions.) 1.1.1 What is the partial derivative of the loss L(y (1)) with respect to the parameter w1, ie. ∂L(y (1)) ∂w1 , in this network? Show your work and simplify the expression as much as possible. You can assume that all values are positive for R [Show More]

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