From 9eee507d732f6a3b98ca383ecec9508ca6fac737 Mon Sep 17 00:00:00 2001 From: Michael Zhang Date: Fri, 10 Nov 2023 00:42:46 -0600 Subject: [PATCH] 1b progress --- assignments/hwk03/hw3_sol.typ | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) diff --git a/assignments/hwk03/hw3_sol.typ b/assignments/hwk03/hw3_sol.typ index 80dc96a..c944f40 100644 --- a/assignments/hwk03/hw3_sol.typ +++ b/assignments/hwk03/hw3_sol.typ @@ -38,4 +38,28 @@ Solved as: &= - sum_t (r^t - y^t) v_h x_h (1-tanh^2(ww_2 dot xx)) \ $ +Updates: + +- $Delta v_h = eta sum_t (r^t-y^t) z^t_h$ +- $Delta w_(1,j) = eta sum_t (r^t - y^t) v_h x_h cases(0 "if" ww_1 dot xx <0, 1 "otherwise")$ +- $Delta w_(2,j) = eta sum_t (r^t - y^t) v_h x_h (1-tanh^2(ww_2 dot xx))$ + = Problem 1b + +- $E(ww,vv|XX) = - sum_t r^t log y^t + (1 - r^t) log (1 - y^t)$ +- $y^t = "sigmoid"(v_2 z_2 + v_1 z_1 + v_0)$ +- $z^t_1 = "ReLU"(w_2 x^t_2 + w_1 x^t_1 + w_0)$ +- $z^t_2 = tanh(w_2 x^t_2 + w_1 x^t_1 + w_0)$ + +Updates: + +- + Same as above: + $Delta v_h = eta sum_t (r^t-y^t) z^t_h$ + +- $ + frac(diff E, diff w_j) &= - sum_t (frac(diff E, diff y^t) frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j)) + (frac(diff E, diff y^t) frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ + &= - sum_t frac(diff E, diff y^t) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ + &= - sum_t (frac(r^t, y^t) - frac(1-r^t, 1-y^t)) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ + &= - sum_t (frac(r^t-y^t, y^t (1-y^t))) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ + $ \ No newline at end of file