diff --git a/Notebooks/Chap07/7_1_Backpropagation_in_Toy_Model.ipynb b/Notebooks/Chap07/7_1_Backpropagation_in_Toy_Model.ipynb index 1dd8bb0..9f3e7bd 100644 --- a/Notebooks/Chap07/7_1_Backpropagation_in_Toy_Model.ipynb +++ b/Notebooks/Chap07/7_1_Backpropagation_in_Toy_Model.ipynb @@ -4,7 +4,7 @@ "metadata": { "colab": { "provenance": [], - "authorship_tag": "ABX9TyP5wHK5E7/el+vxU947K3q8", + "authorship_tag": "ABX9TyPmaYT+KLPAmZxse087Eisa", "include_colab_link": true }, "kernelspec": { @@ -281,7 +281,7 @@ "\\frac{\\partial \\ell_i}{\\partial h_{3}} =\\frac{\\partial f_{3}}{\\partial h_{3}} \\frac{\\partial \\ell_i}{\\partial f_{3}} .\n", "\\end{equation}\n", "\n", - "The left-hand side asks how $\\ell_i$ changes when $h_{3}$ changes. The right-hand side says we can decompose this into (i) how $ell_i$ changes when $f_{3}$ changes and how $f_{3}$ changes when $h_{3}$ changes. So you get a chain of events happening: $h_{3}$ changes $f_{3}$, which changes $\\ell_i$, and the derivatives represent the effects of this chain. Notice that we computed the first of these derivatives already and is $2 (f_3-y)$. We calculated $f_{3}$ in step 1. The second term is the derivative of $\\beta_{3} + \\omega_{3}h_{3}$ with respect to $h_3$ which is simply $\\omega_3$. \n", + "The left-hand side asks how $\\ell_i$ changes when $h_{3}$ changes. The right-hand side says we can decompose this into (i) how $\\ell_i$ changes when $f_{3}$ changes and how $f_{3}$ changes when $h_{3}$ changes. So you get a chain of events happening: $h_{3}$ changes $f_{3}$, which changes $\\ell_i$, and the derivatives represent the effects of this chain. Notice that we computed the first of these derivatives already and is $2 (f_3-y)$. We calculated $f_{3}$ in step 1. The second term is the derivative of $\\beta_{3} + \\omega_{3}h_{3}$ with respect to $h_3$ which is simply $\\omega_3$. \n", "\n", "We can continue in this way, computing the derivatives of the output with respect to these intermediate quantities:\n", "\n",