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2024-02-17 12:35:18 -05:00
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Notebooks/Chap06/6_5_Adam.ipynb
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@@ -4,7 +4,6 @@
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@@ -169,7 +168,7 @@
{ {
"cell_type": "markdown", "cell_type": "markdown",
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"Because the function changes much faster in $\\phi_1$ than in $\\phi_0$, there is no great step size to choose. If we set the step size so that it makes sensible progress in the $\\phi_1$ direction, then it takes many iterations to converge. If we set the step size so that we make sensible progress in the $\\phi_{0}$ direction, then the path oscillates in the $\\phi_1$ direction. \n", "Because the function changes much faster in $\\phi_1$ than in $\\phi_0$, there is no great step size to choose. If we set the step size so that it makes sensible progress in the $\\phi_1$ direction, then it takes many iterations to converge. If we set the step size so that we make sensible progress in the $\\phi_0$ direction, then the path oscillates in the $\\phi_1$ direction. \n",
"\n", "\n",
"This motivates Adam. At the core of Adam is the idea that we should just determine which way is downhill along each axis (i.e. left/right for $\\phi_0$ or up/down for $\\phi_1$) and move a fixed distance in that direction." "This motivates Adam. At the core of Adam is the idea that we should just determine which way is downhill along each axis (i.e. left/right for $\\phi_0$ or up/down for $\\phi_1$) and move a fixed distance in that direction."
], ],
@@ -285,4 +284,4 @@
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} }
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} }