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Fix typos in the Adam optimizer #15

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Fix typos in the Adam optimizer #15

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12 changes: 6 additions & 6 deletions doc/LectureNotes/chapteroptimization.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -2727,7 +2727,7 @@
},
"source": [
"$$\n",
"\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
"\\hat{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
"$$"
]
},
Expand All @@ -2739,7 +2739,7 @@
},
"source": [
"$$\n",
"\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
"\\hat{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
"$$"
]
},
Expand All @@ -2751,7 +2751,7 @@
},
"source": [
"$$\n",
"\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
"\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\hat{\\mathbf{m}}_t \\over \\sqrt{\\hat{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
"$$"
]
},
Expand Down Expand Up @@ -2786,8 +2786,8 @@
"Like in RMSprop, the effective step size of a parameter depends on the\n",
"magnitude of its gradient squared. To understand this better, let us\n",
"rewrite this expression in terms of the variance\n",
"$\\boldsymbol{\\sigma}_t^2 = \\boldsymbol{\\mathbf{s}}_t -\n",
"(\\boldsymbol{\\mathbf{m}}_t)^2$. Consider a single parameter $\\theta_t$. The\n",
"$\\hat{\\sigma}_t^2 = \\hat{\\mathbf{s}}_t -\n",
"(\\hat{\\mathbf{m}}_t)^2$. Consider a single parameter $\\theta_t$. The\n",
"update rule for this parameter is given by"
]
},
Expand All @@ -2799,7 +2799,7 @@
},
"source": [
"$$\n",
"\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n",
"\\Delta \\theta_{t+1}= -\\eta_t { \\hat{\\mathbf{m}}_t \\over \\sqrt{\\hat{\\sigma}_t^2 + \\hat{m}_t^2 }+\\epsilon}.\n",
"$$"
]
},
Expand Down