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Merge pull request #239 from tsreaper/lesson-3-fix 

Fix incorrect formula in Perceptron.ipynb of lesson 3
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Pikachú 2023-10-27 15:07:19 +03:00 committed by GitHub
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lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb
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@ -166,7 +166,7 @@
" \\end{cases} \\\\\n",
"$$\n",
"\n",
"However, a generic linear model should also have a bias, i.e. ideally we should compute $y$ as $y=f(\\mathbf{w}^{\\mathrm{T}}\\mathbf{x})+\\mathbf{b}$. To simplify our model, we can get rid of this bias term by adding one more dimension to our input features, which always equals to 1:"
"However, a generic linear model should also have a bias, i.e. ideally we should compute $y$ as $y=f(\\mathbf{w}^{\\mathrm{T}}\\mathbf{x}+\\mathbf{b})$. To simplify our model, we can get rid of this bias term by adding one more dimension to our input features, which always equals to 1:"
]
},
{
@ -215,7 +215,7 @@
" \n",
"We will use the process of **gradient descent**. Starting with some initial random weights $\\mathbf{w}^{(0)}$, we will adjust weights on each step of the training using the gradient of $E$:\n",
"\n",
"$$\\mathbf{w}^{\\tau + 1}=\\mathbf{w}^{\\tau} - \\eta \\nabla E(\\mathbf{w}) = \\mathbf{w}^{\\tau} + \\eta \\mathbf{x}_{n} t_{n}$$\n",
"$$\\mathbf{w}^{\\tau + 1}=\\mathbf{w}^{\\tau} - \\eta \\nabla E(\\mathbf{w}) = \\mathbf{w}^{\\tau} + \\eta\\sum_{n \\in \\mathcal{M}}\\mathbf{x}_{n} t_{n}$$\n",
"\n",
"where $\\eta$ is a **learning rate**, and $\\tau\\in\\mathbb{N}$ - number of iteration.\n",
"\n",