Fix incorrect formula in Perceptron.ipynb of lesson 3

caizhi.wcz · caizhi.wcz · commit ef6570ab4167 · 2023-08-10T09:34:15.000+08:00
diff --git a/lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb b/lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb
@@ -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",
