From ef6570ab4167f608226f6dc57bbb0d213b78c090 Mon Sep 17 00:00:00 2001 From: "caizhi.wcz" Date: Thu, 10 Aug 2023 09:34:15 +0800 Subject: [PATCH] Fix incorrect formula in Perceptron.ipynb of lesson 3 --- lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb b/lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb index d356632f..6df73e93 100644 --- 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",