From 592d4b55188e0bb6581f27778ea5806a7ae14365 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Quentin=20Gallou=C3=A9dec?= <45557362+qgallouedec@users.noreply.github.com> Date: Tue, 4 Oct 2022 22:34:00 +0200 Subject: [PATCH] desired output -> label --- README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index b149587..f65360d 100644 --- a/README.md +++ b/README.md @@ -117,7 +117,7 @@ First of all, let's focus on the backpropagation of the gradient with an example Let's consider a network with a hidden layer. The weight matrix of the layer $`L`$ is denoted $`W^{(L)}`$. The bias vector of the layer $`L`$ is denoted $`B^{(L)}`$. We choose the sigmoid function, denoted $`\sigma`$, as the activation function. The output vector of the layer $`L`$ before activation is denoted $`Z^{(L)}`$. The output vector of the layer $`L`$ after activation is denoted $`A^{(L)}`$. By convention, we note $`A^{(0)}`$ the network input vector. Thus $`Z^{(L+1)} = W^{(L+1)}A^{(L)} + B^{(L+1)}`$ and $`A^{(L+1)} = \sigma\left(Z^{(L+1)}\right)`$. In our example, the output is $`\hat{Y} = A^{(2)}`$. -Let $`Y`$ be the desired output. We use mean squared error (MSE) as the cost function. Thus, the cost is $`C = \frac{1}{N_{out}}\sum_{i=1}^{N_{out}} (\hat{y_i} - y_i)^2`$. +Let $`Y`$ be the labels (desired output). We use mean squared error (MSE) as the cost function. Thus, the cost is $`C = \frac{1}{N_{out}}\sum_{i=1}^{N_{out}} (\hat{y_i} - y_i)^2`$. 1. Prove that $`\sigma' = \sigma \times (1-\sigma)`$ 2. Express $`\frac{\partial C}{\partial A^{(2)}}`$, i.e. the vector of $`\frac{\partial C}{\partial a^{(2)}_i}`$ as a function of $`A^{(2)}`$ and $`Y`$. @@ -138,8 +138,8 @@ N = 30 # number of input data d_in = 3 # input dimension d_h = 3 # number of neurons in the hidden layer d_out = 2 # output dimension (number of neurons of the output layer) -data = np.random.rand(N, d_in) # create a random input -labels = np.random.rand(N, d_out) # create a random desired output +data = np.random.rand(N, d_in) # create a random data +labels = np.random.rand(N, d_out) # create a random labels # Forward pass a0 = data # the data are the input of the first layer -- GitLab