From e6c6759277c3e1275cec23a7eeca091997891013 Mon Sep 17 00:00:00 2001
From: Sucio <esteban.cosserat@gmail.com>
Date: Fri, 10 Nov 2023 08:39:51 +0100
Subject: [PATCH] Update Rapport.ipynb
---
Rapport.ipynb | 9 ++++++---
1 file changed, 6 insertions(+), 3 deletions(-)
diff --git a/Rapport.ipynb b/Rapport.ipynb
index ff5895c..9bf5fef 100644
--- a/Rapport.ipynb
+++ b/Rapport.ipynb
@@ -466,18 +466,21 @@
"\n",
"## Réseaux de Neurones Artificiels\n",
"\n",
- "$$Z^{L+1}=W^{L+1}A^{L}+B^{L+1}$$\n",
- "\n",
- "$$A^{L+1}=\\sigma(Z^{L+1})$$\n",
+ "$Z^{L+1}=W^{L+1}A^{L}+B^{L+1}\\\\\n",
+ "A^{L+1}=\\sigma(Z^{L+1})$\n",
"\n",
"$$C = \\frac{1}{N_{out}}\\sum_{i=1}^{N_{out}} (\\hat{y_i} - y_i)^2$$\n",
"\n",
"### 1\n",
"\n",
"$$\\sigma(x)=\\frac{1}{1+e^{-x}} $$\n",
+ "\n",
"$$\\Rightarrow \\sigma'(x)=\\frac{-e^{-x}}{-(1+e^{-x})^2} $$\n",
+ "\n",
"$$\\Rightarrow \\sigma'(x)=\\frac{1}{1+e^{-x}}(\\frac{1+e^{-x}-1}{1+e^{-x}}) $$\n",
+ "\n",
"$$\\Rightarrow \\sigma'(x)=\\sigma(\\frac{1+e^{-x}}{1+e^{-x}}-\\frac{1}{1+e^{-x}}) $$\n",
+ "\n",
"$$\\Rightarrow \\sigma'(x)=\\sigma(1-\\sigma)$$\n",
"\n",
"### 2\n",
--
GitLab