diff --git a/Rapport.ipynb b/Rapport.ipynb
index 8655f08bb0cfb04e2298936dc127b5d8fde25ce8..e8c60ae4d9645762fe1cf15739c05c38eb761c2e 100644
--- a/Rapport.ipynb
+++ b/Rapport.ipynb
@@ -496,101 +496,73 @@
"\n",
"### 3\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial Z^{(2)}}=\\frac{\\partial C}{\\partial A^{(2)}}\\frac{\\partial A^{(2)}}{\\partial Z^{(2)}} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial Z^{(2)}}=\\frac{\\partial C}{\\partial A^{(2)}}\\frac{\\partial A^{(2)}}{\\partial Z^{(2)}} $$\n",
- "$$\n",
- "A^{(2)}=\\sigma (Z^{(2)}) $$\n",
- "$$\n",
- "\\frac{\\partial A^{(2)}}{\\partial Z^{(2)}}=A^{(2)}(1-A^{(2)}) $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial Z^{(2)}}=\\frac{\\partial C}{\\partial A^{(2)}}[A^{(2)}(1-A^{(2)})]\n",
+ "$$A^{(2)}=\\sigma (Z^{(2)}) $$\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial A^{(2)}}{\\partial Z^{(2)}}=A^{(2)}(1-A^{(2)}) $$\n",
+ "\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial Z^{(2)}}=\\frac{\\partial C}{\\partial A^{(2)}}[A^{(2)}(1-A^{(2)})]$$\n",
"\n",
"### 4\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial W^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial W^{(2)}} $$\n",
+ "\n",
+ "$$Z^{(2)}=W^{(2)}A^{(1)}+B^{(2)} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial W^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial W^{(2)}} $$\n",
- "$$\n",
- "Z^{(2)}=W^{(2)}A^{(1)}+B^{(2)} $$\n",
- "$$\n",
- "\\frac{\\partial Z^{(2)}}{\\partial W^{(2)}}=A^{(1)} $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial W^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}A^{(1)}\n",
+ "$$\\frac{\\partial Z^{(2)}}{\\partial W^{(2)}}=A^{(1)} $$\n",
"\n",
- "$$\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial W^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}A^{(1)}$$\n",
"\n",
"### 5\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial B^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial B^{(2)}} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial B^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial B^{(2)}} $$\n",
- "$$\n",
- "Z^{(2)}=W^{(2)}A^{(1)}+B^{(2)} $$\n",
- "$$\n",
- "\\frac{\\partial Z^{(2)}}{\\partial B^{(2)}}=1 $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial B^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\n",
+ "$$Z^{(2)}=W^{(2)}A^{(1)}+B^{(2)} $$\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial Z^{(2)}}{\\partial B^{(2)}}=1 $$\n",
+ "\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial B^{(2)}}=\\frac{\\partial C}{\\partial Z^{(2)}}$$\n",
"\n",
"### 6\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial A^{(1)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial A^{(1)}} $$\n",
+ "\n",
+ "$$Z^{(2)}=W^{(2)}A^{(1)}+B^{(2)} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial A^{(1)}}=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial A^{(1)}} $$\n",
- "$$\n",
- "Z^{(2)}=W^{(2)}A^{(1)}+B^{(2)} $$\n",
- "$$\n",
- "\\frac{\\partial Z^{(2)}}{\\partial A^{(1)}}=W^{(2)} $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial A^{(1)}}=\\frac{\\partial C}{\\partial Z^{(2)}}W^{(2)}\n",
+ "$$\\frac{\\partial Z^{(2)}}{\\partial A^{(1)}}=W^{(2)} $$\n",
"\n",
- "$$\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial A^{(1)}}=\\frac{\\partial C}{\\partial Z^{(2)}}W^{(2)}$$\n",
"\n",
"### 7\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial Z^{(1)}}=\\frac{\\partial C}{\\partial A^{(1)}}\\frac{\\partial A^{(1)}}{\\partial Z^{(1)}} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial Z^{(1)}}=\\frac{\\partial C}{\\partial A^{(1)}}\\frac{\\partial A^{(1)}}{\\partial Z^{(1)}} $$\n",
- "$$\n",
- "A^{(1)}=\\sigma (Z^{(1)}) $$\n",
- "$$\n",
- "\\frac{\\partial A^{(1)}}{\\partial Z^{(1)}}=A^{(1)}(1-A^{(1)}) $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial Z^{(1)}}=\\frac{\\partial C}{\\partial A^{(1)}}[A^{(1)}(1-A^{(1)})]\n",
+ "$$A^{(1)}=\\sigma (Z^{(1)}) $$\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial A^{(1)}}{\\partial Z^{(1)}}=A^{(1)}(1-A^{(1)}) $$\n",
+ "\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial Z^{(1)}}=\\frac{\\partial C}{\\partial A^{(1)}}[A^{(1)}(1-A^{(1)})]$$\n",
"\n",
"### 8\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial W^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}\\frac{\\partial Z^{(1)}}{\\partial W^{(1)}} $$\n",
+ "\n",
+ "$$Z^{(1)}=W^{(1)}A^{(0)}+B^{(1)} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial W^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}\\frac{\\partial Z^{(1)}}{\\partial W^{(1)}} $$\n",
- "$$\n",
- "Z^{(1)}=W^{(1)}A^{(0)}+B^{(1)} $$\n",
- "$$\n",
- "\\frac{\\partial Z^{(1)}}{\\partial W^{(1)}}=A^{(0)} $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial W^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}A^{(0)}\n",
+ "$$\\frac{\\partial Z^{(1)}}{\\partial W^{(1)}}=A^{(0)} $$\n",
"\n",
- "$$\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial W^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}A^{(0)}$$\n",
"\n",
"### 9\n",
"\n",
- "$$\n",
+ "$$\\frac{\\partial C}{\\partial B^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}\\frac{\\partial Z^{(1)}}{\\partial B^{(1)}} $$\n",
"\n",
- "\\frac{\\partial C}{\\partial B^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}\\frac{\\partial Z^{(1)}}{\\partial B^{(1)}} $$\n",
- "$$\n",
- "Z^{(1)}=W^{(1)}A^{(0)}+B^{(1)} $$\n",
- "$$\n",
- "\\frac{\\partial Z^{(1)}}{\\partial B^{(1)}}=1 $$\n",
- "$$\n",
- "\\Rightarrow \\frac{\\partial C}{\\partial B^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}\n",
+ "$$Z^{(1)}=W^{(1)}A^{(0)}+B^{(1)} $$\n",
"\n",
- "$$\n"
+ "$$\\frac{\\partial Z^{(1)}}{\\partial B^{(1)}}=1 $$\n",
+ "\n",
+ "$$\\Rightarrow \\frac{\\partial C}{\\partial B^{(1)}}=\\frac{\\partial C}{\\partial Z^{(1)}}$$\n"
]
},
{
@@ -598,8 +570,8 @@
"metadata": {},
"source": [
"### 10\n",
- "$loss=\\frac{1}{N_{out}}\\sum_{i=1}^{N_{out}}-(y_i*log(\\hat{y_i})+(1-y_1)*log(1-\\hat{y_i}))\n",
- "$"
+ "\n",
+ "$$loss=\\frac{1}{N_{out}}\\sum_{i=1}^{N_{out}}-(y_i*log(\\hat{y_i})+(1-y_1)*log(1-\\hat{y_i}))$$"
]
},
{