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      Readme.md
  2. +415
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      main.ipynb

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Readme.md View File

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# Exam
$$ \frac{\partial E}{\partial w_{jk}}= -e_j\cdot \sigma\left(\sum_i w_{ij} o\_i\right) \left(1-\sigma\left(\sum\_i w\_{ij} o\_i\right) \right) o\_i $$
$$w_{New} = w_{old}-\alpha \frac{\partial E}{\partial w} $$
## Doing step by step
```
def af(x):
sigmoid = 1/(1+np.exp(-x))
return sigmoid
import numpy as np
inN = 3
hiN= 4
outN=3
lr= 0.4
#weight W11 W21 W31
# W12 W22 W32
# .....
np.random.seed(53)
wih=np.random.rand(hiN, inN)-0.5
who=np.random.rand(outN, hiN)-0.5
print("Wih: ", wih)
print("Who: ", who)
Wih: [[ 0.34666241 0.06116554 -0.0451246 ]
[-0.14782509 0.08585138 0.03574974]
[ 0.32745628 -0.2354578 -0.02162094]
[-0.15221498 -0.36552168 -0.24002265]]
Who: [[-0.45236532 -0.1057067 -0.12838381 0.05673292]
[ 0.39749455 -0.33265411 -0.09279358 0.15235334]
[ 0.06774908 0.06651886 0.0243551 0.10758002]]
```
## Feedforward
```
inputList = [0.32, 0.27, 0.18]
inputs = np.array(inputList, ndmin=2).T
Xh = np.dot(wih, inputs)
print('Xh: ', Xh)
Oh = af(Xh)
print('Oh:', Oh)
# computing output
Xo = np.dot(who, Oh)
print('Xo: ', Xo)
Oo = af(Xo)
print('Oo: ', Oo)
Xh: [[ 0.11932424]
[-0.0176892 ]
[ 0.03732063]
[-0.19060372]]
Oh: [[0.52979571]
[0.49557782]
[0.50932908]
[0.45249281]]
Xo: [[-0.33176547]
[ 0.06741123]
[ 0.12994239]]
Oo: [[0.41781112]
[0.51684643]
[0.53243996]]
```
## Backpropagation
```
inputList = [0.32, 0.27, 0.18]
targetList = [0.82, 0.25, 0.44]
inputs = np.array(inputList, ndmin=2).T
target = np.array(targetList, ndmin=2).T
#computting hidden layer
Xh = np.dot(wih, inputs)
Oh = af(Xh)
# computing output
Xo = np.dot(who, Oh)
Oo = af(Xo)
# Output error
oe = target-Oo
# E propagation
hiddenE = np.dot(who.T, oe)
# updating weights
#who+=lr*np.dot(oe*Oo*(1-Oo), Oh.T)
#wih+=lr*np.dot(hiddenE*Oh*(1-Oh), inputs.T)
#print('New wih: ', wih)
#print('New who: ', who)
NewW=who-lr*np.dot(-oe*Oo*(1-Oo),Oh.T)
NewW
array([[-0.43163327, -0.08631366, -0.10845266, 0.07443995],
[ 0.38337319, -0.34586342, -0.10636942, 0.14029244],
[ 0.06287227, 0.06195702, 0.01966668, 0.10341479]])
newWho=who-lr*np.dot(-oe*Oo*(1-Oo), Oh.T)
newWho
array([[-0.43163327, -0.08631366, -0.10845266, 0.07443995],
[ 0.38337319, -0.34586342, -0.10636942, 0.14029244],
[ 0.06287227, 0.06195702, 0.01966668, 0.10341479]])
```
## Using class
```
import numpy as np
class NeuralNetwork:
# init method
def __init__(self, inputN,hiddenN, outputN, lr):
# creates a NN with three layers (input, hidden, output)
# inputN - Number of input nodes
# hiddenN - Number of hidden nodes
self.inN=inputN
self.hiN=hiddenN
self.outN=outputN
self.lr=lr
#weight W11 W21 W31
# W12 W22 W32
# .....
np.random.seed(53)
self.wih=np.random.rand(self.hiN, self.inN)-0.5
self.who=np.random.rand(self.outN,self.hiN)-0.5
print("Wih: ", self.wih)
print("Who: ", self.who)
pass
# NN computing method
def feedforward(self, inputList):
# computing hidden output
inputs = np.array(inputList, ndmin=2).T
self.Xh = np.dot(self.wih, inputs)
print('Xh: ', self.Xh)
self.af = lambda x:1/(1+np.exp(-x))
self.Oh = self.af(self.Xh)
print('Oh:', self.Oh)
# computing output
self.Xo = np.dot(self.who, self.Oh)
print('Xo: ', self.Xo)
self.Oo = self.af(self.Xo)
print('Oo: ', self.Oo)
pass
# NN trainning method
def backpropagation(self, inputList, targetList):
# data
lr = self.lr
inputs = np.array(inputList, ndmin=2).T
target = np.array(targetList, ndmin=2).T
#computting hidden layer
Xh = np.dot(self.wih, inputs)
af = lambda x:1/(1+np.exp(-x))
Oh = af(Xh)
# computing output
Xo = np.dot(self.who, Oh)
Oo = af(Xo)
# Output error
oe = target-Oo
# E propagation
hiddenE = np.dot(self.who.T, oe)
# updating weights
self.who+=lr*np.dot(oe*Oo*(1-Oo), Oh.T)
self.wih+=lr*np.dot(hiddenE*Oh*(1-Oh), inputs.T)
return self.wih, self.who
```
```
NN = NeuralNetwork(3,4,3,0.4)
Wih: [[ 0.34666241 0.06116554 -0.0451246 ]
[-0.14782509 0.08585138 0.03574974]
[ 0.32745628 -0.2354578 -0.02162094]
[-0.15221498 -0.36552168 -0.24002265]]
Who: [[-0.45236532 -0.1057067 -0.12838381 0.05673292]
[ 0.39749455 -0.33265411 -0.09279358 0.15235334]
[ 0.06774908 0.06651886 0.0243551 0.10758002]]
```
```
NN.feedforward([0.32, 0.27, 0.18])
Xh: [[ 0.11932424]
[-0.0176892 ]
[ 0.03732063]
[-0.19060372]]
Oh: [[0.52979571]
[0.49557782]
[0.50932908]
[0.45249281]]
Xo: [[-0.33176547]
[ 0.06741123]
[ 0.12994239]]
Oo: [[0.41781112]
[0.51684643]
[0.53243996]]
```
```
NN.backpropagation([0.32, 0.27, 0.18], [0.82, 0.25, 0.44])
(array([[ 0.33727924, 0.05324849, -0.05040263],
[-0.14654184, 0.08693412, 0.03647157],
[ 0.32652462, -0.23624388, -0.02214499],
[-0.15309598, -0.36626503, -0.24051822]]),
array([[-0.43163327, -0.08631366, -0.10845266, 0.07443995],
[ 0.38337319, -0.34586342, -0.10636942, 0.14029244],
[ 0.06287227, 0.06195702, 0.01966668, 0.10341479]]))
```

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main.ipynb View File

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{
"cells": [
{
"cell_type": "markdown",
"id": "77c1109a-ca7c-4005-908e-e89b22de92ff",
"metadata": {},
"source": [
"# Exam\n",
"$$ \\frac{\\partial E}{\\partial w_{jk}}= -e_j\\cdot \\sigma\\left(\\sum_i w_{ij} o_i\\right) \\left(1-\\sigma\\left(\\sum_i w_{ij} o_i\\right) \\right) o_i $$\n",
"\n",
"$$w_{New} = w_{old}-\\alpha \\frac{\\partial E}{\\partial w} $$"
]
},
{
"cell_type": "markdown",
"id": "9878b172-ce84-4d7d-822b-a2c0bda6b7cf",
"metadata": {},
"source": [
"## Doing step by step"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "bafc3aff-e2eb-43cf-9d8e-6a7e252be593",
"metadata": {},
"outputs": [],
"source": [
"def af(x):\n",
" sigmoid = 1/(1+np.exp(-x))\n",
" return sigmoid"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7a83cf35-172a-436c-8e68-ed6ae9e2eeba",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wih: [[ 0.34666241 0.06116554 -0.0451246 ]\n",
" [-0.14782509 0.08585138 0.03574974]\n",
" [ 0.32745628 -0.2354578 -0.02162094]\n",
" [-0.15221498 -0.36552168 -0.24002265]]\n",
"Who: [[-0.45236532 -0.1057067 -0.12838381 0.05673292]\n",
" [ 0.39749455 -0.33265411 -0.09279358 0.15235334]\n",
" [ 0.06774908 0.06651886 0.0243551 0.10758002]]\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"inN = 3\n",
"hiN= 4\n",
"outN=3\n",
"lr= 0.4\n",
" \n",
"#weight W11 W21 W31\n",
"# W12 W22 W32\n",
"# .....\n",
"np.random.seed(53) \n",
"wih=np.random.rand(hiN, inN)-0.5\n",
"who=np.random.rand(outN, hiN)-0.5\n",
"print(\"Wih: \", wih)\n",
"print(\"Who: \", who)"
]
},
{
"cell_type": "markdown",
"id": "8c2a8d42-b5e2-40c4-9220-50e8cc42ed7e",
"metadata": {},
"source": [
"## Feedforward"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c3e66fc9-a311-4d30-b312-08e6519f4069",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Xh: [[ 0.11932424]\n",
" [-0.0176892 ]\n",
" [ 0.03732063]\n",
" [-0.19060372]]\n",
"Oh: [[0.52979571]\n",
" [0.49557782]\n",
" [0.50932908]\n",
" [0.45249281]]\n",
"Xo: [[-0.33176547]\n",
" [ 0.06741123]\n",
" [ 0.12994239]]\n",
"Oo: [[0.41781112]\n",
" [0.51684643]\n",
" [0.53243996]]\n"
]
}
],
"source": [
"inputList = [0.32, 0.27, 0.18]\n",
"inputs = np.array(inputList, ndmin=2).T\n",
"Xh = np.dot(wih, inputs)\n",
"print('Xh: ', Xh)\n",
"\n",
"Oh = af(Xh)\n",
"print('Oh:', Oh)\n",
"\n",
"# computing output \n",
"Xo = np.dot(who, Oh)\n",
"print('Xo: ', Xo)\n",
"Oo = af(Xo)\n",
"print('Oo: ', Oo)"
]
},
{
"cell_type": "markdown",
"id": "87b902d1-0046-425f-8ade-def73a605374",
"metadata": {},
"source": [
"## Backpropagation"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9703ca9c-9a8d-4f4a-bc89-f3984620ef1f",
"metadata": {},
"outputs": [],
"source": [
"inputList = [0.32, 0.27, 0.18]\n",
"targetList = [0.82, 0.25, 0.44]"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b335a7d5-33bf-4af0-930b-794c77bdc116",
"metadata": {},
"outputs": [],
"source": [
"inputs = np.array(inputList, ndmin=2).T\n",
"target = np.array(targetList, ndmin=2).T\n",
" \n",
"#computting hidden layer\n",
"Xh = np.dot(wih, inputs)\n",
"Oh = af(Xh)\n",
" \n",
"# computing output \n",
"Xo = np.dot(who, Oh)\n",
"Oo = af(Xo)\n",
" \n",
"# Output error\n",
"oe = target-Oo\n",
"# E propagation\n",
"hiddenE = np.dot(who.T, oe)\n",
" \n",
"# updating weights\n",
"#who+=lr*np.dot(oe*Oo*(1-Oo), Oh.T) \n",
"#wih+=lr*np.dot(hiddenE*Oh*(1-Oh), inputs.T) \n",
"#print('New wih: ', wih)\n",
"#print('New who: ', who)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "0164f74a-ee41-4cf4-92d3-72dfdc85d3bc",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.43163327, -0.08631366, -0.10845266, 0.07443995],\n",
" [ 0.38337319, -0.34586342, -0.10636942, 0.14029244],\n",
" [ 0.06287227, 0.06195702, 0.01966668, 0.10341479]])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"NewW=who-lr*np.dot(-oe*Oo*(1-Oo),Oh.T)\n",
"NewW"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "becd14fd-c1bf-400e-995d-c3ffee8167f5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.43163327, -0.08631366, -0.10845266, 0.07443995],\n",
" [ 0.38337319, -0.34586342, -0.10636942, 0.14029244],\n",
" [ 0.06287227, 0.06195702, 0.01966668, 0.10341479]])"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"newWho=who-lr*np.dot(-oe*Oo*(1-Oo), Oh.T)\n",
"newWho"
]
},
{
"cell_type": "markdown",
"id": "03cba5b5-7d31-464a-b56f-04004efe67b2",
"metadata": {},
"source": [
"## Using class"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "de8798ec-ddf2-40d2-bdd3-ed9d82059829",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"\n",
"class NeuralNetwork:\n",
" # init method\n",
" def __init__(self, inputN,hiddenN, outputN, lr):\n",
" # creates a NN with three layers (input, hidden, output)\n",
" # inputN - Number of input nodes\n",
" # hiddenN - Number of hidden nodes\n",
" self.inN=inputN\n",
" self.hiN=hiddenN\n",
" self.outN=outputN\n",
" self.lr=lr\n",
" \n",
" #weight W11 W21 W31\n",
" # W12 W22 W32\n",
" # .....\n",
" np.random.seed(53) \n",
" self.wih=np.random.rand(self.hiN, self.inN)-0.5\n",
" self.who=np.random.rand(self.outN,self.hiN)-0.5\n",
" print(\"Wih: \", self.wih)\n",
" print(\"Who: \", self.who)\n",
" pass\n",
" \n",
" # NN computing method\n",
" def feedforward(self, inputList):\n",
" # computing hidden output\n",
" inputs = np.array(inputList, ndmin=2).T\n",
" self.Xh = np.dot(self.wih, inputs)\n",
" print('Xh: ', self.Xh)\n",
" self.af = lambda x:1/(1+np.exp(-x))\n",
" self.Oh = self.af(self.Xh)\n",
" print('Oh:', self.Oh)\n",
" \n",
" # computing output \n",
" self.Xo = np.dot(self.who, self.Oh)\n",
" print('Xo: ', self.Xo)\n",
" self.Oo = self.af(self.Xo)\n",
" print('Oo: ', self.Oo)\n",
" pass\n",
" \n",
" # NN trainning method \n",
" def backpropagation(self, inputList, targetList):\n",
" # data\n",
" lr = self.lr \n",
" inputs = np.array(inputList, ndmin=2).T\n",
" target = np.array(targetList, ndmin=2).T\n",
" \n",
" #computting hidden layer\n",
" Xh = np.dot(self.wih, inputs)\n",
" af = lambda x:1/(1+np.exp(-x))\n",
" Oh = af(Xh)\n",
" \n",
" # computing output \n",
" Xo = np.dot(self.who, Oh)\n",
" Oo = af(Xo)\n",
" \n",
" # Output error\n",
" oe = target-Oo\n",
" # E propagation\n",
" hiddenE = np.dot(self.who.T, oe)\n",
" \n",
" # updating weights\n",
" self.who+=lr*np.dot(oe*Oo*(1-Oo), Oh.T) \n",
" self.wih+=lr*np.dot(hiddenE*Oh*(1-Oh), inputs.T) \n",
" return self.wih, self.who"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e38c98a0-2edc-4733-a2e0-d911f44236a1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wih: [[ 0.34666241 0.06116554 -0.0451246 ]\n",
" [-0.14782509 0.08585138 0.03574974]\n",
" [ 0.32745628 -0.2354578 -0.02162094]\n",
" [-0.15221498 -0.36552168 -0.24002265]]\n",
"Who: [[-0.45236532 -0.1057067 -0.12838381 0.05673292]\n",
" [ 0.39749455 -0.33265411 -0.09279358 0.15235334]\n",
" [ 0.06774908 0.06651886 0.0243551 0.10758002]]\n"
]
}
],
"source": [
"NN = NeuralNetwork(3,4,3,0.4)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "87a9faaa-d8f8-4ea7-b098-d3e8cf06fea8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Xh: [[ 0.11932424]\n",
" [-0.0176892 ]\n",
" [ 0.03732063]\n",
" [-0.19060372]]\n",
"Oh: [[0.52979571]\n",
" [0.49557782]\n",
" [0.50932908]\n",
" [0.45249281]]\n",
"Xo: [[-0.33176547]\n",
" [ 0.06741123]\n",
" [ 0.12994239]]\n",
"Oo: [[0.41781112]\n",
" [0.51684643]\n",
" [0.53243996]]\n"
]
}
],
"source": [
"NN.feedforward([0.32, 0.27, 0.18])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "6ef426d3-3f6d-448d-9fe0-41c044a30fed",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([[ 0.33727924, 0.05324849, -0.05040263],\n",
" [-0.14654184, 0.08693412, 0.03647157],\n",
" [ 0.32652462, -0.23624388, -0.02214499],\n",
" [-0.15309598, -0.36626503, -0.24051822]]),\n",
" array([[-0.43163327, -0.08631366, -0.10845266, 0.07443995],\n",
" [ 0.38337319, -0.34586342, -0.10636942, 0.14029244],\n",
" [ 0.06287227, 0.06195702, 0.01966668, 0.10341479]]))"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"NN.backpropagation([0.32, 0.27, 0.18], [0.82, 0.25, 0.44])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ab4fc050-df3d-470c-aede-629357e44df5",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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