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"class Value:\n",
"\n",
" def __init__(self, data, _children=(), _op='', label=''):\n",
" self.data = data\n",
" self.grad = 0.0\n",
" self._prev = set(_children)\n",
" self._op = _op\n",
" self.label = label\n",
"\n",
"\n",
" def __repr__(self): # This basically allows us to print nicer looking expressions for the final output\n",
" return f\"Value(data={self.data})\"\n",
"\n",
" def __add__(self, other):\n",
" out = Value(self.data + other.data, (self, other), '+')\n",
" return out\n",
"\n",
" def __mul__(self, other):\n",
" out = Value(self.data * other.data, (self, other), '*')\n",
" return out"
],
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"a = Value(2.0, label='a')\n",
"b = Value(-3.0, label='b')\n",
"c = Value(10.0, label='c')\n",
"e = a*b; e.label='e'\n",
"d= e + c; d.label='d'\n",
"f = Value(-2.0, label='f')\n",
"L = d*f; L.label='L'\n",
"L"
]
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{
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"source": [
"from graphviz import Digraph\n",
"\n",
"def trace(root):\n",
" #Builds a set of all nodes and edges in a graph\n",
" nodes, edges = set(), set()\n",
" def build(v):\n",
" if v not in nodes:\n",
" nodes.add(v)\n",
" for child in v._prev:\n",
" edges.add((child, v))\n",
" build(child)\n",
" build(root)\n",
" return nodes, edges\n",
"\n",
"def draw_dot(root):\n",
" dot = Digraph(format='svg', graph_attr={'rankdir': 'LR'}) #LR == Left to Right\n",
"\n",
" nodes, edges = trace(root)\n",
" for n in nodes:\n",
" uid = str(id(n))\n",
" #For any value in the graph, create a rectangular ('record') node for it\n",
" dot.node(name = uid, label = \"{ %s | data %.4f | grad %.4f }\" % ( n.label, n.data, n.grad), shape='record')\n",
" if n._op:\n",
" #If this value is a result of some operation, then create an op node for it\n",
" dot.node(name = uid + n._op, label=n._op)\n",
" #and connect this node to it\n",
" dot.edge(uid + n._op, uid)\n",
"\n",
" for n1, n2 in edges:\n",
" #Connect n1 to the node of n2\n",
" dot.edge(str(id(n1)), str(id(n2)) + n2._op)\n",
"\n",
" return dot"
],
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"------------------"
],
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"source": [
"### **Implementing the Neuron Mathematical Mode**"
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""
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"#Inputs x1, x2 of the neuron\n",
"x1 = Value(2.0, label='x1')\n",
"x2 = Value(0.0, label='x2')\n",
"\n",
"#Weights w1, w2 of the neuron - The synaptic values\n",
"w1 = Value(-3.0, label='w1')\n",
"w2 = Value(1.0, label='w2')\n",
"\n",
"#The bias of the neuron\n",
"b = Value(6.7, label='b')"
],
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"id": "3rGi-UXPu0lq"
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{
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"x1w1 = x1*w1; x1w1.label = 'x1*w1'\n",
"x2w2 = x2*w2; x2w2.label = 'x2*w2'\n",
"\n",
"#The summation\n",
"x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1*w1 + x2*w2'"
],
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{
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"source": [
"#n is basically the cell body, but without the activation function\n",
"n = x1w1x2w2 + b; n.label = 'n'"
],
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"id": "i33UWc5Yvh5e"
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"draw_dot(n)"
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},
{
"cell_type": "markdown",
"source": [
"Now, we have to get the output i.e. by having the dot product with the activation function.\n",
"\n",
"So we have to implement the tanh function"
],
"metadata": {
"id": "TrUjY3Xrw0TP"
}
},
{
"cell_type": "markdown",
"source": [
"Now, tanh is a hyperbolic expression. So it doesnt just contain +, -, it also has exponetials. So we have to create that function first in our Value object.\n",
"\n",
" \n",
"\n",
"\n"
],
"metadata": {
"id": "fd6oiWGaxEIb"
}
},
{
"cell_type": "markdown",
"source": [
"So now, lets update our Value object"
],
"metadata": {
"id": "hAXPXTquy8KN"
}
},
{
"cell_type": "code",
"source": [
"import math"
],
"metadata": {
"id": "JlYxBvFK0AjA"
},
"execution_count": 7,
"outputs": []
},
{
"cell_type": "code",
"source": [
"class Value:\n",
"\n",
" def __init__(self, data, _children=(), _op='', label=''):\n",
" self.data = data\n",
" self.grad = 0.0\n",
" self._prev = set(_children)\n",
" self._op = _op\n",
" self.label = label\n",
"\n",
"\n",
" def __repr__(self): # This basically allows us to print nicer looking expressions for the final output\n",
" return f\"Value(data={self.data})\"\n",
"\n",
" def __add__(self, other):\n",
" out = Value(self.data + other.data, (self, other), '+')\n",
" return out\n",
"\n",
" def __mul__(self, other):\n",
" out = Value(self.data * other.data, (self, other), '*')\n",
" return out\n",
"\n",
" def tanh(self):\n",
" x = self.data\n",
" t = (math.exp(2*x) - 1)/(math.exp(2*x) + 1)\n",
" out = Value(t, (self, ), 'tanh')\n",
" return out"
],
"metadata": {
"id": "4XPxg_t3wl35"
},
"execution_count": 8,
"outputs": []
},
{
"cell_type": "code",
"source": [
"#Inputs x1, x2 of the neuron\n",
"x1 = Value(2.0, label='x1')\n",
"x2 = Value(0.0, label='x2')\n",
"\n",
"#Weights w1, w2 of the neuron - The synaptic values\n",
"w1 = Value(-3.0, label='w1')\n",
"w2 = Value(1.0, label='w2')\n",
"\n",
"#The bias of the neuron\n",
"b = Value(6.7, label='b')\n",
"\n",
"x1w1 = x1*w1; x1w1.label = 'x1*w1'\n",
"x2w2 = x2*w2; x2w2.label = 'x2*w2'\n",
"\n",
"#The summation\n",
"x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1*w1 + x2*w2'"
],
"metadata": {
"id": "S3HaLbW_zvne"
},
"execution_count": 9,
"outputs": []
},
{
"cell_type": "code",
"source": [
"#n is basically the cell body, but without the activation function\n",
"n = x1w1x2w2 + b; n.label = 'n'\n",
"\n",
"#Now we pass n to the activation function\n",
"\n",
"o = n.tanh(); o.label = 'o'"
],
"metadata": {
"id": "UuUWxrHQzzYG"
},
"execution_count": 10,
"outputs": []
},
{
"cell_type": "code",
"source": [
"draw_dot(o)"
],
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"colab": {
"base_uri": "https://localhost:8080/",
"height": 322
},
"id": "j8zlrUnLz8F4",
"outputId": "9ea436d3-3701-4bb8-9fad-7dd9e14cbbe9"
},
"execution_count": 11,
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{
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"source": [
"We have recieved that output. So now, tanh is our little 'micrograd supported' node here, as an operation :)"
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