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{
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"metadata": {
"colab": {
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
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{
"cell_type": "code",
"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"
],
"metadata": {
"id": "T0rN8d146jvF"
},
"execution_count": 1,
"outputs": []
},
{
"cell_type": "code",
"source": [
"import math"
],
"metadata": {
"id": "JlYxBvFK0AjA"
},
"execution_count": 2,
"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._backward = lambda: None #Its an empty function by default. This is what will do that gradient calculation at each of the operations.\n",
" self._prev = set(_children)\n",
" self._op = _op\n",
" self.label = label\n",
"\n",
"\n",
" def __repr__(self):\n",
" return f\"Value(data={self.data})\"\n",
"\n",
" def __add__(self, other):\n",
" out = Value(self.data + other.data, (self, other), '+')\n",
"\n",
" def backward():\n",
" self.grad += 1.0 * out.grad #Adding it on\n",
" other.grad += 1.0 * out.grad #Adding it on\n",
"\n",
" out._backward = backward\n",
" return out\n",
"\n",
" def __mul__(self, other):\n",
" out = Value(self.data * other.data, (self, other), '*')\n",
"\n",
" def backward():\n",
" self.grad += other.data * out.grad #Adding it on\n",
" other.grad += self.data * out.grad #Adding it on\n",
"\n",
" out._backward = backward\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",
"\n",
" def backward():\n",
" self.grad += 1 - (t**2) * out.grad #Adding it on\n",
"\n",
" out._backward = backward\n",
" return out\n",
"\n",
" def backward(self):\n",
"\n",
" topo = []\n",
" visited = set()\n",
" def build_topo(v):\n",
" if v not in visited:\n",
" visited.add(v)\n",
" for child in v._prev:\n",
" build_topo(child)\n",
" topo.append(v)\n",
"\n",
" build_topo(self)\n",
"\n",
" self.grad = 1.0\n",
" for node in reversed(topo):\n",
" node._backward()"
],
"metadata": {
"id": "XBafkiKxJ-in"
},
"execution_count": 3,
"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(6.8813735870195432, 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'\n",
"\n",
"#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",
"o = n.tanh(); o.label = 'o'"
],
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"id": "S3HaLbW_zvne"
},
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"outputs": []
},
{
"cell_type": "code",
"source": [
"#o.grad = 1.0\n",
"o.backward()\n",
"\n",
"draw_dot(o)"
],
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"colab": {
"base_uri": "https://localhost:8080/",
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},
"id": "P6OmwdXGGoJZ",
"outputId": "b5f3e9c2-c28f-4272-c328-db0c0536f5b5"
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{
"output_type": "execute_result",
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"--------------------"
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"id": "476LQxU3FXL4"
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"cell_type": "markdown",
"source": [
"### **Updating the Value object**"
],
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"id": "vP0ZtM9HFX9p"
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"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._backward = lambda: None #Its an empty function by default. This is what will do that gradient calculation at each of the operations.\n",
" self._prev = set(_children)\n",
" self._op = _op\n",
" self.label = label\n",
"\n",
"\n",
" def __repr__(self):\n",
" return f\"Value(data={self.data})\"\n",
"\n",
" def __add__(self, other):\n",
" other = other if isinstance(other, Value) else Value(other)\n",
" out = Value(self.data + other.data, (self, other), '+')\n",
"\n",
" def backward():\n",
" self.grad += 1.0 * out.grad\n",
" other.grad += 1.0 * out.grad\n",
"\n",
" out._backward = backward\n",
" return out\n",
"\n",
" def __mul__(self, other):\n",
" other = other if isinstance(other, Value) else Value(other)\n",
" out = Value(self.data * other.data, (self, other), '*')\n",
"\n",
" def backward():\n",
" self.grad += other.data * out.grad\n",
" other.grad += self.data * out.grad\n",
" out._backward = backward\n",
" return out\n",
"\n",
" def __rmul__(self, other): #other * self\n",
" return self * other\n",
"\n",
" def __truediv__(self, other): #self/other\n",
" return self * other**-1\n",
"\n",
" def __neg__(self):\n",
" return self * -1\n",
"\n",
" def __sub__(self, other): #self - other\n",
" return self + (-other)\n",
"\n",
" def __pow__(self, other):\n",
" assert isinstance(other, (int, float)), \"only supporting int/float powers for now\"\n",
" out = Value(self.data ** other, (self, ), f\"**{other}\")\n",
"\n",
" def backward():\n",
" self.grad += (other * (self.data ** (other - 1))) * out.grad\n",
"\n",
" out._backward = backward\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",
"\n",
" def backward():\n",
" self.grad += 1 - (t**2) * out.grad\n",
"\n",
" out._backward = backward\n",
" return out\n",
"\n",
" def exp(self):\n",
" x = self.data\n",
" out = Value(math.exp(x), (self, ), 'exp') #We merged t and out, into just out\n",
"\n",
" def backward():\n",
" self.grad += out.data * out.grad\n",
"\n",
" out._backward = backward\n",
" return out\n",
"\n",
" def backward(self):\n",
"\n",
" topo = []\n",
" visited = set()\n",
" def build_topo(v):\n",
" if v not in visited:\n",
" visited.add(v)\n",
" for child in v._prev:\n",
" build_topo(child)\n",
" topo.append(v)\n",
"\n",
" build_topo(self)\n",
"\n",
" self.grad = 1.0\n",
" for node in reversed(topo):\n",
" node._backward()"
],
"metadata": {
"id": "tA0zbyEwFbD5"
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{
"cell_type": "code",
"source": [
"x1 = Value(2.0, label='x1')\n",
"x2 = Value(0.0, label='x2')\n",
"\n",
"w1 = Value(-3.0, label='w1')\n",
"w2 = Value(1.0, label='w2')\n",
"\n",
"b = Value(6.8813735870195432, label='b')\n",
"\n",
"x1w1 = x1*w1; x1w1.label = 'x1*w1'\n",
"x2w2 = x2*w2; x2w2.label = 'x2*w2'\n",
"\n",
"x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1*w1 + x2*w2'\n",
"\n",
"n = x1w1x2w2 + b; n.label = 'n'\n",
"\n",
"#o = n.tanh(); o.label = 'o'\n",
"\n",
"#Spliting up of the tanh function\n",
"\n",
"e = (2*n).exp()\n",
"o = (e - 1) / (e + 1)\n",
"o.label = 'o'"
],
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"id": "Ounbj2XwHSZ1"
},
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},
{
"cell_type": "code",
"source": [
"o.backward()\n",
"\n",
"draw_dot(o)"
],
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"colab": {
"base_uri": "https://localhost:8080/",
"height": 360
},
"id": "FomTAJvaIFcb",
"outputId": "c1de2563-fad8-4049-9b37-84254d4b45c1"
},
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{
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"---------------"
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"**Hence, we have now split the tanh function and the additional operations have also been added!** \\\n",
"\\\n",
"**Plus, we are also getting the same output as before: o and the inputs & weights :)**"
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