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import math
import numpy as np
import matplotlib.pyplot as plt
import random
from typing import Any
def f(x):
return 3*x**2 + 2*x + 4
def sigmoid(x):
return 1/(1+math.exp(-x))
def modsigmoid(x):
return 2/(1+math.exp(abs(x)))
class Value:
def __init__(self, data, _children = (), _op='', label = ''):
self.data = data
self.grad = 0.0 # represents derivative of the parent node with respec to current node
self._prev = set(_children)
self._backward = lambda: None
self._op = _op
self.label = label
def __repr__(self):
return f'Value(data={self.data})'
def __add__(self, other):
other = other if isinstance(other, Value) else Value(other)
out = Value(self.data+other.data, (self, other), '+')
def _backward():
self.grad += 1.0*out.grad # out and self are addresses here, so if it gets executed in outer node then out == currentnode and self and other == children, so even if we are assigning a different address to out in current node, since out was used in this node, out will be current node when executing the function
other.grad += 1.0*out.grad
out._backward = _backward
return out
def __mul__(self, other):
other = other if isinstance(other, Value) else Value(other)
out = Value(self.data*other.data, (self, other), '*')
def _backward():
self.grad += other.data*out.grad
other.grad += self.data*out.grad
out._backward = _backward
return out
def __pow__(self, other):
assert isinstance(other,(int, float))
out = Value(self.data**other, (self,), f'**{other}')
def _backward():
self.grad += other*(self.data**(other-1))*out.grad
out._backward = _backward
return out
def __rmul__(self, other): # other*self
return self*other
def __truediv__(self, other):
return self*other**-1
def __neg__(self):
return self*-1
def __sub__(self, other):
return self + (-other)
def __radd__(self, other):
return self + other
def tanh(self):
x = self.data
t = (math.exp(2*x) - 1)/(math.exp(2*x) + 1)
out = Value(t, (self, ), 'tanh')
def _backward():
self.grad += (1 - t**2)*out.grad
out._backward = _backward
return out
def sin(self):
x = self.data
out = Value(math.sin(x), (self, ), 'sin')
def _backward():
self.grad += math.cos(x)*out.grad
out._backward = _backward
return out
def cos(self):
x = self.data
out = Value(math.cos(x), (self, ), 'cos')
def _backward():
self.grad += -math.sin(x)*out.grad
out._backward = _backward
return out
def tan(self):
x = self.data
out = Value(math.tan(x), (self, ), 'tan')
def _backward():
self.grad += (1/math.cos(x)**2)*out.grad
out._backward = _backward
return out
def cot(self):
x = self.data
out = Value(math.cot(x), (self, ), 'cot')
def _backward():
self.grad += -(1/math.sin(x)**2)*out.grad
out._backward = _backward
return out
def sinh(self):
x = self.data
out = Value(math.sinh(x), (self, ), 'sinh')
def _backward():
self.grad += math.cosh(x)*out.grad
out._backward = _backward
return out
def cosh(self):
x = self.data
out = Value(math.cosh(x), (self, ), 'sinh')
def _backward():
self.grad += math.sinh(x)*out.grad
out._backward = _backward
return out
def exp(self):
x = self.data
out = Value(math.exp(x), (self,), 'exp')
def _backward():
self.grad += out.data*out.grad
out._backward = _backward
return out
def reLu(self):
x = self.data
out = Value(max(0, x), (self, ), 'reLu')
def _backward():
if x > 0:
self.grad += out.grad
else:
self.grad += 0
out._backward = _backward
return out
def sigmoid(self):
x = self.data
s = sigmoid(x)
out = Value(s, (self,), 'sigmoid')
def _backward():
self.grad += s*(1 - s)*out.grad
out._backward = _backward
return out
def log(self):
x = self.data
# print(x)
out = Value(math.log(x), (self,), 'log')
def _backward():
self.grad += (1/x)*out.grad
out._backward = _backward
return out
def modsigmoid(self):
x = self.data
s = modsigmoid(x)
out = Value(s, (self,), 'modsigmoid')
def _backward():
if x >= 0:
self.grad += -((2*x)/(x*(1+x)**2))*out.grad
else:
self.grad += -((2*x)/(-x*(1-x)**2))*out.grad
out._backward = _backward
return out
def sinc(self):
if x == 0:
print('error 0 not valdid input')
return
x = self.data
out = Value(math.sinx(x)/x, (self, ), 'sinc')
def _backward():
self.grad += ((2*x*math.sin(x) - (x**2)*math.cos(x))/(x**4))*out.grad
out._backward = _backward
return out
def backward(self):
topo = []
visited = set()
def build_topo(v):
if v not in visited:
visited.add(v)
for child in v._prev:
build_topo(child)
topo.append(v)
build_topo(self)
self.grad = 1.0
for node in reversed(topo):
node._backward()
class Neuron:
def __init__(self, nin, activation='sigmoid'):
self.w = [Value(random.uniform(-2, 2)) for _ in range(nin)]
self.b = Value(random.uniform(-2, 2))
self.activation = activation
def parameters(self):
return self.w + [self.b]
def __call__(self, x): # Neuron()(x)
act = sum((xi*wi for xi, wi in zip(x, self.w)), self.b)
if self.activation == 'sigmoid':
out = act.sigmoid()
if self.activation == 'reLu':
out = act.reLu()
if self.activation == 'modsigmoid':
out = act.modsigmoid()
if self.activation == '':
return act
return out
class Layer:
def __init__(self, nin, nout, activation='sigmoid'):
self.neurons = [Neuron(nin, activation=activation) for _ in range(nout)]
def parameters(self):
return [p for neuron in self.neurons for p in neuron.parameters()]
def __call__(self, x):
outs = [n(x) for n in self.neurons]
return outs[0] if len(outs) == 1 else outs
class MLP:
def __init__(self, nin, nouts):
sz = [nin] + nouts
self.layers = [Layer(sz[i], sz[i+1]) for i in range(len(nouts))]
def __call__(self, x):
for layer in self.layers:
x = layer(x)
return x
def parameters(self):
return [p for layer in self.layers for p in layer.parameters()]
def fit(n, X, Y, epochs, learning_rate):
for k in range(epochs):
ypred = [n(x) for x in X]
loss = sum([(yout - ygt)**2 for ygt, yout in zip(Y, ypred)])
# resets all the grad to zero for our new weight and biases
for node in n.parameters():
node.grad = 0
# deposits all the gradients in the nodes
loss.backward()
# subtracts all the values by a fraction of gradient decent
for node in n.parameters():
node.data -= learning_rate*node.grad
# print(k, loss)
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