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https://github.com/guezoloic/neural-network.git
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99 lines
3.4 KiB
Python
99 lines
3.4 KiB
Python
import math
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import random
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# transform all numbers between 0 and 1
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def sigmoid(x):
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return 1 / (1 + math.exp(-x))
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# sigmoid's derivation
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def sigmoid_deriv(x):
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y = sigmoid(x)
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return y * (1 - y)
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# neuron class
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class Neuron:
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"""
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z: linear combination of inputs and weights plus bias (pre-activation)
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y : output of the activation function (sigmoid(z))
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w : list of weights, one for each input
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"""
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def __init__(self, isize):
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# number of inputs to this neuron
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self.isize = isize
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# importance to each input
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self.weight = [random.uniform(-1, 1) for _ in range(self.isize)]
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# importance of the neuron
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self.bias = random.uniform(-1, 1)
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# last z (linear combination) value
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self.z = 0
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# last output sigmoid(z)
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self.last_output = 0
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def forward(self, x):
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# computes the weighted sum of inputs and add the bias
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self.z = sum(w * xi for w, xi in zip(self.weight, x)) + self.bias
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# normalize the output between 0 and 1
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self.last_output = sigmoid(self.z)
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return self.last_output
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# adjust weight and bias
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def backward(self, x, dcost_dy, learning_rate):
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"""
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x : list of input values to the neuron
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dcost_dy : derivate of the cost function `(2 * (output - target))`
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learning_rate : learning factor (adjust the speed of weight/bias change during training)
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weight -= learning_rate * dC/dy * dy/dz * dz/dw
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bias -= learning_rate * dC/dy * dy/dz * dz/db
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"""
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# dy/dz: derivate of the sigmoid activation
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dy_dz = sigmoid_deriv(self.z)
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# dz/dw = x
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dz_dw = x
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# dz/db = 1
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dz_db = 1
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for i in range(self.isize):
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# update all weights by `learning_rate * cost * derivate sigmoid * dz/dw`
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self.weight[i] -= learning_rate * dcost_dy * dy_dz * dz_dw[i]
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# update bias by`learning_rate * cost * derivate sigmoid * dz/db`
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self.bias -= learning_rate * dcost_dy * dy_dz * dz_db
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# def forward(self, inputs: list[float]) -> float:
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# assert len(inputs) == self.isize, "error: incorrect inputs number"
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# total = sum(self.weight[i] * inputs[i] for i in range(self.isize)) + self.bias
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# return sigmoid(total)
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# def train(self, inputs: list[float], target: float, learning_rate: float = 0.1):
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# assert len(inputs) == self.isize, "error: incorrect inputs number"
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# z = sum(self.weight[i] * inputs[i] for i in range(self.isize)) + self.bias
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# output = sigmoid(z)
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# error = output - target
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# d_sigmoid = output * (1 - output)
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# dz = error * d_sigmoid
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# for i in range(self.isize):
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# self.weight[i] -= learning_rate * dz * inputs[i]
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# self.bias -= learning_rate * dz
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# class Layer:
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# def __init__(self, input_size, output_size):
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# self.size = output_size
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# self.neurons = [Neuron(output_size) for _ in range(input_size)]
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# def forward(self, inputs):
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# return [n.forward(inputs) for n in self.neurons]
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# def train(self, inputs: list[float], targets: list[float], learning_rate: float = 0.1):
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# outputs = self.forward(inputs)
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# errors = [outputs[i] - targets[i] for i in range(self.size)]
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# for i in range(self.neurons):
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# self.neurons[i].train(inputs, errors[i], learning_rate)
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