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https://github.com/guezoloic/neural-network.git
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refactor(network.py): annotate Neuron constructor (comments other functions)
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220
network.py
220
network.py
@@ -1,6 +1,7 @@
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import math
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import random
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def sigmoid(x: float) -> float:
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return 1 / (1 + math.exp(-x))
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@@ -9,123 +10,154 @@ def sigmoid_deriv(x: float) -> float:
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y: float = 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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def __init__(self, input_size: int) -> None:
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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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Set up the neuron's parameters (weights, and bias)
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:param input_size: Number of incomming inputs (must be > 0)
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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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# Store input dimensions for structural consistency
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self._input_size: int = input_size
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def forward(self, x, activate=True):
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"""
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x : list of input values to the neuron
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"""
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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 if activate
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last_output = sigmoid(self.z) if activate else self.z
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# Scale each input influence using random weights.
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self._weight: list[float] = [
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random.uniform(-1., 1.) for _ in range(input_size)
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]
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return last_output
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# Initialize a shift to the activation threshold with a random bias
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self._bias: float = random.uniform(-1., 1.)
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# adjust weight and bias of neuron
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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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def __repr__(self) -> str:
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jmp: int = int(math.sqrt(self._input_size))
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text: list[str] = []
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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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for i in range(0, self._input_size, jmp):
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line: str = str.join("", str(self._weight[i: (i + jmp)]))
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text.append(line)
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assert len(dz_dw) >= self.isize, "too many value for input size"
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return f"weight:\n{str.join("\n", text)}\nbias: {self._bias}"
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# dz/db = 1
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dz_db = 1
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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, input_size):
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# # number of inputs to this neuron
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# self._input_size = input_size
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# # importance to each input
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# self._weight = [random.uniform(-1, 1) for _ in range(self._input_size)]
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# # importance of the neuron
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# self._bias = random.uniform(-1, 1)
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for i in range(self.isize):
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# update each weight `weight -= learning_rate * dC/dy * dy/dz * x_i`
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self.weight[i] -= learning_rate * dcost_dy * dy_dz * dz_dw[i]
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# def forward(self, x, activate=True):
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# """
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# x : list of input values to the neuron
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# """
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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 if activate
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# last_output = sigmoid(self.z) if activate else self.z
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# update bias: bias -= learning_rate * dC/dy * dy/dz * dz/db
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self.bias -= learning_rate * dcost_dy * dy_dz * dz_db
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# return last_output
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# return gradient vector len(input) dimension
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return [dcost_dy * dy_dz * w for w in self.weight]
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# # adjust weight and bias of neuron
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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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class Layer:
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def __init__(self, input_size, output_size):
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"""
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input_size : size of each neuron input
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output_size : size of neurons
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"""
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self.size = output_size
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# list of neurons
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self.neurons = [Neuron(input_size) for _ in range(output_size)]
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# assert len(dz_dw) >= self.isize, "too many value for input size"
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def forward(self, inputs, activate=True):
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self.inputs = inputs
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# give the same inputs to each neuron in the layer
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return [neuron.forward(inputs, activate) for neuron in self.neurons]
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# # dz/db = 1
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# dz_db = 1
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# adjust weight and bias of the layer (all neurons)
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def backward(self, dcost_dy_list, learning_rate=0.1):
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# init layer gradient vector len(input) dimention
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input_gradients = [0.0] * len(self.inputs)
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# for i in range(self.isize):
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# # update each weight `weight -= learning_rate * dC/dy * dy/dz * x_i`
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# self.weight[i] -= learning_rate * dcost_dy * dy_dz * dz_dw[i]
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for i, neuron in enumerate(self.neurons):
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dcost_dy = dcost_dy_list[i]
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grad_to_input = neuron.backward(self.inputs, dcost_dy, learning_rate)
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# # update bias: bias -= learning_rate * dC/dy * dy/dz * dz/db
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# self.bias -= learning_rate * dcost_dy * dy_dz * dz_db
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# accumulate the input gradients from all neurons
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for j in range(len(grad_to_input)):
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input_gradients[j] += grad_to_input[j]
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# # return gradient vector len(weight) dimension
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# return [dcost_dy * dy_dz * w for w in self.weight]
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# return layer gradient
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return input_gradients
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# def __repr__(self):
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# pass
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class NeuralNetwork:
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def __init__(self, layer_size):
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self.layers = [Layer(layer_size[i], layer_size[i+1]) for i in range(len(layer_size) - 1)]
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# class Layer:
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# def __init__(self, input_size, output_size):
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# """
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# input_size : size of each neuron input
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# output_size : size of neurons
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# """
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# self.size = output_size
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# # list of neurons
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# self.neurons = [Neuron(input_size) for _ in range(output_size)]
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def forward(self, inputs):
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output = inputs
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for i, layer in enumerate(self.layers):
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activate = (i != len(self.layers) - 1) # deactivate sigmoid latest neuron
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output = layer.forward(output, activate=activate)
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return output
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# def forward(self, inputs, activate=True):
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# self.inputs = inputs
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# # give the same inputs to each neuron in the layer
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# return [neuron.forward(inputs, activate) for neuron in self.neurons]
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def backward(self, inputs, targets, learning_rate=0.1):
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"""
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target must be a list with the same length that the final layer
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input
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"""
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output = self.forward(inputs)
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# # adjust weight and bias of the layer (all neurons)
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# def backward(self, dcost_dy_list, learning_rate=0.1):
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# # init layer gradient vector len(input) dimention
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# input_gradients = [0.0] * len(self.inputs)
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# computes the initial gradient of the cost function for each neuron
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# by using Mean Squared Error's derivate: dC/dy = 2 * (output - target)
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dcost_dy_list = [2 * (o - t) for o, t in zip(output, targets)]
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# for i, neuron in enumerate(self.neurons):
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# dcost_dy = dcost_dy_list[i]
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# grad_to_input = neuron.backward(self.inputs, dcost_dy, learning_rate)
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grad = dcost_dy_list
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for layer in reversed(self.layers):
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# backpropagate the gradient of the layer to update weights and biases
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grad = layer.backward(grad, learning_rate)
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# # accumulate the input gradients from all neurons
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# for j in range(len(grad_to_input)):
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# input_gradients[j] += grad_to_input[j]
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# return final gradient
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return grad
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# # return layer gradient
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# return input_gradients
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if __name__ == "__main__":
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print("you might want to run main.py instead of network.py")
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# class NeuralNetwork:
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# def __init__(self, layer_size):
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# self.layers = [Layer(layer_size[i], layer_size[i+1]) for i in range(len(layer_size) - 1)]
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# def forward(self, inputs):
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# output = inputs
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# for i, layer in enumerate(self.layers):
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# activate = (i != len(self.layers) - 1) # deactivate sigmoid latest neuron
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# output = layer.forward(output, activate=activate)
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# return output
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# def backward(self, inputs, targets, learning_rate=0.1):
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# """
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# target must be a list with the same length that the final layer
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# input
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# """
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# output = self.forward(inputs)
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# # computes the initial gradient of the cost function for each neuron
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# # by using Mean Squared Error's derivate: dC/dy = 2 * (output - target)
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# dcost_dy_list = [2 * (o - t) for o, t in zip(output, targets)]
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# grad = dcost_dy_list
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# for layer in reversed(self.layers):
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# # backpropagate the gradient of the layer to update weights and biases
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# grad = layer.backward(grad, learning_rate)
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# # return final gradient
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# return grad
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# if __name__ == "__main__":
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# print("you might want to run main.py instead of network.py")
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