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神经网络/main.py
211
神经网络/main.py
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@ -34,7 +34,6 @@ class NeuralNetwork:
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:param epsilon: 极小值，默认为1e-9
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"""
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print("正在初始化神经网络...", end="")
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if not (
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len(structure) >= 3
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and all(x >= 1 if isinstance(x, int) else False for x in structure)
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@ -55,66 +54,18 @@ class NeuralNetwork:
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# 神经网络层数（定义，第0层为输入层，第l层为隐含层（l=1,2,...,L-1），第L层为输出层（L为神经网络层数），深度为L+1）
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self.layer_counts = len(structure) - 1
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# 初始化是否训练
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self.training = True
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numpy.random.seed(seed) # 设置随机种子
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self.parameters = {0: {}}
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# 初始化神经网络参数
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for layer_index in range(1, self.layer_counts + 1):
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self.parameters[layer_index] = {
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"activate": (
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activate := (
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self.output_activate
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if layer_index == self.layer_counts
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else self.hidden_activate
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)
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), # 激活函数
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"weight": self._init_weight(
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activate=activate,
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previous_layer_neuron_counts=self.structure[layer_index - 1],
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current_layer_neuron_counts=(
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current_layer_neuron_counts := self.structure[layer_index]
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),
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), # 权重，维度为[当前层神经元数，上一层神经元数]，适配加权输入=权重*输入+平移
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"bias": numpy.zeros((current_layer_neuron_counts, 1)), # 平移
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}
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self.parameters = {}
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# 初始化模式（包括训练模式和推理模式）
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self.training = None
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# 初始化随机种子
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self.seed = seed
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# 初始化极小值
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self.epsilon = epsilon
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print("已完成")
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def _init_weight(
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self,
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activate: Literal["relu", "linear", "softmax"],
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previous_layer_neuron_counts: int,
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current_layer_neuron_counts: int,
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) -> numpy.floating:
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"""
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初始化权重
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:param activate: 激活函数
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:param previous_layer_neuron_counts: 上一层神经元数
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:param current_layer_neuron_counts: 当前层神经元数
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:return: 初始化后的权重，维度为[当前层神经元数，上一层神经元数]
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"""
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weight = numpy.random.randn(
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current_layer_neuron_counts, previous_layer_neuron_counts
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)
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match activate:
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case "relu":
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return weight * numpy.sqrt(
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2 / previous_layer_neuron_counts
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) # 使用He初始化权重方法
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case "linear":
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return weight * numpy.sqrt(
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2 / previous_layer_neuron_counts
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) # 使用He初始化权重方法
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case "softmax":
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return weight * numpy.sqrt(
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2 / (previous_layer_neuron_counts + current_layer_neuron_counts)
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) # 使用Xavier初始化权重方法
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def train(
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self,
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X: numpy.ndarray,
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@ -145,7 +96,10 @@ class NeuralNetwork:
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raise RuntimeError(
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"输入和真实输出应为数组，其中输入维度应为[输入神经元数, 样本数]，真实输出维度应为[输出神经元数, 样本数]，样本数应需相同"
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)
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# 默认为训练模式
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self.training = True
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# 初始化神经网络参数
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self._init_parameters()
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# 归一化输入
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self.parameters[0].update({"activation": self._normalize(input=X)})
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@ -174,12 +128,80 @@ class NeuralNetwork:
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epoch += 1
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try:
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with open("neural_network.pkl", "wb") as file:
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pickle.dump(self, file, protocol=pickle.HIGHEST_PROTOCOL)
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print(f"模型保存成功")
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except Exception as exception:
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raise RuntimeError(f"模型保存失败：{str(exception)}") from exception
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# 保存神经网络参数
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self._save_parameters()
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def _init_parameters(self) -> None:
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"""
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初始化神经网络参数
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:return: 无
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"""
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self.parameters = {0: {}}
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# 初始化神经网络参数
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for layer_index in range(1, self.layer_counts + 1):
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self.parameters[layer_index] = {
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"activate": (
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activate := (
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self.output_activate
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if layer_index == self.layer_counts
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else self.hidden_activate
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)
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), # 激活函数
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"weight": self._init_weight(
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activate=activate,
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previous_layer_neuron_counts=self.structure[layer_index - 1],
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current_layer_neuron_counts=(
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current_layer_neuron_counts := self.structure[layer_index]
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),
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), # 权重，维度为[当前层神经元数，上一层神经元数]，适配加权输入=权重*输入+平移
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"bias": self._init_bias(
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current_layer_neuron_counts=current_layer_neuron_counts
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), # 平移
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}
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def _init_weight(
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self,
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activate: str,
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previous_layer_neuron_counts: int,
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current_layer_neuron_counts: int,
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) -> numpy.ndarray: # pyright: ignore[reportReturnType]
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"""
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初始化权重
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:param activate: 激活函数
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:param previous_layer_neuron_counts: 上一层神经元数
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:param current_layer_neuron_counts: 当前层神经元数
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:return: 初始化后的权重，维度为[当前层神经元数，上一层神经元数]
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"""
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# 设置随机种子
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numpy.random.seed(self.seed)
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# 基于正态分布生成权重
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weight = numpy.random.randn(
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current_layer_neuron_counts, previous_layer_neuron_counts
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)
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match activate:
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case "relu":
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return weight * numpy.sqrt(
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2 / previous_layer_neuron_counts
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) # 使用He初始化权重方法
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case "linear":
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return weight * numpy.sqrt(
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2 / previous_layer_neuron_counts
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) # 使用He初始化权重方法
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case "softmax":
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return weight * numpy.sqrt(
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2 / (previous_layer_neuron_counts + current_layer_neuron_counts)
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) # 使用Xavier初始化权重方法
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def _init_bias(
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self,
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current_layer_neuron_counts: int,
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) -> numpy.ndarray:
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"""
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初始化平移
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:param current_layer_neuron_counts: 当前层神经元数
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:return: 初始化后的平移，维度为[当前层神经元数, 1]
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"""
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return numpy.zeros((current_layer_neuron_counts, 1))
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def _normalize(
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self,
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@ -206,7 +228,7 @@ class NeuralNetwork:
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def _forward_propagate(self) -> None:
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"""
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前向传播
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:return: 输出层的输出预测，维度为[输出神经元数, 样本数]
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:return: 输出层的预测输出，维度为[输出神经元数, 样本数]
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"""
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for layer_index in range(1, self.layer_counts + 1):
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self.parameters[layer_index].update(
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@ -229,9 +251,9 @@ class NeuralNetwork:
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def _activate(
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self,
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activate: Literal["relu", "linear", "softmax"],
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activate: str,
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input: numpy.ndarray,
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) -> numpy.ndarray:
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) -> numpy.ndarray: # pyright: ignore[reportReturnType]
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"""
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激活
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:param activate: 激活函数
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@ -385,23 +407,66 @@ class NeuralNetwork:
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}
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)
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def _reason(self, input: numpy.ndarray) -> numpy.ndarray:
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def _save_parameters(self) -> None:
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"""
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保存神经网络参数
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:return: 无
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"""
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with open("parameters.pkl", "wb") as file:
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pickle.dump(
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obj=self.parameters,
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file=file,
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protocol=pickle.HIGHEST_PROTOCOL,
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)
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def reason(self, X: numpy.ndarray) -> numpy.ndarray:
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"""
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推理
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:param input: 输入，维度为[输入神经元数, 样本数]
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:return: 输出，维度为[输出神经元数, 样本数]
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:param X: 输入，维度为[输入神经元数, 样本数]
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:return: 预测输出，维度为[输出神经元数, 样本数]
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"""
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print(f"基于已训练神经网络进行推理...")
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if not (
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X.shape[0] == self.structure[0] if isinstance(X, numpy.ndarray) else False
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):
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raise RuntimeError("输入应为数组，输入维度应为[输入神经元数, 样本数]")
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# 默认为推理模式
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self.training = False
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# 加载神经网络参数
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self._load_parameters()
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# 归一化输入
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self.parameters[0].update({"activation": self._normalize(input=input)})
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self.parameters[0].update({"activation": self._normalize(input=X)})
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return self._forward_propagate()
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# 前向传播
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self._forward_propagate()
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return self.parameters[self.layer_counts]["activation"]
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def _load_parameters(self) -> None:
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"""
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加载神经网络参数
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:return: 无
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"""
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with open("parameters.pkl", "rb") as file:
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self.parameters = pickle.load(file=file)
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# 校验神经网络参数
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for layer_index in range(1, self.layer_counts + 1):
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if not (
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self.parameters[layer_index]["weight"].shape
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== (self.structure[layer_index], self.structure[layer_index - 1])
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and self.parameters[layer_index]["bias"].shape
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== (self.structure[layer_index], 1)
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if isinstance(self.parameters[layer_index]["weight"], numpy.ndarray)
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and isinstance(self.parameters[layer_index]["bias"], numpy.ndarray)
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else False
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):
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raise RuntimeError("神经网络参数中权重和偏置的维度与神经网络结构不匹配")
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# 测试代码
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if __name__ == "__main__":
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X = numpy.random.randn(2, 100)
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X = numpy.random.randn(2, 5000)
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# 真实函数：y = 2*x1 + 3*x2 + 1
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y_true = 2 * X[0:1, :] ** 2 + 3 * X[1:2, :] + 1
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@ -412,5 +477,9 @@ if __name__ == "__main__":
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# 训练
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neural_network.train(
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X=X, y_true=y_true, target_loss=0.1, epochs=1_000, learning_rate=0.05
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X=X, y_true=y_true, target_loss=0.01, epochs=1_000, learning_rate=0.1
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)
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print(f"推理结果：{y_true[:, 0:5]}")
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print(f"推理结果：{neural_network.reason(X=X)[:, 0:5]}")
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