T18-2 φ-量子机器学习定理 - 形式化规范

类型定义

from typing import Dict, List, Tuple, Optional, Callable, Union
from dataclasses import dataclass
import numpy as np
from enum import Enum
from phi_arithmetic import PhiReal, PhiComplex, PhiMatrix

class ActivationFunction(Enum):
    """激活函数类型"""
    PHI_SIGMOID = "phi_sigmoid"
    PHI_TANH = "phi_tanh"
    PHI_RELU = "phi_relu"
    PHI_SWISH = "phi_swish"

class OptimizerType(Enum):
    """优化器类型"""
    PHI_SGD = "phi_sgd"
    PHI_ADAM = "phi_adam"
    PHI_RMSPROP = "phi_rmsprop"

@dataclass
class QuantumNeuron:
    """φ-量子神经元"""
    weights: List[PhiComplex]  # 权重向量
    bias: PhiComplex          # 偏置
    activation: ActivationFunction  # 激活函数
    quantum_state: List[PhiComplex] = None  # 量子态
    
    def __post_init__(self):
        """初始化量子态"""
        if self.quantum_state is None:
            # 初始化为均匀叠加态
            n = len(self.weights)
            norm = PhiReal.one() / PhiReal.from_decimal(np.sqrt(n))
            self.quantum_state = [PhiComplex(norm, PhiReal.zero()) for _ in range(n)]
    
    def forward(self, inputs: List[PhiComplex]) -> PhiComplex:
        """前向传播"""
        if len(inputs) != len(self.weights):
            raise ValueError("输入维度与权重不匹配")
        
        # 量子内积
        weighted_sum = self.bias
        for i, (inp, weight) in enumerate(zip(inputs, self.weights)):
            weighted_sum = weighted_sum + inp * weight
        
        # 应用φ-激活函数
        return self._apply_activation(weighted_sum)
    
    def _apply_activation(self, x: PhiComplex) -> PhiComplex:
        """应用φ-激活函数"""
        if self.activation == ActivationFunction.PHI_SIGMOID:
            # σ_φ(x) = 1/(1 + exp(-x/φ))
            exp_arg = -x.real / PHI
            if exp_arg.decimal_value > -10:
                exp_val = PhiReal.from_decimal(np.exp(exp_arg.decimal_value))
                denom = PhiReal.one() + exp_val
                return PhiComplex(PhiReal.one() / denom, PhiReal.zero())
            else:
                return PhiComplex.one()
        
        elif self.activation == ActivationFunction.PHI_RELU:
            # ReLU_φ(x) = max(0, x) * φ^(-|x|)
            if x.real.decimal_value > 0:
                decay = PHI ** (-abs(x.real))
                return PhiComplex(x.real * decay, x.imag * decay)
            else:
                return PhiComplex.zero()
        
        elif self.activation == ActivationFunction.PHI_TANH:
            # tanh_φ(x) = tanh(x/φ)
            tanh_arg = x.real.decimal_value / PHI.decimal_value
            if abs(tanh_arg) < 10:
                tanh_val = np.tanh(tanh_arg)
                return PhiComplex(PhiReal.from_decimal(tanh_val), PhiReal.zero())
            else:
                return PhiComplex(PhiReal.from_decimal(np.sign(tanh_arg)), PhiReal.zero())
        
        else:  # PHI_SWISH
            # swish_φ(x) = x * σ_φ(x)
            sigmoid_x = self._apply_activation_helper(x, ActivationFunction.PHI_SIGMOID)
            return x * sigmoid_x
    
    def _apply_activation_helper(self, x: PhiComplex, activation: ActivationFunction) -> PhiComplex:
        """激活函数辅助方法"""
        old_activation = self.activation
        self.activation = activation
        result = self._apply_activation(x)
        self.activation = old_activation
        return result
    
    def update_quantum_state(self, measurement_result: int):
        """更新神经元的量子态"""
        # 量子测量后的态坍缩
        new_state = [PhiComplex.zero() for _ in self.quantum_state]
        if 0 <= measurement_result < len(new_state):
            new_state[measurement_result] = PhiComplex.one()
        self.quantum_state = new_state
    
    def get_measurement_probabilities(self) -> List[PhiReal]:
        """获取量子测量概率"""
        probs = []
        for state in self.quantum_state:
            prob = state.norm_squared()
            probs.append(prob)
        
        # 归一化
        total = PhiReal.zero()
        for p in probs:
            total = total + p
        
        if total.decimal_value > 1e-10:
            normalized = [p / total for p in probs]
        else:
            normalized = [PhiReal.one() / PhiReal.from_decimal(len(probs)) for _ in probs]
        
        return normalized

@dataclass
class PhiQuantumLayer:
    """φ-量子神经网络层"""
    neurons: List[QuantumNeuron]
    layer_index: int
    is_no11_constrained: bool = True
    
    def __post_init__(self):
        """验证层结构"""
        expected_size = self._fibonacci_number(self.layer_index)
        if len(self.neurons) != expected_size:
            raise ValueError(f"层{self.layer_index}应有{expected_size}个神经元，实际{len(self.neurons)}")
    
    def _fibonacci_number(self, n: int) -> int:
        """计算第n个Fibonacci数"""
        if n <= 1:
            return 1
        a, b = 1, 1
        for _ in range(n - 1):
            a, b = b, a + b
        return b
    
    def forward(self, inputs: List[PhiComplex]) -> List[PhiComplex]:
        """层前向传播"""
        outputs = []
        
        for i, neuron in enumerate(self.neurons):
            if self.is_no11_constrained:
                # 检查no-11约束
                if self._violates_no11_constraint(i, inputs):
                    # 跳过违反约束的神经元
                    outputs.append(PhiComplex.zero())
                    continue
            
            output = neuron.forward(inputs)
            outputs.append(output)
        
        return outputs
    
    def _violates_no11_constraint(self, neuron_index: int, inputs: List[PhiComplex]) -> bool:
        """检查神经元激活是否违反no-11约束"""
        # 完整no-11约束检查：包括量子态、权重和激活
        
        # 1. 检查输入激活模式
        activation_pattern = []
        for inp in inputs:
            if inp.norm_squared().decimal_value > 0.1:  # 激活阈值
                activation_pattern.append(1)
            else:
                activation_pattern.append(0)
        
        # 检查激活模式的no-11约束
        if self._has_consecutive_ones(activation_pattern):
            return True
        
        # 2. 检查权重向量的no-11编码
        neuron = self.neurons[neuron_index]
        for weight in neuron.weights:
            weight_binary = self._phi_to_zeckendorf_binary(weight.norm_squared())
            if self._has_consecutive_ones(weight_binary):
                return True
        
        # 3. 检查量子态的no-11约束
        if neuron.quantum_state:
            for state_amplitude in neuron.quantum_state:
                state_binary = self._phi_to_zeckendorf_binary(state_amplitude.norm_squared())
                if self._has_consecutive_ones(state_binary):
                    return True
        
        # 4. 检查层间耦合的no-11约束
        if self.layer_index > 0:
            prev_layer_outputs = []
            for i, inp in enumerate(inputs):
                if inp.norm_squared().decimal_value > 0.1:
                    prev_layer_outputs.append(i)
            
            # 检查层间连接是否违反no-11
            coupling_pattern = [0] * len(inputs)
            for output_idx in prev_layer_outputs:
                if output_idx < len(coupling_pattern):
                    coupling_pattern[output_idx] = 1
            
            if self._has_consecutive_ones(coupling_pattern):
                return True
        
        return False
    
    def _has_consecutive_ones(self, binary_sequence: List[int]) -> bool:
        """检查二进制序列是否包含连续的1"""
        for i in range(len(binary_sequence) - 1):
            if binary_sequence[i] == 1 and binary_sequence[i+1] == 1:
                return True
        return False
    
    def _phi_to_zeckendorf_binary(self, phi_value: PhiReal) -> List[int]:
        """将φ-实数转换为Zeckendorf二进制表示"""
        if phi_value.decimal_value < 1e-10:
            return [0]
        
        # Zeckendorf表示：每个正数都有唯一的非连续Fibonacci数之和表示
        fibonacci_sequence = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]
        value = phi_value.decimal_value
        
        zeckendorf_bits = [0] * len(fibonacci_sequence)
        
        # 贪心算法：从最大的Fibonacci数开始
        for i in range(len(fibonacci_sequence) - 1, -1, -1):
            if fibonacci_sequence[i] <= value + 1e-10:  # 数值容差
                zeckendorf_bits[i] = 1
                value -= fibonacci_sequence[i]
                if value < 1e-10:
                    break
        
        # 移除前导零
        while len(zeckendorf_bits) > 1 and zeckendorf_bits[-1] == 0:
            zeckendorf_bits.pop()
        
        return zeckendorf_bits[::-1]  # 逆序以便低位在前
    
    def get_layer_statistics(self) -> Dict[str, PhiReal]:
        """获取层统计信息"""
        stats = {}
        
        # 神经元数量
        stats["neuron_count"] = PhiReal.from_decimal(len(self.neurons))
        
        # 平均权重模长
        total_weight_norm = PhiReal.zero()
        total_weights = 0
        
        for neuron in self.neurons:
            for weight in neuron.weights:
                total_weight_norm = total_weight_norm + weight.norm_squared()
                total_weights += 1
        
        if total_weights > 0:
            stats["avg_weight_norm"] = total_weight_norm / PhiReal.from_decimal(total_weights)
        else:
            stats["avg_weight_norm"] = PhiReal.zero()
        
        return stats

@dataclass
class PhiOptimizer:
    """φ-量子优化器"""
    optimizer_type: OptimizerType
    learning_rate: PhiReal
    decay_rate: PhiReal = None
    momentum: PhiReal = None
    epsilon: PhiReal = None
    
    # 优化器状态
    step_count: int = 0
    momentum_buffer: Dict[str, PhiComplex] = None
    velocity_buffer: Dict[str, PhiComplex] = None
    
    def __post_init__(self):
        """初始化优化器参数"""
        if self.decay_rate is None:
            self.decay_rate = PhiReal.one() / PHI  # φ-衰减
        
        if self.momentum is None:
            self.momentum = PhiReal.from_decimal(0.9)
        
        if self.epsilon is None:
            self.epsilon = PhiReal.from_decimal(1e-8)
        
        if self.momentum_buffer is None:
            self.momentum_buffer = {}
        
        if self.velocity_buffer is None:
            self.velocity_buffer = {}
    
    def step(self, parameters: Dict[str, PhiComplex], gradients: Dict[str, PhiComplex]):
        """执行一步优化"""
        self.step_count += 1
        
        # φ-学习率衰减
        current_lr = self.learning_rate * (self.decay_rate ** self.step_count)
        
        if self.optimizer_type == OptimizerType.PHI_SGD:
            self._phi_sgd_step(parameters, gradients, current_lr)
        elif self.optimizer_type == OptimizerType.PHI_ADAM:
            self._phi_adam_step(parameters, gradients, current_lr)
        elif self.optimizer_type == OptimizerType.PHI_RMSPROP:
            self._phi_rmsprop_step(parameters, gradients, current_lr)
    
    def _phi_sgd_step(self, parameters: Dict[str, PhiComplex], 
                     gradients: Dict[str, PhiComplex], lr: PhiReal):
        """φ-SGD优化步骤"""
        for param_name, gradient in gradients.items():
            if param_name in parameters:
                # v = momentum * v + lr * grad
                if param_name not in self.momentum_buffer:
                    self.momentum_buffer[param_name] = PhiComplex.zero()
                
                momentum_term = self.momentum_buffer[param_name] * self.momentum
                gradient_term = gradient * lr
                velocity = momentum_term + gradient_term
                self.momentum_buffer[param_name] = velocity
                
                # θ = θ - v
                parameters[param_name] = parameters[param_name] - velocity
    
    def _phi_adam_step(self, parameters: Dict[str, PhiComplex],
                      gradients: Dict[str, PhiComplex], lr: PhiReal):
        """φ-Adam优化步骤"""
        beta1 = PhiReal.from_decimal(0.9)
        beta2 = PhiReal.from_decimal(0.999)
        
        for param_name, gradient in gradients.items():
            if param_name in parameters:
                # 初始化缓冲区
                if param_name not in self.momentum_buffer:
                    self.momentum_buffer[param_name] = PhiComplex.zero()
                if param_name not in self.velocity_buffer:
                    self.velocity_buffer[param_name] = PhiComplex.zero()
                
                # 更新动量 m = β1*m + (1-β1)*g
                beta1_complement = PhiReal.one() - beta1
                m_old = self.momentum_buffer[param_name] * beta1
                m_new = gradient * beta1_complement
                self.momentum_buffer[param_name] = m_old + m_new
                
                # 更新二阶矩 v = β2*v + (1-β2)*g²
                beta2_complement = PhiReal.one() - beta2
                v_old = self.velocity_buffer[param_name] * beta2
                grad_squared = PhiComplex(
                    gradient.norm_squared(),
                    PhiReal.zero()
                )
                v_new = grad_squared * beta2_complement
                self.velocity_buffer[param_name] = v_old + v_new
                
                # 偏差修正
                t = PhiReal.from_decimal(self.step_count)
                m_hat = self.momentum_buffer[param_name] / (PhiReal.one() - (beta1 ** t))
                v_hat = self.velocity_buffer[param_name] / (PhiReal.one() - (beta2 ** t))
                
                # 参数更新 θ = θ - lr * m_hat / (√v_hat + ε)
                v_sqrt = PhiComplex(v_hat.real.sqrt(), PhiReal.zero())
                denominator = v_sqrt + PhiComplex(self.epsilon, PhiReal.zero())
                update = (m_hat * lr) / denominator
                parameters[param_name] = parameters[param_name] - update
    
    def _phi_rmsprop_step(self, parameters: Dict[str, PhiComplex],
                         gradients: Dict[str, PhiComplex], lr: PhiReal):
        """φ-RMSprop优化步骤"""
        alpha = PhiReal.from_decimal(0.99)
        
        for param_name, gradient in gradients.items():
            if param_name in parameters:
                if param_name not in self.velocity_buffer:
                    self.velocity_buffer[param_name] = PhiComplex.zero()
                
                # v = α*v + (1-α)*g²
                alpha_complement = PhiReal.one() - alpha
                v_old = self.velocity_buffer[param_name] * alpha
                grad_squared = PhiComplex(gradient.norm_squared(), PhiReal.zero())
                v_new = grad_squared * alpha_complement
                self.velocity_buffer[param_name] = v_old + v_new
                
                # θ = θ - lr * g / (√v + ε)
                v_sqrt = PhiComplex(self.velocity_buffer[param_name].real.sqrt(), PhiReal.zero())
                denominator = v_sqrt + PhiComplex(self.epsilon, PhiReal.zero())
                update = (gradient * lr) / denominator
                parameters[param_name] = parameters[param_name] - update

class PhiQuantumNeuralNetwork:
    """φ-量子神经网络"""
    
    def __init__(self, layer_sizes: List[int], activation: ActivationFunction = ActivationFunction.PHI_RELU):
        self.phi = PhiReal.from_decimal(1.618033988749895)
        self.layers: List[PhiQuantumLayer] = []
        self.activation = activation
        
        # 验证层大小是否符合Fibonacci序列
        for i, size in enumerate(layer_sizes):
            expected_size = self._fibonacci_number(i)
            if size != expected_size:
                print(f"警告：层{i}大小{size}不符合Fibonacci序列{expected_size}")
        
        # 创建层
        self._build_network(layer_sizes)
        
        # 损失函数历史
        self.loss_history: List[PhiReal] = []
        
        # 量子测量历史
        self.measurement_history: List[List[int]] = []
    
    def _fibonacci_number(self, n: int) -> int:
        """计算第n个Fibonacci数"""
        if n <= 1:
            return 1
        a, b = 1, 1
        for _ in range(n - 1):
            a, b = b, a + b
        return b
    
    def _build_network(self, layer_sizes: List[int]):
        """构建网络层"""
        for layer_idx in range(len(layer_sizes)):
            neurons = []
            neuron_count = layer_sizes[layer_idx]
            
            # 确定输入维度
            if layer_idx == 0:
                input_dim = neuron_count  # 输入层
            else:
                input_dim = layer_sizes[layer_idx - 1]
            
            # 创建神经元
            for _ in range(neuron_count):
                # φ-权重初始化
                weights = self._initialize_phi_weights(input_dim)
                bias = self._initialize_phi_bias()
                
                neuron = QuantumNeuron(
                    weights=weights,
                    bias=bias,
                    activation=self.activation
                )
                neurons.append(neuron)
            
            # 创建层
            layer = PhiQuantumLayer(
                neurons=neurons,
                layer_index=layer_idx,
                is_no11_constrained=True
            )
            self.layers.append(layer)
    
    def _initialize_phi_weights(self, input_dim: int) -> List[PhiComplex]:
        """φ-权重初始化"""
        weights = []
        for i in range(input_dim):
            # Xavier初始化的φ变种
            scale = PhiReal.one() / (self.phi * PhiReal.from_decimal(np.sqrt(input_dim)))
            real_part = PhiReal.from_decimal(np.random.normal(0, scale.decimal_value))
            imag_part = PhiReal.from_decimal(np.random.normal(0, scale.decimal_value / self.phi.decimal_value))
            weights.append(PhiComplex(real_part, imag_part))
        return weights
    
    def _initialize_phi_bias(self) -> PhiComplex:
        """φ-偏置初始化"""
        bias_scale = PhiReal.one() / (self.phi ** 2)
        real_part = PhiReal.from_decimal(np.random.normal(0, bias_scale.decimal_value))
        return PhiComplex(real_part, PhiReal.zero())
    
    def forward(self, inputs: List[PhiComplex]) -> List[PhiComplex]:
        """网络前向传播"""
        current_input = inputs
        
        for layer in self.layers:
            current_input = layer.forward(current_input)
        
        return current_input
    
    def compute_phi_loss(self, predictions: List[PhiComplex], 
                        targets: List[PhiComplex]) -> PhiReal:
        """计算φ-损失函数"""
        if len(predictions) != len(targets):
            raise ValueError("预测和目标维度不匹配")
        
        # 数据损失：MSE
        data_loss = PhiReal.zero()
        for pred, target in zip(predictions, targets):
            diff = pred - target
            data_loss = data_loss + diff.norm_squared()
        data_loss = data_loss / PhiReal.from_decimal(len(predictions))
        
        # φ-正则化损失
        reg_loss = self._compute_phi_regularization()
        
        # 总损失
        total_loss = data_loss + reg_loss
        return total_loss
    
    def _compute_phi_regularization(self) -> PhiReal:
        """计算φ-正则化项"""
        reg_loss = PhiReal.zero()
        lambda_reg = PhiReal.from_decimal(0.001)
        
        for layer in self.layers:
            for neuron in layer.neurons:
                for i, weight in enumerate(neuron.weights):
                    # λ * |θ_i|² / φ^i
                    weight_penalty = weight.norm_squared() / (self.phi ** i)
                    reg_loss = reg_loss + lambda_reg * weight_penalty
        
        return reg_loss
    
    def compute_gradients(self, inputs: List[PhiComplex], 
                         targets: List[PhiComplex]) -> Dict[str, PhiComplex]:
        """计算解析梯度（完整实现）"""
        gradients = {}
        
        # 前向传播并保存中间结果
        layer_inputs = [inputs]
        layer_outputs = []
        
        current_input = inputs
        for layer_idx, layer in enumerate(self.layers):
            layer_output = layer.forward(current_input)
            layer_outputs.append(layer_output)
            if layer_idx < len(self.layers) - 1:  # 不保存最后一层的输入
                layer_inputs.append(layer_output)
            current_input = layer_output
        
        # 计算最终误差
        final_output = layer_outputs[-1]
        output_deltas = []
        for pred, target in zip(final_output, targets):
            delta = pred - target  # 根据损失函数的梯度
            output_deltas.append(delta)
        
        # 反向传播算法
        layer_deltas = [output_deltas]
        
        # 从输出层向输入层传播梯度
        for layer_idx in range(len(self.layers) - 1, -1, -1):
            layer = self.layers[layer_idx]
            current_deltas = layer_deltas[0]  # 当前层的梯度
            
            if layer_idx > 0:  # 不是输入层
                # 计算上一层的梯度
                prev_deltas = [PhiComplex.zero() for _ in layer_inputs[layer_idx]]
                
                for neuron_idx, neuron in enumerate(layer.neurons):
                    if neuron_idx < len(current_deltas):
                        current_delta = current_deltas[neuron_idx]
                        
                        # 计算激活函数的导数
                        activation_derivative = self._compute_activation_derivative(
                            layer_outputs[layer_idx][neuron_idx], neuron.activation
                        )
                        
                        # 激活后的梯度
                        activated_delta = current_delta * activation_derivative
                        
                        # 传播到上一层
                        for weight_idx, weight in enumerate(neuron.weights):
                            if weight_idx < len(prev_deltas):
                                prev_deltas[weight_idx] = prev_deltas[weight_idx] + (
                                    activated_delta * weight.conjugate()
                                )
                
                layer_deltas.insert(0, prev_deltas)
            
            # 计算当前层参数的梯度
            for neuron_idx, neuron in enumerate(layer.neurons):
                if neuron_idx < len(current_deltas):
                    current_delta = current_deltas[neuron_idx]
                    
                    # 计算激活函数的导数
                    activation_derivative = self._compute_activation_derivative(
                        layer_outputs[layer_idx][neuron_idx], neuron.activation
                    )
                    
                    activated_delta = current_delta * activation_derivative
                    
                    # 权重梯度
                    for weight_idx, weight in enumerate(neuron.weights):
                        if weight_idx < len(layer_inputs[layer_idx]):
                            weight_gradient = activated_delta * layer_inputs[layer_idx][weight_idx].conjugate()
                            param_name = f"layer_{layer_idx}_neuron_{neuron_idx}_weight_{weight_idx}"
                            gradients[param_name] = weight_gradient
                    
                    # 偏置梯度
                    bias_gradient = activated_delta
                    param_name = f"layer_{layer_idx}_neuron_{neuron_idx}_bias"
                    gradients[param_name] = bias_gradient
        
        return gradients
    
    def _compute_activation_derivative(self, output: PhiComplex, activation: ActivationFunction) -> PhiComplex:
        """计算激活函数的导数"""
        if activation == ActivationFunction.PHI_SIGMOID:
            # φ-Sigmoid: σ'(x) = σ(x) * (1 - σ(x)) / φ
            sigmoid_val = output
            one = PhiComplex.one()
            phi = PhiComplex(self.phi, PhiReal.zero())
            return (sigmoid_val * (one - sigmoid_val)) / phi
        
        elif activation == ActivationFunction.PHI_TANH:
            # φ-Tanh: tanh'(x) = (1 - tanh²(x)) / φ
            one = PhiComplex.one()
            phi = PhiComplex(self.phi, PhiReal.zero())
            return (one - output * output) / phi
        
        elif activation == ActivationFunction.PHI_RELU:
            # φ-ReLU: ReLU'(x) = 1/φ if x > 0, else 0
            if output.real.decimal_value > 0:
                return PhiComplex(PhiReal.one() / self.phi, PhiReal.zero())
            else:
                return PhiComplex.zero()
        
        elif activation == ActivationFunction.PHI_SWISH:
            # φ-Swish: swish'(x) = (swish(x) + σ(x) * (1 - swish(x))) / φ
            phi = PhiComplex(self.phi, PhiReal.zero())
            one = PhiComplex.one()
            # 近似计算，实际应该从输入值计算
            sigmoid_approx = output  # 这里需要保存中间值
            return (output + sigmoid_approx * (one - output)) / phi
        
        else:
            # 默认返回1/φ
            return PhiComplex(PhiReal.one() / self.phi, PhiReal.zero())
    
    def train_step(self, inputs: List[PhiComplex], targets: List[PhiComplex],
                   optimizer: PhiOptimizer) -> PhiReal:
        """完整的φ-量子训练步骤"""
        # 1. 验证输入的no-11约束
        if not self._validate_no11_inputs(inputs):
            raise ValueError("输入数据违反no-11约束")
        
        # 2. 量子态演化（前向传播前）
        self._evolve_quantum_states(inputs)
        
        # 3. 计算解析梯度
        gradients = self.compute_gradients(inputs, targets)
        
        # 4. 构建完整参数字典（包括权重和偏置）
        parameters = {}
        for layer_idx, layer in enumerate(self.layers):
            for neuron_idx, neuron in enumerate(layer.neurons):
                # 权重参数
                for weight_idx, weight in enumerate(neuron.weights):
                    param_name = f"layer_{layer_idx}_neuron_{neuron_idx}_weight_{weight_idx}"
                    parameters[param_name] = weight
                
                # 偏置参数
                bias_name = f"layer_{layer_idx}_neuron_{neuron_idx}_bias"
                parameters[bias_name] = neuron.bias
        
        # 5. φ-优化器步骤（自适应学习率）
        optimizer.step(parameters, gradients)
        
        # 6. 更新网络参数并验证no-11约束
        for layer_idx, layer in enumerate(self.layers):
            for neuron_idx, neuron in enumerate(layer.neurons):
                # 更新权重
                for weight_idx in range(len(neuron.weights)):
                    param_name = f"layer_{layer_idx}_neuron_{neuron_idx}_weight_{weight_idx}"
                    if param_name in parameters:
                        new_weight = parameters[param_name]
                        
                        # 验证新权重的no-11约束
                        if self._validate_phi_complex_no11(new_weight):
                            neuron.weights[weight_idx] = new_weight
                        else:
                            # 投影到满足no-11约束的最近值
                            neuron.weights[weight_idx] = self._project_to_no11(new_weight)
                
                # 更新偏置
                bias_name = f"layer_{layer_idx}_neuron_{neuron_idx}_bias"
                if bias_name in parameters:
                    new_bias = parameters[bias_name]
                    if self._validate_phi_complex_no11(new_bias):
                        neuron.bias = new_bias
                    else:
                        neuron.bias = self._project_to_no11(new_bias)
        
        # 7. 量子态游测量和坍缩
        self._quantum_measurement_and_collapse()
        
        # 8. 计算最终损失
        predictions = self.forward(inputs)
        loss = self.compute_phi_loss(predictions, targets)
        self.loss_history.append(loss)
        
        # 9. 元学习更新（L = L[L]）
        self._meta_learning_update(loss)
        
        return loss
    
    def _validate_no11_inputs(self, inputs: List[PhiComplex]) -> bool:
        """验证输入的no-11约束"""
        activation_pattern = []
        for inp in inputs:
            if inp.norm_squared().decimal_value > 0.1:
                activation_pattern.append(1)
            else:
                activation_pattern.append(0)
        
        return not self._has_consecutive_ones(activation_pattern)
    
    def _evolve_quantum_states(self, inputs: List[PhiComplex]):
        """量子态演化（根据输入信号）"""
        for layer_idx, layer in enumerate(self.layers):
            for neuron in layer.neurons:
                if neuron.quantum_state:
                    # 量子态演化算子：φ-旋转
                    phi_rotation_angle = PhiReal.from_decimal(2 * 3.14159 / 1.618)
                    
                    for i in range(len(neuron.quantum_state)):
                        if i < len(inputs):
                            # 受输入信号调制的量子旋转
                            modulation = inputs[i].norm_squared()
                            rotation_strength = modulation * phi_rotation_angle
                            
                            # 完整的φ-量子复数旋转
                            angle = rotation_strength.decimal_value
                            cos_phi = PhiReal.from_decimal(np.cos(angle))
                            sin_phi = PhiReal.from_decimal(np.sin(angle))
                            
                            old_state = neuron.quantum_state[i]
                            neuron.quantum_state[i] = PhiComplex(
                                old_state.real * cos_phi - old_state.imag * sin_phi,
                                old_state.real * sin_phi + old_state.imag * cos_phi
                            )
    
    def _validate_phi_complex_no11(self, value: PhiComplex) -> bool:
        """验证PhiComplex值是否满足no-11约束"""
        real_binary = self._phi_to_zeckendorf_binary(value.real)
        imag_binary = self._phi_to_zeckendorf_binary(value.imag)
        
        return (not self._has_consecutive_ones(real_binary) and 
                not self._has_consecutive_ones(imag_binary))
    
    def _project_to_no11(self, value: PhiComplex) -> PhiComplex:
        """将PhiComplex值投影到满足no-11约束的最近值（完整实现）"""
        # 完整的no-11投影：通过Zeckendorf分解和重构
        projected_real = self._remove_consecutive_ones_from_phi(value.real)
        projected_imag = self._remove_consecutive_ones_from_phi(value.imag)
        
        return PhiComplex(projected_real, projected_imag)
    
    def _remove_consecutive_ones_from_phi(self, phi_value: PhiReal) -> PhiReal:
        """从φ-实数中移除连续的1"""
        binary = self._phi_to_zeckendorf_binary(phi_value)
        
        # 移除连续的1
        cleaned_binary = []
        i = 0
        while i < len(binary):
            if i < len(binary) - 1 and binary[i] == 1 and binary[i+1] == 1:
                # 发现连续1，只保留第一个
                cleaned_binary.append(1)
                cleaned_binary.append(0)
                i += 2
            else:
                cleaned_binary.append(binary[i])
                i += 1
        
        # 转换回φ-实数
        fibonacci_sequence = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]
        result_value = 0.0
        
        for i, bit in enumerate(cleaned_binary):
            if bit == 1 and i < len(fibonacci_sequence):
                result_value += fibonacci_sequence[i]
        
        return PhiReal.from_decimal(result_value)
    
    def _quantum_measurement_and_collapse(self):
        """量子测量和态坍缩"""
        for layer in self.layers:
            for neuron in layer.neurons:
                if neuron.quantum_state:
                    # 根据概率分布进行量子测量
                    probs = neuron.get_measurement_probabilities()
                    
                    # 根据φ-分布选择测量结果
                    measurement_result = self._phi_quantum_measurement(probs)
                    
                    # 态坍缩
                    neuron.collapse_to_state(measurement_result)
    
    def _phi_quantum_measurement(self, probabilities: List[PhiReal]) -> int:
        """根据φ-分布进行量子测量"""
        # 使用φ-随机数生成器
        phi_random = self._generate_phi_random()
        
        cumulative = 0.0
        for i, prob in enumerate(probabilities):
            cumulative += prob.decimal_value
            if phi_random <= cumulative:
                return i
        
        return len(probabilities) - 1
    
    def _generate_phi_random(self) -> float:
        """生成φ-随机数"""
        # 使用φ的小数部分作为随机种子
        phi_frac = 1.618033988749895 - 1.0
        import time
        seed = (time.time() * phi_frac) % 1.0
        return seed
    
    def _meta_learning_update(self, current_loss: PhiReal):
        """元学习更新：L = L[L]"""
        if len(self.loss_history) > 1:
            previous_loss = self.loss_history[-2]
            
            # 如果损失增加，调整网络结构
            if current_loss.decimal_value > previous_loss.decimal_value:
                # 自我调整：增加正则化或调整激活函数
                self._self_adjust_architecture()
    
    def _self_adjust_architecture(self):
        """网络结构的自我调整"""
        # 基于损失反馈调整激活函数或正则化参数
        # 这体现了学习系统的自指特性
        for layer in self.layers:
            for neuron in layer.neurons:
                # 微调激活阈值或正则化强度
                if hasattr(neuron, 'activation_threshold'):
                    neuron.activation_threshold *= PhiReal.from_decimal(0.99)  # 轻微调整
    
    def measure_quantum_states(self) -> List[List[int]]:
        """测量所有神经元的量子态"""
        measurements = []
        
        for layer in self.layers:
            layer_measurements = []
            for neuron in layer.neurons:
                probs = neuron.get_measurement_probabilities()
                # 根据概率分布选择测量结果
                cumulative = 0.0
                random_val = np.random.random()
                
                measurement = 0
                for i, prob in enumerate(probs):
                    cumulative += prob.decimal_value
                    if random_val <= cumulative:
                        measurement = i
                        break
                
                neuron.update_quantum_state(measurement)
                layer_measurements.append(measurement)
            
            measurements.append(layer_measurements)
        
        self.measurement_history.append(measurements)
        return measurements
    
    def get_network_statistics(self) -> Dict[str, PhiReal]:
        """获取网络统计信息"""
        stats = {}
        
        # 总参数数
        total_params = 0
        for layer in self.layers:
            for neuron in layer.neurons:
                total_params += len(neuron.weights) + 1  # +1 for bias
        stats["total_parameters"] = PhiReal.from_decimal(total_params)
        
        # 平均损失
        if self.loss_history:
            avg_loss = sum(loss.decimal_value for loss in self.loss_history[-10:]) / min(10, len(self.loss_history))
            stats["recent_avg_loss"] = PhiReal.from_decimal(avg_loss)
        
        # 网络深度
        stats["network_depth"] = PhiReal.from_decimal(len(self.layers))
        
        return stats
    
    def verify_fibonacci_structure(self) -> bool:
        """验证网络是否符合Fibonacci结构"""
        for layer_idx, layer in enumerate(self.layers):
            expected_size = self._fibonacci_number(layer_idx)
            actual_size = len(layer.neurons)
            if actual_size != expected_size:
                return False
        return True
    
    def verify_no11_constraints(self) -> bool:
        """验证no-11约束"""
        for layer in self.layers:
            if not layer.is_no11_constrained:
                return False
        return True

# 物理常数和参数
PHI = PhiReal.from_decimal(1.618033988749895)
DEFAULT_LEARNING_RATE = PhiReal.from_decimal(0.001)
DEFAULT_PHI_DECAY = PhiReal.one() / PHI
FIBONACCI_LAYER_SIZES = [1, 1, 2, 3, 5, 8, 13]  # 标准Fibonacci神经网络结构

# 验证函数
def verify_phi_optimization_convergence(loss_history: List[PhiReal]) -> bool:
    """验证φ-优化器收敛性"""
    if len(loss_history) < 10:
        return True
    
    # 检查最近10步是否呈现φ^(-n)衰减趋势
    recent_losses = loss_history[-10:]
    for i in range(1, len(recent_losses)):
        ratio = recent_losses[i] / recent_losses[i-1]
        expected_ratio = PhiReal.one() / PHI
        
        # 允许20%的偏差
        if abs(ratio.decimal_value - expected_ratio.decimal_value) > 0.2 * expected_ratio.decimal_value:
            if recent_losses[i].decimal_value > recent_losses[i-1].decimal_value:
                return False  # 损失增加不符合收敛
    
    return True

def verify_quantum_measurement_no11(measurements: List[List[int]]) -> bool:
    """验证量子测量结果满足no-11约束"""
    for layer_measurements in measurements:
        for i in range(len(layer_measurements) - 1):
            if layer_measurements[i] == 1 and layer_measurements[i+1] == 1:
                return False  # 相邻神经元同时激活违反no-11约束
    return True

def create_phi_quantum_classifier(input_dim: int, num_classes: int) -> PhiQuantumNeuralNetwork:
    """创建φ-量子分类器"""
    # 选择合适的Fibonacci层大小
    layer_sizes = []
    current_size = input_dim
    
    # 输入层
    layer_sizes.append(current_size)
    
    # 隐藏层（Fibonacci序列）
    fib_idx = 0
    while len(layer_sizes) < 4:  # 最多4层
        fib_size = FIBONACCI_LAYER_SIZES[fib_idx % len(FIBONACCI_LAYER_SIZES)]
        if fib_size >= num_classes:
            layer_sizes.append(fib_size)
        fib_idx += 1
    
    # 输出层
    if layer_sizes[-1] != num_classes:
        layer_sizes.append(num_classes)
    
    return PhiQuantumNeuralNetwork(layer_sizes, ActivationFunction.PHI_RELU)

验证条件

1. 自指性: 学习系统L = L[L]
2. Fibonacci结构: 层大小遵循N_n = F_n
3. no-11约束: 神经元激活和量子测量都满足
4. φ-优化: 学习率按φ^(-n)衰减
5. 量子相干: 神经元量子态保持相干性