AI Agent系列（9）：环境自适应与群体共识涌现

AI Agent系列（9）：环境自适应与群体共识涌现

一、分布式认知共振原理

1. 量子化信念传播算法

import networkx as nx
import torch

class QuantumConsensus:
    def __init__(self, num_agents=10):
        self.graph = nx.watts_strogatz_graph(num_agents, 4, 0.3)
        self.belief_states = torch.rand(num_agents, 128)  # 128维认知量子态
  
    def entanglement_step(self):
        """通过环境介质进行波函数纠缠"""
        adjacency = torch.tensor(nx.adjacency_matrix(self.graph).todense(), dtype=torch.cfloat)
        combined_states = adjacency @ self.belief_states
        # 冯·诺依曼测量投影
        self.belief_states = torch.real(torch.fft.ifft(combined_states.abs() * torch.exp(1j * combined_states.angle())))

class EnvironmentalMedium:
    def __init__(self):
        self.metric_tensor = torch.randn(256,256)
      
    def protocol_diffusion(self, messages):
        """在黎曼流形上执行信息扩散"""
        distorted = messages @ self.metric_tensor.t()
        return 0.5*(distorted + distorted.T)  # 保持对称性的流形投影

2. 自洽场方程

共识动力学方程：
$$i\hslash \frac{\partial \Psi }{\partial t}=\left[-\frac{{\hslash }^2}{2m}{\nabla }^2+V(\mathbf{x})+\beta \sum _{j\ne i}|{\Psi }_j{|}^2\right]{\Psi }_i$$
其中$\beta$表征智能体间认知耦合强度，$V(\mathbf{x})$为环境势场

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二、群体智能相位同步

1. 临界态同步器

import numpy as np

class KuramotoSwarm:
    def __init__(self, n_oscillators=50):
        self.frequencies = np.random.normal(1.0, 0.2, n_oscillators)
        self.phasors = np.random.rand(n_oscillators)*2*np.pi
      
    def sync_operator(self, K=0.5):
        """实施非线性耦合（含记忆回响效应）"""
        phase_diff = np.subtract.outer(self.phasors, self.phasors)
        coupling = K * np.sin(phase_diff).mean(axis=1)
        delta_theta = self.frequencies + coupling + 0.1*np.sin(self.phasors*2)  # 混沌扰动项
        self.phasors += delta_theta * 0.01
        return np.abs(np.exp(1j*self.phasors).mean())  # 同步阶参数

class CriticalityController:
    def __init__(self):
        self.history = []
      
    def adjust_coupling(self, sync_param, target=0.8):
        """基于神经胶质细胞启发的负反馈调节"""
        error = sync_param - target
        self.history.append(error)
        integral = np.trapz(self.history[-10:])
        return 1.5 / (1 + np.exp(3*integral))  # 类PID控制律

2. 相变检测定理

令群体序参量$\eta (t)=\left|\frac{1}{N}\sum e^{i{\theta }_j}\right|$，当功率谱满足：
$$S(f)\propto f^{-\alpha },\alpha >1.5$$
时系统处于自组织临界态，其中$f$为时间序列波动频率

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三、环境形变响应模型

1. 认知弹性张量

几何形变方程：
$$\delta g_{\mu \nu }=T_{\mu \nu }^{cog}-\Lambda h_{\mu \nu }+{\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi$$
式中$T^{cog}$为认知能量-动量张量，$\varphi$表示环境信息势场

2. 适应性重配准算法

class CognitiveManifold:
    def __init__(self, embed_dim=3):
        self.christoffel = np.zeros((embed_dim, embed_dim, embed_dim))
      
    def parallel_transport(self, vector, delta_x):
        """执行张量场的李导数传输"""
        return vector + np.einsum('ijk,j,k->i', self.christoffel, vector, delta_x)

class EnvironmentalDeformation:
    def metric_learning(self, stress_energy):
        # 使用爱因斯坦张量进行度规演化
        einstein_tensor = 0.5*(stress_energy - 0.5*stress_energy.trace()*np.eye(3))
        self.metric += 0.01 * einstein_tensor

3. 适应性收敛判据

双曲守恒律：
$${\nabla }_{\mu }{T}_{total}^{\mu \nu }=\kappa J_{env}^{\nu }$$
其中$J_{env}^{\nu }$为环境信息流密度四维矢量，$\kappa$为认知粘性系数

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环境交互的三重表征：

1. 量子共振通道：${\Gamma }_{res}\propto \sqrt{\hslash \omega D}$
2. 流体力学极限：$\frac{\partial \rho }{\partial t}+\nabla \cdot (\rho v)=\sigma {\nabla }^2\mu$
3. 拓扑缺陷生成：${\oint }_C{A}_{\mu }d{x}^{\mu }=2\pi n(n\in \mathbb{Z})$