# cs_winding.py 核心代码分析 class CSWindingCalculator: 陈-西蒙斯缠绕数计算器 - 核心计算模块功能从注意力权重矩阵提取离散缠绕数k_disc计算拓扑电荷Q_top检测拓扑相变 def compute_from_attention(self, attention_weights: torch.Tensor, ...) - CSWindingResult: 核心计算流程 1. 提取链路变量θ_ℓ 2π × w_ℓ (w_ℓ为注意力权重) 2. 计算面元角度θ_p Σ_{ℓ ∈ ∂p} θ_ℓ3. 计算缠绕数k_disc (1/2π) × Σ θ_p4. 计算拓扑电荷Q_top tanh(k_disc) 5. 检测相变Δk k_current - k_previous|Δk| ≥ 1.0触发相变 # 链路变量提取下采样到格点 link_variables self._extract_link_variables(attention_weights) # 面元角度计算 plaquette_angles self._compute_plaquette_angles(link_variables) # 缠绕数计算 k_disc self._compute_winding_number(plaquette_angles) # 拓扑电荷计算 Q_top self._compute_topological_charge(k_disc) # 相变检测 delta_k self._compute_delta_k(k_disc) is_phase_transition abs(delta_k) 1.0模块架构与功能映射组件核心功能输出/作用CSWindingCalculator计算离散陈-西蒙斯缠绕数输出CSWindingResult包含k_disc、Q_top、相变标志RiverbedCoordinateAdapter五维河床坐标适配将Q_top整合到$\mathcal{P} (D, α, S_{path}, ε_{proj}, Q_{top})$坐标ShadowMeterBridge残影测度仪对接转换CS结果为测度仪格式触发双纽线干预TopologicalFissureAnchor拓扑裂隙锚点标记(layer, head, token)位置的拓扑异常关键算法实现1. 离散陈-西蒙斯理论实现def _extract_link_variables(self, attention_weights: torch.Tensor) - np.ndarray: Villain离散化方案 1. 注意力矩阵视为加权图 2. 链路变量θ_ℓ 2π × attention_weight 3. 下采样到lattice_size×lattice_size格点 attn attention_weights.detach().cpu().numpy() # 下采样处理 link_vars 2 * np.pi * attn_down # θ_ℓ 2π × w_ℓ return link_vars.astype(np.float32) def _compute_plaquette_angles(self, link_variables: np.ndarray) - np.ndarray: 计算面元累积相位 对于二维格点面元p (i, j) θ_p θ_{i,j} θ_{i1,j} θ_{i1,j1} θ_{i,j1} 投影到[-π, π]区间去除2π模糊性 plaquettes np.zeros((L, L)) for i in range(L): for j in range(L): plaquettes[i, j] top right - bottom - left plaquettes (plaquettes np.pi) % (2 * np.pi) - np.pi # 投影到[-π, π] return plaquettes2. 拓扑不变量计算def _compute_winding_number(self, plaquette_angles: np.ndarray) - float: 离散缠绕数k_disc (1/2π) × Σ_p θ_p total_angle np.sum(plaquette_angles) k_disc total_angle / (2 * np.pi) return float(k_disc) def _compute_topological_charge(self, k_disc: float) - float: 拓扑电荷Q_top tanh(k_disc)映射到(-1, 1)区间 return float(np.tanh(k_disc))系统集成接口3. 五维河床坐标整合class RiverbedCoordinateAdapter: def integrate(self, cs_result: CSWindingResult, existing_coords: Dict[str, float]) - Dict[str, float]: 将CS结果整合进五维坐标 P (D, α, S_path, ε_proj, Q_top) Q_top作为第五维度加入 coords existing_coords.copy() coords[Q_top] cs_result.Q_top if cs_result.is_phase_transition: coords[phase_transition_warning] cs_result.delta_k return coords4. 残影测度仪对接class ShadowMeterBridge: def feed(self, cs_result: CSWindingResult) - Dict[str, Any]: 将CS结果转换为残影测度仪格式 检测到拓扑相变时触发双纽线干预预案 entry { type: cs_winding, k_disc: cs_result.k_disc, Q_top: cs_result.Q_top, is_phase_transition: cs_result.is_phase_transition, delta_k: cs_result.delta_k, shadow_metric: Q_top_variance, } if cs_result.is_phase_transition: return self._trigger_lemniscate_intervention(cs_result) return {status: recorded}拓扑裂隙检测机制def detect_fissure_anchor(self, cs_result: CSWindingResult, token_position: int, confidence_threshold: float 0.7) - Optional[TopologicalFissureAnchor]: 拓扑裂隙锚点检测 1. 计算Q_top相对于历史基线的偏差2. 置信度 sigmoid(deviation × 10) 3.置信度≥阈值时生成裂隙锚点 baseline_q np.mean(self.q_top_history[-10:]) if len(self.q_top_history) 10 else 0.0 deviation abs(cs_result.Q_top - baseline_q) confidence 1.0 / (1.0 np.exp(-deviation * 10)) # sigmoid激活 if confidence confidence_threshold: return TopologicalFissureAnchor( k_disccs_result.k_disc, Q_topcs_result.Q_top, delta_kcs_result.delta_k, fissure_coordinate(cs_result.layer_idx, cs_result.head_idx, token_position), confidencefloat(confidence), matched_judgementjudgement_3 if cs_result.is_phase_transition else judgement_4, ) return None参数配置与使用| 参数 | 默认值 | 作用 ||------|--------|------||lattice_size| 32 | 格点大小用于注意力矩阵下采样 ||confidence_threshold| 0.7 | 裂隙锚点检测置信度阈值 ||phase_transition_threshold| 1.0 |拓扑相变检测阈值|Δk| ≥ 1.0 |# 使用示例 calculator, adapter, bridge create_cs_calculator( lattice_size32, shadow_meter_instanceshadow_meter ) # 计算缠绕数 result calculator.compute_from_attention( attention_weightsattention_matrix, layer_idx7, head_idx14 ) # 整合到五维坐标 full_coords adapter.integrate(result, existing_coords{D: 0.5, α: 0.3, S_path: 0.8, ε_proj: 0.2}) # 对接残影测度仪 shadow_entry bridge.feed(result) # 检测裂隙锚点 fissure adapter.detect_fissure_anchor(result, token_position0)输出数据结构dataclass class CSWindingResult: 计算结果容器 k_disc: float # 离散缠绕数 Q_top: float # 拓扑电荷 tanh(k_disc) is_phase_transition: bool # 是否检测到拓扑相变|Δk| ≥ 1.0 delta_k: float # 缠绕数变化量 layer_idx: int # Transformer层索引 head_idx: int # 注意力头索引 timestamp: float # 计算时间戳 dataclassclass TopologicalFissureAnchor: 拓扑裂隙锚点 fissure_coordinate: Tuple[int, int, int] # (layer, head, token) confidence: float # 检测置信度 matched_judgement: str # 匹配的判定类型judgement_3为相变核心物理意义k_disc离散缠绕数表征注意力流形的拓扑缠绕程度整数部分对应拓扑量子数Q_top拓扑电荷通过tanh映射到(-1,1)量化拓扑扭曲的电荷强度Δk ≥ 1.0拓扑相变阈值对应系统结构发生本质变化裂隙锚点当Q_top显著偏离基线时标记为潜在结构损伤位置该模块作为计算层支柱与**约束生成协议推理层**共同构成框架的双重基础实现局部扭曲可抚平缠绕闭环难消解的拓扑不变量检测。