当神经网络学会“讲逻辑”：聊聊神经符号学习中的约束嵌入

import torch
import torch.nn.functional as F

def logic_constraint_embedding(user_preferences, movie_scores):
    """
    user_preferences: 用户对各类别的偏好分数 [batch_size, categories]
    movie_scores: 用户对电影的预测评分 [batch_size, movies]
    
    约束：科幻偏好高 -> 《星际穿越》分数高
    """
    # 假设科幻类别索引为0，《星际穿越》索引为5
    sci_fi_pref = user_preferences[:, 0]  # 科幻偏好
    interstellar_score = movie_scores[:, 5]  # 《星际穿越》预测分
    
    # 将逻辑蕴含转换为损失：如果科幻偏好高，但电影分数低，则惩罚
    # 蕴含逻辑 p -> q 等价于 max(0, p - q)
    constraint_loss = torch.relu(sci_fi_pref - interstellar_score)
    
    return constraint_loss.mean()

def mutual_exclusion_constraint(preferences):
    """
    preferences: 用户对不同度假地类型的偏好 [batch_size, types]
    假设索引：0=极冷地, 1=极热地
    """
    cold_pref = preferences[:, 0]
    hot_pref = preferences[:, 1]
    
    # 互斥约束：两者不应该同时高
    # 使用乘积惩罚两者都高的情况
    mutual_loss = cold_pref * hot_pref
    
    return mutual_loss.mean()

class ConstrainedModel:
    def train_step(self, data, labels):
        # 主任务预测
        predictions = self.model(data)
        
        # 主损失（如交叉熵）
        main_loss = F.cross_entropy(predictions, labels)
        
        # 逻辑约束损失
        logic_loss = 0.0
        
        # 添加各种约束
        logic_loss += self.consistency_constraint(predictions)
        logic_loss += self.mutual_exclusion_constraint(predictions)
        
        # 组合损失
        total_loss = main_loss + self.lambda_param * logic_loss
        
        return total_loss
    
    def consistency_constraint(self, predictions):
        """一致性约束示例"""
        # 假设我们的预测包含一些互斥的属性
        batch_size, num_features = predictions.shape
        
        # 简化的示例：某些特征组合不应同时出现
        loss = torch.tensor(0.0, device=predictions.device)
        
        # 示例约束：特征0和特征3不应同时高
        feature_0 = predictions[:, 0]
        feature_3 = predictions[:, 3]
        
        # 当两者都超过阈值时施加惩罚
        threshold = 0.7
        mask = (feature_0 > threshold) & (feature_3 > threshold)
        loss = (feature_0[mask] * feature_3[mask]).sum()
        
        return loss

def fuzzy_and(tensor1, tensor2):
    """模糊逻辑与操作"""
    return torch.min(tensor1, tensor2)

def fuzzy_or(tensor1, tensor2):
    """模糊逻辑或操作"""
    return torch.max(tensor1, tensor2)

def fuzzy_implication(p, q):
    """模糊蕴含 p -> q"""
    # 使用卢卡西维茨蕴含
    return torch.clamp(1 - p + q, 0, 1)

def complex_constraint_example(user_features, item_features):
    """
    复杂规则示例：
    (年轻用户 AND 科技爱好者) -> 可能喜欢最新电子产品
    """
    is_young = user_features[:, AGE_COL] < 0.3  # 标准化后的年龄
    likes_tech = user_features[:, TECH_COL] > 0.7
    
    # 模糊逻辑组合
    antecedent = fuzzy_and(is_young.float(), likes_tech.float())
    
    # 结论：喜欢最新电子产品
    should_like_new_tech = item_features[:, NEW_TECH_COL]
    
    # 计算蕴含损失
    constraint = fuzzy_implication(antecedent, should_like_new_tech)
    
    # 我们希望蕴含尽可能为真（接近1）
    loss = 1 - constraint.mean()
    
    return loss

# 约束权重调优示例
class AdaptiveConstraintWeight:
    def __init__(self, num_constraints, lr=0.01):
        self.weights = torch.nn.Parameter(torch.ones(num_constraints))
        self.optimizer = torch.optim.Adam([self.weights], lr=lr)
    
    def adjust_weights(self, constraint_violations):
        """
        根据约束违反程度自适应调整权重
        constraint_violations: 各约束的违反程度
        """
        # 违反程度高的约束获得更高权重
        weight_update = torch.softmax(constraint_violations, dim=0)
        self.weights.data = weight_update