引言

图基础模型(Graph Foundation Model, GFM)是近年来图机器学习领域的重要发展方向,旨在通过大规模图数据的预训练,构建能够跨领域泛化的通用图表示学习模型。与语言模型、视觉模型的基础模型范式类似,图基础模型试图解决图神经网络(GNN)在实际应用中面临的挑战:

  1. 标签稀疏性:大多数图数据缺乏足够的标注
  2. 领域迁移困难:在一个领域训练的GNN难以直接应用于其他领域
  3. 计算效率:大规模图的训练成本高昂
  4. 异质性:不同领域的图结构差异显著

图基础模型定义

图基础模型(Graph Foundation Model)是指在大规模、多样化的图数据上进行预训练的神经网络,能够通过微调或提示学习的方式,快速适应下游图任务。

class GraphFoundationModel:
    """
    图基础模型接口定义
    
    核心特性:
    1. 预训练:在大规模图数据上学习通用图表示
    2. 迁移:通过微调/提示适应下游任务
    3. 泛化:跨领域、跨任务的能力
    """
    
    def __init__(self, backbone: GNNArchitecture):
        self.backbone = backbone
        self.pretrain_objectives = []
        self.prompt_strategy = None
    
    def pretrain(self, graphs: List[Graph]):
        """多图预训练"""
        for objective in self.pretrain_objectives:
            for graph in graphs:
                loss = objective(graph)
                loss.backward()
    
    def finetune(self, task_graph: Graph, labels: Labels):
        """任务微调"""
        pass
    
    def prompt(self, task_graph: Graph, task_description: str):
        """提示学习"""
        pass

1. 图预训练的挑战

1.1 图数据的异质性

与自然语言和图像不同,图数据具有高度的异质性:

异质性维度表现示例
结构异质节点度数分布、聚类系数差异大社交网络 vs 分子图
特征异质节点/边特征维度、类型不同蛋白质特征 vs 引用网络
语义异质任务目标、标签含义不同节点分类 vs 链接预测
规模异质节点数、边数差异巨大万级 vs 十亿级节点

1.2 预训练的风险

# 预训练-微调差异导致的负迁移风险
class NegativeTransferRisk:
    """
    预训练图模型可能在以下情况下产生负迁移:
    """
    
    risks = {
        "structural_mismatch": {
            "description": "预训练和微调图的拓扑结构差异大",
            "symptom": "微调性能显著低于从头训练",
            "mitigation": "图增强、结构正则化"
        },
        "feature_distribution_shift": {
            "description": "节点特征分布随时间变化",
            "symptom": "时序图上的性能下降",
            "mitigation": "持续预训练、领域适应"
        },
        "task_interference": {
            "description": "多任务预训练导致任务间干扰",
            "symptom": "某些下游任务性能下降",
            "mitigation": "任务解耦、提示学习"
        },
        "overfitting_to_pretraining": {
            "description": "预训练目标与下游任务不一致",
            "symptom": "预训练损失低但微调效果差",
            "mitigation": "设计任务对齐的预训练目标"
        }
    }

2. 图自监督预训练方法

2.1 代理任务分类

图预训练的核心是设计有效的自监督学习(SSL)目标:

图预训练代理任务
    │
    ├─ 节点级代理
    │    ├─ 上下文预测
    │    │    ├─ 属性掩码(Attribute Masking)
    │    │    ├─ 上下文预测(Context Prediction)
    │    │    └─ 邻居对比(N Contrast)
    │    │
    │    └─ 特征重构
    │         ├─ 自编码器(Graph Autoencoder)
    │         └─ 对比学习(GraphCL等)
    │
    ├─ 图级代理
    │    ├─ 图级表示对比
    │    │    ├─ 对比学习(InfoGraph, SUBG-CON)
    │    │    └─ 知识蒸馏
    │    │
    │    └─ 图生成
    │         ├─ 节点/边预测
    │         └─ 图重建
    │
    └─ 跨层次代理
         ├─ 局部-全局一致性
         └─ 多尺度对比

2.2 属性掩码(Attribute Masking)

节点/边属性掩码

class AttributeMaskingPretrain:
    """
    属性掩码预训练
    
    核心思想:随机掩码节点或边的属性,让模型学习恢复
    """
    
    def __init__(self, mask_ratio=0.15):
        self.mask_ratio = mask_ratio
    
    def pretrain_step(self, graph: Graph, model: GNN):
        """一步预训练"""
        # 1. 掩码节点属性
        masked_graph, mask = self.mask_node_features(graph)
        
        # 2. 前向传播
        node_repr = model(masked_graph)
        
        # 3. 预测被掩码的属性
        masked_nodes = torch.where(mask)[0]
        pred_features = self.predict_features(node_repr[masked_nodes])
        true_features = graph.x[masked_nodes]
        
        # 4. 计算损失
        loss = F.mse_loss(pred_features, true_features)
        
        return loss
    
    def mask_node_features(self, graph: Graph):
        """掩码节点特征"""
        num_nodes = graph.num_nodes
        num_mask = int(num_nodes * self.mask_ratio)
        
        # 随机选择要掩码的节点
        mask_idx = torch.randperm(num_nodes)[:num_mask]
        mask = torch.zeros(num_nodes, dtype=torch.bool)
        mask[mask_idx] = True
        
        # 保存原始特征并掩码
        original_x = graph.x.clone()
        graph.x[mask_idx] = 0  # 或用特殊掩码token
        
        return graph, mask
 
 
# 边属性掩码
class EdgeAttributeMasking:
    """边属性掩码:掩码边的类型或权重"""
    
    def pretrain_step(self, graph: Graph, model: GNN):
        # 掩码边属性
        num_edges = graph.edge_index.shape[1]
        mask_idx = torch.randperm(num_edges)[:int(num_edges * 0.15)]
        
        original_edge_attr = graph.edge_attr.clone()
        graph.edge_attr[mask_idx] = 0
        
        # 模型前向
        node_repr = model(graph)
        
        # 预测边属性
        edge_repr = self.edge_representation(node_repr, graph.edge_index)
        pred_edge_attr = self.edge_predictor(edge_repr[mask_idx])
        
        loss = F.cross_entropy(pred_edge_attr, original_edge_attr[mask_idx])
        
        return loss

掩码策略对比

策略描述适用场景
随机掩码随机选择节点/边进行掩码通用
结构感知掩码基于度数、重要性选择异质图
属性感知掩码优先掩码罕见属性特征丰富的图
图级掩码掩码整个子图图级任务

2.3 图对比学习

InfoGraph: 局部-全局对比

class InfoGraphPretrain:
    """
    InfoGraph: 最大化局部表示与全局表示的互信息
    
    论文: InfoGraph: Unsupervised and Semi-supupervised Graph-Level Representation Learning via Mutual Information Maximization
    """
    
    def __init__(self, temperature=0.5):
        self.temperature = temperature
        self.discriminator = MLPProjector()
    
    def pretrain(self, graphs: List[Graph], model: GNN):
        """InfoGraph预训练"""
        total_loss = 0
        
        for graph in graphs:
            # 1. 获取局部表示(节点级)
            local_repr = model(graph)  # [num_nodes, hidden_dim]
            
            # 2. 获取全局表示(图级)
            graph_repr = readout(local_repr)  # [1, hidden_dim]
            
            # 3. 对比损失:拉近正样本,排斥负样本
            pos_score = self.calculate_positive_score(local_repr, graph_repr)
            neg_score = self.calculate_negative_score(local_repr, graph_repr)
            
            # 4. InfoNCE损失
            loss = self.info_nce(pos_score, neg_score)
            total_loss += loss
        
        return total_loss / len(graphs)
    
    def info_nce(self, pos_score, neg_scores):
        """InfoNCE损失"""
        pos_exp = torch.exp(pos_score / self.temperature)
        neg_exp = torch.sum(torch.exp(neg_scores / self.temperature), dim=-1)
        
        return -torch.log(pos_exp / (pos_exp + neg_exp + 1e-8))

GraphCL: 图增强对比

class GraphCLPretrain:
    """
    GraphCL: 图对比学习的系统研究
    
    核心思想:通过对图进行不同的增强,构造对比学习的正负样本
    """
    
    def __init__(self):
        self.augmentations = [
            NodeDropout(),
            EdgePerturbation(ratio=0.1),
            AttributeMasking(ratio=0.1),
            SubgraphSampling(ratio=0.5),
        ]
    
    def pretrain(self, graph: Graph, model: GNN):
        # 1. 构造两个增强视图
        aug1 = self.random_augment(graph)
        aug2 = self.random_augment(graph)
        
        # 2. 获取表示
        repr1 = model(self.aug(aug1))
        repr2 = model(self.aug(aug2))
        
        # 3. 对比损失
        loss = self.contrastive_loss(repr1, repr2)
        
        return loss
    
    def random_augment(self, graph: Graph) -> Graph:
        """随机选择一种增强方式"""
        aug = random.choice(self.augmentations)
        return aug.apply(graph)
 
 
class NodeDropout:
    """节点丢弃增强"""
    
    def __init__(self, p=0.2):
        self.p = p
    
    def apply(self, graph: Graph) -> Graph:
        num_nodes = graph.num_nodes
        keep_idx = torch.rand(num_nodes) > self.p
        keep_idx = keep_idx.nonzero().squeeze()
        
        # 重新索引
        new_index_map = -torch.ones(num_nodes, dtype=torch.long)
        new_index_map[keep_idx] = torch.arange(len(keep_idx))
        
        # 更新边
        new_edge_index = new_index_map[graph.edge_index]
        valid_edges = (new_edge_index[0] >= 0) & (new_edge_index[1] >= 0)
        
        return Graph(
            x=graph.x[keep_idx],
            edge_index=new_edge_index[:, valid_edges],
            edge_attr=graph.edge_attr[valid_edges] if graph.edge_attr else None
        )
 
 
class SubgraphSampling:
    """子图采样增强"""
    
    def __init__(self, ratio=0.5):
        self.ratio = ratio
    
    def apply(self, graph: Graph) -> Graph:
        # 随机游走采样子图
        start_nodes = torch.randint(0, graph.num_nodes, (int(graph.num_nodes * self.ratio),))
        sub_nodes = self.random_walk_subgraph(graph, start_nodes)
        
        return self.extract_subgraph(graph, sub_nodes)

2.4 上下文预测(Context Prediction)

class ContextPredictionPretrain:
    """
    上下文预测预训练
    
    让模型预测一个节点属于哪个子图(上下文)
    来自: Hu et al. "Pre-training Graph Neural Networks"
    """
    
    def __init__(self, k_hop=2, num_contexts=50):
        self.k_hop = k_hop
        self.num_contexts = num_contexts
        self.context_encoder = GNN()
    
    def pretrain(self, graph: Graph, model: GNN):
        # 1. 采样锚点节点
        anchor_nodes = self.sample_anchor_nodes(graph)
        
        # 2. 获取锚点表示
        node_repr = model(graph)
        anchor_repr = node_repr[anchor_nodes]
        
        # 3. 构建上下文样本
        positive_contexts, negative_contexts = self.sample_contexts(
            graph, anchor_nodes
        )
        
        # 4. 编码上下文
        pos_context_repr = self.context_encoder(positive_contexts)
        neg_context_repr = self.context_encoder(negative_contexts)
        
        # 5. 上下文预测损失
        pos_score = torch.sum(anchor_repr * pos_context_repr, dim=-1)
        neg_score = torch.sum(anchor_repr * neg_context_repr, dim=-1)
        
        loss = self.contrastive_loss(pos_score, neg_score)
        
        return loss
    
    def sample_contexts(self, graph, anchor_nodes):
        """采样正负上下文"""
        positive = []
        negative = []
        
        for node in anchor_nodes:
            # 正样本:k-hop邻居子图
            pos_subgraph = self.extract_khop_subgraph(graph, node, self.k_hop)
            positive.append(pos_subgraph)
            
            # 负样本:随机子图
            neg_node = torch.randint(0, graph.num_nodes, (1,)).item()
            neg_subgraph = self.extract_khop_subgraph(graph, neg_node, self.k_hop)
            negative.append(neg_subgraph)
        
        return positive, negative

3. 图基础模型架构

3.1 通用图骨干网络

class UniversalGraphBackbone(nn.Module):
    """
    通用图骨干网络
    
    设计原则:
    1. 架构无关:支持多种GNN变体
    2. 尺度无关:可处理不同规模的图
    3. 异质性无关:通过参数化处理不同特征
    """
    
    def __init__(
        self,
        input_dim: int,
        hidden_dim: int,
        num_layers: int,
        gnn_type: str = "GAT",  # GCN, GAT, GraphSAINT, GPS
        dropout: float = 0.1,
    ):
        super().__init__()
        
        # 输入投影
        self.input_proj = nn.Linear(input_dim, hidden_dim)
        
        # GNN层
        self.gnn_layers = nn.ModuleList([
            self._create_gnn_layer(gnn_type, hidden_dim)
            for _ in range(num_layers)
        ])
        
        # 层归一化
        self.norms = nn.ModuleList([
            nn.LayerNorm(hidden_dim)
            for _ in range(num_layers)
        ])
        
        self.dropout = nn.Dropout(dropout)
    
    def _create_gnn_layer(self, gnn_type, hidden_dim):
        """创建指定类型的GNN层"""
        if gnn_type == "GCN":
            return GCNConv(hidden_dim, hidden_dim)
        elif gnn_type == "GAT":
            return GATConv(hidden_dim, hidden_dim // 8, heads=8)
        elif gnn_type == "GraphSAINT":
            return SAGEConv(hidden_dim, hidden_dim)
        elif gnn_type == "GPS":
            return GPSLayer(hidden_dim, num_heads=8)
        else:
            raise ValueError(f"Unknown GNN type: {gnn_type}")
    
    def forward(self, graph: Graph) -> Tensor:
        x = self.input_proj(graph.x)
        
        for gnn, norm in zip(self.gnn_layers, self.norms):
            h = gnn(x, graph.edge_index)
            h = norm(h)
            h = F.relu(h)
            h = self.dropout(h)
            
            # 残差连接
            x = x + h
        
        return x

3.2 异质图Transformer

class HeterogeneousGraphTransformer(nn.Module):
    """
    异质图Transformer
    
    处理具有多种节点类型和边类型的图
    """
    
    def __init__(
        self,
        num_node_types: int,
        num_edge_types: int,
        hidden_dim: int,
        num_layers: int,
    ):
        super().__init__()
        
        # 节点类型嵌入
        self.node_type_embedding = nn.Embedding(num_node_types, hidden_dim)
        
        # 边类型嵌入
        self.edge_type_embedding = nn.Embedding(num_edge_types, hidden_dim)
        
        # 异质注意力
        self.layers = nn.ModuleList([
            HeterophilicAttentionLayer(hidden_dim)
            for _ in range(num_layers)
        ])
    
    def forward(self, graph: HeteroGraph) -> Dict[str, Tensor]:
        # 初始化节点表示
        h = {
            ntype: graph.x[ntype] + self.node_type_embedding(
                torch.full((graph.x[ntype].shape[0],), 
                          self.type_id_map[ntype])
            )
            for ntype in graph.node_types
        }
        
        # 多层Transformer
        for layer in self.layers:
            h = layer(h, graph.edge_index_dict)
        
        return h
 
 
class HeterophilicAttentionLayer(nn.Module):
    """异质感知注意力层"""
    
    def __init__(self, hidden_dim):
        super().__init__()
        self.query_proj = nn.Linear(hidden_dim, hidden_dim)
        self.key_proj = nn.Linear(hidden_dim, hidden_dim)
        self.value_proj = nn.Linear(hidden_dim, hidden_dim)
        
        # 边类型特定的投影
        self.edge_proj = nn.Linear(hidden_dim, hidden_dim)
    
    def forward(self, h_dict, edge_index_dict):
        """处理异质边"""
        new_h = {}
        
        for (src_type, rel_type, dst_type), edge_index in edge_index_dict.items():
            src_h = h_dict[src_type]
            dst_h = h_dict[dst_type]
            
            # 注意力计算
            q = self.query_proj(dst_h)
            k = self.key_proj(src_h)
            v = self.value_proj(src_h)
            
            # 边类型信息
            edge_h = self.edge_proj(
                self.edge_type_embedding(
                    torch.full((edge_index.shape[1],), 
                              self.edge_type_id_map[rel_type])
                )
            )
            
            # 注意力分数
            attn = (q[edge_index[1]] * (k[edge_index[0]] + edge_h)).sum(-1)
            attn = F.softmax(attn, dim=0)
            
            # 聚合
            new_h[dst_type] = (attn.unsqueeze(-1) * (v[edge_index[0]] + edge_h)).sum(dim=0)
        
        return new_h

4. 跨领域迁移学习

4.1 迁移策略

class GraphTransferLearning:
    """
    图迁移学习策略
    """
    
    strategies = {
        "full_finetune": {
            "description": "全量微调所有参数",
            "pros": ["适应性强", "性能最优"],
            "cons": ["计算成本高", "容易过拟合"],
            "适用": "标注数据充足"
        },
        "linear_probe": {
            "description": "冻结骨干网络,只微调分类头",
            "pros": ["高效", "不易过拟合"],
            "cons": ["表达能力受限"],
            "适用": "标注数据有限"
        },
        "adapter": {
            "description": "添加适配器模块",
            "pros": ["参数高效", "可多任务"],
            "cons": ["需要设计适配器"],
            "适用": "多任务场景"
        },
        "prompt": {
            "description": "图提示学习",
            "pros": ["无需微调", "任务灵活"],
            "cons": ["需要设计提示"],
            "适用": "零样本场景"
        }
    }

4.2 图适配器(GraphAdapter)

class GraphAdapter(nn.Module):
    """
    图适配器模块
    
    在预训练模型基础上添加少量可学习参数
    """
    
    def __init__(self, hidden_dim, adapter_dim=64):
        super().__init__()
        
        # 下投影 + 非线性 + 上投影
        self.down_proj = nn.Linear(hidden_dim, adapter_dim)
        self.activation = nn.GELU()
        self.up_proj = nn.Linear(adapter_dim, hidden_dim)
        
        # 残差缩放
        self.scale = nn.Parameter(torch.ones(1) * 0.1)
    
    def forward(self, x):
        return x + self.scale * self.up_proj(self.activation(self.down_proj(x)))
 
 
class AdapterGNN(nn.Module):
    """带适配器的GNN"""
    
    def __init__(self, base_gnn: GNN, adapter_dim=64):
        super().__init__()
        self.base_gnn = base_gnn
        
        # 每层后添加适配器
        self.adapters = nn.ModuleList([
            GraphAdapter(base_gnn.hidden_dim, adapter_dim)
            for _ in range(base_gnn.num_layers)
        ])
    
    def forward(self, graph):
        h = self.base_gnn.input_proj(graph.x)
        
        for gnn, adapter, norm in zip(
            self.base_gnn.gnn_layers,
            self.adapters,
            self.base_gnn.norms
        ):
            h = gnn(h, graph.edge_index)
            h = norm(h)
            h = adapter(h)  # 应用适配器
            h = F.relu(h)
        
        return h
 
 
# 训练时:只更新适配器和分类头
def train_with_adapter(model, graph, labels):
    optimizer = torch.optim.Adam([
        {"params": model.adapters.parameters(), "lr": 1e-3},
        {"params": model.classifier.parameters(), "lr": 1e-3},
        # 可选:解冻部分GNN层
        {"params": model.base_gnn.gnn_layers[-2:], "lr": 1e-4},
    ])
    
    # 冻结基础GNN参数
    for param in model.base_gnn.input_proj.parameters():
        param.requires_grad = False
    for param in model.base_gnn.gnn_layers[:-2].parameters():
        param.requires_grad = False

4.3 图提示学习(Graph Prompt Learning)

class GraphPromptLearning:
    """
    图提示学习
    
    通过设计图特定的提示,使预训练模型适应下游任务
    """
    
    def __init__(self, base_model: GNN):
        self.base_model = base_model
        self.prompt_tokens = nn.Parameter(torch.randn(10, base_model.hidden_dim))
    
    def prompt(self, graph: Graph, task_type: str) -> Graph:
        """
        应用提示
        
        Args:
            graph: 输入图
            task_type: "node", "edge", "graph"
        """
        # 获取节点表示
        node_repr = self.base_model(graph)
        
        # 添加任务特定的提示
        if task_type == "node":
            # 节点级任务:添加节点提示
            graph.prompt_h = node_repr + self.prompt_tokens[:5]
        elif task_type == "graph":
            # 图级任务:添加图级提示
            graph_repr = self.readout(node_repr)
            graph.prompt_h = graph_repr + self.prompt_tokens[-5:]
        
        return graph
    
    def predict(self, prompted_graph):
        """基于提示进行预测"""
        return self.classifier(prompted_graph.prompt_h)
 
 
# GraphPrompt设计
class GraphPromptPool:
    """图提示池:学习多个可组合的提示"""
    
    def __init__(self, num_prompts=10, prompt_dim=64, hidden_dim=512):
        # 提示池
        self.prompt_embeddings = nn.Parameter(
            torch.randn(num_prompts, prompt_dim)
        )
        
        # 投影层
        self.prompt_proj = nn.Linear(prompt_dim, hidden_dim)
    
    def get_prompt(self, task_id):
        """获取指定任务的提示"""
        return self.prompt_proj(self.prompt_embeddings[task_id])
    
    def compose_prompts(self, task_ids):
        """组合多个提示"""
        prompts = self.prompt_embeddings[task_ids]
        return self.prompt_proj(prompts.mean(dim=0))

5. 大规模图预训练实践

5.1 图采样策略

class GraphSamplingPretraining:
    """
    大规模图采样预训练
    
    核心思想:通过采样处理大规模图,构造mini-batch进行训练
    """
    
    def __init__(self, model: GNN, sampler: Sampler):
        self.model = model
        self.sampler = sampler
    
    def pretrain(self, large_graph: LargeGraph, num_epochs=100):
        """大规模图预训练"""
        
        for epoch in range(num_epochs):
            # 1. 采样子图batch
            subgraphs = self.sampler.sample(large_graph, batch_size=32)
            
            # 2. 在子图上计算预训练损失
            total_loss = 0
            for subgraph in subgraphs:
                loss = self.compute_pretrain_loss(subgraph)
                total_loss += loss
            
            # 3. 反向传播
            total_loss.backward()
            self.optimizer.step()
            self.optimizer.zero_grad()
    
    def compute_pretrain_loss(self, subgraph):
        """计算预训练损失"""
        # 使用掩码特征重建
        masked_subgraph = self.mask_features(subgraph)
        node_repr = self.model(masked_subgraph)
        
        # 预测被掩码的特征
        pred = self.decoder(node_repr[masked_subgraph.mask])
        target = subgraph.x[masked_subgraph.mask]
        
        return F.mse_loss(pred, target)
 
 
class GraphSAINTSampler:
    """GraphSAINT采样器"""
    
    def __init__(self, sample_coverage=0.6):
        self.sample_coverage = sample_coverage
    
    def sample(self, graph, batch_size):
        """GraphSAINT采样"""
        # 1. 计算节点采样概率
        node_probs = self.compute_sampling_probability(graph)
        
        # 2. 采样节点
        sampled_nodes = torch.multinomial(node_probs, batch_size, replacement=True)
        
        # 3. 构建子图
        subgraphs = []
        for nodes in sampled_nodes.split(batch_size // 4):  # 分成多个子图
            subgraph = self.extract_subgraph(graph, nodes)
            subgraph.normalization = self.compute_subgraph_norm(
                graph, nodes, node_probs
            )
            subgraphs.append(subgraph)
        
        return subgraphs
    
    def compute_sampling_probability(self, graph):
        """计算节点采样概率(基于度数)"""
        degrees = degree(graph.edge_index[0], graph.num_nodes)
        probs = degrees.float()
        probs = probs / probs.sum()
        return probs

5.2 分布式图预训练

class DistributedGraphPretraining:
    """
    分布式图预训练
    """
    
    def __init__(self, num_workers=4):
        self.num_workers = num_workers
        self.workers = []
        
        # 图分区器
        self.partitioner = GraphPartitioner()
        
        # 参数服务器
        self.param_server = ParameterServer()
    
    def pretrain(self, large_graph: LargeGraph):
        """分布式预训练"""
        
        # 1. 图分区
        partitions = self.partitioner.partition(large_graph, self.num_workers)
        
        # 2. 启动工作进程
        for i, partition in enumerate(partitions):
            worker = GraphPretrainWorker(
                worker_id=i,
                local_graph=partition,
                param_server=self.param_server
            )
            self.workers.append(worker)
            worker.start()
        
        # 3. 同步训练
        for epoch in range(num_epochs):
            # 各worker本地计算梯度
            for worker in self.workers:
                worker.compute_gradients()
            
            # 参数服务器聚合梯度
            self.param_server.aggregate_gradients()
            
            # 更新参数
            self.param_server.update_params()
            
            # 广播新参数
            self.param_server.broadcast_params()
 
 
class GraphPartitioner:
    """图分区器"""
    
    def partition(self, graph, num_parts):
        """METIS风格图分区"""
        # 使用图分区算法(如METIS、 Chaco)
        partition_ids = metis_partition(graph, k=num_parts)
        
        partitions = [[] for _ in range(num_parts)]
        for node_id, part_id in enumerate(partition_ids):
            partitions[part_id].append(node_id)
        
        return partitions

6. 图基础模型评估

6.1 基准数据集

class GraphBenchmark:
    """图学习基准"""
    
    benchmarks = {
        # 生物医疗
        "OGBG-Mol": {
            "description": "OGB分子性质预测",
            "tasks": ["node", "edge", "graph"],
            "scale": "medium"
        },
        "PCQM4Mv2": {
            "description": "量子化学性质预测",
            "num_nodes": "3.8M",
            "task": "link prediction"
        },
        
        # 网络分析
        "WikiCS": {
            "description": "计算机科学论文分类",
            "num_nodes": "11K",
            "task": "node classification"
        },
        "ArXiv": {
            "description": "学术引用网络",
            "num_nodes": "169K",
            "task": "node classification"
        },
        
        # 推荐系统
        "Amazon-Coauthor": {
            "description": "电商合著者网络",
            "task": "node classification"
        },
        
        # 代码理解
        "CodeXGLUE": {
            "description": "代码图理解",
            "task": "graph classification"
        }
    }

6.2 评估指标

class GraphModelEvaluator:
    """图模型评估器"""
    
    metrics = {
        "node_classification": ["Accuracy", "F1", "AUC-ROC", "Precision", "Recall"],
        "graph_classification": ["Accuracy", "F1", "ROC-AUC", "AP"],
        "link_prediction": ["AUC-ROC", "Hits@K", "MRR"],
        "edge_classification": ["Accuracy", "F1"]
    }
    
    def evaluate(self, model, test_data, metric="Accuracy"):
        """全面评估"""
        model.eval()
        
        if test_data.task_type == "node":
            preds = model.predict_node(test_data.graph)
            targets = test_data.labels
        elif test_data.task_type == "graph":
            preds = model.predict_graph(test_data.graphs)
            targets = test_data.labels
        else:
            preds = model.predict_link(test_data.graph)
            targets = test_data.labels
        
        return self.compute_metrics(preds, targets, metric)
    
    def cross_domain_evaluation(self, model, source_data, target_data):
        """跨领域评估"""
        # 源域评估
        source_metrics = self.evaluate(model, source_data)
        
        # 目标域评估(零样本/微调后)
        target_metrics_zero = self.evaluate(model, target_data)  # 零样本
        target_metrics_finetune = self.evaluate_with_finetune(
            model, source_data, target_data
        )  # 微调后
        
        return {
            "source": source_metrics,
            "target_zero_shot": target_metrics_zero,
            "target_finetuned": target_metrics_finetune,
            "transfer_gain": target_metrics_finetune - target_metrics_zero
        }

7. 应用场景

7.1 分子性质预测

class MolecularPropertyPrediction:
    """
    分子性质预测:图基础模型的典型应用
    
    预训练策略:
    1. 属性掩码:掩码原子类型、电荷等
    2. 上下文预测:预测化学子结构
    3. 图级预测:预测分子指纹
    """
    
    def __init__(self, pretrained_gnn):
        self.model = pretrained_gnn
        self.property_predictor = MLP(hidden_dim * 2, num_properties)
    
    def predict(self, molecule_graph):
        """预测分子性质"""
        # 获取分子表示
        mol_repr = self.model(molecule_graph)
        
        # 预测性质
        properties = self.property_predictor(mol_repr)
        
        return properties
 
 
# 预训练+微调流程
def molecular_pretrain_finetune():
    # 1. 大规模分子图预训练
    molecular_graphs = load_molecular_dataset(num_graphs=1000000)
    
    pretrain_model = GraphFoundationModel(
        backbone=GNN(hidden_dim=512, num_layers=8),
        objectives=[
            AttributeMasking(mask_ratio=0.15),
            ContextPrediction(k_hop=2),
            GraphContrastiveLoss(temperature=0.5)
        ]
    )
    
    pretrain_model.pretrain(molecular_graphs)
    
    # 2. 保存预训练权重
    save_checkpoint(pretrain_model, "molecular_gnn_pretrain.pt")
    
    # 3. 微调到具体性质预测任务
    task_graphs = load_qm9_dataset()  # QM9数据集
    
    finetune_model = MolecularPropertyPrediction(pretrain_model.backbone)
    
    for epoch in range(100):
        for batch in task_graphs:
            loss = finetune_model.train_step(batch)
            loss.backward()
            optimizer.step()

7.2 代码理解

class CodeUnderstanding:
    """
    代码理解:AST图表示学习
    """
    
    def pretrain_on_code(self, code_graphs):
        """代码图预训练"""
        pretrain_objectives = [
            # 1. 掩码节点类型
            AttributeMasking(
                attribute_types=["token_type", "data_type", "scope_level"]
            ),
            
            # 2. 掩码AST边类型
            EdgeAttributeMasking(
                attribute_types=["edge_type"]  # parent, child, next_sibling等
            ),
            
            # 3. 数据流上下文预测
            ContextPrediction(
                subgraph_extractor="data_flow"
            )
        ]
        
        return pretrain_objectives

7.3 推荐系统

class GraphBasedRecommendation:
    """
    图推荐系统:用户-物品交互建模
    """
    
    def pretrain_on_recommendation(self, interaction_graphs):
        """推荐图预训练"""
        pretrain_objectives = [
            # 1. 掩码节点特征
            AttributeMasking(
                attributes=["user_features", "item_features"]
            ),
            
            # 2. 链接预测(交互预测)
            LinkPredictionContrastive(),
            
            # 3. 图对比学习
            GraphCL(augmentations=[
                NodeDropout(p=0.1),
                EdgePerturbation(ratio=0.05),
            ])
        ]
        
        return pretrain_objectives

8. 总结与展望

8.1 当前进展

方向代表工作核心贡献
预训练目标GPT-GNN, GraphCL, InfoGraph设计有效的SSL目标
架构设计Hu et al.预训练框架通用GNN骨干
迁移学习GraphPrompt, Adapter参数高效迁移
大规模GLEM, Open Graph Benchmark亿级节点处理
异质图HAN, HGT异质图Transformer

8.2 未来方向

  1. 更大规模的预训练:探索十亿级节点的图预训练
  2. 更通用的表示:设计真正的”图GPT”
  3. 提示学习:类比LLM的提示工程
  4. 多模态图:结合文本、图像的异构多模态图
  5. 动态图:时序图、演化图的预训练

参考资料