Project: 030_Subgraph_Federated_Learning_for_Local_Generalizati | Function: train (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Core local training function that implements the FedLoG algorithm including local fitting with head/tail degree branches, global synthetic data generation, feature scaling, and local generalization using condensed knowledge from reliable data.

**KEY TERMS:** {
  "alpha": "α weight parameter for degree-based branch combination",
  "output_metric_head": "phead predictions from head degree branch",
  "output_metric_tail": "ptail predictions from tail degree branch",
  "syn_feat_head": "Vk,head learnable synthetic nodes for head degree",
  "syn_feat_tail": "Vk,tail learnable synthetic nodes for tail degree",
  "cls_cd_scaler": "γk class-wise adaptive factor for feature scaling"
}

**CONTEXT CODE:**                 outputs.append(output)
                ys.append(y_output)

                epoch_loss += loss

            if len(outputs) != 1 :
                outputs = torch.cat(outputs)
                ys = torch.cat(ys)
            else :
                outputs = torch.Tensor(outputs[0])
                ys = torch.LongTensor(ys[0])

            epoch_loss /= train_mask_part.sum()

            # _____________
            # eval pretrain
            self.embedder.eval()
            self.classifier.eval()

            outputs = []
            ys = []

            optimizer.zero_grad()

            h = self.embedder(local_graph.x.to(gpu), local_graph.edge_index.to(gpu))

            if len(train_idx) >= self.args.batch_size :
                train_batch = np.random.choice(train_idx, size=self.args.batch_size, replace=False).tolist()
                for d in train_batch:
                    train_idx.remove(d)
            else :
                train_batch = train_idx
            
            output = self.classifier(h).cpu().detach()
            y_output = local_graph.y.cpu().detach()

            test_acc = accuracy(output[test_mask_part.cpu().detach()], y_output[test_mask_part.cpu().detach()])

            if best_acc <= test_acc : 
                best_acc = test_acc

                patience = 0
                self.transfer_to_server(global_dict, cid, 'client_weights', (self.get_parameters(self.embedder), self.get_parameters(self.classifier), self.get_parameters(self.clsf_head), self.get_parameters(self.clsf_tail)), lock)

            else : 
                patience += 1

            if patience == 10 :
                break

    def train(self, cid, gpu, global_dict, cur_round, lock, mode='train'):
    
        '''Train the network on the training set'''
        raise NotImplementedError("Function implementation has been masked for testing")
    
    def test(self, cid, gpu, global_dict, cur_round, lock, mode='test'):
        '''Evaluate the network on the entire test set'''

        self.embedder = self.embedder.to(gpu) 
        self.classifier = self.classifier.to(gpu) 
        self.clsf_head = self.clsf_head.to(gpu)
        self.clsf_tail = self.clsf_tail.to(gpu)
        self.syn_feat_head = torch.nn.Parameter(self.syn_feat_head.to(gpu))
        self.syn_feat_tail = torch.nn.Parameter(self.syn_feat_tail.to(gpu))
        self.syn_adj = self.syn_adj.to(gpu)
        local_graph = self.local_graphs[cid].to(gpu)
        local_graph_unseen = self.local_graphs[-1].to(gpu)

        with torch.no_grad():
            self.embedder.eval()
            self.clsf_head.eval()
            self.clsf_tail.eval()
            self.classifier.eval()
            
            loss_fn = torch.nn.NLLLoss()

            if mode == 'valid' :
                mask = local_graph.val_mask
            elif mode == 'test' : 
                mask = local_graph.test_mask

            h = self.embedder(local_graph.x.to(gpu), local_graph.edge_index.to(gpu))
            h_unseen = self.embedder(local_graph_unseen.x.to(gpu), local_graph_unseen.edge_index.to(gpu))

            syn_h_head = self.embedder(self.syn_feat_head, self.syn_adj)
            syn_proto_head = syn_h_head.view(
                [self.n_way, self.k_shot, syn_h_head.shape[1]])
            syn_proto_head = syn_proto_head.mean(1)

            syn_h_tail = self.embedder(self.syn_feat_tail, self.syn_adj)
            syn_proto_tail = syn_h_tail.view(
                [self.n_way, self.k_shot, syn_h_tail.shape[1]])
            syn_proto_tail = syn_proto_tail.mean(1)
            
            # ___________________
            # Task-specific graph 
            edge1 = []
            for i in range(self.n_way * self.k_shot, self.n_way * self.k_shot+len(h)):
                temp = [i] * self.n_way * self.k_shot
                edge1.extend(temp)
            edge1 = torch.LongTensor(edge1)
            edge2 = torch.LongTensor(
                list(range(self.n_way * self.k_shot)) * len(h))
            edge_index = torch.stack((edge2, edge1)).to(gpu)

            edge1 = []
            for i in range(self.n_way * self.k_shot, self.n_way * self.k_shot+len(h_unseen)):
                temp = [i] * self.n_way * self.k_shot
                edge1.extend(temp)
            edge1 = torch.LongTensor(edge1)
            edge2 = torch.LongTensor(
                list(range(self.n_way * self.k_shot)) * len(h_unseen))
            edge_index_unseen = torch.stack((edge2, edge1)).to(gpu)

            # ________________________
            # neighborhood information
            edge_index_wo_self = remove_self_loops(local_graph.edge_index)[0]
            adj_matrix = SparseTensor(row=edge_index_wo_self[0], col=edge_index_wo_self[1], 
                                    sparse_sizes=(h.size(0), h.size(0)))
            neighbor = adj_matrix @ h
            norm = adj_matrix.sum(0)
            norm[norm == 0] = 1
            neighbor = neighbor / norm.unsqueeze(1)

            edge_index_wo_self_unseen = remove_self_loops(local_graph_unseen.edge_index)[0]
            adj_matrix_unseen = SparseTensor(row=edge_index_wo_self_unseen[0], col=edge_index_wo_self_unseen[1], 
                                    sparse_sizes=(h_unseen.size(0), h_unseen.size(0)))
            neighbor_unseen = adj_matrix_unseen @ h_unseen
            norm_unseen = adj_matrix_unseen.sum(0)
            norm_unseen[norm_unseen == 0] = 1
            neighbor_unseen = neighbor_unseen / norm_unseen.unsqueeze(1)

            # ______________________
            # clsf - Task adaptation
            neighbor, embeds_epi_head = self.clsf_head(h, neighbor, syn_h_head, edge_index) 
            neighbor, embeds_epi_tail = self.clsf_tail(h, neighbor, syn_h_tail, edge_index) 

            neighbor_unseen, embeds_epi_head_unseen = self.clsf_head(h_unseen, neighbor_unseen, syn_h_head, edge_index_unseen) 
            neighbor_unseen, embeds_epi_tail_unseen = self.clsf_tail(h_unseen, neighbor_unseen, syn_h_tail, edge_index_unseen) 

            # __________
            # Prediction
            dists_output_metric_head = euclidean_dist(
                embeds_epi_head, syn_proto_head)
            dists_output_metric_tail = euclidean_dist(
                embeds_epi_tail, syn_proto_tail)

            output_metric_head = F.log_softmax(-dists_output_metric_head, dim=1)
            output_metric_softmax_head = F.softmax(-dists_output_metric_head, dim=1)
            output_metric_tail = F.log_softmax(-dists_output_metric_tail, dim=1)


Complete the function implementation replacing "raise NotImplementedError".