迁移学习（六）：多任务学习

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for each task i:
    g_i = loss_i 的反向传播
    for each other task j:
        if g_i . g_j < 0:                     # 冲突
            g_i = g_i - proj(g_i, g_j)        # 去掉冲突分量
final_gradient = 所有修改后梯度的均值

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import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.utils.data import DataLoader, Dataset
import torchvision
import numpy as np
from typing import List, Dict, Optional

# ===== 网络架构 =====

class SharedEncoder(nn.Module):
    """共享主干网络：ResNet-18 的前 3 个 block。"""
    def __init__(self):
        super().__init__()
        resnet = torchvision.models.resnet18(pretrained=False)
        self.stem = nn.Sequential(
            resnet.conv1, resnet.bn1, resnet.relu, resnet.maxpool)
        self.layer1 = resnet.layer1
        self.layer2 = resnet.layer2
        self.layer3 = resnet.layer3

    def forward(self, x):
        x = self.stem(x)
        x = self.layer1(x)
        x = self.layer2(x)
        return self.layer3(x)

class TaskHead(nn.Module):
    """任务专属的分类或回归头。"""
    def __init__(self, in_channels, num_outputs, task_type='classification'):
        super().__init__()
        self.task_type = task_type
        self.pool = nn.AdaptiveAvgPool2d(1)
        self.fc = nn.Sequential(
            nn.Linear(in_channels, 256), nn.ReLU(), nn.Dropout(0.5),
            nn.Linear(256, num_outputs))

    def forward(self, x):
        return self.fc(self.pool(x).flatten(1))

class MultiTaskNet(nn.Module):
    """硬参数共享：共享编码器 + 任务专属头部。"""
    def __init__(self, task_configs):
        super().__init__()
        self.encoder = SharedEncoder()
        self.heads = nn.ModuleDict({
            cfg['name']: TaskHead(256, cfg['num_classes'], cfg['type'])
            for cfg in task_configs
        })

    def forward(self, x):
        features = self.encoder(x)
        return {name: head(features) for name, head in self.heads.items()}

# ===== PCGrad =====

class PCGrad:
    """投影冲突梯度（Yu et al., NeurIPS 2020）"""
    def __init__(self, optimizer, task_names):
        self.optimizer = optimizer
        self.task_names = task_names

    @staticmethod
    def _project(g_i, g_j):
        dot = torch.dot(g_i, g_j)
        if dot < 0:
            g_i = g_i - (dot / (g_j.norm() ** 2 + 1e-8)) * g_j
        return g_i

    def step(self, losses):
        # 1. 各任务在共享参数上的扁平化梯度
        grads = {}
        for name in self.task_names:
            self.optimizer.zero_grad()
            losses[name].backward(retain_graph=True)
            grads[name] = torch.cat([
                p.grad.flatten() for p in self.optimizer.param_groups[0]['params']
                if p.grad is not None
            ]).clone()

        # 2. 两两投影掉冲突分量
        modified = {}
        for i, ni in enumerate(self.task_names):
            g = grads[ni].clone()
            for j, nj in enumerate(self.task_names):
                if i != j:
                    g = self._project(g, grads[nj])
            modified[ni] = g

        # 3. 使用修改后梯度的均值更新优化器
        avg_grad = sum(modified.values()) / len(modified)
        self.optimizer.zero_grad()
        idx = 0
        for p in self.optimizer.param_groups[0]['params']:
            if p.grad is not None:
                n = p.numel()
                p.grad = avg_grad[idx:idx + n].view_as(p)
                idx += n
        self.optimizer.step()

# ===== GradNorm =====

class GradNorm:
    """梯度归一化以自适应平衡损失（Chen et al., ICML 2018）"""
    def __init__(self, model, task_names, alpha=1.5, lr=0.025):
        self.model = model
        self.task_names = task_names
        self.alpha = alpha
        self.weights = nn.Parameter(torch.ones(len(task_names)))
        self.weight_optim = optim.Adam([self.weights], lr=lr)
        self.initial_losses = None

    def step(self, losses):
        if self.initial_losses is None:
            self.initial_losses = {n: l.item() for n, l in losses.items()}

        weighted = [self.weights[i] * losses[n]
                    for i, n in enumerate(self.task_names)]
        total = sum(weighted)

        # 只在共享编码器上计算各任务的梯度范数
        shared_params = list(self.model.encoder.parameters())
        grad_norms = []
        for wl in weighted:
            grads = torch.autograd.grad(
                wl, shared_params, retain_graph=True, create_graph=True)
            grad_norms.append(
                torch.norm(torch.cat([g.flatten() for g in grads])))

        avg_norm = sum(grad_norms) / len(grad_norms)
        avg_ratio = sum(
            losses[n].item() / (self.initial_losses[n] + 1e-8)
            for n in self.task_names) / len(self.task_names)

        # GradNorm 损失：让 ||w_t * grad_t|| 趋向 avg_norm * r_t^alpha
        gn_loss = sum(
            torch.abs(grad_norms[i] - avg_norm * (
                (losses[n].item() / (self.initial_losses[n] + 1e-8))
                / (avg_ratio + 1e-8)) ** self.alpha)
            for i, n in enumerate(self.task_names))

        self.weight_optim.zero_grad()
        gn_loss.backward()
        self.weight_optim.step()
        # 重新归一化权重，确保权重之和等于任务数
        with torch.no_grad():
            self.weights.data *= len(self.task_names) / self.weights.sum()

        return total, {n: self.weights[i].item()
                       for i, n in enumerate(self.task_names)}

# ===== 训练器 =====

class MTLTrainer:
    """多任务训练器，支持 uniform、PCGrad 和 GradNorm"""
    def __init__(self, model, task_configs, device='cpu', method='uniform'):
        self.model = model.to(device)
        self.device = device
        self.task_configs = {c['name']: c for c in task_configs}
        self.task_names = [c['name'] for c in task_configs]
        self.method = method
        self.optimizer = optim.Adam(model.parameters(), lr=1e-3)

        if method == 'pcgrad':
            self.pcgrad = PCGrad(self.optimizer, self.task_names)
        elif method == 'gradnorm':
            self.gradnorm = GradNorm(model, self.task_names)

    def _losses(self, outputs, targets):
        losses = {}
        for n in self.task_names:
            if self.task_configs[n]['type'] == 'classification':
                losses[n] = F.cross_entropy(outputs[n], targets[n])
            else:
                losses[n] = F.mse_loss(outputs[n], targets[n])
        return losses

    def train_epoch(self, loader, epoch):
        self.model.train()
        stats = {n: 0.0 for n in self.task_names + ['total']}
        for batch in loader:
            inputs = batch['input'].to(self.device)
            targets = {n: batch[n].to(self.device) for n in self.task_names}
            outputs = self.model(inputs)
            losses = self._losses(outputs, targets)

            if self.method == 'uniform':
                total = sum(losses.values())
                self.optimizer.zero_grad()
                total.backward()
                self.optimizer.step()
            elif self.method == 'pcgrad':
                self.pcgrad.step(losses)
                total = sum(l.item() for l in losses.values())
            elif self.method == 'gradnorm':
                total, _ = self.gradnorm.step(losses)
                self.optimizer.zero_grad()
                total.backward()
                self.optimizer.step()

            for n in self.task_names:
                stats[n] += (losses[n].item()
                             if isinstance(losses[n], torch.Tensor)
                             else losses[n])
            stats['total'] += (total.item()
                               if isinstance(total, torch.Tensor) else total)
        nb = len(loader)
        return {k: v / nb for k, v in stats.items()}

    @torch.no_grad()
    def evaluate(self, loader):
        self.model.eval()
        correct = {n: 0 for n in self.task_names}
        total = 0
        for batch in loader:
            inputs = batch['input'].to(self.device)
            targets = {n: batch[n].to(self.device) for n in self.task_names}
            outputs = self.model(inputs)
            total += inputs.size(0)
            for n in self.task_names:
                if self.task_configs[n]['type'] == 'classification':
                    correct[n] += (outputs[n].argmax(1) == targets[n]).sum().item()
        return {n: 100.0 * correct[n] / total for n in self.task_names}

# ===== 演示 =====

class DummyMTLDataset(Dataset):
    def __init__(self, n=1000):
        self.n = n
    def __len__(self):
        return self.n
    def __getitem__(self, i):
        return {
            'input': torch.randn(3, 32, 32),
            'task1': torch.randint(0, 10, ()).item(),
            'task2': torch.randint(0, 5, ()).item(),
        }

def main():
    configs = [
        {'name': 'task1', 'num_classes': 10, 'type': 'classification'},
        {'name': 'task2', 'num_classes': 5,  'type': 'classification'},
    ]
    device = 'cuda' if torch.cuda.is_available() else 'cpu'
    loader = DataLoader(DummyMTLDataset(1000), batch_size=32, shuffle=True)
    test_loader = DataLoader(DummyMTLDataset(200), batch_size=32)

    for method in ['uniform', 'pcgrad', 'gradnorm']:
        print(f"\n{'=' * 50}\nMethod: {method}\n{'=' * 50}")
        model = MultiTaskNet(configs)
        trainer = MTLTrainer(model, configs, device, method=method)
        for epoch in range(10):
            stats = trainer.train_epoch(loader, epoch)
            metrics = trainer.evaluate(test_loader)
            print(f"Epoch {epoch+1}: "
                  + " ".join(f"{k}={v:.4f}" for k, v in stats.items())
                  + " | "
                  + " ".join(f"{k}={v:.1f}%" for k, v in metrics.items()))

if __name__ == '__main__':
    main()

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import torch
from collections import defaultdict
from typing import Callable, Dict, List

def grad_conflict_logger(
    model: torch.nn.Module,
    losses: Dict[str, torch.Tensor],
    shared_param_filter: Callable[[str], bool] = lambda n: "shared" in n,
) -> Dict[str, float]:
    """计算共享参数上的各任务梯度，并返回任务对之间的余弦相似度。

    Args:
        model: 包含共享主干和任务头的 nn.Module。
        losses: 字典 {任务名: 标量损失张量}，均来自同一次前向传播。
        shared_param_filter: 用于筛选共享参数名称的谓词函数。

    Returns:
        扁平字典，包含每对无序任务的 cos(task_i, task_j)，以及各任务梯度范数。
        调用方需跨 batch 绘制直方图。
    """
    shared_params = [p for n, p in model.named_parameters()
                     if shared_param_filter(n) and p.requires_grad]
    grads: Dict[str, torch.Tensor] = {}
    for tname, loss in losses.items():
        # retain_graph=True 以支持对每个任务单独反向传播
        g = torch.autograd.grad(
            loss, shared_params, retain_graph=True, allow_unused=False,
        )
        grads[tname] = torch.cat([gi.reshape(-1) for gi in g])  # 拉平为向量

    out: Dict[str, float] = {}
    names = list(grads.keys())
    for n in names:
        out[f"||g_{n}||"] = grads[n].norm().item()
    for i in range(len(names)):
        for j in range(i + 1, len(names)):
            a, b = grads[names[i]], grads[names[j]]
            denom = a.norm() * b.norm() + 1e-12
            out[f"cos({names[i]},{names[j]})"] = (a @ b / denom).item()
    return out

# 在训练循环中使用（此时尚未调用 .backward() —— 日志函数会自行处理）。
# 日志记录后，再进行一次前向+反向以计算组合损失并执行优化步。

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import torch
from typing import List

def cagrad_step(grads: List[torch.Tensor], c: float = 0.5,
                n_iters: int = 5, lr: float = 0.5) -> torch.Tensor:
    """通过 CAGrad 计算组合梯度。grads: T 个扁平梯度张量的列表。"""
    G = torch.stack(grads)                          # [T, d]
    T = G.shape[0]
    g0 = G.mean(dim=0)                              # 平均梯度
    g0_norm = g0.norm() + 1e-12

    # 对偶变量：每个任务一个 lambda，位于单纯形上（和为 1，非负）。
    lam = torch.full((T,), 1.0 / T, device=G.device)

    GG = G @ G.t()                                  # [T, T] 格拉姆矩阵
    g0G = G @ g0                                    # [T] 各任务与平均梯度的点积

    for _ in range(n_iters):
        gw = (lam.unsqueeze(0) @ G).squeeze(0)      # 加权梯度
        gw_norm = gw.norm() + 1e-12
        # 对偶目标关于 lambda 的梯度
        dlam = (GG @ lam) / gw_norm + c * g0G / g0_norm
        lam = lam - lr * dlam
        lam = torch.clamp(lam, min=0.0)
        s = lam.sum()
        if s > 0:
            lam = lam / s                           # 投影回单纯形

    gw = (lam.unsqueeze(0) @ G).squeeze(0)
    gw_norm = gw.norm() + 1e-12
    g_star = g0 + (c * g0_norm / gw_norm) * gw
    return g_star