75_TPU集成：Google Cloud加速

// 简化的脉动阵列伪代码表示
void systolic_array(float input_matrix[M][K], float weight_matrix[K][N], float output_matrix[M][N]) {
  // 初始化处理单元阵列
  ProcessingElement PE[ARRAY_SIZE][ARRAY_SIZE];
  
  // 数据流入阶段：权重和输入数据分别从不同方向输入
  for (int t = 0; t < M + N + K - 1; t++) {
    // 在每个时钟周期同步传输数据
    for (int i = 0; i < ARRAY_SIZE; i++) {
      for (int j = 0; j < ARRAY_SIZE; j++) {
        // 执行乘累加运算
        PE[i][j].compute();
        // 将结果传递给下一个处理单元
        PE[i][j].pass_result();
      }
    }
  }
  
  // 收集输出结果
  for (int i = 0; i < M; i++) {
    for (int j = 0; j < N; j++) {
      output_matrix[i][j] = PE[i][j].get_result();
    }
  }
}

# 创建单个TPU v4虚拟机
gcloud compute tpus tpu-vm create tpu-vm-name \
  --zone=us-central2-b \
  --accelerator-type=v4-8 \
  --version=tpu-vm-v4-base

# 连接到TPU VM
gcloud compute tpus tpu-vm ssh tpu-vm-name --zone=us-central2-b

# 安装PyTorch XLA
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu
pip install cloud-tpu-client==0.10 https://storage.googleapis.com/tpu-pytorch/wheels/torch_xla-2.0-cp39-cp39-linux_x86_64.whl

# 安装JAX
pip install --upgrade jax jaxlib

# 查看TPU状态
gcloud compute tpus tpu-vm describe tpu-vm-name --zone=us-central2-b

# 查看TPU性能指标
gcloud compute tpus tpu-vm logs tpu-vm-name --zone=us-central2-b

# 更新系统
pip install --upgrade pip

# 安装PyTorch基础包
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu

# 安装PyTorch XLA
pip install cloud-tpu-client==0.10 https://storage.googleapis.com/tpu-pytorch/wheels/torch_xla-2.0-cp39-cp39-linux_x86_64.whl

# 验证安装
python -c "import torch; import torch_xla; import torch_xla.core.xla_model as xm; print(xm.xla_device())"

import torch
import torch_xla
import torch_xla.core.xla_model as xm
import torch_xla.distributed.xla_multiprocessing as xmp
import torch.nn as nn
import torch.optim as optim

# 定义简单模型
class SimpleModel(nn.Module):
    def __init__(self):
        super(SimpleModel, self).__init__()
        self.fc1 = nn.Linear(784, 512)
        self.relu = nn.ReLU()
        self.fc2 = nn.Linear(512, 10)
    
    def forward(self, x):
        x = x.view(-1, 784)
        x = self.fc1(x)
        x = self.relu(x)
        x = self.fc2(x)
        return x

# 训练函数
def train_fn(rank, world_size):
    # 获取TPU设备
    device = xm.xla_device()
    
    # 移动模型到TPU
    model = SimpleModel().to(device)
    
    # 定义损失函数和优化器
    criterion = nn.CrossEntropyLoss()
    optimizer = optim.SGD(model.parameters(), lr=0.01)
    
    # 创建模拟数据
    inputs = torch.randn(64, 1, 28, 28).to(device)
    targets = torch.randint(0, 10, (64,)).to(device)
    
    # 训练循环
    for epoch in range(10):
        # 前向传播
        outputs = model(inputs)
        loss = criterion(outputs, targets)
        
        # 反向传播
        optimizer.zero_grad()
        loss.backward()
        
        # 同步梯度并更新权重
        xm.optimizer_step(optimizer)
        
        # 标记步骤完成
        xm.mark_step()
        
        if rank == 0:
            print(f'Epoch {epoch+1}, Loss: {loss.item()}')

# 启动分布式训练
if __name__ == '__main__':
    xmp.spawn(train_fn, args=(8,), nprocs=8, start_method='fork')

import torch
import torch_xla
import torch_xla.core.xla_model as xm
import torch_xla.distributed.parallel_loader as pl
import torch_xla.distributed.xla_multiprocessing as xmp
from transformers import AutoModelForSequenceClassification, AutoTokenizer, Trainer, TrainingArguments
from datasets import load_dataset

# 加载数据集
dataset = load_dataset('glue', 'mrpc')

def train_fn(rank, world_size):
    # 获取TPU设备
    device = xm.xla_device()
    
    # 加载模型和分词器
    model_name = 'bert-base-uncased'
    tokenizer = AutoTokenizer.from_pretrained(model_name)
    model = AutoModelForSequenceClassification.from_pretrained(model_name, num_labels=2)
    model.to(device)
    
    # 预处理函数
    def preprocess_function(examples):
        return tokenizer(examples['sentence1'], examples['sentence2'], truncation=True)
    
    # 预处理数据集
    tokenized_datasets = dataset.map(preprocess_function, batched=True)
    
    # 设置训练参数
    training_args = TrainingArguments(
        output_dir='./results',
        evaluation_strategy='epoch',
        learning_rate=2e-5,
        per_device_train_batch_size=16,
        per_device_eval_batch_size=16,
        num_train_epochs=3,
        weight_decay=0.01,
        push_to_hub=False,
        # TPU特定配置
        use_xla=True,
        tpu_num_cores=world_size,
    )
    
    # 创建Trainer
    trainer = Trainer(
        model=model,
        args=training_args,
        train_dataset=tokenized_datasets['train'],
        eval_dataset=tokenized_datasets['validation'],
        tokenizer=tokenizer,
    )
    
    # 开始训练
    trainer.train()

# 启动分布式训练
if __name__ == '__main__':
    xmp.spawn(train_fn, args=(8,), nprocs=8, start_method='fork')

# 梯度累积示例
def train_with_grad_accumulation(model, dataloader, optimizer, device, accumulation_steps=8):
    model.train()
    total_loss = 0
    
    for step, (inputs, targets) in enumerate(dataloader):
        inputs, targets = inputs.to(device), targets.to(device)
        
        # 前向传播
        outputs = model(inputs)
        loss = criterion(outputs, targets)
        loss = loss / accumulation_steps  # 缩放损失
        
        # 反向传播
        loss.backward()
        total_loss += loss.item() * accumulation_steps
        
        # 累积梯度后更新权重
        if (step + 1) % accumulation_steps == 0:
            xm.optimizer_step(optimizer)
            optimizer.zero_grad()
            xm.mark_step()
            
            if xm.get_ordinal() == 0:
                print(f'Step {step+1}, Loss: {total_loss/(step+1)}')

# 安装JAX
pip install --upgrade jax jaxlib

# 验证TPU连接
python -c "import jax; print(jax.devices())"

import jax
import jax.numpy as jnp

# 创建TPU设备上的数组
x = jnp.ones((1024, 1024))

# 矩阵乘法 - 自动利用TPU脉动阵列
y = jnp.dot(x, x)

# JIT编译优化
@jax.jit
def matmul_fn(a, b):
    return jnp.dot(a, b)

# 自动微分
def loss_fn(params, inputs, targets):
    # 简化的损失函数
    return jnp.mean((jnp.dot(inputs, params) - targets)**2)

# 梯度计算
grad_fn = jax.grad(loss_fn)

# 并行计算
@jax.pmap
def parallel_matmul(a, b):
    return jnp.dot(a, b)

import jax
import jax.numpy as jnp
from jax import pmap

# 启用TPU后端
jax.config.update('jax_platform_name', 'tpu')

# 定义分块矩阵乘法
def block_matmul(x, y, block_size=256):
    # 将大矩阵分成小块
    x_blocks = x.reshape(x.shape[0] // block_size, block_size, -1)
    y_blocks = y.reshape(y.shape[0] // block_size, block_size, -1)
    
    # 定义块级矩阵乘法
    @pmap
    def compute_block_pair(x_block, y_block):
        return jnp.dot(x_block, y_block)
    
    # 并行计算所有块对
    return compute_block_pair(x_blocks, y_blocks)

# 在8个TPU核心上并行计算
with jax.profiler.trace("/tmp/tpu_profile"):
    x = jnp.ones((8192, 8192))  # 64MB矩阵
    y = jnp.ones((8192, 8192))
    z = block_matmul(x, y)
    print(f"矩阵乘法完成，结果形状: {z.shape}")

import jax
import jax.numpy as jnp
import flax.linen as nn
import optax
from flax.training import train_state

# 定义简单的神经网络
class MLP(nn.Module):
    features: list
    
    @nn.compact
    def __call__(self, x):
        for feat in self.features[:-1]:
            x = nn.relu(nn.Dense(feat)(x))
        x = nn.Dense(self.features[-1])(x)
        return x

# 初始化模型和优化器
def create_train_state(rng):
    model = MLP(features=[512, 256, 10])
    params = model.init(rng, jnp.ones([1, 784]))['params']
    tx = optax.adam(learning_rate=0.001)
    return train_state.TrainState.create(apply_fn=model.apply, params=params, tx=tx)

# 定义训练步骤
@jax.jit
def train_step(state, batch):
    def loss_fn(params):
        logits = state.apply_fn({'params': params}, batch['image'])
        loss = optax.softmax_cross_entropy_with_integer_labels(logits, batch['label'])
        return jnp.mean(loss)
    
    grad_fn = jax.value_and_grad(loss_fn)
    loss, grads = grad_fn(state.params)
    state = state.apply_gradients(grads=grads)
    return state, loss

# 并行训练
@jax.pmap
def parallel_train_step(state, batch):
    return train_step(state, batch)

# 主训练循环
def train_loop(rng, num_epochs, train_ds):
    rng, init_rng = jax.random.split(rng)
    state = create_train_state(init_rng)
    
    for epoch in range(num_epochs):
        epoch_loss = 0
        for batch in train_ds:
            state, loss = train_step(state, batch)
            epoch_loss += loss
        
        print(f'Epoch {epoch+1}, Loss: {epoch_loss/len(train_ds)}')
    
    return state

# 启动训练
if __name__ == '__main__':
    rng = jax.random.PRNGKey(0)
    # 这里应该有实际的数据集加载代码
    # train_ds = load_and_preprocess_dataset()
    # state = train_loop(rng, 10, train_ds)

import jax
import jax.numpy as jnp
import optax

# 定义混合精度训练函数
def create_mixed_precision_train_step(forward_fn, optimizer):
    # 前向传播使用BF16
    def forward_bf16(params, x, y):
        x_bf16 = x.astype(jnp.bfloat16)
        y_pred = forward_fn(params, x_bf16)
        loss = jnp.mean((y_pred.astype(jnp.float32) - y)**2)
        return loss
    
    # 创建梯度函数
    grad_fn = jax.value_and_grad(forward_bf16)
    
    # 训练步骤
    @jax.jit
    def train_step(params, opt_state, x, y):
        loss, grads = grad_fn(params, x, y)
        updates, opt_state = optimizer.update(grads, opt_state)
        params = optax.apply_updates(params, updates)
        return params, opt_state, loss
    
    return train_step

import flax.linen as nn
from flax import serialization

# 定义支持梯度检查点的Transformer层
class CheckpointedTransformerLayer(nn.Module):
    hidden_size: int
    num_heads: int
    dropout_rate: float = 0.1
    
    @nn.compact
    def __call__(self, inputs, attention_mask=None, deterministic=True):
        # 使用nn.remat启用梯度检查点
        @nn.remat
        def attention_block(x):
            # 自注意力子层
            attention_output = nn.MultiHeadDotProductAttention(
                num_heads=self.num_heads,
                qkv_features=self.hidden_size,
                dropout_rate=self.dropout_rate
            )(x, x, x, mask=attention_mask, deterministic=deterministic)
            attention_output = nn.LayerNorm()(x + attention_output)
            return attention_output
        
        @nn.remat
        def feed_forward_block(x):
            # 前馈网络子层
            ff_output = nn.Dense(self.hidden_size * 4)(x)
            ff_output = nn.gelu(ff_output)
            ff_output = nn.Dropout(rate=self.dropout_rate)(ff_output, deterministic=deterministic)
            ff_output = nn.Dense(self.hidden_size)(ff_output)
            ff_output = nn.LayerNorm()(x + ff_output)
            return ff_output
        
        # 执行检查点化的前向传播
        x = attention_block(inputs)
        x = feed_forward_block(x)
        return x

import jax
import jax.numpy as jnp

# 定义数据并行训练步骤
@jax.pmap
def data_parallel_train_step(params, batch, rng):
    # 为每个设备创建独立的随机数生成器
    device_rng = jax.random.fold_in(rng, jax.lax.axis_index('batch'))
    
    # 前向传播和损失计算
    def loss_fn(p):
        logits = model.apply({'params': p}, batch['inputs'], rngs={'dropout': device_rng})
        loss = jnp.mean(optax.softmax_cross_entropy_with_integer_labels(logits, batch['targets']))
        return loss
    
    # 计算梯度
    loss, grads = jax.value_and_grad(loss_fn)(params)
    
    # 跨设备同步梯度（全部归约）
    grads = jax.lax.pmean(grads, 'batch')
    loss = jax.lax.pmean(loss, 'batch')
    
    # 更新参数
    updates, opt_state = optimizer.update(grads, opt_state)
    params = optax.apply_updates(params, updates)
    
    return params, opt_state, loss

import jax
import jax.numpy as jnp
import optax

# 创建分片优化器
def create_sharded_optimizer(base_optimizer, num_shards):
    # 包装基础优化器
    @optax.inject_hyperparams
    def sharded_optimizer(learning_rate=1e-3):
        # 获取基础优化器
        tx = base_optimizer(learning_rate=learning_rate)
        
        # 自定义更新函数
        def update_fn(updates, state, params=None):
            # 分片处理更新
            sharded_updates = jax.tree_util.tree_map(
                lambda u: jnp.reshape(u, (num_shards, -1)), updates
            )
            
            # 应用分片更新
            sharded_new_updates, new_state = tx.update(sharded_updates, state, params)
            
            # 合并分片结果
            new_updates = jax.tree_util.tree_map(
                lambda u: jnp.reshape(u, (-1,)), sharded_new_updates
            )
            
            return new_updates, new_state
        
        return optax.GradientTransformation(
            init=tx.init,
            update=update_fn
        )
    
    return sharded_optimizer

# 使用示例
sharded_adam = create_sharded_optimizer(optax.adam, num_shards=8)
optimizer = sharded_adam(learning_rate=1e-4)

import jax
import jax.numpy as jnp
from jax.experimental import mesh_utils
from jax.sharding import Mesh, PartitionSpec, NamedSharding

# 创建设备网格
devices = mesh_utils.create_device_mesh((8, 8))  # 假设8×8的设备网格
mesh = Mesh(devices, ('data', 'model'))

# 定义分片规格
x_sharding = NamedSharding(mesh, PartitionSpec('data', None))  # 数据维度分片
model_sharding = NamedSharding(mesh, PartitionSpec(None, 'model'))  # 模型维度分片

# 加载分片数据
x = jax.device_put(jnp.ones((1024, 512)), x_sharding)

# 定义并应用分片模型
params = jax.device_put(initial_params, model_sharding)

# 执行分片计算
@jax.jit
@partial(jax.vmap, in_axes=(0, None), out_axes=0)
def parallel_forward(x_batch, params):
    return model.apply({'params': params}, x_batch)

outputs = parallel_forward(x, params)

import jax
import jax.numpy as jnp
from jax.profiler import trace, device_memory_profile

# 启用性能分析
with trace("/tmp/tpu_profile"):
    # 执行要分析的操作
    x = jnp.ones((1024, 1024))
    for _ in range(100):
        x = jnp.dot(x, x)
    
    # 等待所有操作完成
    jax.block_until_ready(x)

# 分析设备内存使用
with device_memory_profile():
    # 内存密集型操作
    y = jnp.ones((4096, 4096))
    z = jnp.dot(y, y)
    jax.block_until_ready(z)

import jax
import jax.numpy as jnp

# 优化前：Python控制流导致重复编译
def slow_function(x, condition):
    if condition:  # Python控制流
        return jnp.sin(x)
    else:
        return jnp.cos(x)

# 优化后：使用JAX的函数式控制流
def fast_function(x, condition):
    # 使用jnp.where代替Python条件语句
    return jnp.where(condition, jnp.sin(x), jnp.cos(x))

# 优化前：未批处理的操作
def slow_batch_processing(data):
    results = []
    for i in range(data.shape[0]):
        # 每个样本单独处理，导致多次编译
        results.append(jnp.sum(data[i]))
    return jnp.array(results)

# 优化后：向量化批处理
def fast_batch_processing(data):
    # 单次向量化操作，仅编译一次
    return jnp.sum(data, axis=1)