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深入理解GPU内存分配:机器学习工程师的实用指南与实验

2024-11-29 19:04

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预留与分配

PyTorch预留了更多内存,但只分配所需的内存。这样做是为了在需要更多内存时能够快速分配,而不是进行昂贵的预留操作。我们只关心内存分配,而不关心预留。

def test_reservation_vs_allocation():
     print(f"Base memory reserved: {torch.cuda.memory_reserved(device_id)}")
     print(f"Base memory allocated: {torch.cuda.memory_allocated(device_id)}")
 
     # Allocate some memory
     x = torch.randn((1024,), dtype=torch.float32, device=device)
     print(f"Memory after allocation (reserved): {torch.cuda.memory_reserved(device_id)}")
     print(f"Memory after allocation (allocated): {torch.cuda.memory_allocated(device_id)}")
 
     # Cleanup
     del x
     print(f"Memory after cleanup (reserved): {torch.cuda.memory_reserved(device_id)}")
     print(f"Memory after cleanup (allocated): {torch.cuda.memory_allocated(device_id)}")
 
     torch.cuda.empty_cache()
     print(f"Memory after empty_cache (reserved): {torch.cuda.memory_reserved(device_id)}")
     print(f"Memory after empty_cache (allocated): {torch.cuda.memory_allocated(device_id)}")
 
 """
 Output:
 
 Base memory reserved: 0
 Base memory allocated: 0
 Memory after allocation (reserved): 2097152
 Memory after allocation (allocated): 4096
 Memory after cleanup (reserved): 2097152
 Memory after cleanup (allocated): 0
 Memory after empty_cache (reserved): 0
 Memory after empty_cache (allocated): 0
 """

当删除变量x或当x超出作用域时,x的内存被释放,但仍然为将来使用而预留。只有在调用torch.cuda.empty_cache()时,才会释放预留的内存。

这里的torch.cuda.memory_allocated()将返回PyTorch在此进程上分配的内存。如果有另一个进程正在使用一些GPU内存,将返回0。为了获取真实的GPU内存使用情况,可以使用以下函数。

import subprocess
 
 
 def get_gpu_memory_used(gpu_id):
     """
    Returns the amount of memory used on the specified GPU in bytes.
 
    Parameters:
    gpu_id (int): The ID of the GPU (e.g., 0 for "cuda:0", 1 for "cuda:1").
 
    Returns:
    int: The amount of memory used on the GPU in bytes.
    """
     try:
         # Run the nvidia-smi command to get memory usage
         result = subprocess.run(
            ["nvidia-smi", "--query-gpu=memory.used", "--format=csv,nounits,noheader", f"--id={gpu_id}"],
             stdout=subprocess.PIPE,
             text=True
        )
 
         # Get the used memory in MiB from the result
         used_memory_mib = int(result.stdout.strip())
 
         # Convert MiB to bytes (1 MiB = 1024 * 1024 bytes)
         used_memory_bytes = used_memory_mib * 1024 * 1024
 
         return used_memory_bytes
 
     except Exception as e:
         print(f"Error occurred: {e}")
         return None

数据类型

float32需要4字节的内存,bfloat16需要2字节,我们可以绘制一些数据类型所需的内存图。

图1:不同数据类型的内存分配

def test_dtype_memory_allocation():
     dtypes = [torch.float32, torch.float16, torch.bfloat16, torch.int32, torch.int64, torch.uint8, torch.int8, torch.uint16]
     memories = []
     for dtype in dtypes:
         base_memory = get_gpu_memory_used(device_id)
         x = torch.ones((1024,), dtype=dtype, device=device)
         memory_after_allocation = get_gpu_memory_used(device_id)
         memories.append((memory_after_allocation - base_memory) // 1024)
         del x
         torch.cuda.empty_cache()
     fig = plt.figure(figsize=(7, 4))
     fig.set_tight_layout(True)
     plt.bar([str(d) for d in dtypes], memories)
     plt.xlabel("Data type")
     plt.ylabel("Bytes per element")
     plt.title("Memory allocation for different data types")
     plt.xticks(rotation=45)
     plt.show()

内存块

内存以512字节的块分配。当创建一个张量时,它被分配到下一个可用的块中。对于形状为(800,)的float32张量,不是分配800 * 4 = 3200字节,而是分配3584(512 * 7)字节。

图2:不同张量大小的内存分配。

def test_memory_allocation_relationship():
     """
    For different sizes of tensors, check the memory allocated on GPU.
    """
     memories = []
     sizes = 1050
     for i in tqdm(range(sizes)):
         base_memory = get_gpu_memory_used(device_id)
         x = torch.randn((i,), dtype=torch.float32, device=device)
         memory_after_allocation = get_gpu_memory_used(device_id)
         memories.append(memory_after_allocation - base_memory)
         del x
         torch.cuda.empty_cache()
     plt.plot(memories)
     plt.xlabel("Size of float32 tensor")
     plt.ylabel("Memory allocated (bytes)")
     plt.title("Memory allocation for different tensor sizes")
     plt.show()

可训练参数(单个线性层前向传播)

接下来我们将看一个单一的线性层。进行前向传播,并计算所需的内存。

def test_single_linear_layer_forward_allocation():
     # Disable cublas
     # import os; os.environ["CUBLAS_WORKSPACE_CONFIG"] = ":0:0"
 
     print(f"Base memory: {torch.cuda.memory_allocated(device_id)}")
 
     model = nn.Linear(256, 250, device=device, dtype=torch.float32)
     print(f"Memory after model allocation: {torch.cuda.memory_allocated(device_id)}")
 
     x = torch.randn((1, 256,), dtype=torch.float32, device=device)
     print(f"Memory after input allocation: {torch.cuda.memory_allocated(device_id)}")
 
     y = model(x)
     final_memory = torch.cuda.memory_allocated(device_id)
     print(f"Memory after forward pass: {final_memory}")
 
     # Memory calculations
     w_mem = len(model.weight.flatten()) * model.weight.dtype.itemsize
     # Get the higher multiple of 512
     w_mem_as_chunks = (w_mem + 511) // 512 * 512
     print(f"{model.weight.shape=}, {w_mem=}, {w_mem_as_chunks=}")
 
     b_mem = len(model.bias) * model.bias.dtype.itemsize
     b_mem_as_chunks = (b_mem + 511) // 512 * 512
     print(f"{model.bias.shape=}, {b_mem=}, {b_mem_as_chunks=}")
 
     x_mem = (len(x.flatten()) * x.dtype.itemsize + 511) // 512 * 512
     y_mem = (len(y.flatten()) * y.dtype.itemsize + 511) // 512 * 512
     print(f"{x_mem=}, {y_mem=}")
 
     total_memory_expected = w_mem_as_chunks + b_mem_as_chunks + x_mem + y_mem
 
     cublas_workspace_size = 8519680
     memory_with_cublas = total_memory_expected + cublas_workspace_size
     print(f"{total_memory_expected=}, {memory_with_cublas=}")
     
     assert final_memory == memory_with_cublas
 
     del model, x, y
     torch.cuda.empty_cache()
     print(f"Memory after cleanup: {torch.cuda.memory_allocated(device_id)}")
 
     torch._C._cuda_clearCublasWorkspaces()
     print(f"Memory after clearing cublas workspace: {torch.cuda.memory_allocated(device_id)}")
 
 """
 Output:
 Base memory: 0
 Memory after model allocation: 257024
 Memory after input allocation: 258048
 Memory after forward pass: 8778752
 model.weight.shape=torch.Size([250, 256]), w_mem=256000, w_mem_as_chunks=256000
 model.bias.shape=torch.Size([250]), b_mem=1000, b_mem_as_chunks=1024
 x_mem=1024, y_mem=1024
 total_memory_expected=259072, memory_with_cublas=8778752
 Memory after cleanup: 8519680
 Memory after clearing cublas workspace: 0
 """

model有一个形状为(256, 250)的float32 weight矩阵,占用(256 * 250 * 4) = 256,000字节,这正好是内存块大小512的倍数(512 * 500 = 256,000)。但是bias有250个float32需要占用(250 * 4) = 1000字节。而512的更高倍数是2,(512 * 2) = 1024字节。x和y是形状为(256,)的张量,所以它们各占用1024字节。总内存 = weight + bias + x + y

当我们将所有内容加起来时,应该得到259,072字节(256,000 + 1024 + 1024 + 1024)。但是实际观察到的大小是8,778,752字节。这额外的8,519,680字节来自分配cuBLAS工作空间。

这是为快速矩阵乘法操作预留的内存空间。对于某些matmul操作,会分配一个新的8,519,680字节的块。这个大小可能会根据GPU和Python环境而变化。当调用torch.cuda.empty_cache()时,cublas内存不会消失。它需要torch._C._cuda_clearCublasWorkspaces()来实际清除它。也可以设置环境变量os.environ["CUBLAS_WORKSPACE_CONFIG"] = ":0:0"来禁用cublas工作空间。但这可能是一种以牺牲执行速度为代价来优化内存的方法,所以我们使用默认就好。

梯度(单个线性层反向传播)

使用相同的模型,运行loss.backward()。为简单起见假设损失为loss = y.sum()。

def test_single_linear_layer_backward_allocation():
     print(f"Base memory: {torch.cuda.memory_allocated(device_id)}")
 
     model = nn.Linear(256, 250, device=device, dtype=torch.float32)
     x = torch.randn((1, 256,), dtype=torch.float32, device=device)
     y = model(x)
 
     print(f"Memory after forward pass: {torch.cuda.memory_allocated(device_id)}")
     y.sum().backward()
     final_memory = torch.cuda.memory_allocated(device_id)
     print(f"Memory after backward pass: {final_memory}")
 
     # Memory calculations
     next_chunk = lambda n: (n + 511) // 512 * 512
     units = model.weight.dtype.itemsize  # 4 bytes for float32
     mem = next_chunk(len(model.weight.flatten()) * units)
     mem += next_chunk(len(model.bias) * units)
     print(f"Excepted model memory: {mem}")
 
     x_mem = next_chunk(len(x.flatten()) * units)
     y_mem = next_chunk(len(y.flatten()) * units)
     print(f"{x_mem=}, {y_mem=}")
     mem += x_mem + y_mem
 
     # Gradient memory
     w_grad_mem = next_chunk(len(model.weight.grad.flatten()) * units)
     b_grad_mem = next_chunk(len(model.bias.grad.flatten()) * units)
     print(f"{model.weight.grad.shape=}, {w_grad_mem=}")
     print(f"{model.bias.grad.shape=}, {b_grad_mem=}")
     mem += w_grad_mem + b_grad_mem
 
     mem += 2 * 8519680  # cublas_size doubled
     print(f"Total memory expected: {mem}")
     assert final_memory == mem
 
     del model, x, y
     torch.cuda.empty_cache()
     print(f"Memory after cleanup: {torch.cuda.memory_allocated(device_id)}")
 
     torch._C._cuda_clearCublasWorkspaces()
     print(f"Memory after clearing cublas workspace: {torch.cuda.memory_allocated(device_id)}")
 
 """
 Output:
 Base memory: 0
 Memory after forward pass: 8778752
 Memory after backward pass: 17555456
 Excepted model memory: 257024
 x_mem=1024, y_mem=1024
 model.weight.grad.shape=torch.Size([250, 256]), w_grad_mem=256000
 model.bias.grad.shape=torch.Size([250]), b_grad_mem=1024
 Total memory expected: 17555456
 Memory after cleanup: 17039360
 Memory after clearing cublas workspace: 0
 """

由于每个具有requires_grad=True的模型参数都会有一个.grad成员来存储底层张量的梯度,所以模型的大小会翻倍。

这次分配了2个cublas工作空间内存块,假设一个用于前向传播,一个用于反向传播。此时cublas何时确切地分配新块还不确定。

中间张量(多层前馈网络)

当模型在推理模式下运行时,没有自动求导图,不需要存储中间张量。所以内存量只是简单地将每一层的内存相加。

在需要跟踪计算图的训练模式下情况会有所不同。当有多个串行应用的操作时,比如在前馈网络或任何深度网络中,自动求导图需要记住这些操作的中间张量。存储需求取决于它们的偏导数操作的性质。这些中间张量在反向传播过程中从内存中清除。我们看一些例子:x是输入,w是需要梯度的参数(w.requires_grad = True)。

让我们看看更深网络的实现:

def test_multi_layer_forward():
     print(f"Base memory: {torch.cuda.memory_allocated(device_id)}")
 
     inference_mode = False
     n_layers = 1
     model = nn.Sequential(*[
         nn.Sequential(
             nn.Linear(200, 100),
             nn.ReLU(),  # No trainable params
             nn.Linear(100, 200),
             nn.Sigmoid(),  # No trainable params
        )
         for _ in range(n_layers)
    ]).to(device_id)
     batch_size = 5
     x = torch.randn((batch_size, 200), device=device_id)
     with torch.inference_mode(inference_mode):
         y = model(x)
 
     final_memory = torch.cuda.memory_allocated(device_id)
     print(f"Memory after forward pass: {final_memory}")
 
     # Computed memory
     next_chunk = lambda n: (n + 511) // 512 * 512
     mem = 0
     unit = model[0][0].weight.dtype.itemsize
     for block in model:
         for layer in block:
             if isinstance(layer, nn.Linear):
                 mem += next_chunk(len(layer.weight.flatten()) * unit)
                 mem += next_chunk(len(layer.bias) * unit)
                 if not inference_mode:
                     # Gotta store the input
                     mem += next_chunk(layer.in_features * batch_size * unit)
     mem += next_chunk(len(y.flatten()) * unit)
     mem += 8519680  # cublas_size
     if inference_mode:
         mem += next_chunk(len(y.flatten()) * unit)
     print(f"Total memory expected: {mem}")
     assert final_memory == mem

在像BatchNorm1d、LayerNorm、RMSNorm这样的归一化层中,在与参数w相乘之前,有一个对输入x的操作,如(x — x.mean()) / (x.std() + 1e-6) * w。操作数(x — x.mean()) / (x.std() + 1e-6)是需要存储的中间输出。并且可能还有其他状态,如running_mean、running_std或forward()方法中的中间张量需要考虑。其中一些中间张量我们无法访问,所以我们无法确定发生了什么。当包含批量大小时,这变得更加复杂。

def test_layer_norm():
     print(f"Base memory: {torch.cuda.memory_allocated(device_id)}")
     x = torch.rand((10,), device=device_id)
     w = torch.rand((10,), requires_grad=True, device=device_id)
     # Layer Norm
     y = (x - x.mean()) / (x.std() + 1e-6) * w
     final_memory = torch.cuda.memory_allocated(device_id)
     print(f"Memory after forward pass: {final_memory}")
 
     # Memory calculations
     next_chunk = lambda n: (n + 511) // 512 * 512
     mem = next_chunk(len(x.flatten()) * x.dtype.itemsize)
     mem += next_chunk(len(w.flatten()) * w.dtype.itemsize)
     mem += next_chunk(len(y.flatten()) * y.dtype.itemsize)
     mem += next_chunk(len(x.flatten()) * x.dtype.itemsize)  # intermediate
     print(f"Total memory expected: {mem}")
     assert final_memory == mem

反向传播非常相似,但有一些变化:

def test_multi_layer_backward():
     print(f"Base memory: {torch.cuda.memory_allocated(device_id)}")
 
     n_layers = 1
     model = nn.Sequential(*[
         nn.Sequential(
             nn.Linear(200, 100),
             nn.ReLU(),  # No trainable params
             nn.Linear(100, 200),
             nn.Sigmoid(),  # No trainable params
        )
         for _ in range(n_layers)
    ]).to(device_id)
     batch_size = 5
     x = torch.randn((batch_size, 200), device=device_id)
     y = model(x)
     print(f"Memory after forward pass: {torch.cuda.memory_allocated(device_id)}")
     y.sum().backward()
     final_memory = torch.cuda.memory_allocated(device_id)
     print(f"Memory after backward pass: {final_memory}")
 
     # Computed memory
     next_chunk = lambda n: (n + 511) // 512 * 512
     mem = 0
     unit = model[0][0].weight.dtype.itemsize
     for block in model:
         for layer in block:
             if isinstance(layer, nn.Linear):
                 mem += next_chunk(len(layer.weight.flatten()) * unit) * 2   # Weights and gradients
                 mem += next_chunk(len(layer.bias) * unit) * 2               # Biases and gradients
                 # mem += next_chunk(layer.in_features * batch_size * unit) # Intermediate tensors are cleared
     mem += next_chunk(len(y.flatten()) * unit)
     mem += 2 * 8519680                                                      # cublas_size doubled
     mem += next_chunk(len(y.flatten()) * unit)
     print(f"Total memory expected: {mem}")
     assert final_memory == mem

优化器(单个线性层反向传播)

我们观察一些优化步骤的内存分配。

def test_single_linear_layer_with_optimizer():
     # Disable cublas
     import os; os.environ["CUBLAS_WORKSPACE_CONFIG"] = ":0:0"
 
     memory_timeline_real = []
     add = lambda e: memory_timeline_real.append({"event": e, "memory": torch.cuda.memory_allocated(device_id)})
     add("baseline")
 
     in_size = 256
     out_size = 250
     batch_size = 100
     model = nn.Linear(in_size, out_size, device=device, dtype=torch.float32)
     add("model_allocation")
 
     optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
     add("optimizer_init")
 
     x = torch.randn((batch_size, in_size,), dtype=torch.float32, device=device)
     add("input_allocation")
 
     def step(n):
         optimizer.zero_grad()
         add(f"optim_zero_grad_{n}")
 
         y = model(x)
         add(f"forward_{n}")
 
         y.sum().backward()
         add(f"backward_{n}")
 
         optimizer.step()
         del y
         add(f"optim_step_{n}")
 
     for i in range(4):
         step(i + 1)
 
     # Bar chart with even name on x-axis and total_memory on y-axis
     fig = plt.figure(figsize=(15, 7))
     fig.set_tight_layout(True)
     plt.ylim((0, 1_300_000))
     plt.bar([event["event"] for event in memory_timeline_real], [event["memory"] for event in memory_timeline_real])
     plt.xlabel("Event")
     plt.ylabel("Total memory allocated (bytes)")
     plt.title(f"Memory allocation during training ({type(optimizer)})")
     plt.xticks(rotation=45)
     plt.show()

图3:使用SGD优化器在训练的各个阶段的内存分配

图4:使用Adam优化器在训练的各个阶段的内存分配

直到backward_1,我们看到内存分配如预期。当optimizer.step()结束时,在这个特定的代码中删除了y,所以该内存被释放。在底层优化器会获取额外的内存(等于可训练参数的大小)来更新它们,并在更新后释放该内存。这在图中没有显示。更详细的时间图可以在下图5中看到。

对于Adam对每个可训练参数都有一阶矩和二阶矩。所以它总是在内存中保留2倍的模型大小。这是这段代码中训练最耗费内存的部分。

图5:按毫秒计的内存分配时间图。

现在让我们尝试手动计算这些内存需求:

# Memory calculations (continuing from previous code block)
     units = model.weight.dtype.itemsize
     memory_timeline = []
     all_keys = ["trainable_params", "input", "output", "gradient", "intermediate_tensors", "optimizer_state"]
     def update_memory(event: str, update: dict):
         prev_state = memory_timeline[-1] if memory_timeline else {k: 0 for k in all_keys}
         new_state = {k: prev_state.get(k, 0) + update.get(k, 0) for k in all_keys}
         new_state["event"] = event
         memory_timeline.append(new_state)
     next_chunk = lambda n: (n + 511) // 512 * 512
 
     update_memory("baseline", {})
 
     # Model memory
     model_mem = next_chunk(len(model.weight.flatten()) * units)
     model_mem += next_chunk(len(model.bias) * units)
     update_memory("model_allocation", {"trainable_params": model_mem})
     update_memory("optimizer_init", {})
 
     # Input memory
     x_mem = next_chunk(len(x.flatten()) * units)
     update_memory("input_allocation", {"input": x_mem})
     update_memory("optim_zero_grad_1", {})
 
     # Forward
     y_mem = next_chunk(batch_size * out_size * units)
     # Add any intermediate tensors here.
     update_memory("forward_1", {"output": y_mem})  # , "intermediate_tensors": ...})
 
     # Backward
     grad_mem = next_chunk(len(model.weight.grad.flatten()) * units)
     grad_mem += next_chunk(len(model.bias.grad.flatten()) * units)
     # Clear any intermediate tensors here.
     update_memory("backward_1", {"gradient": grad_mem})  # "intermediate_tensors": ...})
 
     # Optimizer memory
     if isinstance(optimizer, torch.optim.SGD):
         # SGD has parameters in memory. They are cleared after each step.
         optimizer_mem = 0
     elif isinstance(optimizer, torch.optim.Adam):
         # Adam has parameters and 2 momentum buffers. Parameters are cleared after each step.
         optimizer_mem = 2 * model_mem
     else:
         raise
     update_memory("optim_step_1", {"optimizer_state": optimizer_mem, "output": -y_mem})
 
     for step in range(2, 5):
         update_memory(f"optim_zero_grad_{step}", {"gradient": -grad_mem})
         update_memory(f"forward_{step}", {"output": y_mem})
         update_memory(f"backward_{step}", {"gradient": grad_mem})
         update_memory(f"optim_step_{step}", {"output": -y_mem})
 
     # Make totals
     for event in memory_timeline:
         event["total"] = sum([v for v in event.values() if isinstance(v, int)])
 
     # Plot memory timeline
     import pandas as pd
     df = pd.DataFrame(memory_timeline, columns=all_keys + ["event"])
     df.set_index("event", inplace=True, drop=True)
     df.plot(kind='bar', stacked=True, figsize=(15, 7), ylim=(0, 1_300_000), xlabel="Event", ylabel="Total memory allocated (bytes)", title=f"Memory allocation expected ({type(optimizer)})")
     plt.tight_layout()
     plt.xticks(rotation=45)
     plt.show()
 
     # Compare the two timelines
     for i, (real, expected) in enumerate(zip(memory_timeline_real, memory_timeline)):
         assert real["memory"] == expected["total"], f"Memory mismatch at {real['event']}: {real['memory']} != {expected['total']}"

图6:使用SGD优化器在训练的不同阶段的内存使用分段

图7:使用Adam优化器在训练的不同阶段的内存使用分段

在手动计算内存分配后,我们的计算与观察结果相匹配。这次实际上可以看到内存分配到各种张量的分段。例如,Adam的状态占用了两倍的模型大小。梯度(红色)的不同变化。如果向继续测试,还可以尝试向这个模型添加更多层,添加中间张量并在适当的时候删除它们。这应该在这些条形图中创建另一个代表中间张量的分段。

总结

结合上面的每个概念我们可以回答主要问题:

最后一个问题就是,我们只处理了前馈层,那么CNN、Transformers、RNN等呢?首先CNN是类似前馈层的操作,所以我们可以根据他的计算规则进行计算,而Transformers、RNN都基础操作的组合,我们计算了一个前馈层可以根据他们的架构进行组合计算。我们已经掌握了计算前馈层内存需求的方法,所以我们可以自己解决这些问题!

来源:DeepHub IMBA内容投诉

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