(Beta) Implementing High-Performance Transformers with Scaled Dot Product Attention (SDPA)

Created On: Mar 15, 2023 | Last Updated: Oct 09, 2024 | Last Verified: Nov 05, 2024

Author: Driss Guessous

Summary

In this tutorial, we want to highlight a new torch.nn.functional function that can be helpful for implementing transformer architectures. The function is named torch.nn.functional.scaled_dot_product_attention. For detailed description of the function, see the PyTorch documentation. This function has already been incorporated into torch.nn.MultiheadAttention and torch.nn.TransformerEncoderLayer.

Overview

At a high level, this PyTorch function calculates the scaled dot product attention (SDPA) between query, key, and value according to the definition found in the paper Attention is all you need. While this function can be written in PyTorch using existing functions, a fused implementation can provide large performance benefits over a naive implementation.

Fused implementations

For CUDA tensor inputs, the function will dispatch into one of the following implementations:

• FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness

• Memory-Efficient Attention

• A PyTorch implementation defined in C++

Note

This tutorial requires PyTorch 2.0.0 or later.

import torch
import torch.nn as nn
import torch.nn.functional as F
device = "cuda" if torch.cuda.is_available() else "cpu"

# Example Usage:
query, key, value = torch.randn(2, 3, 8, device=device), torch.randn(2, 3, 8, device=device), torch.randn(2, 3, 8, device=device)
F.scaled_dot_product_attention(query, key, value)

tensor([[[-1.3321, -0.3489,  0.3015, -0.3912,  0.9867,  0.3137, -0.0691,
          -1.2593],
         [-1.0882,  0.2506,  0.6491,  0.1360,  0.5238, -0.2448, -0.0820,
          -0.6171],
         [-1.0012,  0.3990,  0.6441, -0.0277,  0.5325, -0.2564, -0.0607,
          -0.6404]],

        [[ 0.6091,  0.0708,  0.6188,  0.3252, -0.1598,  0.4197, -0.2335,
           0.0630],
         [ 0.5285,  0.3890, -0.2649,  0.3706, -0.3839,  0.1963, -0.6242,
           0.2312],
         [ 0.4048,  0.0762,  0.3777,  0.4689, -0.2978,  0.2754, -0.6429,
           0.1037]]], device='cuda:0')

Explicit Dispatcher Control

While the function will implicitly dispatch to one of the three implementations, the user can also explicitly control the dispatch via the use of a context manager. This context manager allows users to explicitly disable certain implementations. If a user wants to ensure the function is indeed using the fastest implementation for their specific inputs, the context manager can be used to sweep through measuring performance.

# Lets define a helpful benchmarking function:
import torch.utils.benchmark as benchmark
def benchmark_torch_function_in_microseconds(f, *args, **kwargs):
    t0 = benchmark.Timer(
        stmt="f(*args, **kwargs)", globals={"args": args, "kwargs": kwargs, "f": f}
    )
    return t0.blocked_autorange().mean * 1e6

# Lets define the hyper-parameters of our input
batch_size = 32
max_sequence_len = 1024
num_heads = 32
embed_dimension = 32

dtype = torch.float16

query = torch.rand(batch_size, num_heads, max_sequence_len, embed_dimension, device=device, dtype=dtype)
key = torch.rand(batch_size, num_heads, max_sequence_len, embed_dimension, device=device, dtype=dtype)
value = torch.rand(batch_size, num_heads, max_sequence_len, embed_dimension, device=device, dtype=dtype)

print(f"The default implementation runs in {benchmark_torch_function_in_microseconds(F.scaled_dot_product_attention, query, key, value):.3f} microseconds")

# Lets explore the speed of each of the 3 implementations
from torch.nn.attention import SDPBackend, sdpa_kernel


with sdpa_kernel(SDPBackend.MATH):
    math_time=benchmark_torch_function_in_microseconds(F.scaled_dot_product_attention, query, key, value)
    print(f"The math implementation runs in {math_time:.3f} microseconds")

with sdpa_kernel(SDPBackend.FLASH_ATTENTION):
    try:
        flash_time=benchmark_torch_function_in_microseconds(F.scaled_dot_product_attention, query, key, value)
        print(f"The flash attention implementation runs in {flash_time:.3f} microseconds")
    except RuntimeError:
        print("FlashAttention is not supported. See warnings for reasons.")

with sdpa_kernel(SDPBackend.EFFICIENT_ATTENTION):
    try:
        efficient_time=benchmark_torch_function_in_microseconds(F.scaled_dot_product_attention, query, key, value)
        print(f"The memory efficient implementation runs in {efficient_time:.3f} microseconds")
    except RuntimeError:
        print("EfficientAttention is not supported. See warnings for reasons.")

The default implementation runs in 2329.051 microseconds
The math implementation runs in 87412.133 microseconds
The flash attention implementation runs in 2330.251 microseconds
The memory efficient implementation runs in 4350.980 microseconds

Hardware dependence

Depending on what machine you ran the above cell on and what hardware is available, your results might be different. - If you don’t have a GPU and are running on CPU then with FP32 the context manager will have no effect and all three runs should return similar timings. - Depending on what compute capability your graphics card supports flash attention or memory efficient might have failed.

Causal Self Attention

Below is an example implementation of a multi-headed causal self attention block inspired by Andrej Karpathy NanoGPT repository.

class CausalSelfAttention(nn.Module):

    def __init__(self, num_heads: int, embed_dimension: int, bias: bool=False, is_causal: bool=False, dropout:float=0.0):
        super().__init__()
        assert embed_dimension % num_heads == 0
        # key, query, value projections for all heads, but in a batch
        self.c_attn = nn.Linear(embed_dimension, 3 * embed_dimension, bias=bias)
        # output projection
        self.c_proj = nn.Linear(embed_dimension, embed_dimension, bias=bias)
        # regularization
        self.dropout = dropout
        self.resid_dropout = nn.Dropout(dropout)
        self.num_heads = num_heads
        self.embed_dimension = embed_dimension
        # Perform causal masking
        self.is_causal = is_causal

    def forward(self, x):
        # calculate query, key, values for all heads in batch and move head forward to be the batch dim
        query_projected = self.c_attn(x)

        batch_size = query_projected.size(0)
        embed_dim = query_projected.size(2)
        head_dim = embed_dim // (self.num_heads * 3)

        query, key, value = query_projected.chunk(3, -1)
        query = query.view(batch_size, -1, self.num_heads, head_dim).transpose(1, 2)
        key = key.view(batch_size, -1, self.num_heads, head_dim).transpose(1, 2)
        value = value.view(batch_size, -1, self.num_heads, head_dim).transpose(1, 2)

        if self.training:
            dropout = self.dropout
            is_causal = self.is_causal
        else:
            dropout = 0.0
            is_causal = False

        y = F.scaled_dot_product_attention(query, key, value, attn_mask=None, dropout_p=dropout, is_causal=is_causal)
        y = y.transpose(1, 2).view(batch_size, -1, self.num_heads * head_dim)

        y = self.resid_dropout(self.c_proj(y))
        return y


num_heads = 8
heads_per_dim = 64
embed_dimension = num_heads * heads_per_dim
dtype = torch.float16
model = CausalSelfAttention(num_heads=num_heads, embed_dimension=embed_dimension, bias=False, is_causal=True, dropout=0.1).to("cuda").to(dtype).eval()
print(model)

CausalSelfAttention(
  (c_attn): Linear(in_features=512, out_features=1536, bias=False)
  (c_proj): Linear(in_features=512, out_features=512, bias=False)
  (resid_dropout): Dropout(p=0.1, inplace=False)
)

NestedTensor and Dense tensor support

SDPA supports both NestedTensor and Dense tensor inputs. NestedTensors handle the case where the input is a batch of variable length sequences without needing to pad each sequence to the maximum length in the batch. For more information about NestedTensors see torch.nested and NestedTensors Tutorial.

import random
def generate_rand_batch(
    batch_size,
    max_sequence_len,
    embed_dimension,
    pad_percentage=None,
    dtype=torch.float16,
    device="cuda",
):
    if not pad_percentage:
        return (
            torch.randn(
                batch_size,
                max_sequence_len,
                embed_dimension,
                dtype=dtype,
                device=device,
            ),
            None,
        )
    # Random sequence lengths
    seq_len_list = [
        int(max_sequence_len * (1 - random.gauss(pad_percentage, 0.01)))
        for _ in range(batch_size)
    ]
    # Make random entry in the batch have max sequence length
    seq_len_list[random.randint(0, batch_size - 1)] = max_sequence_len
    return (
        torch.nested.nested_tensor(
            [
                torch.randn(seq_len, embed_dimension,
                            dtype=dtype, device=device)
                for seq_len in seq_len_list
            ]
        ),
        seq_len_list,
    )

random_nt, _ = generate_rand_batch(32, 512, embed_dimension, pad_percentage=0.5, dtype=dtype, device=device)
random_dense, _ = generate_rand_batch(32, 512, embed_dimension, pad_percentage=None, dtype=dtype, device=device)

# Currently the fused implementations don't support ``NestedTensor`` for training
model.eval()

with sdpa_kernel(SDPBackend.FLASH_ATTENTION):
    try:
        print(f"Random NT runs in {benchmark_torch_function_in_microseconds(model, random_nt):.3f} microseconds")
        print(f"Random Dense runs in {benchmark_torch_function_in_microseconds(model, random_dense):.3f} microseconds")
    except RuntimeError:
        print("FlashAttention is not supported. See warnings for reasons.")

/usr/local/lib/python3.10/dist-packages/torch/nested/__init__.py:226: UserWarning:

The PyTorch API of nested tensors is in prototype stage and will change in the near future. (Triggered internally at ../aten/src/ATen/NestedTensorImpl.cpp:178.)

Random NT runs in 562.866 microseconds
Random Dense runs in 948.493 microseconds

Using SDPA with torch.compile

With the release of PyTorch 2.0, a new feature called torch.compile() has been introduced, which can provide significant performance improvements over eager mode. Scaled dot product attention is fully composable with torch.compile(). To demonstrate this, let’s compile the CausalSelfAttention module using torch.compile() and observe the resulting performance improvements.

batch_size = 32
max_sequence_len = 256
x = torch.rand(batch_size, max_sequence_len,
               embed_dimension, device=device, dtype=dtype)
print(
    f"The non compiled module runs in  {benchmark_torch_function_in_microseconds(model, x):.3f} microseconds")


compiled_model = torch.compile(model)
# Let's compile it
compiled_model(x)
print(
    f"The compiled module runs in  {benchmark_torch_function_in_microseconds(compiled_model, x):.3f} microseconds")

The non compiled module runs in  415.917 microseconds
The compiled module runs in  517.206 microseconds

The exact execution time is dependent on machine, however the results for mine: The non compiled module runs in 166.616 microseconds The compiled module runs in 166.726 microseconds That is not what we were expecting. Let’s dig a little deeper. PyTorch comes with an amazing built-in profiler that you can use to inspect the performance characteristics of your code.

from torch.profiler import profile, record_function, ProfilerActivity
activities = [ProfilerActivity.CPU]
if device == 'cuda':
    activities.append(ProfilerActivity.CUDA)

with profile(activities=activities, record_shapes=False) as prof:
    with record_function(" Non-Compilied Causal Attention"):
        for _ in range(25):
            model(x)
print(prof.key_averages().table(sort_by="cuda_time_total", row_limit=10))


with profile(activities=activities, record_shapes=False) as prof:
    with record_function("Compiled Causal Attention"):
        for _ in range(25):
            compiled_model(x)
print(prof.key_averages().table(sort_by="cuda_time_total", row_limit=10))

# For even more insights, you can export the trace and use ``chrome://tracing`` to view the results
#
# .. code-block:: python
#
#    prof.export_chrome_trace("compiled_causal_attention_trace.json").

-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
                                                   Name    Self CPU %      Self CPU   CPU total %     CPU total  CPU time avg     Self CUDA   Self CUDA %    CUDA total  CUDA time avg    # of Calls
-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
                         Non-Compilied Causal Attention         0.00%       0.000us         0.00%       0.000us       0.000us      10.593ms       102.09%      10.593ms      10.593ms             1
                         Non-Compilied Causal Attention        21.86%       2.429ms        77.90%       8.656ms       8.656ms       0.000us         0.00%      10.376ms      10.376ms             1
                                           aten::linear         1.13%     125.161us        28.70%       3.189ms      63.781us       0.000us         0.00%       7.767ms     155.332us            50
                                           aten::matmul         2.32%     257.724us        24.81%       2.756ms      55.129us       0.000us         0.00%       7.767ms     155.332us            50
                                               aten::mm        15.75%       1.750ms        20.12%       2.235ms      44.707us       7.767ms        74.85%       7.767ms     155.332us            50
         ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_tn         0.00%       0.000us         0.00%       0.000us       0.000us       5.560ms        53.58%       5.560ms     222.385us            25
                     aten::scaled_dot_product_attention         1.94%     215.363us        17.96%       1.995ms      79.809us       0.000us         0.00%       2.609ms     104.380us            25
              aten::_scaled_dot_product_flash_attention         2.96%     328.913us        16.02%       1.780ms      71.195us       0.000us         0.00%       2.609ms     104.380us            25
                         aten::_flash_attention_forward         3.60%     400.038us        11.00%       1.223ms      48.900us       2.609ms        25.15%       2.609ms     104.380us            25
void pytorch_flash::flash_fwd_kernel<pytorch_flash::...         0.00%       0.000us         0.00%       0.000us       0.000us       2.609ms        25.15%       2.609ms     104.380us            25
-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
Self CPU time total: 11.112ms
Self CUDA time total: 10.376ms

-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
                                                   Name    Self CPU %      Self CPU   CPU total %     CPU total  CPU time avg     Self CUDA   Self CUDA %    CUDA total  CUDA time avg    # of Calls
-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
                              Compiled Causal Attention         0.00%       0.000us         0.00%       0.000us       0.000us      10.506ms       101.21%      10.506ms      10.506ms             1
                              Compiled Causal Attention         9.09%       1.013ms        77.07%       8.587ms       8.587ms       0.000us         0.00%      10.381ms      10.381ms             1
                                  Torch-Compiled Region         8.74%     974.078us        65.72%       7.322ms     292.882us       0.000us         0.00%      10.381ms     415.250us            25
                                       CompiledFunction        27.31%       3.043ms        56.97%       6.348ms     253.919us       0.000us         0.00%      10.381ms     415.250us            25
                                               aten::mm         9.90%       1.103ms        14.60%       1.626ms      32.525us       7.771ms        74.86%       7.771ms     155.424us            50
         ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_tn         0.00%       0.000us         0.00%       0.000us       0.000us       5.563ms        53.59%       5.563ms     222.534us            25
              aten::_scaled_dot_product_flash_attention         2.25%     251.072us        15.07%       1.679ms      67.154us       0.000us         0.00%       2.610ms     104.403us            25
                         aten::_flash_attention_forward         3.64%     405.660us        11.07%       1.234ms      49.351us       2.610ms        25.14%       2.610ms     104.403us            25
void pytorch_flash::flash_fwd_kernel<pytorch_flash::...         0.00%       0.000us         0.00%       0.000us       0.000us       2.610ms        25.14%       2.610ms     104.403us            25
ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_stages_3...         0.00%       0.000us         0.00%       0.000us       0.000us       2.208ms        21.27%       2.208ms      88.314us            25
-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
Self CPU time total: 11.142ms
Self CUDA time total: 10.381ms

The previous code snippet generates a report of the top 10 PyTorch functions that consumed the most GPU execution time, for both the compiled and non-compiled module. The analysis reveals that the majority of time spent on the GPU is concentrated on the same set of functions for both modules. The reason for this here is that torch.compile is very good at removing the framework overhead associated with PyTorch. If your model is launching large, efficient CUDA kernels, which in this case CausalSelfAttention is, then the overhead of PyTorch can be hidden.

In reality, your module does not normally consist of a singular CausalSelfAttention block. When experimenting with Andrej Karpathy NanoGPT repository, compiling the module took the time per train step from: 6090.49ms to 3273.17ms! This was done on commit: ae3a8d5 of NanoGPT training on the Shakespeare dataset.

Using SDPA with attn_bias subclasses

# As of PyTorch 2.3, we have added a new submodule that contains tensor subclasses.
# Designed to be used with ``torch.nn.functional.scaled_dot_product_attention``.
# The module is named ``torch.nn.attention.bias`` and contains the following two
# utilities for generating causal attention variants:
#
# - ``torch.nn.attention.bias.causal_upper_left``
# - ``torch.nn.attention.bias.causal_lower_right``
#
# .. note::
#    The current argument ``is_causal`` in ``torch.nn.functional.scaled_dot_product_attention``
#    is the same as using ``torch.nn.attention.bias.causal_upper_left``.
#

from torch.nn.attention.bias import causal_lower_right, causal_upper_left

batch_size = 32
sequence_length_q = 2
sequence_length_kv = 10
num_heads = 16
embed_dimension = 32

dtype = torch.float16

query = torch.rand(batch_size, num_heads, sequence_length_q, embed_dimension, device=device, dtype=dtype)
key = torch.rand(batch_size, num_heads, sequence_length_kv, embed_dimension, device=device, dtype=dtype)
value = torch.rand(batch_size, num_heads, sequence_length_kv, embed_dimension, device=device, dtype=dtype)

upper_left_bias = causal_upper_left(sequence_length_q, sequence_length_kv)
lower_right_bias = causal_lower_right(sequence_length_q, sequence_length_kv)

print(type(upper_left_bias))
print(type(lower_right_bias))

assert type(upper_left_bias) == type(lower_right_bias)
assert issubclass(type(upper_left_bias), torch.Tensor)

# As you can see from the previous output, are the same type ``torch.nn.attention.bias.CausalBias``
# and subclass ``torch.Tensor``

# Lets see what these tensors look like
print(upper_left_bias)
print(lower_right_bias)

# Upper Left Bias aligns the causal attention mask to the upper left corner of the attention scores matrix.
# This only has an impact when the attention scores matrix is not square, which is common for decoding use cases.
# Another way of thinking about this concept is that when you use upper left bias,
# the 0th token in the query is aligned to the 0th token in the key, while for lower right bias,
# Assuming the attention score matrix is two dimensional, ``attn_score[0][0]`` is the attention score
# between the 0th token in the query and the 0th token in the key.
# For lower right bias, the sequence of q is aligned so that the last token in q is aligned to the last token in k
# (for example, ``attn_score[-1][-1])`` is all True since the last token in q is at the same position as the last token in k
# even if the sequence length of q and k are different.

# These objects are intended to be used with sdpa
out_upper_left = F.scaled_dot_product_attention(query, key, value, upper_left_bias)
out_lower_right = F.scaled_dot_product_attention(query, key, value, lower_right_bias)
out_is_causal = F.scaled_dot_product_attention(query, key, value, is_causal=True)

assert torch.allclose(out_upper_left, out_is_causal)
assert not torch.allclose(out_upper_left, out_lower_right)

# These attention biases should also be compatible with torch.compile
compiled_sdpa = torch.compile(F.scaled_dot_product_attention, fullgraph=True)
out_upper_left = compiled_sdpa(query, key, value, upper_left_bias)

<class 'torch.nn.attention.bias.CausalBias'>
<class 'torch.nn.attention.bias.CausalBias'>
tensor([[ True, False, False, False, False, False, False, False, False, False],
        [ True,  True, False, False, False, False, False, False, False, False]])
tensor([[ True,  True,  True,  True,  True,  True,  True,  True,  True, False],
        [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True]])

Conclusion

In this tutorial, we have demonstrated the basic usage of torch.nn.functional.scaled_dot_product_attention. We have shown how the sdpa_kernel context manager can be used to assert a certain implementation is used on GPU. As well, we built a simple CausalSelfAttention module that works with NestedTensor and is torch compilable. In the process we have shown how to the profiling tools can be used to explore the performance characteristics of a user defined module.