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

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 2329.801 microseconds
The math implementation runs in 87430.357 microseconds
The flash attention implementation runs in 2336.004 microseconds
The memory efficient implementation runs in 4312.427 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 563.060 microseconds
Random Dense runs in 948.656 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  416.172 microseconds
The compiled module runs in  511.366 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      10.512ms       101.26%      10.512ms      10.512ms             1
                         Non-Compilied Causal Attention        19.65%       2.162ms        73.57%       8.097ms       8.097ms       0.000us         0.00%      10.382ms      10.382ms             1
                                           aten::linear         1.10%     120.710us        27.13%       2.986ms      59.728us       0.000us         0.00%       7.770ms     155.399us            50
                                           aten::matmul         2.16%     237.583us        23.29%       2.563ms      51.260us       0.000us         0.00%       7.770ms     155.399us            50
                                               aten::mm        14.84%       1.634ms        19.01%       2.093ms      41.856us       7.770ms        74.84%       7.770ms     155.399us            50
         ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_tn         0.00%       0.000us         0.00%       0.000us       0.000us       5.566ms        53.61%       5.566ms     222.623us            25
                     aten::scaled_dot_product_attention         1.91%     209.734us        17.38%       1.913ms      76.533us       0.000us         0.00%       2.612ms     104.471us            25
              aten::_scaled_dot_product_flash_attention         2.85%     313.464us        15.48%       1.704ms      68.144us       0.000us         0.00%       2.612ms     104.471us            25
                         aten::_flash_attention_forward         3.51%     386.406us        10.79%       1.188ms      47.507us       2.612ms        25.16%       2.612ms     104.471us            25
void pytorch_flash::flash_fwd_kernel<pytorch_flash::...         0.00%       0.000us         0.00%       0.000us       0.000us       2.612ms        25.16%       2.612ms     104.471us            25
-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
Self CPU time total: 11.007ms
Self CUDA time total: 10.382ms

-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
                                                   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      10.456ms       100.68%      10.456ms      10.456ms             1
                              Compiled Causal Attention         8.49%     940.170us        71.92%       7.968ms       7.968ms       0.000us         0.00%      10.386ms      10.386ms             1
                                  Torch-Compiled Region         8.22%     910.934us        61.38%       6.800ms     272.016us       0.000us         0.00%      10.386ms     415.444us            25
                                       CompiledFunction        25.24%       2.796ms        53.16%       5.889ms     235.579us       0.000us         0.00%      10.386ms     415.444us            25
                                               aten::mm         9.24%       1.023ms        13.76%       1.525ms      30.490us       7.776ms        74.87%       7.776ms     155.520us            50
         ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_tn         0.00%       0.000us         0.00%       0.000us       0.000us       5.567ms        53.60%       5.567ms     222.689us            25
              aten::_scaled_dot_product_flash_attention         2.04%     226.132us        14.16%       1.569ms      62.760us       0.000us         0.00%       2.610ms     104.403us            25
                         aten::_flash_attention_forward         3.51%     388.527us        10.35%       1.147ms      45.885us       2.610ms        25.13%       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        25.13%       2.610ms     104.403us            25
ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_stages_3...         0.00%       0.000us         0.00%       0.000us       0.000us       2.209ms        21.27%       2.209ms      88.352us            25
-------------------------------------------------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------  ------------
Self CPU time total: 11.079ms
Self CUDA time total: 10.386ms

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.