Note
Go to the end to download the full example code.
(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
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([[[ 2.0776, -0.6983, 0.7035, -1.6485, -0.7951, -0.3311, 0.1492,
-0.8578],
[ 0.4932, 1.2065, 0.4041, 0.0968, -0.2332, 0.1752, -0.4782,
-0.8079],
[ 0.7532, 1.0582, 0.5769, -0.0881, -0.3975, 0.1011, -0.3719,
-1.0104]],
[[-0.3089, 0.5800, -0.2403, -0.4013, 1.6163, 0.3114, -0.4385,
1.3604],
[-0.7240, 0.5346, -0.1608, -0.6489, 1.3062, 0.3425, -0.1411,
0.9240],
[-0.6395, 0.5294, -0.1754, -0.6034, 1.3402, 0.3328, -0.1917,
1.0248]]], 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 2272.459 microseconds
The math implementation runs in 87384.204 microseconds
The flash attention implementation runs in 2277.315 microseconds
The memory efficient implementation runs in 4341.564 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:250: UserWarning:
The PyTorch API of nested tensors is in prototype stage and will change in the near future. We recommend specifying layout=torch.jagged when constructing a nested tensor, as this layout receives active development, has better operator coverage, and works with torch.compile. (Triggered internally at /pytorch/aten/src/ATen/NestedTensorImpl.cpp:178.)
Random NT runs in 611.695 microseconds
Random Dense runs in 948.388 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 424.367 microseconds
The compiled module runs in 525.241 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 16.42% 2.083ms 71.91% 9.126ms 9.126ms 0.000us 0.00% 10.846ms 10.846ms 1
Non-Compilied Causal Attention 0.00% 0.000us 0.00% 0.000us 0.000us 10.731ms 101.01% 10.731ms 10.731ms 1
aten::linear 0.93% 117.695us 34.04% 4.319ms 86.390us 0.000us 0.00% 8.028ms 160.566us 50
aten::matmul 1.79% 227.338us 30.80% 3.909ms 78.186us 0.000us 0.00% 8.028ms 160.566us 50
aten::mm 9.57% 1.214ms 26.96% 3.421ms 68.427us 7.806ms 73.48% 8.028ms 160.566us 50
ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_tn 0.00% 0.000us 0.00% 0.000us 0.000us 5.582ms 52.54% 5.582ms 223.279us 25
aten::scaled_dot_product_attention 1.64% 207.687us 14.12% 1.792ms 71.684us 0.000us 0.00% 2.818ms 112.714us 25
aten::_scaled_dot_product_flash_attention 2.29% 290.827us 12.48% 1.584ms 63.376us 0.000us 0.00% 2.818ms 112.714us 25
aten::_flash_attention_forward 2.36% 299.166us 9.00% 1.142ms 45.680us 2.818ms 26.52% 2.818ms 112.714us 25
void pytorch_flash::flash_fwd_kernel<Flash_fwd_kerne... 0.00% 0.000us 0.00% 0.000us 0.000us 2.818ms 26.52% 2.818ms 112.714us 25
------------------------------------------------------- ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------
Self CPU time total: 12.691ms
Self CUDA time total: 10.624ms
------------------------------------------------------- ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------
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 10.666ms 100.56% 10.666ms 10.666ms 1
Compiled Causal Attention 7.19% 919.680us 75.56% 9.662ms 9.662ms 0.000us 0.00% 10.607ms 10.607ms 1
Torch-Compiled Region: 0/0 6.75% 862.663us 65.73% 8.405ms 336.195us 0.000us 0.00% 10.607ms 424.272us 25
CompiledFunction 20.78% 2.657ms 56.63% 7.242ms 289.675us 0.000us 0.00% 10.607ms 424.272us 25
aten::mm 6.88% 879.324us 10.78% 1.379ms 27.581us 7.809ms 73.62% 7.809ms 156.174us 50
ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_tn 0.00% 0.000us 0.00% 0.000us 0.000us 5.585ms 52.65% 5.585ms 223.396us 25
aten::_scaled_dot_product_flash_attention 1.64% 209.534us 11.62% 1.486ms 59.456us 0.000us 0.00% 2.798ms 111.923us 25
aten::_flash_attention_forward 2.34% 298.938us 8.48% 1.085ms 43.383us 2.798ms 26.38% 2.798ms 111.923us 25
void pytorch_flash::flash_fwd_kernel<Flash_fwd_kerne... 0.00% 0.000us 0.00% 0.000us 0.000us 2.798ms 26.38% 2.798ms 111.923us 25
ampere_fp16_s1688gemm_fp16_128x128_ldg8_f2f_stages_3... 0.00% 0.000us 0.00% 0.000us 0.000us 2.224ms 20.97% 2.224ms 88.952us 25
------------------------------------------------------- ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------
Self CPU time total: 12.788ms
Self CUDA time total: 10.607ms
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.
Total running time of the script: (0 minutes 7.522 seconds)
