triton/python/tutorials/04-low-memory-dropout.py

"""
Low-Memory Dropout
=================

In this tutorial, you will write a memory-efficient implementation of dropout whose state
will be composed of a single int32 seed. This differs from more traditional implementations of dropout,
whose state is generally composed of a bit mask tensor of the same shape as the input. You will learn about:

- The limitations of naive implementations of Dropout with PyTorch
- Parallel pseudo-random number generation in Triton
"""

# %%
# Baseline
# -------------
# The *dropout* operator was first introduced in [SRIVASTAVA2014]_ as a way to improve the performance
# of deep neural networks in low-data regime (i.e. regularization).
#
# It takes a vector as input and produces a vector of the same shape as output. Each scalar in the
# output has a probability :math:`p` of being changed to zero and otherwise it is copied from the input.
# This forces the network to perform well even when only :math:`1 - p` scalars from the input are available.
#
# At evaluation time we want to use the full power of the network so we set :math:`p=0`. Naively this would
# increase the norm of the output (which can be a bad thing, e.g. it can lead to artificial decrease
# in the output softmax temperature). To prevent this we multiply the output by :math:`\frac{1}{1 - p}`, which
# keeps the norm consistent regardless of the dropout probability.
#
# Let's first take a look at the baseline implementation.


import tabulate
import torch

import triton
import triton.language as tl


@triton.jit
def _dropout(
        x_ptr,  # pointer to the input
        x_keep_ptr,  # pointer to a mask of 0s and 1s
        output_ptr,  # pointer to the output
        n_elements,  # number of elements in the `x` tensor
        p,  # probability that an element of `x` is changed to zero
        BLOCK_SIZE: tl.constexpr,
):
    pid = tl.program_id(axis=0)
    block_start = pid * BLOCK_SIZE
    offsets = block_start + tl.arange(0, BLOCK_SIZE)
    mask = offsets < n_elements
    # Load data
    x = tl.load(x_ptr + offsets, mask=mask)
    x_keep = tl.load(x_keep_ptr + offsets, mask=mask)
    # The line below is the crucial part, described in the paragraph above!
    output = tl.where(x_keep, x / (1 - p), 0.0)
    # Write-back output
    tl.store(output_ptr + offsets, output, mask=mask)


def dropout(x, x_keep, p):
    output = torch.empty_like(x)
    assert x.is_contiguous()
    n_elements = x.numel()
    grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),)
    _dropout[grid](x, x_keep, output, n_elements, p, BLOCK_SIZE=1024)
    return output


# Input tensor
x = torch.randn(size=(10,)).cuda()
# Dropout mask
p = 0.5
x_keep = (torch.rand(size=(10,)) > p).to(torch.int32).cuda()
#
output = dropout(x, x_keep=x_keep, p=p)
print(tabulate.tabulate([
    ["input"] + x.tolist(),
    ["keep mask"] + x_keep.tolist(),
    ["output"] + output.tolist()
]))

# %%
# Seeded dropout
# -------------
# Above implementation of dropout works fine, but it can be a bit awkward to deal with. Firstly
# we need to store the dropout mask for backpropagation. Secondly, dropout state management can get
# very tricky when using recompute/checkpointing (e.g. see all the notes about `preserve_rng_state` in
# https://pytorch.org/docs/1.9.0/checkpoint.html). In this tutorial we'll describe an alternative implementation
# that (1) has a smaller memory footprint; (2) requires less data movement; and (3) simplifies the management
# of persisting randomness across multiple invocations of the kernel.
#
# Pseudorandom number generation in Triton is simple! In this tutorial we will use the
# :code:`triton.language.rand` function which generates a block of uniformly distributed :code:`float32`
# values in [0, 1), given a seed and a block of :code:`int32` offsets. But if you need it, Triton also provides
# other :ref:`random number generation strategies <Random Number Generation>`.
#
# .. note::
#    Triton's implementation of PRNG is based on the Philox algorithm (described on [SALMON2011]_).
#
# Let's put it all together.


@triton.jit
def _seeded_dropout(
        x_ptr,
        output_ptr,
        n_elements,
        p,
        seed,
        BLOCK_SIZE: tl.constexpr,
):
    # compute memory offsets of elements handled by this instance
    pid = tl.program_id(axis=0)
    block_start = pid * BLOCK_SIZE
    offsets = block_start + tl.arange(0, BLOCK_SIZE)
    # load data from x
    mask = offsets < n_elements
    x = tl.load(x_ptr + offsets, mask=mask)
    # randomly prune it
    random = tl.rand(seed, offsets)
    x_keep = random > p
    # write-back
    output = tl.where(x_keep, x / (1 - p), 0.0)
    tl.store(output_ptr + offsets, output, mask=mask)


def seeded_dropout(x, p, seed):
    output = torch.empty_like(x)
    assert x.is_contiguous()
    n_elements = x.numel()
    grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),)
    _seeded_dropout[grid](x, output, n_elements, p, seed, BLOCK_SIZE=1024)
    return output


x = torch.randn(size=(10,)).cuda()
# Compare this to the baseline - dropout mask is never instantiated!
output = seeded_dropout(x, p=0.5, seed=123)
output2 = seeded_dropout(x, p=0.5, seed=123)
output3 = seeded_dropout(x, p=0.5, seed=512)

print(tabulate.tabulate([
    ["input"] + x.tolist(),
    ["output (seed = 123)"] + output.tolist(),
    ["output (seed = 123)"] + output2.tolist(),
    ["output (seed = 512)"] + output3.tolist()
]))

# %%
# Et Voilà! We have a triton kernel that applies the same dropout mask provided the seed is the same!
# If you'd like explore further applications of pseudorandomness in GPU programming, we encourage you
# to explore the `triton/language/random` folder!

# %%
# Exercises
# -------------
# 1. Extend the kernel to operate over a matrix and use a vector of seeds - one per row.
# 2. Add support for striding.
# 3. (challenge) Implement a kernel for sparse Johnson-Lindenstrauss transform which generates the projection matrix one the fly each time using a seed.

# %%
# References
# --------------
#
# .. [SALMON2011] John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw, "Parallel Random Numbers: As Easy as 1, 2, 3", 2011
# .. [SRIVASTAVA2014] Nitish Srivastava and Geoffrey Hinton and Alex Krizhevsky and Ilya Sutskever and Ruslan Salakhutdinov, "Dropout: A Simple Way to Prevent Neural Networks from Overfitting", JMLR 2014