# Copyright 2021 MosaicML. All Rights Reserved.
from __future__ import annotations
import abc
import math
from typing import Optional, Tuple, Union, cast
import numpy as np
import torch
from torch import nn
from torch.nn.common_types import _size_2_t
from composer.algorithms.factorize.factorize_core import LowRankSolution, factorize_conv2d, factorize_matrix
def _clean_latent_size(latent_size: Union[int, float], in_size: int, out_size: int) -> int:
if latent_size < 1: # fraction of input or output channels
latent_channels = int(latent_size * min(in_size, out_size))
return max(1, latent_channels)
return int(latent_size)
def _max_rank_with_possible_speedup(in_channels: int,
out_channels: int,
kernel_size: Optional[_size_2_t] = None) -> int:
# TODO less naive cost model than counting multiply-adds
fan_in = in_channels
if kernel_size is not None:
fan_in *= np.prod(kernel_size)
breakeven = (fan_in * out_channels) / (fan_in + out_channels)
return int(math.ceil(breakeven - 1)) # round down, or 1 lower if divides evenly
[docs]def factorizing_could_speedup(module: torch.nn.Module, latent_size: Union[int, float]):
"""Whether factorizing a module a given amount could possibly yield a benefit.
This computation is based on the number of multiply-add operations involved
in the module's current forward pass versus the number that would be involved
if it were factorized into two modules using the specified latent size. The
operations are assumed to be dense and of the same data type in all cases.
Note that this function returning true does not guarantee a wall-clock
speedup, since splitting one operation into two involves more data movement
and more per-op overhead.
Args:
module (torch.nn.Module): a :py:class:`~torch.nn.Conv2d`, :py:class:`~torch.nn.Linear`,
:py:class:`~FactorizedConv2d`, or :py:class:`~FactorizedLinear`.
latent_size (int or float): number of channels (for convolution) or
features (for linear) in the latent representation. Can be
specified as either an integer > 1 or as float within [0, 1).
In the latter case, the value is interpreted as a fraction of
``min(in_features, out_features)`` for a linear module or
``min(in_channels, out_channels)`` for a convolution.
Returns:
could_speedup:
A ``bool`` indicating whether the provided amount of factorization
could accelerate the provided module. If ``module`` is not one of
the allowed types, always returns ``False``, since there is no
supported way to factorize that module.
"""
if isinstance(module, _FactorizedModule):
return module.should_factorize(latent_size)
elif isinstance(module, torch.nn.Conv2d):
if module.groups > 1:
return False # can't factorize grouped convolutions yet
latent_size = _clean_latent_size(latent_size, module.in_channels, module.out_channels)
max_rank = _max_rank_with_possible_speedup(module.in_channels,
module.out_channels,
kernel_size=cast(_size_2_t, module.kernel_size))
return latent_size <= max_rank
elif isinstance(module, torch.nn.Linear):
latent_size = _clean_latent_size(latent_size, module.in_features, module.out_features)
max_rank = _max_rank_with_possible_speedup(module.in_features, module.out_features)
return latent_size <= max_rank
else:
return False
def _apply_solution_to_module_parameters(solution: LowRankSolution, module0: torch.nn.Module, module1: torch.nn.Module,
transpose: bool) -> None:
error_msg = "Can't apply unititalized solution!"
assert solution.bias is not None, error_msg
assert solution.Wa is not None, error_msg
assert solution.Wb is not None, error_msg
with torch.no_grad():
# first op always has no bias since adds no expressivity
if module0.bias is not None:
assert isinstance(module0.bias, torch.Tensor)
module0.bias = torch.nn.parameter.Parameter(
torch.zeros(solution.rank, dtype=module0.bias.dtype).to(device=module0.bias.device)) # type: ignore
assert isinstance(module1.bias, torch.Tensor)
module1.bias.copy_(solution.bias)
Wa = solution.Wa
Wb = solution.Wb
if transpose:
Wa = torch.transpose(Wa, 0, 1)
Wb = torch.transpose(Wb, 0, 1)
module0.weight = torch.nn.parameter.Parameter(Wa.to(device=module0.weight.device)) # type: ignore
module1.weight = torch.nn.parameter.Parameter(Wb.to(device=module1.weight.device)) # type: ignore
class _FactorizedModule(nn.Module, abc.ABC):
def __init__(self, in_size: int, out_size: int, latent_size: Union[int, float], kernel_size: _size_2_t = 1):
super().__init__()
self.in_size = in_size
self.out_size = out_size
self.latent_size = _clean_latent_size(latent_size, in_size, out_size)
self.kernel_size = kernel_size
def _check_child_modules_present(self):
assert hasattr(self, 'module0'), "module0 must be set during child class __init__!"
assert hasattr(self, 'module1'), "module1 must be set during child class __init__!"
assert isinstance(self.module0, torch.nn.Module)
assert isinstance(self.module1, torch.nn.Module)
def forward(self, input: torch.Tensor): # type: ignore reportIncompatibleMethodOverride
self._check_child_modules_present()
ret = self.module0(input) # type: ignore reportGeneralTypeIssues
if self.module1 is not None:
ret = self.module1(ret) # type: ignore reportGeneralTypeIssues
return ret
def reset_parameters(self):
self._check_child_modules_present()
cast(torch.nn.Module, self.module0).reset_parameters() # type: ignore reportGeneralTypeIssues
cast(torch.nn.Module, self.module1).reset_parameters() # type: ignore reportGeneralTypeIssues
def set_rank(self, input: torch.Tensor, rank: int) -> None:
"""Makes the module factorize using a ``rank``-dimensional latent representation.
``rank`` can be large enough that the factorization increases the
number of multiply-add operations, but not larger than the current
latent rank.
Args:
input: Tensor that can be passed to the model's `forward()` method
rank: dimensionality of the latent representation; this is the
size of the vector space when factorizing linear modules and
the number of channels for convolutional modules.
Raises:
ValueError:
If ``rank`` is larger than the current latent rank
"""
if rank > self.latent_size:
raise ValueError(f"Requested rank {rank} exceeds current rank {self.latent_size}")
if rank == self.latent_size:
return
soln = self.solution_for_rank(input, rank)
self.apply_solution(soln)
def _clean_latent_size(self, latent_size: Union[int, float]):
return _clean_latent_size(latent_size, self.in_size, self.out_size)
def _max_rank_with_speedup(self):
if hasattr(self, 'module1') and self.module1 is not None:
# already factorized, so reducing rank at all helps
return self.latent_size - 1
else:
# not factorized yet; has to factorize enough to be worthwhile
return _max_rank_with_possible_speedup(self.in_size, self.out_size, kernel_size=self.kernel_size)
def should_factorize(self, proposed_rank: Union[int, float]) -> bool:
"""Whether factorizing with a given rank would reduce the number of multiply-add operations."""
proposed_rank = self._clean_latent_size(proposed_rank)
return proposed_rank <= self._max_rank_with_speedup()
@abc.abstractmethod
def _create_child_modules(self) -> Tuple[torch.nn.Module, torch.nn.Module]:
"""This is used to populate the self.module0 and self.module1 attributes; it's not part of __init__ because the
logic to initialize them is subclass-specific and might depend on the shared logic in __init__"""
...
@abc.abstractmethod
def solution_for_rank(self, input: torch.Tensor, rank: int) -> LowRankSolution:
"""Returns a solution that :meth:`~apply_solution` can use to update the module's level of factorization.
This is seperate from :meth:`set_rank` so that one can generate and assess
many possible solutions for a given module before choosing one.
Args:
input: An input to the module used to optimize the solution's
weights. The optimization seeks to preserve the module's
input-output mapping as much as possible subject to the
specified rank constraint.
rank: The number of dimensions in the latent space into which
the input is mapped.
Returns:
solution:
An object encapsulating the new parameters to be used and their
associated mean squared error on the input
"""
...
@abc.abstractmethod
def apply_solution(self, solution: LowRankSolution) -> None:
"""Updates module's child modules to reflect the factorization solution.
This *always* applies the solution and doesn't check whether
using the solution is worthwhile.
Args:
solution: an object encapsulating the new parameters to be used
and their associated mean squared error on the input for
which they were optimized. Can be obtained using
:meth:`~solution_for_rank`.
"""
...
[docs]class FactorizedConv2d(_FactorizedModule):
"""Factorized replacement for :class:`torch.nn.Conv2d`.
Splits the conv2d operation into two smaller conv2d operations, which
are executed sequentially with no nonlinearity in between. This first
conv2d can be thought of as projecting the feature maps into a
lower-dimensional space, similar to PCA. The second produces outputs
of the same shape as the un-factorized version based on the embeddings
within this lower-dimensional space. Note that "dimensionality" here
refers to the number of channels, not the spatial extent or tensor rank.
The first conv2d has a kernel size of ``kernel_size``, while the second
one always has a kernel size of 1x1. For large kernel sizes, the
lower-dimensional space can be nearly as large as
``min(in_channels, out_channels)`` and still yield a reduction in
multiply-add operations. For kernels sizes of 1x1, the breakeven
point is a 2x reduction in channel count, similar to
:class:`~FactorizedLinear`.
See :func:`~composer.factorize.factorize_conv2d` for more details.
Args:
in_channels (int): number of channels in the input image
out_channels (int): number of channels produced by the convolution
kernel_size (int or tuple, optional): size of the convolving kernel
latent_channels (int or float, optional): number of channels in the
latent representation produced by the first small convolution.
Can be specified as either an integer > 1 or as float within
[0, 1). In the latter case, the value is interpreted as a fraction
of ``min(in_features, out_features)`` for each linear module, and
is converted to the equivalent integer value, with a minimum of 1.
**kwargs: other arguments to :class:`torch.nn.Conv2d` are supported
and will be used with the first of the two smaller ``Conv2d``
operations. However, ``groups > 1`` and ``dilation > 1`` are
not currently supported.
Raises:
ValueError:
If ``latent_channels`` is not small enough for factorization
to reduce the number of multiply-add operations. In this regime,
factorization is both slower and less expressive than a
non-factorized operation. Setting
``latent_features`` to :meth:`~max_allowed_latent_channels`
or a smaller value is sufficient to avoid this.
"""
def __init__(self,
in_channels: int,
out_channels: int,
kernel_size: _size_2_t,
latent_channels: Union[int, float] = .25,
**kwargs):
super().__init__(in_size=in_channels,
out_size=out_channels,
latent_size=latent_channels,
kernel_size=kernel_size)
if kwargs.get('groups', 1) > 1:
raise NotImplementedError("Factorizing grouped convolutions is not supported.")
self.kwargs = kwargs
# conv2d factorization code requires most Conv2d arguments, but
# not boolean 'bias'
self.convolution_kwargs = {k: v for k, v in kwargs.items() if k != 'bias'}
self.module0, self.module1 = self._create_child_modules()
def _create_child_modules(self) -> Tuple[torch.nn.Module, torch.nn.Module]:
if not self.should_factorize(self.latent_channels):
raise ValueError(
f"latent_channels {self.latent_size} is not small enough to merit factorization! Must be <= {self._max_rank_with_speedup()}"
)
# this one produces identical output as a regular Conv2d would,
# except with fewer output channels
conv0 = nn.Conv2d(self.in_channels,
self.latent_channels,
self.kernel_size,
bias=False,
**self.convolution_kwargs)
# this one increases the number of output channels
conv1 = nn.Conv2d(self.latent_channels, self.out_channels, kernel_size=1, bias=True)
return conv0, conv1
# wrap shared fields in read-only properties matching the torch conv module API
@property
def in_channels(self) -> int:
"""See :class:`torch.nn.Conv2d`."""
return self.in_size
@property
def out_channels(self) -> int:
"""See :class:`torch.nn.Conv2d`."""
return self.out_size
@property
def latent_channels(self) -> int:
"""The number of of output channels for the first convolution, which is also the number of input channels for
the second convolution."""
return self.latent_size
def solution_for_rank(self, input: torch.Tensor, rank: int) -> LowRankSolution:
weight0 = self.module0.weight
bias0 = self.module0.bias
weight1, bias1 = self.module1.weight, self.module1.bias
assert (bias0 is None) or isinstance(bias0, torch.Tensor)
assert isinstance(bias1, torch.Tensor)
assert isinstance(weight0, torch.Tensor)
assert isinstance(weight1, torch.Tensor)
return factorize_conv2d(input, weight0, weight1, rank=rank, biasA=bias0, biasB=bias1, **self.convolution_kwargs)
def apply_solution(self, solution: LowRankSolution):
self.latent_size = solution.rank
self.module0.out_channels = solution.rank
self.module1.in_channels = solution.rank
_apply_solution_to_module_parameters(solution, self.module0, self.module1, transpose=False)
[docs] @staticmethod
def max_allowed_latent_features(in_features: int, out_features: int, kernel_size: _size_2_t) -> int:
"""Returns the largest latent channel count that reduces the number of multiply-adds.
Args:
in_channels: number of channels in the input image
out_channels: number of channels produced by the convolution
kernel_size: size of the convolving kernel
Returns:
latent_channels: the largest allowable number of latent channels
"""
return _max_rank_with_possible_speedup(in_features, out_features, kernel_size=kernel_size)
@staticmethod
def from_conv2d(module: torch.nn.Conv2d, module_ix: int = -1, **kwargs) -> FactorizedConv2d:
conv = FactorizedConv2d(
in_channels=module.in_channels,
out_channels=module.out_channels,
kernel_size=cast(_size_2_t, module.kernel_size),
stride=module.stride,
padding=module.padding,
dilation=module.dilation,
groups=module.groups,
bias=((module.bias is not None) and (module.bias is not False)),
**kwargs # custom params
)
conv.reset_parameters()
return conv
[docs]class FactorizedLinear(_FactorizedModule):
"""Factorized replacement for :class:`torch.nn.Linear`.
Splits the linear operation into two smaller linear operations, which
are executed sequentially with no nonlinearity in between. This first
linear operation can be thought of as projecting the inputs into a
lower-dimensional space, similar to PCA. The second produces outputs
of the same shape as the un-factorized version based on the embeddings
within this lower-dimensional space.
If the lower-dimensional space is less than half the size of the
smaller of the input and output dimensionality, this factorization
can reduce the number of multiply-adds necessary to compute the output.
However, because larger matrix products tend to utilize the hardware
better, it may take a reduction of more than 2x to get a speedup
in practice.
See :func:`~composer.factorize.factorize_matrix` for more details.
Args:
in_features (int): size of each input sample
out_features (int): size of each output sample
bias (bool): If set to False, the layer will not learn an additive bias.
latent_features (int or float, optional): size of the latent space.
Can be specified as either an integer > 1 or as a float within
[0, 0.5). In the latter case, the value is interpreted as a fraction
of ``min(in_features, out_features)``, and is converted to the
equivalent integer value, with a minimum of 1.
Raises:
ValueError:
If ``latent_features`` is not small enough for factorization
to reduce the number of multiply-add operations. In this regime,
factorization is both slower and less expressive than a
non-factorized operation. Setting
``latent_features < min(in_features, out_features) / 2`` or
using :meth:`~max_allowed_latent_features` is sufficient to avoid
this.
"""
def __init__(self,
in_features: int,
out_features: int,
bias: bool = True,
latent_features: Union[int, float] = .25):
super().__init__(in_size=in_features, out_size=out_features, latent_size=latent_features)
self.bias = bias
self.module0, self.module1 = self._create_child_modules()
def _create_child_modules(self) -> Tuple[torch.nn.Module, torch.nn.Module]:
if not self.should_factorize(self.latent_size):
raise ValueError(
f"latent_features {self.latent_size} is not small enough to merit factorization! Must be <= {self._max_rank_with_speedup()}"
)
module0 = nn.Linear(in_features=self.in_features, out_features=self.latent_size, bias=False)
module1 = nn.Linear(in_features=self.latent_size, out_features=self.out_features, bias=self.bias)
return module0, module1
# wrap shared fields in read-only properties matching the torch conv module API
@property
def in_features(self) -> int:
"""See :class:`torch.nn.Linear`."""
return self.in_size
@property
def out_features(self) -> int:
"""See :class:`torch.nn.Linear`."""
return self.out_size
@property
def latent_features(self) -> int:
"""The dimensionality of the space into which the input is projected by the first matrix in the
factorization."""
return self.latent_size
def solution_for_rank(self, input: torch.Tensor, rank: int) -> LowRankSolution:
assert isinstance(self.module0.weight, torch.Tensor)
assert isinstance(self.module1.weight, torch.Tensor)
assert isinstance(self.module1.bias, torch.Tensor)
weight0 = torch.transpose(self.module0.weight, 0, 1)
weight1 = torch.transpose(self.module1.weight, 0, 1)
bias1 = self.module1.bias
target = self(input)
return factorize_matrix(input, target, weight0, weight1, bias=bias1, rank=rank)
def apply_solution(self, solution: LowRankSolution) -> None:
self.latent_size = solution.rank
self.module0.out_features = solution.rank
self.module1.in_features = solution.rank
_apply_solution_to_module_parameters(solution, self.module0, self.module1, transpose=True)
[docs] @staticmethod
def max_allowed_latent_channels(in_features: int, out_features: int) -> int:
"""Returns the largest latent feature count that reduces the number of multiply-adds.
Args:
in_features: size of each input sample
out_features: size of each output sample
Returns:
latent_features: the largest allowable number of latent features
"""
return _max_rank_with_possible_speedup(in_features, out_features)
@staticmethod
def from_linear(module: torch.nn.Linear, module_ix: int = -1, **kwargs) -> FactorizedLinear:
ret = FactorizedLinear(in_features=module.in_features,
out_features=module.out_features,
bias=((module.bias is not None) and (module.bias is not False)),
**kwargs)
ret.reset_parameters()
return ret