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SM3.py
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SM3.py
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# Copyright 2020 Eleanor Holland
# SPDX-License-Identifier: Apache-2.0
import torch
from torch.optim import Optimizer
class SM3(Optimizer):
"""Implements SM3 algorithm.
It has been proposed in `Memory-Efficient Adaptive Optimization`_.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): coefficient that scale delta before it is applied
to the parameters (default: 0.1)
momentum (float, optional): coefficient used to scale prior updates
before adding. This drastically increases memory usage if
`momentum > 0.0`. This is ignored if the parameter's gradient
is sparse. (default: 0.0)
beta (float, optional): coefficient used for exponential moving
averages (default: 0.0)
eps (float, optional): Term added to square-root in denominator to
improve numerical stability (default: 1e-30)
.. _Memory-Efficient Adaptive Optimization:
https://arxiv.org/abs/1901.11150
"""
def __init__(self, params, lr=0.1, momentum=0.0, beta=0.0, eps=1e-30):
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {0}".format(lr))
if not 0.0 <= momentum < 1.0:
raise ValueError("Invalid momentum: {0}".format(momentum))
if not 0.0 <= beta < 1.0:
raise ValueError("Invalid beta: {0}".format(beta))
if not 0.0 <= eps:
raise ValueError("Invalid eps: {0}".format(eps))
defaults = {'lr': lr, 'momentum': momentum, 'beta': beta, 'eps': eps}
super(SM3, self).__init__(params, defaults)
@torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
momentum = group['momentum']
beta = group['beta']
eps = group['eps']
for p in group['params']:
grad = p.grad
if p is None or grad is None:
continue
state = self.state[p]
shape = grad.shape
rank = len(shape)
# State initialization
if len(state) == 0:
state['step'] = 0
state['momentum_buffer'] = 0.
_add_initial_accumulators(state, grad)
if grad.is_sparse:
# the update is non-linear so indices must be unique
grad.coalesce()
grad_indices = grad._indices()
grad_values = grad._values()
# Transform update_values into sparse tensor
def make_sparse(values):
constructor = grad.new
if grad_indices.dim() == 0 or values.dim() == 0:
return constructor().resize_as_(grad)
return constructor(grad_indices, values, grad.size())
acc = state[_key(0)]
update_values = _compute_sparse_update(beta, acc, grad_values, grad_indices)
self._update_sparse_accumulator(beta, acc, make_sparse(update_values))
# Add small amount for numerical stability
update_values.add_(eps).rsqrt_().mul_(grad_values)
update = make_sparse(update_values)
else:
# Get previous accumulators mu_{t-1}
if rank > 1:
acc_list = [state[_key(i)] for i in range(rank)]
else:
acc_list = [state[_key(0)]]
# Get update from accumulators and gradients
update = _compute_update(beta, acc_list, grad)
# Update accumulators.
self._update_accumulator(beta, acc_list, update)
# Add small amount for numerical stability
update.add_(eps).rsqrt_().mul_(grad)
if momentum > 0.:
m = state['momentum_buffer']
update.mul_(1. - momentum).add_(m, alpha=momentum)
state['momentum_buffer'] = update.detach()
p.sub_(update, alpha=group['lr'])
state['step'] += 1
return loss
def _update_accumulator(self, beta, acc_list, update):
for i, acc in enumerate(acc_list):
nu_max = _max_reduce_except_dim(update, i)
if beta > 0.:
torch.max(acc, nu_max, out=acc)
else:
# No need to compare - nu_max is bigger because of grad ** 2
acc.copy_(nu_max)
def _update_sparse_accumulator(self, beta, acc, update):
nu_max = _max_reduce_except_dim(update.to_dense(), 0).squeeze()
if beta > 0.:
torch.max(acc, nu_max, out=acc)
else:
# No need to compare - nu_max is bigger because of grad ** 2
acc.copy_(nu_max)
def _compute_sparse_update(beta, acc, grad_values, grad_indices):
# In the sparse case, a single accumulator is used.
update_values = torch.gather(acc, 0, grad_indices[0])
if beta > 0.:
update_values.mul_(beta)
update_values.addcmul_(grad_values, grad_values, value=1. - beta)
return update_values
def _compute_update(beta, acc_list, grad):
rank = len(acc_list)
update = acc_list[0].clone()
for i in range(1, rank):
# We rely on broadcasting to get the proper end shape.
update = torch.min(update, acc_list[i])
if beta > 0.:
update.mul_(beta)
update.addcmul_(grad, grad, value=1. - beta)
return update
def _key(i):
# Returns key used for accessing accumulators
return 'accumulator_' + str(i)
def _add_initial_accumulators(state, grad):
# Creates initial accumulators. For a dense tensor of shape (n1, n2, n3),
# then our initial accumulators are of shape (n1, 1, 1), (1, n2, 1) and
# (1, 1, n3). For a sparse tensor of shape (n, *), we use a single
# accumulator of shape (n,).
shape = grad.shape
rank = len(shape)
defaults = {'device': grad.device, 'dtype': grad.dtype}
acc = {}
if grad.is_sparse:
acc[_key(0)] = torch.zeros(shape[0], **defaults)
elif rank == 0:
# The scalar case is handled separately
acc[_key(0)] = torch.zeros(shape, **defaults)
else:
for i in range(rank):
acc_shape = [1] * i + [shape[i]] + [1] * (rank - 1 - i)
acc[_key(i)] = torch.zeros(acc_shape, **defaults)
state.update(acc)
def _max_reduce_except_dim(tensor, dim):
# Computes max along all dimensions except the given dim.
# If tensor is a scalar, it returns tensor.
rank = len(tensor.shape)
result = tensor
if rank > 0:
assert dim < rank
for d in range(rank):
if d != dim:
result = result.max(dim=d, keepdim=True).values
return result