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kfac.py
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import math
import torch
import torch.optim as optim
from utils.kfac_utils import (ComputeCovA, ComputeCovG)
from utils.kfac_utils import update_running_stat
class KFACOptimizer(optim.Optimizer):
def __init__(self,
model,
lr=0.001,
momentum=0.9,
stat_decay=0.95,
damping=0.001,
kl_clip=0.001,
weight_decay=0,
TCov=10,
TInv=100,
batch_averaged=True):
if lr < 0.0:
raise ValueError("Invalid learning rate: {}".format(lr))
if momentum < 0.0:
raise ValueError("Invalid momentum value: {}".format(momentum))
if weight_decay < 0.0:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = dict(lr=lr, momentum=momentum, damping=damping,
weight_decay=weight_decay)
# TODO (CW): KFAC optimizer now only support model as input
super(KFACOptimizer, self).__init__(model.parameters(), defaults)
self.CovAHandler = ComputeCovA()
self.CovGHandler = ComputeCovG()
self.batch_averaged = batch_averaged
self.known_modules = {'Linear', 'Conv2d'}
self.modules = []
self.grad_outputs = {}
self.model = model
self._prepare_model()
self.steps = 0
self.m_aa, self.m_gg = {}, {}
self.Q_a, self.Q_g = {}, {}
self.d_a, self.d_g = {}, {}
self.stat_decay = stat_decay
self.kl_clip = kl_clip
self.TCov = TCov
self.TInv = TInv
def _save_input(self, module, input):
if torch.is_grad_enabled() and self.steps % self.TCov == 0:
aa = self.CovAHandler(input[0].data, module)
# Initialize buffers
if self.steps == 0:
self.m_aa[module] = torch.diag(aa.new(aa.size(0)).fill_(1))
update_running_stat(aa, self.m_aa[module], self.stat_decay)
def _save_grad_output(self, module, grad_input, grad_output):
# Accumulate statistics for Fisher matrices
if self.acc_stats and self.steps % self.TCov == 0:
gg = self.CovGHandler(grad_output[0].data, module, self.batch_averaged)
# Initialize buffers
if self.steps == 0:
self.m_gg[module] = torch.diag(gg.new(gg.size(0)).fill_(1))
update_running_stat(gg, self.m_gg[module], self.stat_decay)
def _prepare_model(self):
count = 0
print(self.model)
print("=> We keep following layers in KFAC. ")
for module in self.model.modules():
classname = module.__class__.__name__
# print('=> We keep following layers in KFAC. <=')
if classname in self.known_modules:
self.modules.append(module)
module.register_forward_pre_hook(self._save_input)
module.register_backward_hook(self._save_grad_output)
print('(%s): %s' % (count, module))
count += 1
def _update_inv(self, m):
"""Do eigen decomposition for computing inverse of the ~ fisher.
:param m: The layer
:return: no returns.
"""
eps = 1e-10 # for numerical stability
self.d_a[m], self.Q_a[m] = torch.symeig(
self.m_aa[m], eigenvectors=True)
self.d_g[m], self.Q_g[m] = torch.symeig(
self.m_gg[m], eigenvectors=True)
self.d_a[m].mul_((self.d_a[m] > eps).float())
self.d_g[m].mul_((self.d_g[m] > eps).float())
@staticmethod
def _get_matrix_form_grad(m, classname):
"""
:param m: the layer
:param classname: the class name of the layer
:return: a matrix form of the gradient. it should be a [output_dim, input_dim] matrix.
"""
if classname == 'Conv2d':
p_grad_mat = m.weight.grad.data.view(m.weight.grad.data.size(0), -1) # n_filters * (in_c * kw * kh)
else:
p_grad_mat = m.weight.grad.data
if m.bias is not None:
p_grad_mat = torch.cat([p_grad_mat, m.bias.grad.data.view(-1, 1)], 1)
return p_grad_mat
def _get_natural_grad(self, m, p_grad_mat, damping):
"""
:param m: the layer
:param p_grad_mat: the gradients in matrix form
:return: a list of gradients w.r.t to the parameters in `m`
"""
# p_grad_mat is of output_dim * input_dim
# inv((ss')) p_grad_mat inv(aa') = [ Q_g (1/R_g) Q_g^T ] @ p_grad_mat @ [Q_a (1/R_a) Q_a^T]
v1 = self.Q_g[m].t() @ p_grad_mat @ self.Q_a[m]
v2 = v1 / (self.d_g[m].unsqueeze(1) * self.d_a[m].unsqueeze(0) + damping)
v = self.Q_g[m] @ v2 @ self.Q_a[m].t()
if m.bias is not None:
# we always put gradient w.r.t weight in [0]
# and w.r.t bias in [1]
v = [v[:, :-1], v[:, -1:]]
v[0] = v[0].view(m.weight.grad.data.size())
v[1] = v[1].view(m.bias.grad.data.size())
else:
v = [v.view(m.weight.grad.data.size())]
return v
def _kl_clip_and_update_grad(self, updates, lr):
# do kl clip
vg_sum = 0
for m in self.modules:
v = updates[m]
vg_sum += (v[0] * m.weight.grad.data * lr ** 2).sum().item()
if m.bias is not None:
vg_sum += (v[1] * m.bias.grad.data * lr ** 2).sum().item()
nu = min(1.0, math.sqrt(self.kl_clip / vg_sum))
for m in self.modules:
v = updates[m]
m.weight.grad.data.copy_(v[0])
m.weight.grad.data.mul_(nu)
if m.bias is not None:
m.bias.grad.data.copy_(v[1])
m.bias.grad.data.mul_(nu)
def _step(self, closure):
# FIXME (CW): Modified based on SGD (removed nestrov and dampening in momentum.)
# FIXME (CW): 1. no nesterov, 2. buf.mul_(momentum).add_(1 <del> - dampening </del>, d_p)
for group in self.param_groups:
weight_decay = group['weight_decay']
momentum = group['momentum']
for p in group['params']:
if p.grad is None:
continue
d_p = p.grad.data
if weight_decay != 0 and self.steps >= 20 * self.TCov:
d_p.add_(weight_decay, p.data)
if momentum != 0:
param_state = self.state[p]
if 'momentum_buffer' not in param_state:
buf = param_state['momentum_buffer'] = torch.zeros_like(p.data)
buf.mul_(momentum).add_(d_p)
else:
buf = param_state['momentum_buffer']
buf.mul_(momentum).add_(1, d_p)
d_p = buf
p.data.add_(-group['lr'], d_p)
def step(self, closure=None):
# FIXME(CW): temporal fix for compatibility with Official LR scheduler.
group = self.param_groups[0]
lr = group['lr']
damping = group['damping']
updates = {}
for m in self.modules:
classname = m.__class__.__name__
if self.steps % self.TInv == 0:
self._update_inv(m)
p_grad_mat = self._get_matrix_form_grad(m, classname)
v = self._get_natural_grad(m, p_grad_mat, damping)
updates[m] = v
self._kl_clip_and_update_grad(updates, lr)
self._step(closure)
self.steps += 1