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Remove the natural gradient stuff while keeping cosmetic changes.

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This commit is contained in:
Daniel Povey 2022-05-30 11:56:11 +08:00
parent 8a96f29a11
commit b01c09a693
2 changed files with 3 additions and 115 deletions
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115
egs/librispeech/ASR/pruned_transducer_stateless4/optim.py
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@ -61,20 +61,6 @@ class Cain(Optimizer):
and a 512x512 one. This does a better job of separating "important"
from "unimportant" directions in activation space, and empirically
improved convergence, final loss function and WERs.
(v) Change the Adam-type update, where the rms update value in each parameter
is the same, to a (diagonal) natural-gradient-type update, where if a
parameter has larger then average gradients, we give it a smaller
update. Because, in principle, this could lead to unbounded update
magnitudes, we limit these by introducing the "max_eff_lr" parameter,
which defines the maximum learning rate "if we had an Adam-type
update". So what we really implement is a cross between Adam and
natural gradient, where larger "max_eff_lr" means more natural-gradient-like
(i.e. more aggressive in directions with small gradients).
We recommend to set max_eff_lr to the initial learning rate ("lr")
in the learning rate schedule so that the update starts out
equivalent to Adam. Empirically this change to natural-gradient-type
update, epecially when combined with a faster-decaying learning rate
schedule, gives faster convergence.
The original Adam algorithm was proposed in `Adam: A Method for Stochastic Optimization`_.
The AdamW variant was proposed in `Decoupled Weight Decay Regularization`_.
@ -84,13 +70,6 @@ class Cain(Optimizer):
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-3)
max_eff_lr (float, optional): maximum effective learning rate for
natural-gradient update; this limits how aggressively we accelerate
directions with small gradients. The idea is that you might want to
leave this constant as the regular learning rate decreasess; but
we can investigate alternatives here. If you set this to <= 0,
it disables the natural-gradient aspect, giving a more ADAM-like
update (in changed co-ordinates)
betas (Tuple[float, float], optional): coefficients used for computing
running averages of gradient and its square (default: (0.9, 0.999))
eps (float, optional): term added to the denominator to improve
@ -122,7 +101,6 @@ class Cain(Optimizer):
self,
params,
lr=1e-3,
max_eff_lr=3e-3,
betas=(0.9, 0.98),
eps=1e-8,
target_rms=0.1,
@ -151,7 +129,6 @@ class Cain(Optimizer):
defaults = dict(
lr=lr,
max_eff_lr=max_eff_lr,
betas=betas,
eps=eps,
target_rms=target_rms,
@ -179,14 +156,11 @@ class Cain(Optimizer):
for group in self.param_groups:
beta1, beta2 = group["betas"]
lr = group["lr"]
max_eff_lr = group["max_eff_lr"]
target_rms = group["target_rms"]
rms_eps = group["rms_eps"]
eps = group["eps"]
rms_max = group["rms_max"]
assert lr <= max_eff_lr
for p in group["params"]:
if p.grad is None:
continue
@ -276,11 +250,8 @@ class Cain(Optimizer):
# Decay the second moment running average coefficient
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
if p.numel() > 1 and max_eff_lr > 0.0:
denom = self._get_denom(state, step, exp_avg_sq, bias_correction2,
eps, lr/max_eff_lr)
else:
denom = (exp_avg_sq.sqrt()).add_(eps)
denom = (exp_avg_sq.sqrt()).add_(eps)
this_delta = grad / denom
@ -302,88 +273,6 @@ class Cain(Optimizer):
return loss
def _get_denom(self,
state: dict,
step: int,
exp_avg_sq: Tensor,
bias_correction2: float,
eps: float,
beta: float):
"""
This function returns a "denominator" value that we'll divide the gradients by
before multiplying by -lr and applying momentum.
Args:
state: state-dict for this parameter, needed for its "alpha" member
step: the current step index
exp_avg_sq: Moving-average of gradient-squared for each element of the current
parameter matrix (possibly after a co-ordinate change).
bias_correction2: A value that will be normally 1.0, but will be less than 1.0
near the start of training or just after we re-estimated the co-ordinate
changes; we can divide exp_avg_sq by this to get an expected gradient-squared.
eps: Epsilon value that prevents division by zero; dimensionally, this is
a gradient magnitude (not squared-gradient magnitude).
beta: A value <= 1.0, e.g. 0.1; it equals lr / max_eff_lr, and represents
the inverse of the "maximum acceleration" we allow the natural gradient to
give, versus regular ADAM. Think of 1/beta as the maximum normalized
gradient root-mean-square value we allow.
We'll explain what this function does by comparing (i) basic ADAM-like updat,e
(ii) basic natural-gradient update, (iii) our update which combines properties
of both.
The basic ADAM-like version of this would be:
denom = (exp_avg_sq.sqrt()).add_(eps),
so after we divide the gradients by this, they will have unit expected squared value.
The natural-gradient version of this would be:
denom = (exp_avg_sq).add_(eps * eps)
base_denom = (exp_avg_sq.sqrt()).add_(eps),
denom = denom * (base_denom / denom).mean()
what this does is: compute 'denom' with no sqrt(), and then scale it in such
a way that ([root-mean-square gradient magnitude] / denom).mean() == 1.0, so
the overall learning speed is about the same as the baseline.
We will be returning:
denom = alpha * (exp_avg_sq) + beta * exp_avg_sq.sqrt() + eps
and are aiming for alpha to satisfy the following condition:
((exp_avg_sq.sqrt() + eps) / denom).mean() == 1.0 (eqn:1)
... (eqn:1) means that the overall learning rate / "rate of progress"
is about the same as if denom was just (exp_avg_sq.sqrt() + eps). Also,
the beta term in "denom" ensures that:
(1/denom) <= 1/beta * (1/adam_denom)
which ensures that the speed of update for any given element will never
be greater than the normal ADAM-type update by more than 1/beta.
The way we update alpha is as follows. We always have the previous iteration's
alpha, call this alpha_prev. We compute:
denom_prev = (alpha_prev * exp_avg_sq) + beta * exp_avg_sq.sqrt() + eps
and:
mean_prev = (exp_avg_sq.sqrt() + eps) / denom).mean()
.. now, mean_prev varies *at most* like 1/alpha, meaning its maximum sensitivity
to alpha is an inverse relationship. So we we update alpha as:
alpha_cur = alpha_prev * mean_prev
(the idea is that this will eventually converge; and meanwhile, we'll just have
a slightly inaccurate alpha). If `step` is large, we'll assume alpha has converged
and always return the denominator with the old alpha.
"""
num_steps = 10 if step < 3 else 2 if step < 100 else 1
for _ in range(num_steps):
# our update for alpha is iterative since there isn't a closed-form solution.
alpha = state["alpha"]
adam_denom = exp_avg_sq.sqrt()
denom = alpha * exp_avg_sq + beta * adam_denom + eps
mean_speed = ((adam_denom + eps) / denom).mean()
alpha.fill_(alpha * mean_speed)
return denom
def _change_coordinates(self,
grad: Tensor,
state: dict,

3
egs/librispeech/ASR/pruned_transducer_stateless4/train.py
View File

@ -872,8 +872,7 @@ def run(rank, world_size, args):
logging.info("Using DDP")
model = DDP(model, device_ids=[rank])
optimizer = Cain(model.parameters(), lr=params.initial_lr,
max_eff_lr=params.initial_lr)
optimizer = Cain(model.parameters(), lr=params.initial_lr)
scheduler = Eden(optimizer, params.lr_batches, params.lr_epochs)