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Version that is passing the tests

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Daniel Povey 2022-06-14 20:45:57 +08:00
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commit c6f62dfc08
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egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
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@ -43,12 +43,14 @@ class NeutralGradient(Optimizer):
at 0.03 and decreases over time, i.e. much higher than other common at 0.03 and decreases over time, i.e. much higher than other common
optimizers. optimizers.
beta: Momentum constants for regular momentum, and stats of gradients. beta: Momentum constants for regular momentum, and stats of gradients.
eps: An epsilon to prevent division by zero
scale_speed: This scales the learning rate for purposes of learning the overall scale scale_speed: This scales the learning rate for purposes of learning the overall scale
of each tensor of each tensor
rms_eps: An epsilon on the rms value of the parameter, such that when the parameter eps: An epsilon to prevent division by zero
param_eps: An epsilon on the rms value of the parameter, such that when the parameter
gets smaller than this we'll start using a fixed learning rate, not gets smaller than this we'll start using a fixed learning rate, not
decreasing with the parameter norm. decreasing with the parameter norm.
cond_eps: An epsilon that limits the condition number of gradient and parameter
covariance matrices
param_max: To prevent parameter tensors getting too large, we will clip elements to param_max: To prevent parameter tensors getting too large, we will clip elements to
-param_max..param_max. -param_max..param_max.
max_size: We will only use the full-covariance (not-diagonal) update for max_size: We will only use the full-covariance (not-diagonal) update for
@ -64,9 +66,10 @@ class NeutralGradient(Optimizer):
params, params,
lr=1e-2, lr=1e-2,
betas=(0.9, 0.98, 0.99), betas=(0.9, 0.98, 0.99),
eps=1e-8,
scale_speed=0.05, scale_speed=0.05,
rms_eps=1.0e-05, eps=1e-8,
param_eps=1.0e-05,
cond_eps=1.0e-08,
param_max=10.0, param_max=10.0,
max_size=1023, max_size=1023,
stats_period=1, stats_period=1,
@ -91,8 +94,8 @@ class NeutralGradient(Optimizer):
) )
if not 0 < scale_speed < 1.0: if not 0 < scale_speed < 1.0:
raise ValueError("Invalid scale_speed value: {}".format(scale_speed)) raise ValueError("Invalid scale_speed value: {}".format(scale_speed))
if not 0.0 < rms_eps < 0.1: if not 0.0 < param_eps < 0.1:
raise ValueError("Invalid rms_eps value: {}".format(rms_eps)) raise ValueError("Invalid param_eps value: {}".format(param_eps))
if not 0.1 < param_max <= 10000.0: if not 0.1 < param_max <= 10000.0:
raise ValueError("Invalid param_max value: {}".format(param_max)) raise ValueError("Invalid param_max value: {}".format(param_max))
if not stats_period > 0: if not stats_period > 0:
@ -106,7 +109,8 @@ class NeutralGradient(Optimizer):
betas=betas, betas=betas,
eps=eps, eps=eps,
scale_speed=0.05, scale_speed=0.05,
rms_eps=rms_eps, param_eps=param_eps,
cond_eps=cond_eps,
param_max=param_max, param_max=param_max,
max_size=max_size, max_size=max_size,
stats_period=stats_period, stats_period=stats_period,
@ -135,7 +139,7 @@ class NeutralGradient(Optimizer):
beta1, beta2, beta3 = group["betas"] beta1, beta2, beta3 = group["betas"]
lr = group["lr"] lr = group["lr"]
scale_speed = group["scale_speed"] scale_speed = group["scale_speed"]
rms_eps = group["rms_eps"] param_eps = group["param_eps"]
eps = group["eps"] eps = group["eps"]
param_max = group["param_max"] param_max = group["param_max"]
max_size = group["max_size"] max_size = group["max_size"]
@ -163,15 +167,18 @@ class NeutralGradient(Optimizer):
p, memory_format=torch.preserve_format p, memory_format=torch.preserve_format
) )
# Exponential moving average of squared gradient value # Exponential moving average of squared gradient value
# after all multiplications. This is used to help state["exp_avg_sq"] = torch.zeros_like(p)
# determine the scalar factor in the update size. It is
# resert after every `estimate_period` minibatches.
kwargs = {'device':p.device, 'dtype':p.dtype} kwargs = {'device':p.device, 'dtype':p.dtype}
if p.numel() > 1: if p.numel() > 1:
state["scalar_exp_avg_sq"] = torch.zeros((), **kwargs)
is_one_axis = (p.numel() in list(p.shape)) # e.g. a bias is_one_axis = (p.numel() in list(p.shape)) # e.g. a bias
if not is_one_axis:
state["ref_exp_avg_sq"] = torch.ones_like(p)
else:
state["param_rms"] = torch.zeros((), **kwargs)
# we learn the scale on the parameters in a way that # we learn the scale on the parameters in a way that
# also emulates Eve. scale_exp_avg_sq is the # also emulates Eve. scale_exp_avg_sq is the
@ -179,14 +186,6 @@ class NeutralGradient(Optimizer):
# scalar scale. # scalar scale.
state["scale_exp_avg_sq"] = torch.zeros((), **kwargs) state["scale_exp_avg_sq"] = torch.zeros((), **kwargs)
state["param_rms"] = torch.zeros((), **kwargs)
# TODO: may have to add some special stuff here if
if is_one_axis:
state["exp_avg_sq"] = torch.zeros_like(p)
else:
state["scalar_exp_avg_sq"] = torch.zeros((), **kwargs)
for dim in range(p.ndim): for dim in range(p.ndim):
size = p.shape[dim] size = p.shape[dim]
if size == 1 or size == p.numel(): if size == 1 or size == p.numel():
@ -195,15 +194,12 @@ class NeutralGradient(Optimizer):
elif size > max_size: elif size > max_size:
# diagonal only... # diagonal only...
state[f"grad_cov_{dim}"] = torch.zeros(size, **kwargs) state[f"grad_cov_{dim}"] = torch.zeros(size, **kwargs)
state[f"proj_{dim}"] = torch.zeros(size, **kwargs) state[f"proj_{dim}"] = torch.ones(size, **kwargs)
else: else:
state[f"grad_cov_{dim}"] = torch.zeros(size, size, state[f"grad_cov_{dim}"] = torch.zeros(size, size,
**kwargs) **kwargs)
state[f"proj_{dim}"] = torch.zeros(size, size, state[f"proj_{dim}"] = torch.eye(size, **kwargs)
**kwargs)
else:
# p.numel() == 1: scalar parameter
state["exp_avg_sq"] = torch.zeros_like(p)
delta = state["delta"] delta = state["delta"]
step = state["step"] step = state["step"]
@ -240,44 +236,62 @@ class NeutralGradient(Optimizer):
delta.add_(p, alpha=scale_delta) delta.add_(p, alpha=scale_delta)
param_rms = state["param_rms"] exp_avg_sq = state["exp_avg_sq"]
if step % 10 == 0: # Decay the second moment running average coefficient
param_rms.copy_((p**2).mean().sqrt()) exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
bias_correction2 = 1 - beta2 ** (step + 1)
if is_one_axis: if is_one_axis:
exp_avg_sq = state["exp_avg_sq"] param_rms = state["param_rms"]
# Decay the second moment running average coefficient if step % 10 == 0:
exp_avg_sq.mul_(beta3).addcmul_(grad, grad, value=1 - beta3) param_rms.copy_((p**2).mean().sqrt())
bias_correction2 = 1 - beta3 ** (step + 1)
grad_rms = (exp_avg_sq.sqrt()).add_(eps) grad_rms = (exp_avg_sq.sqrt()).add_(eps)
this_delta = grad / grad_rms this_delta = grad / grad_rms
alpha = (-(1-beta1) * lr * bias_correction2) * param_rms.clamp(min=param_eps)
alpha = (-(1-beta1) * lr * bias_correction2) * param_rms.clamp(min=rms_eps)
delta.add_(this_delta, alpha=alpha) delta.add_(this_delta, alpha=alpha)
# below, will do: delta.add_(this_delta, alpha=alpha)
else: else:
# The full update. # The full update.
conditioned_grad = self._precondition_grad(p, grad, state, beta3, max_size, # First, if needed, accumulate per-dimension stats from the grad
stats_period, estimate_period, if step % stats_period == 0:
eps, rms_eps) self._accumulate_per_dim_stats(grad, state, beta3, eps)
scalar_exp_avg_sq = state["scalar_exp_avg_sq"]
grad_sq = (grad**2).mean()
conditioned_grad_sq = (conditioned_grad**2).mean()
prod = (grad*conditioned_grad).mean()
cos_angle = prod / (grad_sq * conditioned_grad_sq).sqrt()
if random.random() < 0.001 or cos_angle < 0.0075:
print(f"cos_angle = {cos_angle}, shape={grad.shape}")
#assert grad_sq - grad_sq == 0 if step % estimate_period == 0 or step in [50, 200, 400]:
#assert conditioned_grad_sq - conditioned_grad_sq == 0 self._estimate(p, state, beta3, max_size,
scalar_exp_avg_sq.mul_(beta2).add_(grad_sq, alpha=(1-beta2)) stats_period, estimate_period,
bias_correction2 = 1 - beta2 ** (step + 1) eps, param_eps)
avg_grad_sq = scalar_exp_avg_sq / bias_correction2
scale = param_rms.clamp(min=rms_eps) * (grad_sq / ((avg_grad_sq * conditioned_grad_sq) + 1.0e-20)).sqrt() ref_exp_avg_sq = state["ref_exp_avg_sq"] # computed in self._estimate()
alpha = -lr * (1-beta1) * scale
delta.add_(conditioned_grad, alpha=alpha) # do ** 0.25, not ** 0.5, because we divide this into two factors:
# one to be applied before the grad preconditioning, and one after.
# This keeps the overall transformation on the gradient symmetric
# (if viewed as a matrix of shape (p.numel(), p.numel())
# Note: ref_exp_avg_sq had eps*eps added to it when we created it.
grad_scale = (ref_exp_avg_sq / (exp_avg_sq/bias_correction2 + eps*eps)) ** 0.25
#print(f"grad_scale mean = {grad_scale.mean()}, shape = {p.shape}")
cur_grad = grad * grad_scale
cur_grad = self._precondition_grad(cur_grad, state)
cur_grad *= grad_scale
if True: # testing
# in principle, the cur_grad is supposed to have the same rms as params, on average.
cur_grad_rms = (cur_grad**2).mean().sqrt()
param_rms = (p**2).mean().sqrt()
#print(f"cur_grad_rms={cur_grad_rms}, param_rms={param_rms}")
if random.random() < 0.1:
prod = (grad*cur_grad).mean()
cos_angle = prod / ((grad**2).mean() * (cur_grad**2).mean()).sqrt()
if random.random() < 0.01 or cos_angle < 0.0075:
print(f"cos_angle = {cos_angle}, shape={grad.shape}")
alpha = -lr * (1-beta1)
delta.add_(cur_grad, alpha=alpha)
else: else:
# p.numel() == 1 # p.numel() == 1
# Decay the second moment running average coefficient # Decay the second moment running average coefficient
@ -301,18 +315,135 @@ class NeutralGradient(Optimizer):
return loss return loss
def _precondition_grad(self, def _accumulate_per_dim_stats(self,
p: Tensor, grad: Tensor,
grad: Tensor, state: dict,
state: dict, beta3: float,
beta3: float, eps: float) -> None:
max_size: int, """
stats_period: int, Accumulate some stats for each dimension of the tensor, about the covariance of gradients.
estimate_period: int, """
eps: float, ndim = grad.ndim
rms_eps: float for dim in range(ndim):
size = grad.shape[dim]
if size == 1:
continue
grad_cov = state[f"grad_cov_{dim}"]
if grad_cov.ndim == 1:
# We are treating this dimension diagonally because it is too big.
other_dims = [ i for i in range(ndim) if i != dim]
grad_cov.mul_(beta3).add_((grad**2).mean(dim=other_dims))
else:
# full-covariance stats.
this_beta3 = self._get_this_beta3(beta3, grad.numel(), size)
grad_cov.mul_(this_beta3).add_(self._get_cov(grad, dim),
alpha=(1.0-this_beta3))
def _estimate(self,
p: Tensor,
state: dict,
beta3: float,
max_size: int,
stats_period: int,
estimate_period: int,
eps: float,
param_eps: float
) -> Tensor: ) -> Tensor:
""" """
Estimate the per-dimension projections proj_0, proj_1 and so on, and
ref_exp_avg_sq.
"""
kwargs = {'device':p.device, 'dtype':p.dtype}
ref_exp_avg_sq = torch.ones([1] * p.ndim, **kwargs)
ndim = p.ndim
step = state["step"]
assert step % stats_period == 0
norm_step = step // stats_period
def update_ref_exp_avg_sq(ref_exp_avg_sq, grad_cov_smoothed, dim):
"""
Updates ref_exp_avg_sq, taking into account `grad_cov_smoothed` which is
a tensor of shape (p.shape[dim],) containing the smoothed diagonal covariance
of grads for dimension `dim`.
Returns new ref_exp_avg_sq
"""
if dim > 0:
# We only want to "count" the overall scale of the gradients' variance
# (i.e. mean variance) once, so for all dims other than 0 we normalize
# this out.
grad_cov_smoothed = grad_cov_smoothed / grad_cov_smoothed.mean()
for _ in range(dim + 1, ndim):
grad_cov_smoothed = grad_cov_smoothed.unsqueeze(-1)
return ref_exp_avg_sq * grad_cov_smoothed
for dim in range(ndim):
size = p.shape[dim]
if size == 1:
continue
grad_cov = state[f"grad_cov_{dim}"]
proj = state[f"proj_{dim}"]
if grad_cov.ndim == 1:
# This dim is treated diagonally, because it is too large.
other_dims = [ i for i in range(ndim) if i != dim]
bias_correction3 = 1 - beta3 ** (norm_step + 1)
# _smoothed means we have the eps terms.
param_var_smoothed = (p**2).mean(dim=other_dims) + param_eps*param_eps
if bias_correction3 < 0.9999:
grad_cov = grad_cov / bias_correction3
grad_var_smoothed = grad_cov + eps*eps
ref_exp_avg_sq = update_ref_exp_avg_sq(ref_exp_avg_sq,
grad_var_smoothed,
dim)
if dim != 0:
# If dim != 0, make the grad_var_smoothed and
# param_var_smoothed have the same mean, because when
# preconditioning gradients, we only want to count the
# overall change in scale once.
grad_var_smoothed *= (param_var_smoothed.sum() / grad_var_smoothed.sum())
proj[:] = (param_var_smoothed / grad_var_smoothed).sqrt()
else:
param_cov_smoothed = self._estimate_and_smooth_param_cov(p, dim,
param_eps)
grad_cov_smoothed = self._smooth_grad_cov(p, grad_cov,
eps, norm_step,
beta3)
ref_exp_avg_sq = update_ref_exp_avg_sq(ref_exp_avg_sq,
grad_cov_smoothed.diag(),
dim)
if dim != 0:
# If dim != 0, make the traces of grad_cov_smoothed and
# param_cov_smoothed be the same, because when
# preconditioning gradients, we only want to count the
# overall change in scale once.
grad_cov_smoothed *= (param_cov_smoothed.diag().sum() /
grad_cov_smoothed.diag().sum())
proj[:] = self._estimate_proj(grad_cov_smoothed,
param_cov_smoothed)
state["ref_exp_avg_sq"][:] = ref_exp_avg_sq
def _get_this_beta3(self, beta3: float, numel: int, size: int):
"""
Get a discounting value beta3 (e.g. 0.99) that is used in computing moving
averages of stats. The idea is that the stats are accumulated from a tensor
x that has `numel` elements and `size == x.shape[dim]`, and we want the covariance
of shape (dim, dim). We may need to make beta3 closer to 1 if this means
we'll be getting only very rank-deficient stats each time.
"""
rank_per_iter = numel // size # maximum rank of each iteration's covaraince
safety_factor = 4.0 # should be > 1.0
grad_num_steps_needed = safety_factor * size / rank_per_iter
return max(beta3, 1 - 1. / grad_num_steps_needed)
def _precondition_grad(self,
grad: Tensor,
state: dict) -> Tensor:
"""
Multiply the grad by a positive-semidefinite matrix for each dimension, to Multiply the grad by a positive-semidefinite matrix for each dimension, to
try to make its covariance the same as that of the parameters (up to a try to make its covariance the same as that of the parameters (up to a
scalar constant). scalar constant).
@ -329,67 +460,110 @@ class NeutralGradient(Optimizer):
""" """
cur_grad = grad cur_grad = grad
ndim = grad.ndim
step = state["step"] step = state["step"]
for dim in range(p.ndim): for dim in range(ndim):
size = p.shape[dim] size = grad.shape[dim]
if size == 1: if size == 1:
continue continue
grad_cov = state[f"grad_cov_{dim}"]
proj = state[f"proj_{dim}"] proj = state[f"proj_{dim}"]
if size > max_size: if proj.ndim == 1:
# We are treating this dimension diagonally because it is too big. # We are treating this dimension diagonally because it is too big.
if step % stats_period == 0 or step < 100: proj = proj.reshape(size, *([1] * (ndim-1-dim)))
# for diagonal dims, both re-estimate stats and re-estimate
# transform every `stats_period`, as the re-estimation is
# easy.
other_dims = [ i for i in range(p.ndim) if i != dim]
grad_cov.mul_(beta3).add_((grad**2).mean(dim=other_dims))
# estimate param_var, the variance of the parameters.
param_var = (p**2).mean(dim=other_dims)
factor = ((param_var + rms_eps*rms_eps) / (grad_cov + eps*eps)).sqrt()
# normalize these factors to stop preconditioned-grad mean from getting
# very large or small
factor = factor / factor.mean()
proj[:] = factor
proj = proj.reshape(size, *([1] * (p.ndim-1-dim)))
cur_grad = cur_grad * proj cur_grad = cur_grad * proj
else: else:
# This dimension gets the full-covariance treatment.
grad_num_points = grad.numel() // size
grad_num_steps_needed = 4 * size / grad_num_points
if step % stats_period == 0 or step < 100:
# normally use beta3 for the decay of the decaying-average
# gradient stats, but we may use a value closer to 1 if we
# have to estimate a high-dimensional gradient from very
# low-rank covariance contributions.
this_beta3 = max(beta3, 1 - 1. / grad_num_steps_needed)
grad_cov.mul_(this_beta3).add_(self._get_cov(grad, dim),
alpha=(1.0-this_beta3))
if step % estimate_period == 0 or (step < estimate_period and step in [10,40]):
# Estimate the parameter covariance on this dimension,
# treating the other dimensions of the parameter as we would
# frames. Smooth with the diagonal because there are not
# many points to estimate the covariance from.
param_cov = self._get_cov(p, dim)
min_diag = 0.2
if True: # Smooth parameter
num_points = p.numel() // size
# later we may be able to find a more principled formula for this.
diag_smooth = max(min_diag, dim / (dim + num_points))
diag = param_cov.diag()
param_cov.mul_(1-diag_smooth).add_((diag*diag_smooth+ rms_eps*rms_eps).diag())
if True:
diag_smooth = min_diag # This is likely far from optimal!
diag = grad_cov.diag()
grad_cov = grad_cov * (1-diag_smooth) + (diag*diag_smooth + eps*eps).diag()
proj[:] = self._estimate_proj(grad_cov, param_cov)
cur_grad = self._multiply_on_dim(cur_grad, proj, dim) cur_grad = self._multiply_on_dim(cur_grad, proj, dim)
return cur_grad return cur_grad
def _estimate_and_smooth_param_cov(self, p: Tensor, dim: int,
param_eps: float,
cond_eps: float = 1.0e-10,
min_diag_smooth: float = 0.2) -> Tensor:
"""
Compute a smoothed version of a covariance matrix for one dimension of
a parameter tensor, estimated by treating the other
dimensions as a batch index.
p: The parameter tensor from which we are estimating the covariance
dim: The dimenion that we want the covariances for.
param_eps: A small epsilon value that represents the minimum root-mean-square
parameter value that we'll estimate.
cond_eps: An epsilon value that limits the condition number of the resulting
matrix. Caution: this applies to the variance, not the rms value,
so should be quite small.
Returns:
A non-singular covariance matrix of shape (p.shape[dim], p.shape[dim])
"""
p = p.transpose(dim, -1)
p = p.reshape(-1, p.shape[-1])
(num_outer_products, size) = p.shape
param_cov = torch.matmul(p.t(), p) / p.shape[0]
# later we may be able to find a more principled formula for this.
diag_smooth = max(min_diag_smooth, size / (size + num_outer_products))
diag = param_cov.diag()
extra_diag = (diag * diag_smooth) + (diag.max() * cond_eps +
param_eps * param_eps)
param_cov.mul_(1-diag_smooth).add_(extra_diag.diag())
return param_cov
def _smooth_grad_cov(self,
p: Tensor,
grad_cov: Tensor,
eps: float,
norm_step: int,
beta3: float,
cond_eps: float = 1.0e-10,
min_diag_smooth: float = 0.2) -> Tensor:
"""
Compute a smoothed version of a covariance matrix for one dimension of
a gradient tensor. The covariance stats are supplied; this function
is responsible for making sure it is nonsingular and smoothed with its
diagonal in a reasonably smart way.
p: The parameter tensor from which we are estimating the covariance
of the gradient (over one of its dimensions); only needed for the shape
grad_cov: The moving-average covariance statistics, to be smoothed
eps: An epsilon value that represents a root-mean-square gradient
magnitude, used to avoid zero values
norm_step: The step count that reflects how many times we updated
grad_cov, we assume we have updated it (norm_step + 1) times; this
is just step divided by stats_perio.
beta3: The user-supplied beta value for decaying the gradient covariance
stats
cond_eps: An epsilon value that limits the condition number of the resulting
matrix. Caution: this applies to the variance, not the rms value,
so should be quite small.
min_diag_smooth: A minimum proportion by which we smooth the covariance
with the diagonal.
Returns:
A non-singular covariance matrix of gradients, of shape (p.shape[dim], p.shape[dim])
"""
size = grad_cov.shape[0]
this_beta3 = self._get_this_beta3(beta3, p.numel(), size)
bias_correction3 = 1 - this_beta3 ** (norm_step + 1)
if bias_correction3 < 0.9999:
grad_cov = grad_cov / bias_correction3
rank_per_iter = p.numel() // size # maximum rank of each iteration's covaraince
# the second part of the following formula roughly represents the number of
# frames that have a "large" weight in the stats.
num_iters_in_stats = min(norm_step + 1, 1.0 / (1 - beta3))
# grad_cov_rank is generally suposed to represent the number of
# individual outer products that are represented with significant weight
# in grad_cov
num_outer_products = rank_per_iter * num_iters_in_stats
diag_smooth = max(min_diag_smooth,
size / (size + num_outer_products))
diag = grad_cov.diag()
extra_diag = (diag * diag_smooth) + (diag.max() * cond_eps +
eps * eps)
grad_cov.mul_(1-diag_smooth).add_(extra_diag.diag())
return grad_cov
def _get_cov(self, x: Tensor, dim: int) -> Tensor: def _get_cov(self, x: Tensor, dim: int) -> Tensor:
""" """
Computes the covariance of x over dimension `dim`, returning something Computes the covariance of x over dimension `dim`, returning something
@ -409,6 +583,18 @@ class NeutralGradient(Optimizer):
return torch.matmul(x.transpose(-1, dim), return torch.matmul(x.transpose(-1, dim),
proj).transpose(-1, dim) proj).transpose(-1, dim)
def _multiply_on_dim_diag(self, x: Tensor, proj: Tensor, dim: int) -> Tensor:
"""
Matrix-multiplies x by `proj` on x's dimension numbered `dim`
Args:
x: Tensor to multiply, of arbitrary shape
proj: Symmetric matrix to multiply x by, of shape (x.shape[dim], x.shape[dim])
"""
return torch.matmul(x.transpose(-1, dim),
proj).transpose(-1, dim)
def _estimate_proj(self, grad_cov: Tensor, param_cov: Tensor) -> Tensor: def _estimate_proj(self, grad_cov: Tensor, param_cov: Tensor) -> Tensor:
""" """
Return a symmetric positive definite matrix P such that Return a symmetric positive definite matrix P such that
@ -425,11 +611,12 @@ class NeutralGradient(Optimizer):
param_cov: Covariance of parameters, a symmetric-positive-definite param_cov: Covariance of parameters, a symmetric-positive-definite
matrix [except for roundoff!] of shape (size, size) matrix [except for roundoff!] of shape (size, size)
Returns: Returns:
A matrix P such that (alpha P grad_cov P^T == param_cov) for some A matrix P such that (alpha P grad_cov P^T == param_cov)
real alpha, and such that P.diag().mean() == 1.
""" """
grad_cov = grad_cov + grad_cov.t() # symmetrize grad_cov and param_cov. The projection P only cares about the
C = param_cov + param_cov.t() # we will normalize away any scalar factor. # relative sizes, so doubling both of them does not matter.
G = grad_cov + grad_cov.t()
C = param_cov + param_cov.t()
U, S, V = C.svd() U, S, V = C.svd()
# Using G == grad_cov and C == param_cov, and not writing transpose because # Using G == grad_cov and C == param_cov, and not writing transpose because
@ -451,7 +638,7 @@ class NeutralGradient(Optimizer):
# because C is symmetric, C == U S U^T, we can ignore V. # because C is symmetric, C == U S U^T, we can ignore V.
Q = (U * S.sqrt()).t() Q = (U * S.sqrt()).t()
X = torch.matmul(Q, torch.matmul(grad_cov, Q.t())) X = torch.matmul(Q, torch.matmul(G, Q.t()))
U2, S2, _ = X.svd() U2, S2, _ = X.svd()
# Because X^{-0.5} = U2 S2^{-0.5} U2^T, we have # Because X^{-0.5} = U2 S2^{-0.5} U2^T, we have
@ -464,22 +651,16 @@ class NeutralGradient(Optimizer):
P = torch.matmul(Y, Y.t()) P = torch.matmul(Y, Y.t())
P = P * (1.0 / P.diag().mean()) # normalize size of P.
if random.random() < 0.1: if random.random() < 0.1:
#U, S, V = P.svd()
#if random.random() < 0.1:
# print(f"Min,max eig of P: {S.min().item()},{S.max().item()}")
# TODO: remove this testing code. # TODO: remove this testing code.
assert (P - P.t()).abs().mean() < 0.01 # make sure symmetric. assert (P - P.t()).abs().mean() < 0.01 # make sure symmetric.
# testing... note, this is only true modulo "eps" # testing... note, this is only true modulo "eps"
C_check = torch.matmul(torch.matmul(P, G), P)
C_check = torch.matmul(torch.matmul(P, grad_cov), P) # C_check should equal C
# C_check should equal C, up to a constant. First normalize both C_diff = C_check - C
C_diff = (C_check / C_check.diag().mean()) - (C / C.diag().mean()) # Roundoff can cause significant differences, so use a fairly large
# actually, roundoff can cause significant differences. # threshold of 0.001. We may increase this later or even remove the check.
assert C_diff.abs().mean() < 0.001 assert C_diff.abs().mean() < 0.01 * C.diag().mean()
return P return P
@ -1112,6 +1293,7 @@ def _test_eve_cain():
device = torch.device('cuda') device = torch.device('cuda')
dtype = torch.float32 dtype = torch.float32
fix_random_seed(42)
# these input_magnitudes and output_magnitudes are to test that # these input_magnitudes and output_magnitudes are to test that
# Abel is working as we expect and is able to adjust scales of # Abel is working as we expect and is able to adjust scales of
# different dims differently. # different dims differently.