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Version that is passing the tests
This commit is contained in:
Daniel Povey
parent
e597b68160
commit
c6f62dfc08
@ -43,12 +43,14 @@ class NeutralGradient(Optimizer):
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at 0.03 and decreases over time, i.e. much higher than other common
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optimizers.
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beta: Momentum constants for regular momentum, and stats of gradients.
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eps: An epsilon to prevent division by zero
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scale_speed: This scales the learning rate for purposes of learning the overall scale
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of each tensor
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rms_eps: An epsilon on the rms value of the parameter, such that when the parameter
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eps: An epsilon to prevent division by zero
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param_eps: An epsilon on the rms value of the parameter, such that when the parameter
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gets smaller than this we'll start using a fixed learning rate, not
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decreasing with the parameter norm.
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cond_eps: An epsilon that limits the condition number of gradient and parameter
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covariance matrices
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param_max: To prevent parameter tensors getting too large, we will clip elements to
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-param_max..param_max.
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max_size: We will only use the full-covariance (not-diagonal) update for
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@ -64,9 +66,10 @@ class NeutralGradient(Optimizer):
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params,
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lr=1e-2,
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betas=(0.9, 0.98, 0.99),
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eps=1e-8,
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scale_speed=0.05,
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rms_eps=1.0e-05,
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eps=1e-8,
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param_eps=1.0e-05,
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cond_eps=1.0e-08,
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param_max=10.0,
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max_size=1023,
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stats_period=1,
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@ -91,8 +94,8 @@ class NeutralGradient(Optimizer):
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)
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if not 0 < scale_speed < 1.0:
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raise ValueError("Invalid scale_speed value: {}".format(scale_speed))
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if not 0.0 < rms_eps < 0.1:
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raise ValueError("Invalid rms_eps value: {}".format(rms_eps))
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if not 0.0 < param_eps < 0.1:
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raise ValueError("Invalid param_eps value: {}".format(param_eps))
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if not 0.1 < param_max <= 10000.0:
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raise ValueError("Invalid param_max value: {}".format(param_max))
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if not stats_period > 0:
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@ -106,7 +109,8 @@ class NeutralGradient(Optimizer):
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betas=betas,
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eps=eps,
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scale_speed=0.05,
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rms_eps=rms_eps,
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param_eps=param_eps,
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cond_eps=cond_eps,
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param_max=param_max,
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max_size=max_size,
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stats_period=stats_period,
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@ -135,7 +139,7 @@ class NeutralGradient(Optimizer):
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beta1, beta2, beta3 = group["betas"]
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lr = group["lr"]
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scale_speed = group["scale_speed"]
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rms_eps = group["rms_eps"]
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param_eps = group["param_eps"]
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eps = group["eps"]
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param_max = group["param_max"]
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max_size = group["max_size"]
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@ -163,15 +167,18 @@ class NeutralGradient(Optimizer):
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p, memory_format=torch.preserve_format
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)
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# Exponential moving average of squared gradient value
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# after all multiplications. This is used to help
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# determine the scalar factor in the update size. It is
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# resert after every `estimate_period` minibatches.
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state["exp_avg_sq"] = torch.zeros_like(p)
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kwargs = {'device':p.device, 'dtype':p.dtype}
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if p.numel() > 1:
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state["scalar_exp_avg_sq"] = torch.zeros((), **kwargs)
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is_one_axis = (p.numel() in list(p.shape)) # e.g. a bias
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if not is_one_axis:
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state["ref_exp_avg_sq"] = torch.ones_like(p)
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else:
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state["param_rms"] = torch.zeros((), **kwargs)
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# we learn the scale on the parameters in a way that
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# also emulates Eve. scale_exp_avg_sq is the
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@ -179,14 +186,6 @@ class NeutralGradient(Optimizer):
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# scalar scale.
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state["scale_exp_avg_sq"] = torch.zeros((), **kwargs)
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state["param_rms"] = torch.zeros((), **kwargs)
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# TODO: may have to add some special stuff here if
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if is_one_axis:
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state["exp_avg_sq"] = torch.zeros_like(p)
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else:
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state["scalar_exp_avg_sq"] = torch.zeros((), **kwargs)
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for dim in range(p.ndim):
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size = p.shape[dim]
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if size == 1 or size == p.numel():
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@ -195,15 +194,12 @@ class NeutralGradient(Optimizer):
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elif size > max_size:
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# diagonal only...
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state[f"grad_cov_{dim}"] = torch.zeros(size, **kwargs)
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state[f"proj_{dim}"] = torch.zeros(size, **kwargs)
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state[f"proj_{dim}"] = torch.ones(size, **kwargs)
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else:
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state[f"grad_cov_{dim}"] = torch.zeros(size, size,
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**kwargs)
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state[f"proj_{dim}"] = torch.zeros(size, size,
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**kwargs)
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else:
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# p.numel() == 1: scalar parameter
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state["exp_avg_sq"] = torch.zeros_like(p)
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state[f"proj_{dim}"] = torch.eye(size, **kwargs)
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delta = state["delta"]
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step = state["step"]
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@ -240,44 +236,62 @@ class NeutralGradient(Optimizer):
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delta.add_(p, alpha=scale_delta)
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exp_avg_sq = state["exp_avg_sq"]
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# Decay the second moment running average coefficient
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exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
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bias_correction2 = 1 - beta2 ** (step + 1)
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if is_one_axis:
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param_rms = state["param_rms"]
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if step % 10 == 0:
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param_rms.copy_((p**2).mean().sqrt())
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if is_one_axis:
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exp_avg_sq = state["exp_avg_sq"]
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# Decay the second moment running average coefficient
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exp_avg_sq.mul_(beta3).addcmul_(grad, grad, value=1 - beta3)
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bias_correction2 = 1 - beta3 ** (step + 1)
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grad_rms = (exp_avg_sq.sqrt()).add_(eps)
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this_delta = grad / grad_rms
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alpha = (-(1-beta1) * lr * bias_correction2) * param_rms.clamp(min=rms_eps)
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alpha = (-(1-beta1) * lr * bias_correction2) * param_rms.clamp(min=param_eps)
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delta.add_(this_delta, alpha=alpha)
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# below, will do: delta.add_(this_delta, alpha=alpha)
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else:
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# The full update.
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conditioned_grad = self._precondition_grad(p, grad, state, beta3, max_size,
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# First, if needed, accumulate per-dimension stats from the grad
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if step % stats_period == 0:
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self._accumulate_per_dim_stats(grad, state, beta3, eps)
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if step % estimate_period == 0 or step in [50, 200, 400]:
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self._estimate(p, state, beta3, max_size,
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stats_period, estimate_period,
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eps, rms_eps)
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scalar_exp_avg_sq = state["scalar_exp_avg_sq"]
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grad_sq = (grad**2).mean()
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conditioned_grad_sq = (conditioned_grad**2).mean()
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prod = (grad*conditioned_grad).mean()
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cos_angle = prod / (grad_sq * conditioned_grad_sq).sqrt()
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if random.random() < 0.001 or cos_angle < 0.0075:
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eps, param_eps)
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ref_exp_avg_sq = state["ref_exp_avg_sq"] # computed in self._estimate()
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# do ** 0.25, not ** 0.5, because we divide this into two factors:
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# one to be applied before the grad preconditioning, and one after.
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# This keeps the overall transformation on the gradient symmetric
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# (if viewed as a matrix of shape (p.numel(), p.numel())
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# Note: ref_exp_avg_sq had eps*eps added to it when we created it.
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grad_scale = (ref_exp_avg_sq / (exp_avg_sq/bias_correction2 + eps*eps)) ** 0.25
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#print(f"grad_scale mean = {grad_scale.mean()}, shape = {p.shape}")
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cur_grad = grad * grad_scale
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cur_grad = self._precondition_grad(cur_grad, state)
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cur_grad *= grad_scale
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if True: # testing
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# in principle, the cur_grad is supposed to have the same rms as params, on average.
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cur_grad_rms = (cur_grad**2).mean().sqrt()
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param_rms = (p**2).mean().sqrt()
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#print(f"cur_grad_rms={cur_grad_rms}, param_rms={param_rms}")
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if random.random() < 0.1:
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prod = (grad*cur_grad).mean()
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cos_angle = prod / ((grad**2).mean() * (cur_grad**2).mean()).sqrt()
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if random.random() < 0.01 or cos_angle < 0.0075:
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print(f"cos_angle = {cos_angle}, shape={grad.shape}")
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#assert grad_sq - grad_sq == 0
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#assert conditioned_grad_sq - conditioned_grad_sq == 0
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scalar_exp_avg_sq.mul_(beta2).add_(grad_sq, alpha=(1-beta2))
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bias_correction2 = 1 - beta2 ** (step + 1)
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avg_grad_sq = scalar_exp_avg_sq / bias_correction2
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scale = param_rms.clamp(min=rms_eps) * (grad_sq / ((avg_grad_sq * conditioned_grad_sq) + 1.0e-20)).sqrt()
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alpha = -lr * (1-beta1) * scale
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delta.add_(conditioned_grad, alpha=alpha)
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alpha = -lr * (1-beta1)
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delta.add_(cur_grad, alpha=alpha)
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else:
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# p.numel() == 1
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# Decay the second moment running average coefficient
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@ -301,18 +315,135 @@ class NeutralGradient(Optimizer):
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return loss
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def _precondition_grad(self,
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p: Tensor,
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def _accumulate_per_dim_stats(self,
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grad: Tensor,
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state: dict,
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beta3: float,
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eps: float) -> None:
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"""
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Accumulate some stats for each dimension of the tensor, about the covariance of gradients.
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"""
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ndim = grad.ndim
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for dim in range(ndim):
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size = grad.shape[dim]
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if size == 1:
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continue
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grad_cov = state[f"grad_cov_{dim}"]
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if grad_cov.ndim == 1:
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# We are treating this dimension diagonally because it is too big.
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other_dims = [ i for i in range(ndim) if i != dim]
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grad_cov.mul_(beta3).add_((grad**2).mean(dim=other_dims))
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else:
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# full-covariance stats.
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this_beta3 = self._get_this_beta3(beta3, grad.numel(), size)
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grad_cov.mul_(this_beta3).add_(self._get_cov(grad, dim),
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alpha=(1.0-this_beta3))
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def _estimate(self,
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p: Tensor,
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state: dict,
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beta3: float,
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max_size: int,
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stats_period: int,
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estimate_period: int,
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eps: float,
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rms_eps: float
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param_eps: float
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) -> Tensor:
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"""
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Estimate the per-dimension projections proj_0, proj_1 and so on, and
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ref_exp_avg_sq.
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"""
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kwargs = {'device':p.device, 'dtype':p.dtype}
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ref_exp_avg_sq = torch.ones([1] * p.ndim, **kwargs)
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ndim = p.ndim
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step = state["step"]
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assert step % stats_period == 0
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norm_step = step // stats_period
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def update_ref_exp_avg_sq(ref_exp_avg_sq, grad_cov_smoothed, dim):
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"""
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Updates ref_exp_avg_sq, taking into account `grad_cov_smoothed` which is
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a tensor of shape (p.shape[dim],) containing the smoothed diagonal covariance
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of grads for dimension `dim`.
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Returns new ref_exp_avg_sq
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"""
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if dim > 0:
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# We only want to "count" the overall scale of the gradients' variance
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# (i.e. mean variance) once, so for all dims other than 0 we normalize
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# this out.
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grad_cov_smoothed = grad_cov_smoothed / grad_cov_smoothed.mean()
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for _ in range(dim + 1, ndim):
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grad_cov_smoothed = grad_cov_smoothed.unsqueeze(-1)
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return ref_exp_avg_sq * grad_cov_smoothed
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for dim in range(ndim):
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size = p.shape[dim]
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if size == 1:
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continue
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grad_cov = state[f"grad_cov_{dim}"]
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proj = state[f"proj_{dim}"]
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if grad_cov.ndim == 1:
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# This dim is treated diagonally, because it is too large.
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other_dims = [ i for i in range(ndim) if i != dim]
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bias_correction3 = 1 - beta3 ** (norm_step + 1)
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# _smoothed means we have the eps terms.
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param_var_smoothed = (p**2).mean(dim=other_dims) + param_eps*param_eps
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if bias_correction3 < 0.9999:
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grad_cov = grad_cov / bias_correction3
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grad_var_smoothed = grad_cov + eps*eps
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ref_exp_avg_sq = update_ref_exp_avg_sq(ref_exp_avg_sq,
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grad_var_smoothed,
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dim)
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if dim != 0:
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# If dim != 0, make the grad_var_smoothed and
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# param_var_smoothed have the same mean, because when
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# preconditioning gradients, we only want to count the
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# overall change in scale once.
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grad_var_smoothed *= (param_var_smoothed.sum() / grad_var_smoothed.sum())
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proj[:] = (param_var_smoothed / grad_var_smoothed).sqrt()
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else:
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param_cov_smoothed = self._estimate_and_smooth_param_cov(p, dim,
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param_eps)
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grad_cov_smoothed = self._smooth_grad_cov(p, grad_cov,
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eps, norm_step,
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beta3)
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ref_exp_avg_sq = update_ref_exp_avg_sq(ref_exp_avg_sq,
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grad_cov_smoothed.diag(),
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dim)
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if dim != 0:
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# If dim != 0, make the traces of grad_cov_smoothed and
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# param_cov_smoothed be the same, because when
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# preconditioning gradients, we only want to count the
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# overall change in scale once.
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grad_cov_smoothed *= (param_cov_smoothed.diag().sum() /
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grad_cov_smoothed.diag().sum())
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proj[:] = self._estimate_proj(grad_cov_smoothed,
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param_cov_smoothed)
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state["ref_exp_avg_sq"][:] = ref_exp_avg_sq
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def _get_this_beta3(self, beta3: float, numel: int, size: int):
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"""
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Get a discounting value beta3 (e.g. 0.99) that is used in computing moving
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averages of stats. The idea is that the stats are accumulated from a tensor
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x that has `numel` elements and `size == x.shape[dim]`, and we want the covariance
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of shape (dim, dim). We may need to make beta3 closer to 1 if this means
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we'll be getting only very rank-deficient stats each time.
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"""
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rank_per_iter = numel // size # maximum rank of each iteration's covaraince
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safety_factor = 4.0 # should be > 1.0
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grad_num_steps_needed = safety_factor * size / rank_per_iter
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return max(beta3, 1 - 1. / grad_num_steps_needed)
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def _precondition_grad(self,
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grad: Tensor,
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state: dict) -> Tensor:
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"""
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Multiply the grad by a positive-semidefinite matrix for each dimension, to
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try to make its covariance the same as that of the parameters (up to a
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scalar constant).
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@ -329,67 +460,110 @@ class NeutralGradient(Optimizer):
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"""
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cur_grad = grad
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ndim = grad.ndim
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step = state["step"]
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for dim in range(p.ndim):
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size = p.shape[dim]
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for dim in range(ndim):
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size = grad.shape[dim]
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if size == 1:
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continue
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grad_cov = state[f"grad_cov_{dim}"]
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proj = state[f"proj_{dim}"]
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if size > max_size:
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if proj.ndim == 1:
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# We are treating this dimension diagonally because it is too big.
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if step % stats_period == 0 or step < 100:
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# for diagonal dims, both re-estimate stats and re-estimate
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# transform every `stats_period`, as the re-estimation is
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# easy.
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other_dims = [ i for i in range(p.ndim) if i != dim]
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grad_cov.mul_(beta3).add_((grad**2).mean(dim=other_dims))
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# estimate param_var, the variance of the parameters.
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param_var = (p**2).mean(dim=other_dims)
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factor = ((param_var + rms_eps*rms_eps) / (grad_cov + eps*eps)).sqrt()
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# normalize these factors to stop preconditioned-grad mean from getting
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# very large or small
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factor = factor / factor.mean()
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proj[:] = factor
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proj = proj.reshape(size, *([1] * (p.ndim-1-dim)))
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proj = proj.reshape(size, *([1] * (ndim-1-dim)))
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cur_grad = cur_grad * proj
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else:
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# This dimension gets the full-covariance treatment.
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grad_num_points = grad.numel() // size
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grad_num_steps_needed = 4 * size / grad_num_points
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if step % stats_period == 0 or step < 100:
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# normally use beta3 for the decay of the decaying-average
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# gradient stats, but we may use a value closer to 1 if we
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# have to estimate a high-dimensional gradient from very
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# low-rank covariance contributions.
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this_beta3 = max(beta3, 1 - 1. / grad_num_steps_needed)
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grad_cov.mul_(this_beta3).add_(self._get_cov(grad, dim),
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alpha=(1.0-this_beta3))
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if step % estimate_period == 0 or (step < estimate_period and step in [10,40]):
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# Estimate the parameter covariance on this dimension,
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# treating the other dimensions of the parameter as we would
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# frames. Smooth with the diagonal because there are not
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# many points to estimate the covariance from.
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param_cov = self._get_cov(p, dim)
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min_diag = 0.2
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if True: # Smooth parameter
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num_points = p.numel() // size
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# later we may be able to find a more principled formula for this.
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diag_smooth = max(min_diag, dim / (dim + num_points))
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diag = param_cov.diag()
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param_cov.mul_(1-diag_smooth).add_((diag*diag_smooth+ rms_eps*rms_eps).diag())
|
||||
if True:
|
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diag_smooth = min_diag # This is likely far from optimal!
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diag = grad_cov.diag()
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grad_cov = grad_cov * (1-diag_smooth) + (diag*diag_smooth + eps*eps).diag()
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proj[:] = self._estimate_proj(grad_cov, param_cov)
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cur_grad = self._multiply_on_dim(cur_grad, proj, dim)
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return cur_grad
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|
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def _estimate_and_smooth_param_cov(self, p: Tensor, dim: int,
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param_eps: float,
|
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cond_eps: float = 1.0e-10,
|
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min_diag_smooth: float = 0.2) -> Tensor:
|
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"""
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Compute a smoothed version of a covariance matrix for one dimension of
|
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a parameter tensor, estimated by treating the other
|
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dimensions as a batch index.
|
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|
||||
p: The parameter tensor from which we are estimating the covariance
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dim: The dimenion that we want the covariances for.
|
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param_eps: A small epsilon value that represents the minimum root-mean-square
|
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parameter value that we'll estimate.
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cond_eps: An epsilon value that limits the condition number of the resulting
|
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matrix. Caution: this applies to the variance, not the rms value,
|
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so should be quite small.
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||||
|
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Returns:
|
||||
A non-singular covariance matrix of shape (p.shape[dim], p.shape[dim])
|
||||
"""
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p = p.transpose(dim, -1)
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p = p.reshape(-1, p.shape[-1])
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(num_outer_products, size) = p.shape
|
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param_cov = torch.matmul(p.t(), p) / p.shape[0]
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# later we may be able to find a more principled formula for this.
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diag_smooth = max(min_diag_smooth, size / (size + num_outer_products))
|
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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:
|
||||
"""
|
||||
Computes the covariance of x over dimension `dim`, returning something
|
||||
@ -409,6 +583,18 @@ class NeutralGradient(Optimizer):
|
||||
return torch.matmul(x.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:
|
||||
"""
|
||||
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
|
||||
matrix [except for roundoff!] of shape (size, size)
|
||||
Returns:
|
||||
A matrix P such that (alpha P grad_cov P^T == param_cov) for some
|
||||
real alpha, and such that P.diag().mean() == 1.
|
||||
A matrix P such that (alpha P grad_cov P^T == param_cov)
|
||||
"""
|
||||
grad_cov = grad_cov + grad_cov.t()
|
||||
C = param_cov + param_cov.t() # we will normalize away any scalar factor.
|
||||
# symmetrize grad_cov and param_cov. The projection P only cares about the
|
||||
# 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()
|
||||
|
||||
# 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.
|
||||
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()
|
||||
# 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 = P * (1.0 / P.diag().mean()) # normalize size of P.
|
||||
|
||||
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.
|
||||
assert (P - P.t()).abs().mean() < 0.01 # make sure symmetric.
|
||||
# testing... note, this is only true modulo "eps"
|
||||
|
||||
C_check = torch.matmul(torch.matmul(P, grad_cov), P)
|
||||
# C_check should equal C, up to a constant. First normalize both
|
||||
C_diff = (C_check / C_check.diag().mean()) - (C / C.diag().mean())
|
||||
# actually, roundoff can cause significant differences.
|
||||
assert C_diff.abs().mean() < 0.001
|
||||
C_check = torch.matmul(torch.matmul(P, G), P)
|
||||
# C_check should equal C
|
||||
C_diff = C_check - C
|
||||
# Roundoff can cause significant differences, so use a fairly large
|
||||
# threshold of 0.001. We may increase this later or even remove the check.
|
||||
assert C_diff.abs().mean() < 0.01 * C.diag().mean()
|
||||
|
||||
return P
|
||||
|
||||
@ -1112,6 +1293,7 @@ def _test_eve_cain():
|
||||
device = torch.device('cuda')
|
||||
dtype = torch.float32
|
||||
|
||||
fix_random_seed(42)
|
||||
# these input_magnitudes and output_magnitudes are to test that
|
||||
# Abel is working as we expect and is able to adjust scales of
|
||||
# different dims differently.
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user