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soap.py
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soap.py
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import torch
import torch.nn as nn
import torch.optim as optim
from itertools import chain
# Parts of the code are modifications of Pytorch's AdamW optimizer
# Parts of the code are modifications of code from https://github.com/jiaweizzhao/GaLore/blob/master/galore_torch/galore_projector.py
class SOAP(optim.Optimizer):
"""
Implements SOAP algorithm (https://arxiv.org/abs/2409.11321).
Parameters:
params (`Iterable[nn.parameter.Parameter]`):
Iterable of parameters to optimize or dictionaries defining parameter groups.
lr (`float`, *optional*, defaults to 0.003):
The learning rate to use.
betas (`Tuple[float,float]`, *optional*, defaults to `(0.95, 0.95)`):
Adam's betas parameters (b1, b2).
shampoo_beta (`float`, *optional*, defaults to -1):
If >= 0, use this beta for the preconditioner (L and R in paper, state['GG'] below) moving average instead of betas[1].
eps (`float`, *optional*, defaults to 1e-08):
Adam's epsilon for numerical stability.
weight_decay (`float`, *optional*, defaults to 0.01): weight decay coefficient.
precondition_frequency (`int`, *optional*, defaults to 10):
How often to update the preconditioner.
max_precond_dim (`int`, *optional*, defaults to 10000):
Maximum dimension of the preconditioner.
Set to 10000, so that we exclude most common vocab sizes while including layers.
merge_dims (`bool`, *optional*, defaults to `False`):
Whether or not to merge dimensions of the preconditioner.
precondition_1d (`bool`, *optional*, defaults to `False`):
Whether or not to precondition 1D gradients.
normalize_grads (`bool`, *optional*, defaults to `False`):
Whether or not to normalize gradients per layer.
Helps at large precondition_frequency (~100 in our experiments),
but hurts performance at small precondition_frequency (~10 in our experiments).
data_format (`str`, *optional*, defaults to `channels_first`):
Data format of the input for convolutional layers.
Should be "channels_last" for data_format of NHWC and "channels_first" for NCHW.
correct_bias (`bool`, *optional*, defaults to `True`):
Whether or not to use bias correction in Adam.
"""
def __init__(
self,
params,
lr: float = 3e-3,
betas=(0.95, 0.95),
shampoo_beta: float= -1,
eps: float = 1e-8,
weight_decay: float = 0.01,
precondition_frequency: int=10,
max_precond_dim: int=10000, #
merge_dims: bool = False, # Merge dimensions till the product of the dimensions is less than or equal to max_precond_dim.
precondition_1d: bool = False,
normalize_grads: bool = False,
data_format: str = "channels_first",
correct_bias: bool = True,
):
defaults = {
"lr": lr,
"betas": betas,
"shampoo_beta": shampoo_beta,
"eps": eps,
"weight_decay": weight_decay,
"precondition_frequency": precondition_frequency,
"max_precond_dim": max_precond_dim,
"merge_dims": merge_dims,
"precondition_1d": precondition_1d,
"normalize_grads": normalize_grads,
"correct_bias": correct_bias,
}
super().__init__(params, defaults)
self._data_format = data_format
def merge_dims(self, grad, max_precond_dim):
"""
Merges dimensions of the gradient tensor till the product of the dimensions is less than or equal to max_precond_dim.
"""
assert self._data_format in ["channels_first", "channels_last"]
if self._data_format == "channels_last" and grad.dim() == 4:
grad = grad.permute(0, 3, 1, 2)
shape = grad.shape
new_shape = []
curr_shape = 1
for sh in shape:
temp_shape = curr_shape * sh
if temp_shape > max_precond_dim:
if curr_shape > 1:
new_shape.append(curr_shape)
curr_shape = sh
else:
new_shape.append(sh)
curr_shape = 1
else:
curr_shape = temp_shape
if curr_shape > 1 or len(new_shape)==0:
new_shape.append(curr_shape)
new_grad = grad.reshape(new_shape)
return new_grad
@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.
"""
if closure is None:
loss = None
else:
loss = closure()
for group in self.param_groups:
for p in group["params"]:
if p.grad is None:
continue
grad = p.grad
state = self.state[p]
if "step" not in state:
state["step"] = 0
# State initialization
if "exp_avg" not in state:
# Exponential moving average of gradient values
state["exp_avg"] = torch.zeros_like(grad)
# Exponential moving average of squared gradient values
state["exp_avg_sq"] = torch.zeros_like(grad)
if 'Q' not in state:
self.init_preconditioner(
grad,
state,
precondition_frequency=group['precondition_frequency'],
precondition_1d=group['precondition_1d'],
shampoo_beta=(group['shampoo_beta'] if group['shampoo_beta'] >= 0 else group["betas"][1]),
max_precond_dim=group['max_precond_dim'],
merge_dims=group["merge_dims"],
)
self.update_preconditioner(grad, state,
max_precond_dim=group['max_precond_dim'],
merge_dims=group["merge_dims"],
precondition_1d=group["precondition_1d"])
continue # first step is skipped so that we never use the current gradients in the projection.
# Projecting gradients to the eigenbases of Shampoo's preconditioner
# i.e. projecting to the eigenbases of matrices in state['GG']
grad_projected = self.project(grad, state, merge_dims=group["merge_dims"],
max_precond_dim=group['max_precond_dim'])
exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
beta1, beta2 = group["betas"]
state["step"] += 1
# Decay the first and second moment running average coefficient
# In-place operations to update the averages at the same time
exp_avg.mul_(beta1).add_(grad_projected, alpha=(1.0 - beta1))
exp_avg_sq.mul_(beta2).add_(grad_projected.square(), alpha=(1.0 - beta2))
denom = exp_avg_sq.sqrt().add_(group["eps"])
# Projecting the exponential moving average of gradients to the eigenbases of Shampoo's preconditioner
# i.e. projecting to the eigenbases of matrices in state['GG']
# exp_avg_projected = self.project(exp_avg, state, merge_dims=group["merge_dims"],
# max_precond_dim=group['max_precond_dim'])
exp_avg_projected = exp_avg
step_size = group["lr"]
if group["correct_bias"]:
bias_correction1 = 1.0 - beta1 ** (state["step"])
bias_correction2 = 1.0 - beta2 ** (state["step"])
step_size = step_size * (bias_correction2 ** .5) / bias_correction1
# Projecting back the preconditioned (by Adam) exponential moving average of gradients
# to the original space
norm_grad = self.project_back(exp_avg_projected / denom, state, merge_dims=group["merge_dims"],
max_precond_dim=group['max_precond_dim'])
if group["normalize_grads"]:
norm_grad = norm_grad / (1e-30+torch.mean(norm_grad**2)**0.5)
p.add_(norm_grad, alpha=-step_size)
# From AdamW code: Just adding the square of the weights to the loss function is *not*
# the correct way of using L2 regularization/weight decay with Adam,
# since that will interact with the m and v parameters in strange ways.
#
# Instead we want to decay the weights in a manner that doesn't interact
# with the m/v parameters. This is equivalent to adding the square
# of the weights to the loss with plain (non-momentum) SGD.
# Add weight decay at the end (fixed version)
if group["weight_decay"] > 0.0:
p.add_(p, alpha=(-group["lr"] * group["weight_decay"]))
# Update is done after the gradient step to avoid using current gradients in the projection.
self.update_preconditioner(grad, state,
max_precond_dim=group['max_precond_dim'],
merge_dims=group["merge_dims"],
precondition_1d=group["precondition_1d"])
return loss
def init_preconditioner(self, grad, state, precondition_frequency=10,
shampoo_beta=0.95, max_precond_dim=10000, precondition_1d=False,
merge_dims=False):
"""
Initializes the preconditioner matrices (L and R in the paper).
"""
state['GG'] = [] # Will hold all the preconditioner matrices (L and R in the paper).
if grad.dim() == 1:
if not precondition_1d or grad.shape[0] > max_precond_dim:
state['GG'].append([])
else:
state['GG'].append(torch.zeros(grad.shape[0], grad.shape[0], device=grad.device))
else:
if merge_dims:
grad = self.merge_dims(grad, max_precond_dim)
for sh in grad.shape:
if sh > max_precond_dim:
state['GG'].append([])
else:
state['GG'].append(torch.zeros(sh, sh, device=grad.device))
state['Q'] = None # Will hold all the eigenbases of the preconditioner.
state['precondition_frequency'] = precondition_frequency
state['shampoo_beta'] = shampoo_beta
def project(self, grad, state, merge_dims=False, max_precond_dim=10000):
"""
Projects the gradient to the eigenbases of the preconditioner.
"""
original_shape = grad.shape
if merge_dims:
if grad.dim() == 4 and self._data_format == 'channels_last':
permuted_shape = grad.permute(0, 3, 1, 2).shape
grad = self.merge_dims(grad, max_precond_dim)
for mat in state['Q']:
if len(mat) > 0:
grad = torch.tensordot(
grad,
mat,
dims=[[0], [0]],
)
else:
permute_order = list(range(1, len(grad.shape))) + [0]
grad = grad.permute(permute_order)
if merge_dims:
if self._data_format == 'channels_last' and len(original_shape) == 4:
grad = grad.reshape(permuted_shape).permute(0, 2, 3, 1)
else:
grad = grad.reshape(original_shape)
return grad
def update_preconditioner(self, grad, state,
max_precond_dim=10000, merge_dims=False, precondition_1d=False):
"""
Updates the preconditioner matrices and the eigenbases (L, R, Q_L, Q_R in the paper).
"""
if state["Q"] is not None:
state["exp_avg"] = self.project_back(state["exp_avg"], state, merge_dims=merge_dims, max_precond_dim=max_precond_dim)
if grad.dim() == 1:
if precondition_1d and grad.shape[0] <= max_precond_dim:
state['GG'][0].lerp_(grad.unsqueeze(1) @ grad.unsqueeze(0), 1-state['shampoo_beta'])
else:
if merge_dims:
new_grad = self.merge_dims(grad, max_precond_dim)
for idx, sh in enumerate(new_grad.shape):
if sh <= max_precond_dim:
outer_product = torch.tensordot(
new_grad,
new_grad,
dims=[[*chain(range(idx), range(idx + 1, len(new_grad.shape)))]] * 2,
)
state['GG'][idx].lerp_(outer_product, 1-state['shampoo_beta'])
else:
for idx, sh in enumerate(grad.shape):
if sh <= max_precond_dim:
outer_product = torch.tensordot(
grad,
grad,
# Contracts across all dimensions except for k.
dims=[[*chain(range(idx), range(idx + 1, len(grad.shape)))]] * 2,
)
state['GG'][idx].lerp_(outer_product, 1-state['shampoo_beta'])
if state['Q'] is None:
state['Q'] = self.get_orthogonal_matrix(state['GG'])
if state['step'] > 0 and state['step'] % state['precondition_frequency'] == 0:
state['Q'] = self.get_orthogonal_matrix_QR(state, max_precond_dim, merge_dims)
# state['Q'] = self.get_fast_QR(state, max_precond_dim, merge_dims)
if state["step"] > 0:
state["exp_avg"] = self.project(state["exp_avg"], state, merge_dims=merge_dims, max_precond_dim=max_precond_dim)
def project_back(self, grad, state, merge_dims=False, max_precond_dim=10000):
"""
Projects the gradient back to the original space.
"""
original_shape = grad.shape
if merge_dims:
if self._data_format == 'channels_last' and grad.dim() == 4:
permuted_shape = grad.permute(0, 3, 1, 2).shape
grad = self.merge_dims(grad, max_precond_dim)
for mat in state['Q']:
if len(mat) > 0:
grad = torch.tensordot(
grad,
mat,
dims=[[0], [1]],
)
else:
permute_order = list(range(1, len(grad.shape))) + [0]
grad = grad.permute(permute_order)
if merge_dims:
if self._data_format == 'channels_last' and len(original_shape) == 4:
grad = grad.reshape(permuted_shape).permute(0, 2, 3, 1)
else:
grad = grad.reshape(original_shape)
return grad
def get_orthogonal_matrix(self, mat):
"""
Computes the eigenbases of the preconditioner using torch.linalg.eigh decomposition.
"""
matrix = []
for m in mat:
if len(m) == 0:
matrix.append([])
continue
if m.data.dtype != torch.float:
float_data = False
original_type = m.data.dtype
original_device = m.data.device
matrix.append(m.data.float())
else:
float_data = True
matrix.append(m.data)
final = []
for m in matrix:
if len(m) == 0:
final.append([])
continue
try:
_, Q = torch.linalg.eigh(m+1e-30*torch.eye(m.shape[0], device=m.device))
except:
_, Q = torch.linalg.eigh(m.to(torch.float64)+1e-30*torch.eye(m.shape[0], device=m.device))
Q = Q.to(m.dtype)
Q = torch.flip(Q, [1])
if not float_data:
Q = Q.to(original_device).type(original_type)
final.append(Q)
return final
def get_orthogonal_matrix_QR(self, state, max_precond_dim=10000, merge_dims=False):
"""
Computes the eigenbases of the preconditioner using one round of power iteration
followed by torch.linalg.qr decomposition.
"""
precond_list = state['GG']
orth_list = state['Q']
matrix = []
orth_matrix = []
for m,o in zip(precond_list, orth_list):
if len(m) == 0:
matrix.append([])
orth_matrix.append([])
continue
if m.data.dtype != torch.float:
float_data = False
original_type = m.data.dtype
original_device = m.data.device
matrix.append(m.data.float())
orth_matrix.append(o.data.float())
else:
float_data = True
matrix.append(m.data.float())
orth_matrix.append(o.data.float())
orig_shape = state['exp_avg_sq'].shape
if self._data_format == 'channels_last' and len(orig_shape) == 4:
permuted_shape = state['exp_avg_sq'].permute(0, 3, 1, 2).shape
if merge_dims:
exp_avg_sq = self.merge_dims(state['exp_avg_sq'], max_precond_dim)
else:
exp_avg_sq = state['exp_avg_sq']
final = []
for ind, (m,o) in enumerate(zip(matrix, orth_matrix)):
if len(m)==0:
final.append([])
continue
est_eig = torch.diag(o.T @ m @ o)
sort_idx = torch.argsort(est_eig, descending=True)
exp_avg_sq = exp_avg_sq.index_select(ind, sort_idx)
o = o[:,sort_idx]
power_iter = m @ o
Q, _ = torch.linalg.qr(power_iter)
if not float_data:
Q = Q.to(original_device).type(original_type)
final.append(Q)
if merge_dims:
if self._data_format == 'channels_last' and len(orig_shape) == 4:
exp_avg_sq = exp_avg_sq.reshape(permuted_shape).permute(0, 2, 3, 1)
else:
exp_avg_sq = exp_avg_sq.reshape(orig_shape)
state['exp_avg_sq'] = exp_avg_sq
return final