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import torch.distributed as dist
# copied from https://github.com/KellerJordan/Muon/blob/master/muon.py
def zeropower_via_newtonschulz5(G, steps=5):
"""
Newton-Schulz iteration to compute the zeroth power / orthogonalization of G. We opt to use a
quintic iteration whose coefficients are selected to maximize the slope at zero. For the purpose
of minimizing steps, it turns out to be empirically effective to keep increasing the slope at
zero even beyond the point where the iteration no longer converges all the way to one everywhere
on the interval. This iteration therefore does not produce UV^T but rather something like US'V^T
where S' is diagonal with S_{ii}' ~ Uniform(0.5, 1.5), which turns out not to hurt model
performance at all relative to UV^T, where USV^T = G is the SVD.
"""
assert G.ndim >= 2 # batched Muon implementation by @scottjmaddox, and put into practice in the record by @YouJiacheng
a, b, c = (3.4445, -4.7750, 2.0315)
X = G.bfloat16()
if G.size(-2) > G.size(-1):
X = X.mT
# Ensure spectral norm is at most 1
X = X / (X.norm(dim=(-2, -1), keepdim=True) + 1e-7)
# Perform the NS iterations
for _ in range(steps):
A = X @ X.mT
B = b * A + c * A @ A # quintic computation strategy adapted from suggestion by @jxbz, @leloykun, and @YouJiacheng
X = a * X + B @ X
if G.size(-2) > G.size(-1):
X = X.mT
return X
def normuon_update(grad, momentum, second_momentum, beta=0.95, beta2=0.95, ns_steps=5, nesterov=True):
momentum.lerp_(grad, 1 - beta)
update = grad.lerp_(momentum, beta) if nesterov else momentum
original_shape = None
if update.ndim == 4: # for the case of conv filters
original_shape = update.shape
update = update.reshape(update.size(0), -1)
update = zeropower_via_newtonschulz5(update, steps=ns_steps)
update = update.to(grad.dtype)
if original_shape is not None:
update = update.reshape(original_shape)
################ NorMuon added ###################
vnorm = update.norm(dim=(-2,-1), keepdim=True)
v_mean = torch.mean(update * update, dim=-1, keepdim=True)
second_momentum.lerp_(v_mean, 1 - beta2)
step_size = 1 / second_momentum.sqrt().add_(1e-10)
update.mul_(step_size)
vnorm_new = update.norm(dim=(-2,-1), keepdim=True)
update.mul_(vnorm / (vnorm_new.add_(1e-10))) # This scaling keep the update norm the same as pre-normalization
##################################################
update *= max(1, grad.size(-2) / grad.size(-1))**0.5
return update
# modified from https://github.com/KellerJordan/Muon/blob/master/muon.py
class NorMuon(torch.optim.Optimizer):
def __init__(self, params, lr=0.02, weight_decay=0, momentum=0.95, beta2=0.95):
defaults = dict(lr=lr, weight_decay=weight_decay, momentum=momentum, beta2=beta2)
assert isinstance(params, list) and len(params) >= 1 and isinstance(params[0], torch.nn.Parameter)
params = sorted(params, key=lambda x: x.size(), reverse=True)
super().__init__(params, defaults)
@torch.no_grad()
def step(self, closure=None):
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
params = group["params"]
params_pad = params + [torch.empty_like(params[-1])] * (dist.get_world_size() - len(params) % dist.get_world_size())
for base_i in range(len(params))[::dist.get_world_size()]:
if base_i + dist.get_rank() < len(params):
p = params[base_i + dist.get_rank()]
had_grad = p.grad is not None
if not had_grad:
# continue
p.grad = torch.zeros_like(p) # Force synchronization
state = self.state[p]
if len(state) == 0:
state["momentum_buffer"] = torch.zeros_like(p)
state["second_momentum_buffer"] = torch.zeros_like(p[..., 0:1])
update = normuon_update(p.grad, state["momentum_buffer"], state["second_momentum_buffer"], beta=group["momentum"], beta2=group["beta2"])
if group["weight_decay"] and had_grad:
p.mul_(1 - group["lr"] * group["weight_decay"])
p.add_(update.reshape(p.shape), alpha=-group["lr"])
dist.all_gather(params_pad[base_i:base_i + dist.get_world_size()], params_pad[base_i + dist.get_rank()])
return loss
# modified from https://github.com/KellerJordan/Muon/blob/master/muon.py
class SingleDeviceNorMuon(torch.optim.Optimizer):
"""
Muon variant for usage in non-distributed settings.
"""
def __init__(self, params, lr=0.02, weight_decay=0, momentum=0.95, beta2=0.95):
defaults = dict(lr=lr, weight_decay=weight_decay, momentum=momentum, beta2=beta2)
super().__init__(params, defaults)
@torch.no_grad()
def step(self, closure=None):
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
for p in group["params"]:
had_grad = p.grad is not None
if not had_grad:
# continue
p.grad = torch.zeros_like(p) # Force synchronization
state = self.state[p]
if len(state) == 0:
state["momentum_buffer"] = torch.zeros_like(p)
state["second_momentum_buffer"] = torch.zeros_like(p[...,0:1])
update = normuon_update(p.grad, state["momentum_buffer"], state["second_momentum_buffer"], beta=group["momentum"], beta2=group["beta2"])
if group["weight_decay"] and had_grad:
p.mul_(1 - group["lr"] * group["weight_decay"])
p.add_(update.reshape(p.shape), alpha=-group["lr"])
return loss
def adam_update(grad, buf1, buf2, step, betas, eps):
buf1.lerp_(grad, 1 - betas[0])
buf2.lerp_(grad.square(), 1 - betas[1])
buf1c = buf1 / (1 - betas[0]**step)
buf2c = buf2 / (1 - betas[1]**step)
return buf1c / (buf2c.sqrt() + eps)
class NorMuonWithAuxAdam(torch.optim.Optimizer):
"""
Distributed NorMuon variant paired with an auxiliary Adam optimizer for parameters that are not
compatible with NorMuon. Groups intended for NorMuon should set `use_muon=True`.
"""
def __init__(self, param_groups):
for group in param_groups:
assert "use_muon" in group
if group["use_muon"]:
group["params"] = sorted(group["params"], key=lambda x: x.size(), reverse=True)
group["lr"] = group.get("lr", 0.02)
group["momentum"] = group.get("momentum", 0.95)
group["beta2"] = group.get("beta2", 0.95)
group["weight_decay"] = group.get("weight_decay", 0)
assert set(group.keys()) == {"params", "lr", "momentum", "beta2", "weight_decay", "use_muon"}
else:
group["lr"] = group.get("lr", 3e-4)
group["betas"] = group.get("betas", (0.9, 0.95))
group["eps"] = group.get("eps", 1e-10)
group["weight_decay"] = group.get("weight_decay", 0)
assert set(group.keys()) == {"params", "lr", "betas", "eps", "weight_decay", "use_muon"}
super().__init__(param_groups, dict())
@torch.no_grad()
def step(self, closure=None):
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
if group["use_muon"]:
params = group["params"]
params_pad = params + [torch.empty_like(params[-1])] * (dist.get_world_size() - len(params) % dist.get_world_size())
for base_i in range(len(params))[::dist.get_world_size()]:
if base_i + dist.get_rank() < len(params):
p = params[base_i + dist.get_rank()]
had_grad = p.grad is not None
if not had_grad:
p.grad = torch.zeros_like(p)
state = self.state[p]
if len(state) == 0:
state["momentum_buffer"] = torch.zeros_like(p)
state["second_momentum_buffer"] = torch.zeros_like(p[..., 0:1])
update = normuon_update(p.grad, state["momentum_buffer"], state["second_momentum_buffer"],
beta=group["momentum"], beta2=group["beta2"])
if group["weight_decay"] and had_grad:
p.mul_(1 - group["lr"] * group["weight_decay"])
p.add_(update.reshape(p.shape), alpha=-group["lr"])
dist.all_gather(params_pad[base_i:base_i + dist.get_world_size()], params_pad[base_i + dist.get_rank()])
else:
for p in group["params"]:
had_grad = p.grad is not None
if not had_grad:
p.grad = torch.zeros_like(p)
state = self.state[p]
if len(state) == 0:
state["exp_avg"] = torch.zeros_like(p)
state["exp_avg_sq"] = torch.zeros_like(p)
state["step"] = 0
state["step"] += 1
update = adam_update(p.grad, state["exp_avg"], state["exp_avg_sq"],
state["step"], group["betas"], group["eps"])
if group["weight_decay"] and had_grad:
p.mul_(1 - group["lr"] * group["weight_decay"])
p.add_(update, alpha=-group["lr"])
return loss
class SingleDeviceNorMuonWithAuxAdam(torch.optim.Optimizer):
"""
Non-distributed counterpart to NorMuonWithAuxAdam.
"""
def __init__(self, param_groups):
for group in param_groups:
assert "use_muon" in group
if group["use_muon"]:
group["lr"] = group.get("lr", 0.02)
group["momentum"] = group.get("momentum", 0.95)
group["beta2"] = group.get("beta2", 0.95)
group["weight_decay"] = group.get("weight_decay", 0)
assert set(group.keys()) == {"params", "lr", "momentum", "beta2", "weight_decay", "use_muon"}
else:
group["lr"] = group.get("lr", 3e-4)
group["betas"] = group.get("betas", (0.9, 0.95))
group["eps"] = group.get("eps", 1e-10)
group["weight_decay"] = group.get("weight_decay", 0)
assert set(group.keys()) == {"params", "lr", "betas", "eps", "weight_decay", "use_muon"}
super().__init__(param_groups, dict())
@torch.no_grad()
def step(self, closure=None):
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
if group["use_muon"]:
for p in group["params"]:
had_grad = p.grad is not None
if not had_grad:
p.grad = torch.zeros_like(p)
state = self.state[p]
if len(state) == 0:
state["momentum_buffer"] = torch.zeros_like(p)
state["second_momentum_buffer"] = torch.zeros_like(p[..., 0:1])
update = normuon_update(p.grad, state["momentum_buffer"], state["second_momentum_buffer"],
beta=group["momentum"], beta2=group["beta2"])
if group["weight_decay"] and had_grad:
p.mul_(1 - group["lr"] * group["weight_decay"])
p.add_(update.reshape(p.shape), alpha=-group["lr"])
else:
for p in group["params"]:
had_grad = p.grad is not None
if not had_grad:
p.grad = torch.zeros_like(p)
state = self.state[p]
if len(state) == 0:
state["exp_avg"] = torch.zeros_like(p)
state["exp_avg_sq"] = torch.zeros_like(p)
state["step"] = 0
state["step"] += 1
update = adam_update(p.grad, state["exp_avg"], state["exp_avg_sq"],
state["step"], group["betas"], group["eps"])
if group["weight_decay"] and had_grad:
p.mul_(1 - group["lr"] * group["weight_decay"])
p.add_(update, alpha=-group["lr"])
return loss
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