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Polar Express msign add eps, remove nan_to_num #79

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Merged
ClashLuke merged 3 commits into from
Oct 7, 2025
Merged

Polar Express msign add eps, remove nan_to_num #79

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06b9f6f
Polar Express msign add eps, remove nan_to_num
sozforex Oct 6, 2025
43a09cc
use stochastic_divide_with_eps_ in msign
sozforex Oct 6, 2025
e13785d
fix formatting
sozforex Oct 6, 2025
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15 changes: 10 additions & 5 deletions heavyball/utils.py
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ class OrthoScaleMode(enum.Enum):
)
_torch_compile_double_backward_pattern = re.compile(r"compile.*does not currently support double backward")
_fd_error = (
"You can accelerate startup by globally enabling finite_differences first " #
"You can accelerate startup by globally enabling finite_differences first "
"(via opt.finite_differences=True or by subclassing it)\n"
"Original Error: "
)
Expand Down Expand Up @@ -418,9 +418,13 @@ def zeropower_via_newtonschulz5(G, steps=5, eps=1e-7):


###### START
# Taken from https://github.com/thinking-machines-lab/manifolds/blob/89dcae50f01af59f1e0570289474da3a2ecaa60b/src/msign.py#L47
# Based on https://arxiv.org/pdf/2505.16932v3
# and https://github.com/NoahAmsel/PolarExpress/blob/5454910920ca8c65afda28820cdf9e49b9436ed0/polar_express.py#L69-L82
# and https://github.com/thinking-machines-lab/manifolds/blob/89dcae50f01af59f1e0570289474da3a2ecaa60b/src/msign.py#L47
#
# under the MIT License

# Coefficients are from https://arxiv.org/pdf/2505.16932v3
ABC_LIST: list[tuple[float, float, float]] = [
(8.28721201814563, -23.595886519098837, 17.300387312530933),
(4.107059111542203, -2.9478499167379106, 0.5448431082926601),
Expand All @@ -438,7 +442,7 @@ def zeropower_via_newtonschulz5(G, steps=5, eps=1e-7):
] + [ABC_LIST[-1]]


def msign(G: torch.Tensor, steps: int = 10) -> torch.Tensor:
def msign(G: torch.Tensor, steps: int = 10, eps: float = 1e-7) -> torch.Tensor:
"""
Polar Express algorithm for the matrix sign function:
https://arxiv.org/abs/2505.16932
Expand All @@ -450,7 +454,9 @@ def msign(G: torch.Tensor, steps: int = 10) -> torch.Tensor:
if should_transpose:
x = x.mT

x /= x.norm(dim=(-2, -1), keepdim=True) * 1.01
# x = x / (x.norm(dim=(-2, -1), keepdim=True) * 1.01 + eps)
stochastic_divide_with_eps_(x, x.norm(dim=(-2, -1)) * 1.01, eps)

for step in range(steps):
a, b, c = ABC_LIST_STABLE[step] if step < len(ABC_LIST_STABLE) else ABC_LIST_STABLE[-1]
s = x @ x.mT
Expand All @@ -464,7 +470,6 @@ def msign(G: torch.Tensor, steps: int = 10) -> torch.Tensor:

if should_transpose:
x = x.mT
x = torch.nan_to_num(x)
return x.float()


Expand Down
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