Function polar_express_fn

optimizers/generic_optim.py:192–233

Polar Express Sign Method: https://arxiv.org/pdf/2505.16932 by Noah Amsel, David Persson, Christopher Musco, Robert M. Gower.

(G: torch.Tensor, split_baddbmm: bool = False)

@torch.compile(dynamic=True, fullgraph=True)
def polar_express_fn(G: torch.Tensor, split_baddbmm: bool = False):
    """
    Polar Express Sign Method: https://arxiv.org/pdf/2505.16932
    by Noah Amsel, David Persson, Christopher Musco, Robert M. Gower.
    """
    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) * (1 + 2e-2) + 1e-6)

    # Allocate buffers
    X = X.contiguous()
    C = torch.empty_like(X)

    # Select batched vs unbatched
    if split_baddbmm:
        BX_matmul = torch.bmm if X.ndim > 2 else torch.mm
    else:
        aX_plus_BX = torch.baddbmm if X.ndim > 2 else torch.addmm

    # Perform the iterations
    for a, b, c in polar_express_coeffs:
        A = X @ X.mT
        B = b * A + c * A @ A

        # Referencing X twice causes pytorch to make a defensive copy,
        # resulting in a cudaMemcpyAsync in baddbmm.
        # For large matrices (i.e., the mlp weights), it's faster to split
        # the operation into two kernels to avoid this.
        if split_baddbmm:
            BX_matmul(B, X, out=C)  # C = B @ X
            C.add_(X, alpha=a)      # C = C + a*X  (in-place, X only read)
        else:
            aX_plus_BX(X, B, X, beta=a, out=C)  # C = a * X + B @ X

        X, C = C, X  # Swap references to avoid unnecessary copies

    if G.size(-2) > G.size(-1):
        X = X.mT
    return X


def apply_normuon_variance_reduction(v_chunk, second_momentum_buffer, beta2, red_dim):