Add option to normalize NS input in double precision (#238)

* Add safer normalization in NS

Signed-off-by: Hao Wu <skyw@nvidia.com>

Author: skyw

emerging_optimizers/orthogonalized_optimizers/muon_utils.py

@@ -129,11 +129,21 @@ def get_coefficient_iterator(
     return islice(base, steps)
 
 
-def distributed_normalize_p2(x: torch.Tensor, eps: float, group: torch.distributed.ProcessGroup) -> torch.Tensor:
-    """Normalize a tensor in a distributed way."""
-    x_sq_sum = (x * x).sum()
+def distributed_normalize_p2(
+    x: torch.Tensor, eps: float, group: torch.distributed.ProcessGroup, normalize_in_double: bool = False
+) -> torch.Tensor:
+    """Normalize a tensor by its distributed Frobenius norm.
+
+    When ``normalize_in_double`` is set, the squared sum is accumulated in float64 so that tiny
+    entries do not underflow to zero when squared in float32.
+    """
+    x_sq = x.double() if normalize_in_double else x
+    x_sq_sum = (x_sq * x_sq).sum()
     torch.distributed.all_reduce(x_sq_sum, op=torch.distributed.ReduceOp.SUM, group=group)
-    return x / torch.sqrt(x_sq_sum).clamp_min(eps)
+    norm = torch.sqrt(x_sq_sum).to(x.dtype)
+    if not normalize_in_double:
+        norm.clamp_min_(eps)
+    return x / norm
 
 
 def newton_schulz(
@@ -145,6 +155,7 @@ def newton_schulz(
     transpose: bool | None = None,
     tp_group: torch.distributed.ProcessGroup | None = None,
     use_syrk: bool = False,
+    normalize_in_double: bool = False,
 ) -> torch.Tensor:
     """Use Newton-Schulz iteration to compute the zeroth power / orthogonalization of x.
 
@@ -177,6 +188,10 @@ def newton_schulz(
             If None, will be determined based on the size of the tensor.
         tp_group: The process group for communication if input is distributed.
         use_syrk: Whether to use the Triton kernel for the Newton-Schulz iteration.
+        normalize_in_double: Whether to reduce the Frobenius norm in float64. This keeps the squared
+            sum out of float32 underflow for inputs with very small entries, at the cost of a float64
+            reduction. Without customized kernels, manually handle scaling without triggering a device to host
+            sync are usually more expensive than using double.
 
     Returns:
         The orthogonalization of x.
@@ -192,13 +207,17 @@ def newton_schulz(
     if transpose:
         x = x.mT
 
-    # Ensure spectral norm is at most 1.
-    # NOTE: ``eps`` is a divide-by-zero guard; it must stay well below any realistic ``||x||_F``
-    # yet remain fp32-safe when squared. See issue #229.
+    # Ensure spectral norm is at most 1 by normalizing with the Frobenius norm. Reducing in float64
+    # (``normalize_in_double``) keeps the squared sum out of float32 underflow for tiny-norm inputs.
     if tp_group is not None:
-        X = distributed_normalize_p2(x, eps, tp_group)
+        X = distributed_normalize_p2(x, eps, tp_group, normalize_in_double)
     else:
-        X = torch.nn.functional.normalize(x, p=2, dim=(-2, -1), eps=eps)  # type: ignore[arg-type]
+        if not normalize_in_double:
+            X = torch.nn.functional.normalize(x, p=2, dim=(-2, -1), eps=eps)  # type: ignore[arg-type]
+        else:
+            # eps is ignored when normalize in double.
+            norm = torch.linalg.vector_norm(x, dim=(-2, -1), keepdim=True, dtype=torch.float64).to(x.dtype)
+            X = x / norm
 
     if coefficient_type in _COEFFICIENT_SETS:
         coefficient_sets = _COEFFICIENT_SETS[coefficient_type]

tests/test_muon_utils.py

@@ -121,28 +121,14 @@ def test_newtonschulz5_close_to_reference(self, dim1, dim2):
             rtol=1e-7,
         )
 
-    @parameterized.parameters(1e-2, 1e-6, 1e-9, 1e-12)
-    def test_newtonschulz_small_eps(self, scale):
-        """Orthogonalization depends only on direction, so scaling the input must not change the output.
-
-        Regression test for issue #229: a too-large ``eps`` in the internal ``F.normalize`` divides
-        small-norm inputs by ``eps`` instead of their norm, silently degenerating the output. The
-        orthogonalized result for ``x`` and ``scale * x`` must match for any ``scale > 0``.
-        """
-        x = torch.randn(256, 256, device=self.device, dtype=torch.float32)
-        x = x / x.norm()  # unit Frobenius norm direction
-        ref = muon_utils.newton_schulz(x, steps=5, coefficient_type="quintic")
-        out = muon_utils.newton_schulz(scale * x, steps=5, coefficient_type="quintic")
-        torch.testing.assert_close(
-            out,
-            ref,
-            atol=1e-4,
-            rtol=1e-5,
-            msg=lambda m: (
-                f"newton_schulz not scale-invariant at input scale {scale}: "
-                f"||out||_F={out.norm().item():.4f} vs ||ref||_F={ref.norm().item():.4f}\n{m}"
-            ),
-        )
+    def test_preserve_values_with_underflowed_norm_in_fp64(self):
+        scale = 1e-30
+        x = torch.randn(256, 256, device=self.device, dtype=torch.float32) * scale
+        assert torch.linalg.vector_norm(x) == 0  # should underflow
+        norm_ref = torch.linalg.vector_norm(x, dtype=torch.double)
+        assert norm_ref != 0
+        out = muon_utils.newton_schulz(x, steps=0, normalize_in_double=True)
+        torch.testing.assert_close(x / norm_ref, out, atol=0, rtol=1e-6)
 
     @parameterized.parameters(
         (2, 256, 256),