diff --git a/src/examples/ngpt/train.py b/src/examples/ngpt/train.py
index e07791d7..131c4962 100644
--- a/src/examples/ngpt/train.py
+++ b/src/examples/ngpt/train.py
@@ -35,6 +35,7 @@
     GPUMemoryMonitorCallback,
     GradClipperCallback,
     LMEvaluatorCallbackConfig,
+    MatrixNormalizerCallback,
     ProfilerCallback,
     SchedulerCallback,
     SequenceLengthSchedulerCallback,
@@ -93,6 +94,7 @@ def build_config(run_name: str, overrides: List[str]) -> ExperimentConfig:
             metrics_collect_interval=5,
             cancel_check_interval=5,
         )
+        .with_callback("matrix_normalizer", MatrixNormalizerCallback())
         .with_callback("lr_scheduler", SchedulerCallback(scheduler=CosWithWarmup(warmup_steps=0)))
         .with_callback(
             "seq_len_scheduler",
diff --git a/src/olmo_core/nn/transformer/model.py b/src/olmo_core/nn/transformer/model.py
index 5d8c6eb9..52c5ed16 100644
--- a/src/olmo_core/nn/transformer/model.py
+++ b/src/olmo_core/nn/transformer/model.py
@@ -9,12 +9,13 @@
 
 from olmo_core.config import StrEnum
 from olmo_core.data.utils import get_cumulative_document_lengths
+from olmo_core.distributed.utils import get_local_tensor
 from olmo_core.doc_utils import beta_feature
 from olmo_core.utils import get_default_device
 
 from ..buffer_cache import BufferCache
 from ..layer_norm import LayerNormConfig
-from ..utils import selective_checkpointing_context_fn
+from ..utils import l2_normalize, selective_checkpointing_context_fn
 from .block import TransformerBlock, TransformerBlockConfig
 from .init import InitMethod
 
@@ -434,6 +435,14 @@ def num_flops_per_token(self, seq_len: int) -> int:
 
 
 class NormalizedTransformer(Transformer):
+    """
+    A nGPT transformer implementation.
+
+    .. warning::
+        When training this model you should use the :class:`~olmo_core.train.callbacks.MatrixNormalizerCallback`
+        to re-normalize the weight matrices after each optimizer step.
+    """
+
     def __init__(
         self,
         *,
@@ -474,6 +483,33 @@ def init_weights(
         super().init_weights(max_seq_len=max_seq_len, device=device)
         nn.init.ones_(self.sz)
         self.sz.mul_(self.sz_init_scaling)
+        self.normalize_matrices()
+
+    @torch.no_grad()
+    def normalize_matrices(self):
+        """
+        Normalize the weights in all matrices. This should be called after each optimizer step, which
+        the :class:`~olmo_core.train.callbacks.MatrixNormalizerCallback` will handle for you.
+        """
+        if self.embeddings is not None:
+            self._normalize_matrix(self.embeddings.weight)
+
+        for block in self.blocks:
+            self._normalize_matrix(block.attention.w_q.weight)
+            self._normalize_matrix(block.attention.w_k.weight)
+            self._normalize_matrix(block.attention.w_v.weight)
+            self._normalize_matrix(block.attention.w_out.weight, dim=0)
+
+            self._normalize_matrix(block.feed_forward.w1.weight)
+            self._normalize_matrix(block.feed_forward.w2.weight, dim=0)
+            self._normalize_matrix(block.feed_forward.w3.weight)
+
+        if self.w_out is not None:
+            self._normalize_matrix(self.w_out.weight)
+
+    def _normalize_matrix(self, p: torch.Tensor, dim: int = -1):
+        w = get_local_tensor(p.data)
+        w.copy_(l2_normalize(w, dim=dim))
 
     def forward(
         self,
diff --git a/src/olmo_core/nn/utils.py b/src/olmo_core/nn/utils.py
index 7fdc15ab..72ee5384 100644
--- a/src/olmo_core/nn/utils.py
+++ b/src/olmo_core/nn/utils.py
@@ -39,4 +39,4 @@ def selective_checkpointing_context_fn():
 
 
 def l2_normalize(x: torch.Tensor, dim: int = -1) -> torch.Tensor:
-    return x / x.norm(p=2, dim=dim, keepdim=True)
+    return x / x.float().norm(p=2, dim=dim, keepdim=True).type_as(x)
diff --git a/src/olmo_core/train/callbacks/__init__.py b/src/olmo_core/train/callbacks/__init__.py
index 05505104..c393422e 100644
--- a/src/olmo_core/train/callbacks/__init__.py
+++ b/src/olmo_core/train/callbacks/__init__.py
@@ -12,6 +12,7 @@
 from .garbage_collector import GarbageCollectorCallback
 from .gpu_memory_monitor import GPUMemoryMonitorCallback
 from .grad_clipper import GradClipperCallback
+from .matrix_normalizer import MatrixNormalizerCallback
 from .moe_handler import MoEHandlerCallback
 from .profiler import ProfilerCallback
 from .scheduler import SchedulerCallback
@@ -36,6 +37,7 @@
     "GarbageCollectorCallback",
     "GPUMemoryMonitorCallback",
     "GradClipperCallback",
+    "MatrixNormalizerCallback",
     "ProfilerCallback",
     "SchedulerCallback",
     "SequenceLengthSchedulerCallback",
diff --git a/src/olmo_core/train/callbacks/float8_handler.py b/src/olmo_core/train/callbacks/float8_handler.py
index 4e47829b..679d5299 100644
--- a/src/olmo_core/train/callbacks/float8_handler.py
+++ b/src/olmo_core/train/callbacks/float8_handler.py
@@ -1,4 +1,5 @@
 from dataclasses import dataclass, field
+from typing import ClassVar
 
 from olmo_core.float8 import Float8Config, Float8Handler
 
@@ -18,6 +19,8 @@ class Float8HandlerCallback(Callback):
         on your model prior to training to replace the linear layers with ``Float8Linear`` layers.
     """
 
+    priority: ClassVar[int] = -1
+
     config: Float8Config = field(default_factory=Float8Config)
 
     _handler = None
diff --git a/src/olmo_core/train/callbacks/matrix_normalizer.py b/src/olmo_core/train/callbacks/matrix_normalizer.py
new file mode 100644
index 00000000..e158e215
--- /dev/null
+++ b/src/olmo_core/train/callbacks/matrix_normalizer.py
@@ -0,0 +1,14 @@
+from dataclasses import dataclass
+
+from .callback import Callback
+
+
+@dataclass
+class MatrixNormalizerCallback(Callback):
+    """
+    A callback to be used in conjunction with :class:`~olmo_core.nn.transformer.NormalizedTransformer`
+    (nGPT) models to re-normalize the weight matrices after each optimizer step.
+    """
+
+    def post_train_batch(self):
+        self.trainer.model.normalize_matrices()