diff --git a/kfac_jax/_src/utils/__init__.py b/kfac_jax/_src/utils/__init__.py
index cd5436b..e843352 100644
--- a/kfac_jax/_src/utils/__init__.py
+++ b/kfac_jax/_src/utils/__init__.py
@@ -131,6 +131,9 @@
 invert_psd_matrices = math.invert_psd_matrices
 inverse_sqrt_psd_matrices = math.inverse_sqrt_psd_matrices
 stable_sqrt = math.stable_sqrt
+cosine_similarity = math.cosine_similarity
+make_flattened_func = math.make_flattened_func
+make_flattened_hvp_func = math.make_flattened_hvp_func
 
 del math
 
diff --git a/kfac_jax/_src/utils/math.py b/kfac_jax/_src/utils/math.py
index 3ad4275..0b9ee8d 100644
--- a/kfac_jax/_src/utils/math.py
+++ b/kfac_jax/_src/utils/math.py
@@ -14,16 +14,14 @@
 """K-FAC utilities for various mathematical operations."""
 import functools
 import string
-from typing import Callable, Sequence, Iterable, TypeVar
+from typing import Callable, Iterable, Sequence, TypeVar
 
 import jax
 from jax import lax
 from jax.experimental.sparse import linalg as experimental_splinalg
 import jax.numpy as jnp
 from jax.scipy import linalg
-
 from kfac_jax._src.utils import types
-
 import numpy as np
 import optax
 import tree
@@ -1155,3 +1153,40 @@ def _stable_sqrt_fwd(
 _sqrt_bound_derivative.defjvp(_stable_sqrt_fwd)
 
 stable_sqrt = functools.partial(_sqrt_bound_derivative, max_gradient=1000.0)
+
+
+def cosine_similarity(v1, v2):
+  return jnp.dot(v1, v2) / (jnp.linalg.norm(v1) * jnp.linalg.norm(v2))
+
+
+def make_flattened_func(func, arg):
+  """Returns a function that has flattened input and output."""
+  _, unflatten_func = jax.flatten_util.ravel_pytree(arg)
+  flattened_func = lambda x: jax.flatten_util.ravel_pytree(
+      func(unflatten_func(x))
+  )[0]
+  return flattened_func
+
+
+def make_flattened_hvp_func(grad_func, primals):
+  """Returns a function that computes the Hessian-vector product (HVP).
+
+  Returns an HVP function which takes in and returns a flattened vector.
+
+  Args:
+    grad_func: A function whose JVP will be computed to obtain the HVP.
+    primals: The primals for the HVP.
+  Returns:
+    The flattened HVP function.
+  """
+
+  flattened_primals, _ = jax.flatten_util.ravel_pytree(primals)
+  flattened_grad_func = make_flattened_func(grad_func, primals)
+
+  def hvp_func(flattened_tangents):
+    return jax.jvp(
+        flattened_grad_func, (flattened_primals,), (flattened_tangents,)
+    )[1]
+
+  return hvp_func
+