diff --git a/CHANGELOG.md b/CHANGELOG.md
index b122675e1..8c34b8e36 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -23,6 +23,8 @@ When releasing, please add the new-release-boilerplate to docs/pallas/CHANGELOG.
   * The deprecated module `jax.experimental.export` has been removed. It was replaced
     by {mod}`jax.export` in JAX v0.4.30. See the [migration guide](https://jax.readthedocs.io/en/latest/export/export.html#migration-guide-from-jax-experimental-export)
     for information on migrating to the new API.
+  * The `initial` argument to {func}`jax.nn.softmax` and {func}`jax.nn.log_softmax`
+    has been removed, after being deprecated in v0.4.27.
   * The following deprecated methods and functions in {mod}`jax.export` have
     been removed:
       * `jax.export.DisabledSafetyCheck.shape_assertions`: it had no effect
diff --git a/jax/_src/nn/functions.py b/jax/_src/nn/functions.py
index 861e3d012..5dfaa7b7e 100644
--- a/jax/_src/nn/functions.py
+++ b/jax/_src/nn/functions.py
@@ -22,7 +22,6 @@ import operator
 import math
 import numpy as np
 from typing import Any, Literal
-import warnings
 
 import jax
 import jax.numpy as jnp
@@ -502,7 +501,7 @@ logsumexp = _logsumexp
 def log_softmax(x: ArrayLike,
                 axis: int | tuple[int, ...] | None = -1,
                 where: ArrayLike | None = None,
-                initial: ArrayLike | None | Unspecified = _UNSPECIFIED) -> Array:
+                initial: Unspecified = _UNSPECIFIED) -> Array:
   r"""Log-Softmax function.
 
   Computes the logarithm of the :code:`softmax` function, which rescales
@@ -528,10 +527,9 @@ def log_softmax(x: ArrayLike,
   See also:
     :func:`softmax`
   """
+  # TODO(jakevdp): remove the initial argument after JAX v0.4.40.
   if initial is not _UNSPECIFIED:
-    # Added 2024-4-10
-    warnings.warn("The initial argument to log_softmax is deprecated, and no longer has any effect.",
-                  DeprecationWarning, stacklevel=2)
+    raise TypeError("The initial argument to jax.nn.log_softmax was removed in JAX v0.4.36.")
   del initial
   numpy_util.check_arraylike("log_softmax", x)
   x_arr = jnp.asarray(x)
@@ -551,7 +549,7 @@ def log_softmax(x: ArrayLike,
 def softmax(x: ArrayLike,
             axis: int | tuple[int, ...] | None = -1,
             where: ArrayLike | None = None,
-            initial: ArrayLike | None | Unspecified = _UNSPECIFIED) -> Array:
+            initial: Unspecified = _UNSPECIFIED) -> Array:
   r"""Softmax function.
 
   Computes the function which rescales elements to the range :math:`[0, 1]`
@@ -577,10 +575,9 @@ def softmax(x: ArrayLike,
   See also:
     :func:`log_softmax`
   """
+  # TODO(jakevdp): remove the initial argument after JAX v0.4.40.
   if initial is not _UNSPECIFIED:
-    # Added 2024-4-10
-    warnings.warn("The initial argument to softmax is deprecated, and no longer has any effect.",
-                  DeprecationWarning, stacklevel=2)
+    raise TypeError("The initial argument to jax.nn.softmax was removed in JAX v0.4.36.")
   del initial
   if config.softmax_custom_jvp.value:
     # mypy is confused by the `functools.partial` application in the definition