diff --git a/pywhy_stats/kernel_utils.py b/pywhy_stats/kernel_utils.py
index faae0c3..88b5e0c 100644
--- a/pywhy_stats/kernel_utils.py
+++ b/pywhy_stats/kernel_utils.py
@@ -123,6 +123,18 @@ def compute_kernel(
     -------
     kernel : ArrayLike of shape (n_samples_X, n_samples_X) or (n_samples_X, n_samples_Y)
         The kernel matrix.
+
+    Notes
+    -----
+    If the metric is a callable, it will have either one input for ``X``, or two inputs for ``X`` and
+    ``Y``. If one input is passed in, it is assumed that the kernel operates on the entire array to compute
+    the kernel array. If two inputs are passed in, then it is assumed that the kernel operates on
+    pairwise row vectors from each input array. This callable is parallelized across rows of the input
+    using :func:`~sklearn.metrics.pairwise.pairwise_kernels`. Note that ``(X, Y=None)`` is a valid input
+    signature for the kernel function and would then get passed to the pairwise kernel function. If
+    a callable is passed in, it is generally faster and more efficient if one can define a vectorized
+    operation that operates on the whole array at once. Otherwise, the pairwise kernel function will
+    call the function for each combination of rows in the input arrays.
     """
     # if the width of the kernel is not set, then use the median trick to set the
     # kernel width based on the data X