diff --git a/blackjax/mcmc/mclmc.py b/blackjax/mcmc/mclmc.py
index b65e5b6e4..33f6060c2 100644
--- a/blackjax/mcmc/mclmc.py
+++ b/blackjax/mcmc/mclmc.py
@@ -22,7 +22,7 @@
 from blackjax.base import SamplingAlgorithm
 from blackjax.mcmc.integrators import IntegratorState, noneuclidean_mclachlan
 from blackjax.types import ArrayLike, PRNGKey
-from blackjax.util import generate_unit_vector, pytree_size
+from blackjax.util import generate_unit_vector
 
 __all__ = ["MCLMCInfo", "init", "build_kernel", "mclmc"]
 
@@ -44,12 +44,12 @@ class MCLMCInfo(NamedTuple):
     energy_change: float
 
 
-def init(x_initial: ArrayLike, logdensity_fn, rng_key):
-    l, g = jax.value_and_grad(logdensity_fn)(x_initial)
+def init(position: ArrayLike, logdensity_fn, rng_key):
+    l, g = jax.value_and_grad(logdensity_fn)(position)
 
     return IntegratorState(
-        position=x_initial,
-        momentum=generate_unit_vector(rng_key, x_initial),
+        position=position,
+        momentum=generate_unit_vector(rng_key, position),
         logdensity=l,
         logdensity_grad=g,
     )
@@ -83,8 +83,6 @@ def kernel(
             state, step_size
         )
 
-        dim = pytree_size(position)
-
         # Langevin-like noise
         momentum, dim = partially_refresh_momentum(
             momentum=momentum, rng_key=rng_key, L=L, step_size=step_size
@@ -95,6 +93,7 @@ def kernel(
         ), MCLMCInfo(
             logdensity=logdensity,
             energy_change=kinetic_change - logdensity + state.logdensity,
+            # TODO: Potential bug here, see #625
             kinetic_change=kinetic_change * (dim - 1),
         )
 
diff --git a/blackjax/util.py b/blackjax/util.py
index 9fb461c8d..6f1d49072 100644
--- a/blackjax/util.py
+++ b/blackjax/util.py
@@ -1,6 +1,6 @@
 """Utility functions for BlackJax."""
 from functools import partial
-from typing import Union
+from typing import Callable, Union
 
 import jax.numpy as jnp
 from jax import jit, lax
@@ -8,7 +8,7 @@
 from jax.random import normal, split
 from jax.tree_util import tree_leaves
 
-from blackjax.base import Info, State
+from blackjax.base import Info, SamplingAlgorithm, State, VIAlgorithm
 from blackjax.progress_bar import progress_bar_scan
 from blackjax.types import Array, ArrayLikeTree, ArrayTree, PRNGKey
 
@@ -141,35 +141,39 @@ def index_pytree(input_pytree: ArrayLikeTree) -> ArrayTree:
 
 
 def run_inference_algorithm(
-    rng_key,
-    initial_state_or_position,
-    inference_algorithm,
-    num_steps,
+    rng_key: PRNGKey,
+    initial_state_or_position: ArrayLikeTree,
+    inference_algorithm: Union[SamplingAlgorithm, VIAlgorithm],
+    num_steps: int,
     progress_bar: bool = False,
-    transform=lambda x: x,
+    transform: Callable = lambda x: x,
 ) -> tuple[State, State, Info]:
     """Wrapper to run an inference algorithm.
 
     Parameters
     ----------
-    rng_key : PRNGKey
+    rng_key
         The random state used by JAX's random numbers generator.
-    initial_state_or_position: ArrayLikeTree
+    initial_state_or_position
         The initial state OR the initial position of the inference algorithm. If an initial position
         is passed in, the function will automatically convert it into an initial state.
-    inference_algorithm : Union[SamplingAlgorithm, VIAlgorithm]
+    inference_algorithm
         One of blackjax's sampling algorithms or variational inference algorithms.
-    num_steps : int
-        Number of learning steps.
-    transform:
-        a transformation of the sequence of states to be returned. By default, the states are returned as is.
+    num_steps
+        Number of MCMC steps.
+    progress_bar
+        Whether to display a progress bar.
+    transform
+        A transformation of the trace of states to be returned. This is useful for
+        computing determinstic variables, or returning a subset of the states.
+        By default, the states are returned as is.
 
     Returns
     -------
     Tuple[State, State, Info]
         1. The final state of the inference algorithm.
-        2. The history of states of the inference algorithm.
-        3. The history of the info of the inference algorithm.
+        2. The trace of states of the inference algorithm (contains the MCMC samples).
+        3. The trace of the info of the inference algorithm for diagnostics.
     """
     try:
         initial_state = inference_algorithm.init(initial_state_or_position)
diff --git a/tests/mcmc/test_sampling.py b/tests/mcmc/test_sampling.py
index 2a9fd07c5..879eba550 100644
--- a/tests/mcmc/test_sampling.py
+++ b/tests/mcmc/test_sampling.py
@@ -78,7 +78,7 @@ def run_mclmc(self, logdensity_fn, num_steps, initial_position, key):
         init_key, tune_key, run_key = jax.random.split(key, 3)
 
         initial_state = blackjax.mcmc.mclmc.init(
-            x_initial=initial_position, logdensity_fn=logdensity_fn, rng_key=init_key
+            position=initial_position, logdensity_fn=logdensity_fn, rng_key=init_key
         )
 
         kernel = blackjax.mcmc.mclmc.build_kernel(