diff --git a/pymdp/jax/inference.py b/pymdp/jax/inference.py
index 350d3662..4edd48d5 100644
--- a/pymdp/jax/inference.py
+++ b/pymdp/jax/inference.py
@@ -73,9 +73,9 @@ def step_fn(qs_smooth, xs):
         if isinstance(norm, JAXSparse):
             norm = sparse.todense(norm)
         norm = jnp.where(norm == 0, eps, norm)
-        qs_backward_cond = (qs_j / norm).T
-        qs_joint = qs_backward_cond * qs_smooth
-        qs_smooth = qs_joint.sum(-1)
+        qs_backward_cond = qs_j / norm
+        qs_joint = qs_backward_cond * jnp.expand_dims(qs_smooth, -1)
+        qs_smooth = qs_joint.sum(-2)
         if isinstance(qs_smooth, JAXSparse):
             qs_smooth = sparse.todense(qs_smooth)
         
@@ -106,9 +106,11 @@ def smoothing_ovf(filtered_post, B, past_actions):
 
     joint = lambda b, qs, f: joint_dist_factor(b, qs, past_actions[..., f])
 
-    marginals_and_joints = []
+    marginals_and_joints = ([], [])
     for b, qs, f in zip(B, filtered_post, list(range(nf))):
-        marginals_and_joints.append( joint(b, qs, f) )
+        marginals, joints = joint(b, qs, f)
+        marginals_and_joints[0].append(marginals)
+        marginals_and_joints[1].append(joints)
 
     return marginals_and_joints
 
diff --git a/pymdp/jax/learning.py b/pymdp/jax/learning.py
index 6c681751..32ada016 100644
--- a/pymdp/jax/learning.py
+++ b/pymdp/jax/learning.py
@@ -4,6 +4,7 @@
 
 from .maths import multidimensional_outer, dirichlet_expected_value
 from jax.tree_util import tree_map
+from jaxtyping import Array
 from jax import vmap, nn
 
 def update_obs_likelihood_dirichlet_m(pA_m, obs_m, qs, dependencies_m, lr=1.0):
@@ -58,6 +59,7 @@ def update_state_transition_dirichlet_f(pB_f, actions_f, joint_qs_f, lr=1.0):
     # \otimes is a multidimensional outer product, not just a outer product of two vectors
     # \kappa is an optional learning rate
 
+    joint_qs_f = [joint_qs_f] if isinstance(joint_qs_f, Array) else joint_qs_f
     dfdb = vmap(multidimensional_outer)(joint_qs_f + [actions_f]).sum(axis=0)
     qB_f = pB_f + lr * dfdb