diff --git a/brainpy/_src/math/op_register/ad_support.py b/brainpy/_src/math/op_register/ad_support.py
index 342093ea..57ce9064 100644
--- a/brainpy/_src/math/op_register/ad_support.py
+++ b/brainpy/_src/math/op_register/ad_support.py
@@ -1,51 +1,57 @@
 import functools
 from functools import partial
 
+import jax
 from jax import tree_util
 from jax.core import Primitive
 from jax.interpreters import ad
 
 __all__ = [
-  'defjvp',
+    'defjvp',
 ]
 
 
 def defjvp(primitive, *jvp_rules):
-  """Define JVP rules for any JAX primitive.
+    """Define JVP rules for any JAX primitive.
 
-  This function is similar to ``jax.interpreters.ad.defjvp``.
-  However, the JAX one only supports primitive with ``multiple_results=False``.
-  ``brainpy.math.defjvp`` enables to define the independent JVP rule for
-  each input parameter no matter ``multiple_results=False/True``.
+    This function is similar to ``jax.interpreters.ad.defjvp``.
+    However, the JAX one only supports primitive with ``multiple_results=False``.
+    ``brainpy.math.defjvp`` enables to define the independent JVP rule for
+    each input parameter no matter ``multiple_results=False/True``.
 
-  For examples, please see ``test_ad_support.py``.
+    For examples, please see ``test_ad_support.py``.
 
-  Args:
-    primitive: Primitive, XLACustomOp.
-    *jvp_rules: The JVP translation rule for each primal.
-  """
-  assert isinstance(primitive, Primitive)
-  if primitive.multiple_results:
-    ad.primitive_jvps[primitive] = partial(_standard_jvp, jvp_rules, primitive)
-  else:
-    ad.primitive_jvps[primitive] = partial(ad.standard_jvp, jvp_rules, primitive)
+    Args:
+      primitive: Primitive, XLACustomOp.
+      *jvp_rules: The JVP translation rule for each primal.
+    """
+    assert isinstance(primitive, Primitive)
+    if primitive.multiple_results:
+        ad.primitive_jvps[primitive] = partial(_standard_jvp, jvp_rules, primitive)
+    else:
+        ad.primitive_jvps[primitive] = partial(ad.standard_jvp, jvp_rules, primitive)
 
 
 def _standard_jvp(jvp_rules, primitive: Primitive, primals, tangents, **params):
-  assert primitive.multiple_results
-  val_out = tuple(primitive.bind(*primals, **params))
-  tree = tree_util.tree_structure(val_out)
-  tangents_out = []
-  for rule, t in zip(jvp_rules, tangents):
-    if rule is not None and type(t) is not ad.Zero:
-      r = tuple(rule(t, *primals, **params))
-      tangents_out.append(r)
-      assert tree_util.tree_structure(r) == tree
-  return val_out, functools.reduce(_add_tangents,
-                                   tangents_out,
-                                   tree_util.tree_map(lambda a: ad.Zero.from_value(a), val_out))
+    assert primitive.multiple_results
+    val_out = tuple(primitive.bind(*primals, **params))
+    tree = tree_util.tree_structure(val_out)
+    tangents_out = []
+    for rule, t in zip(jvp_rules, tangents):
+        if rule is not None and type(t) is not ad.Zero:
+            r = tuple(rule(t, *primals, **params))
+            tangents_out.append(r)
+            assert tree_util.tree_structure(r) == tree
+    return val_out, functools.reduce(
+        _add_tangents,
+        tangents_out,
+        tree_util.tree_map(
+            # compatible with JAX 0.4.34
+            lambda a: ad.Zero.from_primal_value(a) if jax.__version__ >= '0.4.34' else ad.Zero.from_value(a),
+            val_out
+        )
+    )
 
 
 def _add_tangents(xs, ys):
-  return tree_util.tree_map(ad.add_tangents, xs, ys, is_leaf=lambda a: isinstance(a, ad.Zero))
-
+    return tree_util.tree_map(ad.add_tangents, xs, ys, is_leaf=lambda a: isinstance(a, ad.Zero))