diff --git a/__init__.py b/__init__.py
new file mode 100644
index 0000000..da10dbd
--- /dev/null
+++ b/__init__.py
@@ -0,0 +1,161 @@
+"""Warp-accelerated PyPose via global monkey-patching.
+
+``import PyposeWarp`` patches ``pypose`` globally so that every
+``import pypose as pp`` yields warp-accelerated Lie constructors.
+
+For code that needs the original (unpatched) constructors — e.g. the EKF
+Jacobian pipeline that relies on ``torch.autograd.functional.jacobian`` —
+use ``import PyposeWarp.generic as pp`` instead.
+"""
+
+import sys
+import types
+from typing import Any, cast
+from functools import partial
+
+import pypose
+from . import pypose_warp
+
+_wp = cast(Any, pypose_warp)
+
+# ====== Save originals before patching ======
+
+_PATCHED_ATTRS = [
+    "so3", "SO3", "se3", "SE3",
+    "SO3_type", "so3_type", "SE3_type", "se3_type",
+    "identity_SO3", "identity_SE3", "identity_so3", "identity_se3",
+    "randn_SO3", "randn_SE3", "randn_so3", "randn_se3",
+    "from_matrix", "euler2SO3", "mat2SO3", "mat2SE3",
+]
+
+_orig: dict[str, Any] = {name: getattr(pypose, name) for name in _PATCHED_ATTRS}
+
+# ====== Build PyposeWarp.generic module ======
+
+generic = types.ModuleType("PyposeWarp.generic")
+generic.__doc__ = (
+    "Original (unpatched) PyPose constructors.  Use this in files that "
+    "need torch.autograd.functional.jacobian compatibility."
+)
+generic.__dict__.update(_orig)
+generic.__package__ = "PyposeWarp"
+
+
+def _generic_getattr(name: str) -> Any:
+    """Delegate non-patched attributes to the real pypose module."""
+    return getattr(pypose, name)
+
+
+generic.__getattr__ = _generic_getattr  # type: ignore[attr-defined]
+sys.modules["PyposeWarp.generic"] = generic
+
+# ====== Warp-backed wrapper functions ======
+
+
+def _wp_identity(orig_fn: Any, warp_ltype: Any) -> Any:
+    def wrapper(*args: Any, **kwargs: Any) -> pypose.LieTensor:
+        result = orig_fn(*args, **kwargs)
+        result.ltype = warp_ltype
+        return result
+    return wrapper
+
+
+def _wp_randn(orig_fn: Any, warp_ltype: Any) -> Any:
+    def wrapper(*args: Any, **kwargs: Any) -> pypose.LieTensor:
+        result = orig_fn(*args, **kwargs)
+        result.ltype = warp_ltype
+        return result
+    return wrapper
+
+
+def wp_from_matrix(mat: Any, ltype: Any, check: bool = True,
+                   rtol: float = 1e-5, atol: float = 1e-5) -> pypose.LieTensor:
+    if ltype is _wp.warpSE3_type:
+        result = _orig["from_matrix"](mat, _orig["SE3_type"], check=check, rtol=rtol, atol=atol)
+        result.ltype = _wp.warpSE3_type
+    elif ltype is _wp.warpSO3_type:
+        result = _orig["from_matrix"](mat, _orig["SO3_type"], check=check, rtol=rtol, atol=atol)
+        result.ltype = _wp.warpSO3_type
+    else:
+        result = _orig["from_matrix"](mat, ltype, check=check, rtol=rtol, atol=atol)
+    return result
+
+
+def wp_euler2SO3(*args: Any, **kwargs: Any) -> pypose.LieTensor:
+    result = _orig["euler2SO3"](*args, **kwargs)
+    result.ltype = _wp.warpSO3_type
+    return result
+
+
+def wp_mat2SO3(*args: Any, **kwargs: Any) -> pypose.LieTensor:
+    result = _orig["mat2SO3"](*args, **kwargs)
+    result.ltype = _wp.warpSO3_type
+    return result
+
+
+def wp_mat2SE3(*args: Any, **kwargs: Any) -> pypose.LieTensor:
+    result = _orig["mat2SE3"](*args, **kwargs)
+    result.ltype = _wp.warpSE3_type
+    return result
+
+
+# ====== Global monkey-patching ======
+
+# Type objects
+pypose.SE3_type = _wp.warpSE3_type
+pypose.SO3_type = _wp.warpSO3_type
+pypose.se3_type = _wp.warpse3_type
+pypose.so3_type = _wp.warpso3_type
+
+# Constructors
+pypose.SO3 = partial(pypose.LieTensor, ltype=_wp.warpSO3_type)
+pypose.so3 = partial(pypose.LieTensor, ltype=_wp.warpso3_type)
+pypose.SE3 = partial(pypose.LieTensor, ltype=_wp.warpSE3_type)
+pypose.se3 = partial(pypose.LieTensor, ltype=_wp.warpse3_type)
+
+# Identity functions
+pypose.identity_SE3 = _wp_identity(_orig["identity_SE3"], _wp.warpSE3_type)
+pypose.identity_SO3 = _wp_identity(_orig["identity_SO3"], _wp.warpSO3_type)
+pypose.identity_se3 = _wp_identity(_orig["identity_se3"], _wp.warpse3_type)
+pypose.identity_so3 = _wp_identity(_orig["identity_so3"], _wp.warpso3_type)
+
+# Randn functions
+pypose.randn_SE3 = _wp_randn(_orig["randn_SE3"], _wp.warpSE3_type)
+pypose.randn_SO3 = _wp_randn(_orig["randn_SO3"], _wp.warpSO3_type)
+pypose.randn_se3 = _wp_randn(_orig["randn_se3"], _wp.warpse3_type)
+pypose.randn_so3 = _wp_randn(_orig["randn_so3"], _wp.warpso3_type)
+
+# Conversion functions
+pypose.from_matrix = wp_from_matrix
+pypose.euler2SO3 = wp_euler2SO3
+pypose.mat2SO3 = wp_mat2SO3
+pypose.mat2SE3 = wp_mat2SE3
+
+# ====== Patch pypose internal module bindings ======
+# These modules bind `so3`, `identity_SO3` etc. at import time via
+# ``from .. import so3, identity_SO3``, so we must patch those bindings
+# directly after global patching.
+
+import pypose.module.imu_preintegrator as _preint  # noqa: E402
+
+_preint.so3 = pypose.so3
+_preint.SO3 = pypose.SO3
+_preint.identity_SO3 = pypose.identity_SO3
+_preint.LieTensor = pypose.LieTensor
+
+# ====== Re-exports ======
+
+from .pypose_warp import to_warp_backend, to_pypose_backend, is_warp_backend  # noqa: E402
+
+
+# ====== Module-level delegation ======
+
+
+def __getattr__(name: str) -> Any:
+    """Delegate unresolved attributes to the (now patched) pypose module."""
+    return getattr(pypose, name)
+
+
+def __dir__() -> list[str]:
+    """Expose both local symbols and pypose public attributes."""
+    return sorted(set(globals().keys()) | set(dir(pypose)))
diff --git a/generic.py b/generic.py
new file mode 100644
index 0000000..ef6e4a1
--- /dev/null
+++ b/generic.py
@@ -0,0 +1,10 @@
+"""Original (unpatched) PyPose constructors for autograd-compatible code.
+
+This module is populated by ``PyposeWarp.__init__`` before monkey-patching.
+Use ``import PyposeWarp.generic as pp`` in files that need
+``torch.autograd.functional.jacobian`` compatibility (e.g. EKF NLS pipeline).
+
+Attributes not explicitly saved (e.g. ``module``, ``optim``, ``vec2skew``)
+are delegated to the real ``pypose`` module via ``__getattr__``; these are
+unaffected by monkey-patching so they work identically either way.
+"""
diff --git a/pypose_warp/__init__.py b/pypose_warp/__init__.py
index 2968ce0..2bfede8 100644
--- a/pypose_warp/__init__.py
+++ b/pypose_warp/__init__.py
@@ -19,6 +19,7 @@
 ]
 _PP_TO_WP = {pp_ltype : wp_ltype for pp_ltype, wp_ltype in _BACKEND_LIST}
 _WP_TO_PP = {wp_ltype : pp_ltype for pp_ltype, wp_ltype in _BACKEND_LIST}
+_ORIG_PP_TYPES = frozenset(pp_ltype for pp_ltype, _ in _BACKEND_LIST)
 
 
 def to_warp_backend(x: pp.LieTensor) -> pp.LieTensor:
@@ -46,7 +47,4 @@ def is_warp_backend(x: pp.LieTensor) -> bool:
 
 
 def is_pypose_backend(x: pp.LieTensor) -> bool:
-    return x.ltype in {
-        pp.SE3_type, pp.SO3_type, pp.RxSO3_type, pp.Sim3_type,
-        pp.se3_type, pp.so3_type, pp.rxso3_type, pp.sim3_type
-    }
+    return x.ltype in _ORIG_PP_TYPES