diff --git a/README.md b/README.md
index 2a54b6f..381d40a 100644
--- a/README.md
+++ b/README.md
@@ -159,66 +159,6 @@ python -m pip install git+https://github.com/pypose/bae.git
    python -m pip install --no-build-isolation -v -e .  # following https://github.com/pytorch/pytorch
    ```
 
-### `torch.compile` with `LieTensor`
-
-Enable the `LieTensor` TorchDynamo compatibility shim before importing either
-`pypose` or `bae`:
-
-```bash
-export BAE_USE_PYPOSE_TORCH_COMPILE=1
-```
-
-The existing ambient-gradient implementation automatically enables the same
-shim, so `BAE_USE_PYPOSE_AMBIENT_GRAD=1` is sufficient when ambient gradients
-are required. The shim can also be installed explicitly before compiling a
-model or residual function:
-
-```python
-import torch
-
-from bae.utils.pypose_compile import install_pypose_torch_compile_monkeypatch
-
-install_pypose_torch_compile_monkeypatch()
-compiled_model = torch.compile(model, fullgraph=True)
-```
-
-With `fullgraph=True`, indexed `sjac=True` parameters retain their sparse
-Jacobian dependency trace without forcing the gathered camera and point blocks
-to escape the compiled graph. This gives Inductor the opportunity to load
-permuted rows directly inside fused kernels. Inductor will decide the most efficient way, 
-whether to materialize standalone indexed tensors when the
-gathered values have multiple downstream consumers, as can happen during
-Jacobian computation. `fullgraph=True` guarantees graph capture but does not ensure 
-particular kernel-fusion or buffer-allocation strategy.
-
-PyTorch cannot currently represent a sparse BSR tensor as a FakeTensor/AOT
-graph output. To compile the residual and sparse-Jacobian traversal together,
-return its dense component tensors from the compiled function and materialize
-the BSR wrapper immediately afterward:
-
-```python
-from bae.autograd.graph import (
-    jacobian_components,
-    materialize_jacobian_components,
-)
-
-def residual_and_jacobian(observations, camera_indices, point_indices):
-    residual = model(observations, camera_indices, point_indices)
-    components = jacobian_components(
-        residual, (model.pose, model.points)
-    )
-    return residual, components
-
-compiled = torch.compile(residual_and_jacobian, fullgraph=True)
-residual, components = compiled(observations, camera_indices, point_indices)
-jacobians = materialize_jacobian_components(components)
-```
-
-The component traversal and Jacobian values are compiled. For one component per
-parameter, as in the BA residual above, BSR materialization is an eager,
-zero-copy wrapper operation. Graphs with multiple contributions to the same
-parameter additionally combine those sparse components after materialization.
-
 ## Agent Skills
 
 This repo includes skills in [.agent/skills](.agent/skills):
diff --git a/doc/compile_lietensor.md b/doc/compile_lietensor.md
new file mode 100644
index 0000000..fac2862
--- /dev/null
+++ b/doc/compile_lietensor.md
@@ -0,0 +1,59 @@
+### `torch.compile` with `LieTensor`
+
+Enable the `LieTensor` TorchDynamo compatibility shim before importing either
+`pypose` or `bae`:
+
+```bash
+export BAE_USE_PYPOSE_TORCH_COMPILE=1
+```
+
+The existing ambient-gradient implementation automatically enables the same
+shim, so `BAE_USE_PYPOSE_AMBIENT_GRAD=1` is sufficient when ambient gradients
+are required. The shim can also be installed explicitly before compiling a
+model or residual function:
+
+```python
+import torch
+
+from bae.utils.pypose_compile import install_pypose_torch_compile_monkeypatch
+
+install_pypose_torch_compile_monkeypatch()
+compiled_model = torch.compile(model, fullgraph=True)
+```
+
+With `fullgraph=True`, indexed `sjac=True` parameters retain their sparse
+Jacobian dependency trace without forcing the gathered camera and point blocks
+to escape the compiled graph. This gives Inductor the opportunity to load
+permuted rows directly inside fused kernels. Inductor will decide the most efficient way, 
+whether to materialize standalone indexed tensors when the
+gathered values have multiple downstream consumers, as can happen during
+Jacobian computation. `fullgraph=True` guarantees graph capture but does not ensure 
+particular kernel-fusion or buffer-allocation strategy.
+
+PyTorch cannot currently represent a sparse BSR tensor as a FakeTensor/AOT
+graph output. To compile the residual and sparse-Jacobian traversal together,
+return its dense component tensors from the compiled function and materialize
+the BSR wrapper immediately afterward:
+
+```python
+from bae.autograd.graph import (
+    jacobian_components,
+    materialize_jacobian_components,
+)
+
+def residual_and_jacobian(observations, camera_indices, point_indices):
+    residual = model(observations, camera_indices, point_indices)
+    components = jacobian_components(
+        residual, (model.pose, model.points)
+    )
+    return residual, components
+
+compiled = torch.compile(residual_and_jacobian, fullgraph=True)
+residual, components = compiled(observations, camera_indices, point_indices)
+jacobians = materialize_jacobian_components(components)
+```
+
+The component traversal and Jacobian values are compiled. For one component per
+parameter, as in the BA residual above, BSR materialization is an eager,
+zero-copy wrapper operation. Graphs with multiple contributions to the same
+parameter additionally combine those sparse components after materialization.