[sparse] Wrong jacobian computation for bcoo_spdot_general
It seems that the Jacobian computed by `bcoo_spdot_general`, invoked through the operator `@` does not organize the values in the correct order.

In order to show the bug, I have written the following code.
```python
import jax
import jax.numpy as jnp
from jax.experimental.sparse.bcoo import BCOO

A_indices = jnp.array([[0, 1], [0, 2], [1, 1], [1, 2], [1, 0]])
A_values = jnp.array([-2.0, 1.0, -1.0, 0.5, 2.0])
A_shape = (2, 3)

B_indices = jnp.array([[0, 2], [2, 1], [0, 3], [1, 3], [1, 0], [0, 0]])
B_values = jnp.array([10.0, 100.0, 1000.0, -5.0, -50.0, -500.0])
B_shape = (3, 4)

def sp_sp_product(v1, v2):
    sparse1 = BCOO((v1, A_indices), shape=A_shape)
    sparse2 = BCOO((v2, B_indices), shape=B_shape)
    return (sparse1 @ sparse2).todense()

def sp_dense_product(v1, v2):
    sparse1 = BCOO((v1, A_indices), shape=A_shape)
    dense2 = BCOO((v2, B_indices), shape=B_shape).todense()
    return sparse1 @ dense2

sp_sp_product_jac = jax.jacfwd(sp_sp_product, argnums=1)(A_values, B_values)
sparse_dense_product_jac = jax.jacfwd(sp_dense_product, argnums=1)(A_values, B_values)

assert jnp.array_equal(
    sp_sp_product_jac, sparse_dense_product_jac
), "The two Jacobian should be the same"
```

`sparse_dense_product_jac` is correct (as it can be verified analitically), while `sp_sp_product_jac` is incorrect since it should be identical to `sparse_dense_product_jac` but it is not.
The shape of `sp_sp_product_jac` in the expected one and the values in `sp_sp_product_jac` seems correct but they are not placed in the expected location. Probably there is a problem in the indices of the sparse jacobian matrix.

diff --git a/jax/experimental/sparse/bcoo.py b/jax/experimental/sparse/bcoo.py
index 1a05057f3..acaaf923d 100644
--- a/jax/experimental/sparse/bcoo.py
+++ b/jax/experimental/sparse/bcoo.py
@@ -84,6 +84,8 @@ def _bcoo_nse(mat, n_batch=0, n_dense=0):
   mask = mask.sum(list(range(n_batch, mask.ndim)))
   return mask.max()
 
+# TODO(jakevdp): add a custom autodiff rule that errors if remove_zeros=True, because
+# it produces wrong values. See https://github.com/google/jax/issues/10163
 def _bcoo_sum_duplicates(data, indices, shape, nse=None, remove_zeros=True):
   if nse is None and isinstance(jnp.array(0), core.Tracer):
     raise ValueError("When used with JIT, vmap, or another transform, sum_duplicates() "
@@ -1229,7 +1231,8 @@ def _bcoo_spdot_general_unbatched(lhs_data, lhs_indices, rhs_data, rhs_indices,
   out_indices = out_indices.at[:, :, lhs_j.shape[-1]:].set(rhs_j[None, :])
   out_indices = out_indices.reshape(len(out_data), out_indices.shape[-1])
   out_nse = (lhs.nse if lhs_j.shape[1] else 1) * (rhs.nse if rhs_j.shape[1] else 1)
-  return _bcoo_sum_duplicates(out_data, out_indices, out_shape, nse=out_nse)
+  # Note: remove_zeros=True is incompatible with autodiff.
+  return _bcoo_sum_duplicates(out_data, out_indices, out_shape, nse=out_nse, remove_zeros=False)
 
 @bcoo_spdot_general_p.def_impl
 def _bcoo_spdot_general_impl(lhs_data, lhs_indices, rhs_data, rhs_indices, *, lhs_spinfo: BCOOInfo, rhs_spinfo: BCOOInfo, dimension_numbers):
@@ -1770,7 +1773,8 @@ class BCOO(JAXSparse):
         If it is smaller than the number required, data will be silently discarded.
       remove_zeros : bool (default=True). If True, remove explicit zeros from the data
         as part of summing duplicates. If False, then explicit zeros at unique indices
-        will remain among the specified elements.
+        will remain among the specified elements. Note: remove_zeros=True is incompatible
+        with autodiff.
     """
     data, indices = _bcoo_sum_duplicates(self.data, self.indices, self.shape,
                                          nse=nse, remove_zeros=remove_zeros)
diff --git a/tests/sparse_test.py b/tests/sparse_test.py
index 241bd2e44..ab3bb18d3 100644
--- a/tests/sparse_test.py
+++ b/tests/sparse_test.py
@@ -1454,6 +1454,38 @@ class BCOOTest(jtu.JaxTestCase):
     self.assertAllClose(jf_dense_0, jf_sparse_0, rtol=tol)
     self.assertAllClose(jf_dense_1, jf_sparse_1, rtol=tol)
 
+  def test_bcoo_spdot_general_ad_bug(self):
+    # Regression test for https://github.com/google/jax/issues/10163
+    A_indices = jnp.array([[0, 1], [0, 2], [1, 1], [1, 2], [1, 0]])
+    A_values = jnp.array([-2.0, 1.0, -1.0, 0.5, 2.0])
+    A_shape = (2, 3)
+
+    B_indices = jnp.array([[0, 2], [2, 1], [0, 3], [1, 3], [1, 0], [0, 0]])
+    B_values = jnp.array([10.0, 100.0, 1000.0, -5.0, -50.0, -500.0])
+    B_shape = (3, 4)
+
+    def sp_sp_product(v1, v2):
+        A = sparse.BCOO((v1, A_indices), shape=A_shape)
+        B = sparse.BCOO((v2, B_indices), shape=B_shape)
+        return (A @ B).todense()
+
+    def sp_de_product(v1, v2):
+        A = sparse.BCOO((v1, A_indices), shape=A_shape)
+        B = sparse.BCOO((v2, B_indices), shape=B_shape).todense()
+        return A @ B
+
+    def de_de_product(v1, v2):
+        sparse1 = sparse.BCOO((v1, A_indices), shape=A_shape).todense()
+        dense2 = sparse.BCOO((v2, B_indices), shape=B_shape).todense()
+        return sparse1 @ dense2
+
+    sp_sp_jac = jax.jacfwd(sp_sp_product, argnums=1)(A_values, B_values)
+    sp_de_jac = jax.jacfwd(sp_de_product, argnums=1)(A_values, B_values)
+    de_de_jac = jax.jacfwd(de_de_product, argnums=1)(A_values, B_values)
+
+    self.assertAllClose(sp_sp_jac, de_de_jac)
+    self.assertAllClose(sp_de_jac, de_de_jac)
+
   @unittest.skipIf(jtu.device_under_test() == "tpu", "TPU has insufficient precision")
   @parameterized.named_parameters(jtu.cases_from_list(
       {"testcase_name": "_{}[n_batch={}]_{}[n_batch={}]_in_axes={}".format(
['tests/sparse_test.py', 'jax/experimental/sparse/bcoo.py']