diff --git a/backpack/extensions/firstorder/batch_dot_grad/base.py b/backpack/extensions/firstorder/batch_dot_grad/base.py
new file mode 100644
index 00000000..041e1447
--- /dev/null
+++ b/backpack/extensions/firstorder/batch_dot_grad/base.py
@@ -0,0 +1,31 @@
+"""Base class for extension ``BatchDotGrad``."""
+
+import torch
+
+from backpack.extensions.firstorder.base import FirstOrderModuleExtension
+
+
+class BatchDotGradBase(FirstOrderModuleExtension):
+    def __init__(self, derivatives, params=None):
+        self.derivatives = derivatives
+        super().__init__(params=params)
+
+    def bias(self, ext, module, g_inp, g_out, bpQuantities):
+        grad_batch = self.derivatives.bias_jac_t_mat_prod(
+            module, g_inp, g_out, g_out[0], sum_batch=False
+        )
+        return self.pairwise_dot(grad_batch)
+
+    def weight(self, ext, module, g_inp, g_out, bpQuantities):
+        grad_batch = self.derivatives.weight_jac_t_mat_prod(
+            module, g_inp, g_out, g_out[0], sum_batch=False
+        )
+        return self.pairwise_dot(grad_batch)
+
+    @staticmethod
+    def pairwise_dot(grad_batch):
+        """Compute pairwise dot products of individual gradients."""
+        # flatten all feature dimensions
+        grad_batch_flat = grad_batch.flatten(start_dim=1)
+        # pairwise dot product
+        return torch.einsum("if,jf->ij", grad_batch_flat, grad_batch_flat)
diff --git a/backpack/extensions/firstorder/batch_dot_grad/linear.py b/backpack/extensions/firstorder/batch_dot_grad/linear.py
index 59c39419..c7af76ce 100644
--- a/backpack/extensions/firstorder/batch_dot_grad/linear.py
+++ b/backpack/extensions/firstorder/batch_dot_grad/linear.py
@@ -1,31 +1,7 @@
-import torch
-
 from backpack.core.derivatives.linear import LinearDerivatives
-from backpack.extensions.firstorder.base import FirstOrderModuleExtension
+from backpack.extensions.firstorder.batch_dot_grad.base import BatchDotGradBase
 
 
-class BatchDotGradLinear(FirstOrderModuleExtension):
+class BatchDotGradLinear(BatchDotGradBase):
     def __init__(self):
-        self.derivatives = LinearDerivatives()
-        super().__init__(params=["bias", "weight"])
-
-    def bias(self, ext, module, g_inp, g_out, bpQuantities):
-        # Return value will be stored in savefield of extension
-        grad_batch = self.derivatives.bias_jac_t_mat_prod(
-            module, g_inp, g_out, g_out[0], sum_batch=False
-        )
-        return self.pairwise_dot(grad_batch)
-
-    def weight(self, ext, module, g_inp, g_out, bpQuantities):
-        # Return value will be stored in savefield of extension
-        grad_batch = self.derivatives.weight_jac_t_mat_prod(
-            module, g_inp, g_out, g_out[0], sum_batch=False
-        )
-        return self.pairwise_dot(grad_batch)
-
-    @staticmethod
-    def pairwise_dot(grad_batch):
-        # flatten all feature dimensions
-        grad_batch_flat = grad_batch.flatten(start_dim=1)
-        # pairwise dot product
-        return torch.einsum("if,jf->ij", grad_batch_flat, grad_batch_flat)
+        super().__init__(derivatives=LinearDerivatives(), params=["bias", "weight"])