diff --git a/curvlinops/_torch_base.py b/curvlinops/_torch_base.py
index dbb27c3..5819228 100644
--- a/curvlinops/_torch_base.py
+++ b/curvlinops/_torch_base.py
@@ -647,7 +647,8 @@ def _check_deterministic(self):
 
         - Two independent applications of matvec onto the same vector yield different
           results
-        - Two independent loss/gradient computations yield different results
+        - Two independent total loss/gradient computations yield different results
+        - If ``FIXED_DATA_ORDER`` is ``True`` and any mini-batch quantity differs.
 
         Note:
             Deterministic checks should be performed on CPU. We noticed that even when
@@ -712,15 +713,28 @@ def _check_deterministic(self):
 
     def __check_deterministic_batch(
         self,
-        Xs,
-        ys,
-        predictions,
-        losses,
-        gradients,
+        Xs: Tuple[Union[Tensor, MutableMapping], Union[Tensor, MutableMapping]],
+        ys: Tuple[Tensor, Tensor],
+        predictions: Tuple[Tensor, Tensor],
+        losses: Tuple[Optional[Tensor], Optional[Tensor]],
+        gradients: Tuple[Optional[List[Tensor]], Optional[List[Tensor]]],
         rtol: float = 1e-5,
         atol: float = 1e-8,
     ):
-        """Check that the data loader always returns the same order of data."""
+        """Compare two outputs of ``self.data_prediction_loss_gradient``.
+
+        Args:
+            Xs: The two data inputs to compare.
+            ys: The two data targets to compare.
+            predictions: The two predictions to compare.
+            losses: The two losses to compare.
+            gradients: The two gradients to compare.
+            rtol: Relative tolerance for comparison. Default is 1e-5.
+            atol: Absolute tolerance for comparison. Default is 1e-8.
+
+        Raises:
+            RuntimeError: If any of the pairs mismatch.
+        """
 
         X1, X2 = Xs
         if isinstance(X1, MutableMapping) and isinstance(X2, MutableMapping):
@@ -754,6 +768,14 @@ def __check_deterministic_batch(
                 raise RuntimeError("Check for deterministic batch gradient failed.")
 
     def __check_deterministic_matvec(self, rtol: float = 1e-5, atol: float = 1e-8):
+        """Probe whether the linear operator's matrix-vector product is deterministic.
+
+        Performs two sequential matrix-vector products and compares them.
+
+        Args:
+            rtol: Relative tolerance for comparison. Defaults to ``1e-5``.
+            atol: Absolute tolerance for comparison. Defaults to ``1e-8``.
+        """
         v = rand(self.shape[1], device=self._device, dtype=self._infer_dtype())
         Av1 = self @ v
         Av2 = self @ v