diff --git a/docs/core_concepts/configuration.md b/docs/core_concepts/configuration.md
index c5fa21d..f724512 100644
--- a/docs/core_concepts/configuration.md
+++ b/docs/core_concepts/configuration.md
@@ -51,6 +51,15 @@ example `{"feature_0": "rbf"}`. Check `numerical_features_` / `categorical_featu
 overrides, rather than guessing the column order.
 ```
 
+At `transform`, array columns are matched by position, so the training and serving
+containers may differ, as in scikit-learn. A `Preprocessor` fitted on a `DataFrame` accepts
+the same data as an array of the same width (for example `df.to_numpy()` in NumPy-based
+serving or an explainer such as `shap.KernelExplainer`). It warns that `X` does not have
+valid feature names and re-infers the numeric columns of an object array. One fitted on an
+array accepts a `DataFrame` of the same width the same way, with a warning that `X` has
+feature names. Input matched by position with a different number of columns raises the usual
+`X has 4 features, but Preprocessor is expecting 3 features as input.` error.
+
 ## Per-feature overrides
 
 Columns rarely want identical treatment. The `feature_preprocessing` dict assigns a strategy
diff --git a/pretab/preprocessor.py b/pretab/preprocessor.py
index a8193b8..3e384f3 100644
--- a/pretab/preprocessor.py
+++ b/pretab/preprocessor.py
@@ -613,7 +613,12 @@ def transform(self, X, embeddings=None, return_array=None):
         Parameters
         ----------
         X : pandas.DataFrame, numpy.ndarray, or dict
-            Input features to transform.
+            Input features to transform. A DataFrame or dict is matched to the fitted
+            columns by name. A NumPy array is matched by position: after a fit on named
+            columns it takes those names (numeric columns of an object array are
+            re-inferred), with scikit-learn's usual warning that ``X`` does not have
+            valid feature names. Likewise, a DataFrame passed after a fit on an array
+            is matched by position, with a warning that ``X`` has feature names.
         embeddings : np.ndarray or list of np.ndarray, optional
             External embeddings to attach to dictionary output. Required when
             embeddings were supplied during ``fit`` and unsupported when the
@@ -632,11 +637,17 @@ def transform(self, X, embeddings=None, return_array=None):
             (or ``return_array=False``); a SciPy CSR matrix (or CSR blocks) when
             ``output_format`` resolves to ``"sparse"``; or a pandas / polars DataFrame
             when configured via :meth:`set_output`.
+
+        Raises
+        ------
+        PretabDataError
+            If input matched by position has a different number of columns than
+            ``n_features_in_``: it could never be routed correctly.
         """
 
         check_is_fitted(self)
 
-        X = to_dataframe(X, copy=True)
+        X = self._align_input(X)
 
         if self.missing_policy == "error":
             self._reject_missing(X)
@@ -822,6 +833,47 @@ def output_dims_(self) -> dict:
                 dims[columns[0]] = width
         return dims
 
+    def _align_input(self, X):
+        """Return ``X`` as a DataFrame whose columns line up with the fitted columns.
+
+        A NumPy array is matched by position. Once the preprocessor was fitted on
+        named columns, an array of the fitted width takes those column labels
+        (numeric columns of an object array are re-inferred), and a DataFrame
+        passed to a preprocessor fitted on an array is matched by position too --
+        both with scikit-learn's usual warning about the missing or unexpected
+        feature names. Any other DataFrame is matched by column label.
+
+        Raises
+        ------
+        PretabDataError
+            If array-like input matched by position has a different number of
+            columns than seen during ``fit``: it could never be routed correctly.
+        """
+        # The ColumnTransformer records the labels it was fitted on whenever they are
+        # all strings; an array fit shows up as the synthetic positional labels.
+        fitted_labels = getattr(self.column_transformer_, "feature_names_in_", None)
+        positional_labels = [f"feature_{i}" for i in range(self.n_features_in_)]
+        fitted_on_array = fitted_labels is not None and list(fitted_labels) == positional_labels
+
+        is_array = isinstance(X, np.ndarray)
+        X = to_dataframe(X, copy=True)
+        if not (is_array or (fitted_on_array and list(X.columns) != positional_labels)):
+            return X
+        if X.shape[1] != self.n_features_in_:
+            raise PretabDataError(
+                f"X has {X.shape[1]} features, but {type(self).__name__} is expecting "
+                f"{self.n_features_in_} features as input."
+            )
+        if fitted_labels is None or list(X.columns) == list(fitted_labels):
+            return X
+        if fitted_on_array:
+            message = f"X has feature names, but {type(self).__name__} was fitted without feature names"
+        else:
+            message = f"X does not have valid feature names, but {type(self).__name__} was fitted with feature names"
+        warnings.warn(message, UserWarning, stacklevel=3)
+        X = X.set_axis(list(fitted_labels), axis=1)
+        return X.infer_objects() if is_array else X
+
     def _output_itemsize(self) -> int:
         """Bytes per element of the dense transformed array.
 
diff --git a/tests/integration/test_preprocessor.py b/tests/integration/test_preprocessor.py
index df9d224..bbc1adf 100644
--- a/tests/integration/test_preprocessor.py
+++ b/tests/integration/test_preprocessor.py
@@ -377,3 +377,52 @@ def test_unknown_feature_preprocessing_key_raises(sample_data):
     X, y = sample_data
     with pytest.raises(InvalidParamError, match="feature_preprocessing"):
         Preprocessor(feature_preprocessing={"nnum1": "minmax"}).fit(X, y)
+
+
+# --- positional input after a named fit (and vice versa) (issue #78) ---------------
+
+
+@pytest.fixture
+def mixed_named_frame():
+    rng = np.random.default_rng(0)
+    frame = pd.DataFrame(
+        {
+            "age": rng.normal(40, 10, 100),
+            "income": rng.normal(50, 10, 100),
+            "city": rng.choice(["a", "b", "c"], 100),
+        }
+    )
+    return frame, rng.normal(size=100)
+
+
+def test_frame_fit_accepts_an_array_of_the_fitted_width(mixed_named_frame):
+    """Regression guard for issue #78: a DataFrame-fitted preprocessor rejected the same
+    data as an array ('columns are missing'), breaking NumPy-based serving and explainers."""
+    from sklearn.linear_model import Ridge
+    from sklearn.pipeline import make_pipeline
+
+    X, y = mixed_named_frame
+    pipe = make_pipeline(Preprocessor(random_state=0), Ridge()).fit(X, y)
+    with pytest.warns(UserWarning, match="does not have valid feature names"):
+        from_array = pipe.predict(X.to_numpy())
+    np.testing.assert_allclose(from_array, pipe.predict(X))
+
+
+def test_array_fit_accepts_a_frame_of_the_fitted_width(mixed_named_frame):
+    X, y = mixed_named_frame
+    numeric = X[["age", "income"]]
+    pre = Preprocessor(numerical_method="minmax").fit(numeric.to_numpy(), y)
+    with pytest.warns(UserWarning, match="fitted without feature names"):
+        from_frame = pre.transform(numeric.rename(columns={"age": "u", "income": "v"}))
+    np.testing.assert_array_equal(from_frame, pre.transform(numeric.to_numpy()))
+
+
+def test_positional_input_of_the_wrong_width_is_rejected(mixed_named_frame):
+    X, y = mixed_named_frame
+    pre = Preprocessor(random_state=0).fit(X, y)
+    with pytest.raises(PretabDataError, match="X has 2 features, but Preprocessor is expecting 3"):
+        pre.transform(X.to_numpy()[:, :2])
+    numeric = X[["age", "income"]]
+    array_fit = Preprocessor(numerical_method="minmax").fit(numeric.to_numpy(), y)
+    with pytest.raises(PretabDataError, match="X has 1 features"):
+        array_fit.transform(X[["age"]])