diff --git a/aeon/classification/convolution_based/_mr_hydra.py b/aeon/classification/convolution_based/_mr_hydra.py
index c9c90a034d..93cdb4f6fe 100644
--- a/aeon/classification/convolution_based/_mr_hydra.py
+++ b/aeon/classification/convolution_based/_mr_hydra.py
@@ -8,11 +8,12 @@
 from sklearn.linear_model import RidgeClassifierCV
 from sklearn.preprocessing import StandardScaler
 
+from aeon.base._base import _clone_estimator
 from aeon.classification import BaseClassifier
 from aeon.classification.convolution_based._hydra import _SparseScaler
 from aeon.transformations.collection.convolution_based import MultiRocket
 from aeon.transformations.collection.convolution_based._hydra import HydraTransformer
-from aeon.utils.validation import check_n_jobs
+from aeon.utils.validation import check_lapack_svd_safe, check_n_jobs
 
 
 class MultiRocketHydraClassifier(BaseClassifier):
@@ -30,6 +31,9 @@ class MultiRocketHydraClassifier(BaseClassifier):
         Number of kernels per group for the Hydra transform.
     n_groups : int, default=64
         Number of groups per dilation for the Hydra transform.
+    estimator : sklearn compatible classifier or None, default=None
+        The estimator used. If None, a RidgeClassifierCV(alphas=np.logspace(-3, 3, 10))
+        is used.
     class_weight{None, “balanced”}, dict or list of dicts, default=None
         From sklearn documentation:
         If None, all classes are assigned equal weights.
@@ -57,6 +61,8 @@ class MultiRocketHydraClassifier(BaseClassifier):
         Number of classes. Extracted from the data.
     classes_ : ndarray of shape (n_classes_)
         Holds the label for each class.
+    estimator_ : sklearn classifier
+        The fitted estimator.
 
     See Also
     --------
@@ -93,12 +99,14 @@ def __init__(
         self,
         n_kernels: int = 8,
         n_groups: int = 64,
+        estimator=None,
         class_weight=None,
         n_jobs: int = 1,
         random_state=None,
     ):
         self.n_kernels = n_kernels
         self.n_groups = n_groups
+        self.estimator = estimator
         self.class_weight = class_weight
         self.n_jobs = n_jobs
         self.random_state = random_state
@@ -130,10 +138,24 @@ def _fit(self, X, y):
 
         Xt = np.concatenate((Xt_hydra, Xt_multirocket), axis=1)
 
-        self.classifier = RidgeClassifierCV(
-            alphas=np.logspace(-3, 3, 10), class_weight=self.class_weight
+        _using_default_estimator = self.estimator is None
+
+        self.estimator_ = _clone_estimator(
+            (
+                RidgeClassifierCV(
+                    alphas=np.logspace(-3, 3, 10), class_weight=self.class_weight
+                )
+                if _using_default_estimator
+                else self.estimator
+            ),
+            self.random_state,
         )
-        self.classifier.fit(Xt, y)
+
+        if _using_default_estimator:
+            n_samples, n_features = Xt.shape
+            check_lapack_svd_safe(n_samples, n_features, "MultiRocketHydraClassifier")
+
+        self.estimator_.fit(Xt, y)
 
         return self
 
@@ -146,4 +168,20 @@ def _predict(self, X) -> np.ndarray:
 
         Xt = np.concatenate((Xt_hydra, Xt_multirocket), axis=1)
 
-        return self.classifier.predict(Xt)
+        return self.estimator_.predict(Xt)
+
+    @classmethod
+    def _get_test_params(cls, parameter_set: str = "default") -> dict:
+        """Return testing parameter settings for the estimator.
+
+        Parameters
+        ----------
+        parameter_set : str, default="default"
+            Name of the set of test parameters to return, for use in tests.
+
+        Returns
+        -------
+        params : dict
+            Parameters to create testing instances of the class.
+        """
+        return {"n_kernels": 2, "n_groups": 2}
diff --git a/aeon/classification/convolution_based/_rocket.py b/aeon/classification/convolution_based/_rocket.py
index 8ff7cc4be4..3fdb7380ee 100644
--- a/aeon/classification/convolution_based/_rocket.py
+++ b/aeon/classification/convolution_based/_rocket.py
@@ -8,13 +8,12 @@
 
 import numpy as np
 from sklearn.linear_model import RidgeClassifierCV
-from sklearn.pipeline import make_pipeline
 from sklearn.preprocessing import StandardScaler
 
 from aeon.base._base import _clone_estimator
 from aeon.classification import BaseClassifier
 from aeon.transformations.collection.convolution_based import Rocket
-from aeon.utils.validation import check_n_jobs
+from aeon.utils.validation import check_lapack_svd_safe, check_n_jobs
 
 
 class RocketClassifier(BaseClassifier):
@@ -139,23 +138,28 @@ def _fit(self, X, y):
             random_state=self.random_state,
         )
         self._scaler = StandardScaler(with_mean=False)
+
+        _using_default_estimator = self.estimator is None
+
         self.estimator_ = _clone_estimator(
             (
                 RidgeClassifierCV(
                     alphas=np.logspace(-3, 3, 10), class_weight=self.class_weight
                 )
-                if self.estimator is None
+                if _using_default_estimator
                 else self.estimator
             ),
             self.random_state,
         )
 
-        self.pipeline_ = make_pipeline(
-            self._transformer,
-            self._scaler,
-            self.estimator_,
-        )
-        self.pipeline_.fit(X, y)
+        X_t = self._transformer.fit_transform(X)
+        X_t = self._scaler.fit_transform(X_t)
+
+        if _using_default_estimator:
+            n_samples, n_features = X_t.shape
+            check_lapack_svd_safe(n_samples, n_features, "RocketClassifier")
+
+        self.estimator_.fit(X_t, y)
 
         return self
 
@@ -172,7 +176,10 @@ def _predict(self, X) -> np.ndarray:
         y : array-like, shape = (n_cases,)
             Predicted class labels.
         """
-        return self.pipeline_.predict(X)
+        X_t = self._transformer.transform(X)
+        X_t = self._scaler.transform(X_t)
+
+        return self.estimator_.predict(X_t)
 
     def _predict_proba(self, X) -> np.ndarray:
         """Predicts labels probabilities for sequences in X.
@@ -187,12 +194,15 @@ def _predict_proba(self, X) -> np.ndarray:
         y : array-like, shape = (n_cases, n_classes_)
             Predicted probabilities using the ordering in classes_.
         """
+        X_t = self._transformer.transform(X)
+        X_t = self._scaler.transform(X_t)
+
         m = getattr(self.estimator_, "predict_proba", None)
         if callable(m):
-            return self.pipeline_.predict_proba(X)
+            return self.estimator_.predict_proba(X_t)
         else:
             dists = np.zeros((len(X), self.n_classes_))
-            preds = self.pipeline_.predict(X)
+            preds = self.estimator_.predict(X_t)
             for i in range(0, len(X)):
                 dists[i, np.where(self.classes_ == preds[i])] = 1
             return dists
diff --git a/aeon/classification/convolution_based/tests/test_mr_hydra.py b/aeon/classification/convolution_based/tests/test_mr_hydra.py
new file mode 100644
index 0000000000..f74af766b6
--- /dev/null
+++ b/aeon/classification/convolution_based/tests/test_mr_hydra.py
@@ -0,0 +1,53 @@
+"""MultiRocketHydra classifier tests."""
+
+from unittest.mock import patch
+
+import pytest
+from sklearn.linear_model import RidgeClassifier
+
+from aeon.classification.convolution_based import MultiRocketHydraClassifier
+from aeon.testing.data_generation import make_example_3d_numpy
+from aeon.utils.validation._dependencies import _check_soft_dependencies
+
+
+@pytest.mark.skipif(
+    not _check_soft_dependencies("torch", severity="none"),
+    reason="skip test if required soft dependency not available",
+)
+def test_mrhydra_calls_lapack_check_with_default_estimator():
+    """Check LAPACK safety when using the default estimator.
+
+    MultiRocketHydra should call check_lapack_svd_safe when estimator is None.
+    """
+    X, y = make_example_3d_numpy(n_cases=10, n_channels=1, n_timepoints=12)
+    clf = MultiRocketHydraClassifier(n_kernels=2, n_groups=2)
+
+    with patch(
+        "aeon.classification.convolution_based._mr_hydra.check_lapack_svd_safe"
+    ) as mock_check:
+        clf.fit(X, y)
+
+    mock_check.assert_called_once()
+    args, _ = mock_check.call_args
+    assert args[2] == "MultiRocketHydraClassifier"
+
+
+@pytest.mark.skipif(
+    not _check_soft_dependencies("torch", severity="none"),
+    reason="skip test if required soft dependency not available",
+)
+def test_mrhydra_skips_lapack_check_with_custom_estimator():
+    """Skip the LAPACK safety check with a custom estimator.
+
+    MultiRocketHydra should not call check_lapack_svd_safe when a custom
+    estimator is supplied.
+    """
+    X, y = make_example_3d_numpy(n_cases=10, n_channels=1, n_timepoints=12)
+    clf = MultiRocketHydraClassifier(n_kernels=2, estimator=RidgeClassifier())
+
+    with patch(
+        "aeon.classification.convolution_based._mr_hydra.check_lapack_svd_safe"
+    ) as mock_check:
+        clf.fit(X, y)
+
+    mock_check.assert_not_called()
diff --git a/aeon/classification/convolution_based/tests/test_rocket.py b/aeon/classification/convolution_based/tests/test_rocket.py
new file mode 100644
index 0000000000..7d33e5ab20
--- /dev/null
+++ b/aeon/classification/convolution_based/tests/test_rocket.py
@@ -0,0 +1,36 @@
+"""Rocket classifier tests."""
+
+from unittest.mock import patch
+
+from sklearn.linear_model import RidgeClassifier
+
+from aeon.classification.convolution_based import RocketClassifier
+from aeon.testing.data_generation import make_example_3d_numpy
+
+
+def test_rocket_calls_lapack_check_with_default_estimator():
+    """RocketClassifier should call check_lapack_svd_safe when estimator is None."""
+    X, y = make_example_3d_numpy(n_cases=10, n_channels=1, n_timepoints=12)
+    clf = RocketClassifier(n_kernels=20)
+
+    with patch(
+        "aeon.classification.convolution_based._rocket.check_lapack_svd_safe"
+    ) as mock_check:
+        clf.fit(X, y)
+
+    mock_check.assert_called_once()
+    args, _ = mock_check.call_args
+    assert args[2] == "RocketClassifier"
+
+
+def test_rocket_skips_lapack_check_with_custom_estimator():
+    """RocketClassifier should not call check_lapack_svd_safe with custom estimator."""
+    X, y = make_example_3d_numpy(n_cases=10, n_channels=1, n_timepoints=12)
+    clf = RocketClassifier(n_kernels=20, estimator=RidgeClassifier())
+
+    with patch(
+        "aeon.classification.convolution_based._rocket.check_lapack_svd_safe"
+    ) as mock_check:
+        clf.fit(X, y)
+
+    mock_check.assert_not_called()
diff --git a/aeon/classification/shapelet_based/_rdst.py b/aeon/classification/shapelet_based/_rdst.py
index ebff3b56c2..9faded6db4 100644
--- a/aeon/classification/shapelet_based/_rdst.py
+++ b/aeon/classification/shapelet_based/_rdst.py
@@ -18,7 +18,7 @@
 from aeon.transformations.collection.shapelet_based import (
     RandomDilatedShapeletTransform,
 )
-from aeon.utils.validation import check_n_jobs
+from aeon.utils.validation import check_lapack_svd_safe, check_n_jobs
 
 
 class RDSTClassifier(BaseClassifier):
@@ -201,7 +201,9 @@ def _fit(self, X, y):
             random_state=self.random_state,
         )
 
-        if self.estimator is None:
+        _using_default_estimator = self.estimator is None
+
+        if _using_default_estimator:
             self.estimator_ = make_pipeline(
                 StandardScaler(with_mean=True),
                 RidgeClassifierCV(
@@ -221,6 +223,10 @@ def _fit(self, X, y):
         if self.save_transformed_data:
             self.transformed_data_ = X_t
 
+        if _using_default_estimator:
+            n_samples, n_features = X_t.shape
+            check_lapack_svd_safe(n_samples, n_features, "RDSTClassifier")
+
         self.estimator_.fit(X_t, y)
 
         return self
diff --git a/aeon/classification/shapelet_based/tests/test_rdst.py b/aeon/classification/shapelet_based/tests/test_rdst.py
index b1e050b313..1ddd7c32b7 100644
--- a/aeon/classification/shapelet_based/tests/test_rdst.py
+++ b/aeon/classification/shapelet_based/tests/test_rdst.py
@@ -1,5 +1,7 @@
 """RDST tests."""
 
+from unittest.mock import patch
+
 import numpy as np
 from sklearn.ensemble import RandomForestClassifier
 
@@ -31,3 +33,33 @@ def test_rdst_estimator_attribute_lifecycle():
 
     assert hasattr(model, "estimator_")
     assert not hasattr(model, "_estimator")
+
+
+def test_rdst_calls_lapack_check_with_default_estimator():
+    """RDSTClassifier should call check_lapack_svd_safe when estimator is None."""
+    X, y = make_example_3d_numpy(n_cases=10, n_channels=1, n_timepoints=12)
+    clf = RDSTClassifier(max_shapelets=5)
+
+    with patch(
+        "aeon.classification.shapelet_based._rdst.check_lapack_svd_safe"
+    ) as mock_check:
+        clf.fit(X, y)
+
+    mock_check.assert_called_once()
+    args, _ = mock_check.call_args
+    assert args[2] == "RDSTClassifier"
+
+
+def test_rdst_skips_lapack_check_with_custom_estimator():
+    """RDSTClassifier should not call check_lapack_svd_safe with a custom estimator."""
+    from sklearn.linear_model import RidgeClassifier
+
+    X, y = make_example_3d_numpy(n_cases=10, n_channels=1, n_timepoints=12)
+    clf = RDSTClassifier(max_shapelets=5, estimator=RidgeClassifier())
+
+    with patch(
+        "aeon.classification.shapelet_based._rdst.check_lapack_svd_safe"
+    ) as mock_check:
+        clf.fit(X, y)
+
+    mock_check.assert_not_called()
diff --git a/aeon/utils/validation/__init__.py b/aeon/utils/validation/__init__.py
index 5ab60b19bf..bcac6e12f6 100644
--- a/aeon/utils/validation/__init__.py
+++ b/aeon/utils/validation/__init__.py
@@ -1,11 +1,14 @@
 """Validation and checking functions for time series."""
 
 __all__ = [
+    "check_lapack_svd_safe",
     "check_n_jobs",
 ]
 
 import os
 
+import numpy as np
+
 
 def check_n_jobs(n_jobs: int) -> int:
     """Check `n_jobs` parameter according to the scikit-learn convention.
@@ -34,3 +37,38 @@ def check_n_jobs(n_jobs: int) -> int:
         return max(1, os.cpu_count() + 1 + n_jobs)
     else:
         return n_jobs
+
+
+def check_lapack_svd_safe(n_samples: int, n_features: int, estimator_name: str) -> None:
+    """Raise an informative error if a matrix is too large for LAPACK SVD.
+
+    Matrices with more than ``2**31 - 1`` elements may overflow 32-bit integer
+    indexing used internally by LAPACK during SVD-based operations.
+
+    Parameters
+    ----------
+    n_samples : int
+        Number of rows in the matrix.
+    n_features : int
+        Number of columns in the matrix.
+    estimator_name : str
+        Name of the calling estimator, used in the error message.
+
+    Raises
+    ------
+    ValueError
+        If ``n_samples * n_features`` exceeds the 32-bit LAPACK indexing limit.
+    """
+    n_elements = int(n_samples) * int(n_features)
+    limit = np.iinfo(np.int32).max
+
+    if n_elements > limit:
+        raise ValueError(
+            f"{estimator_name} cannot process this data because the "
+            f"transformed feature matrix has {n_samples} samples and "
+            f"{n_features} features ({n_elements} elements), exceeding "
+            f"the {limit} element limit for 32-bit LAPACK indexing during "
+            "SVD-based operations. This limitation is independent of "
+            "available RAM. Use an estimator or solver that does not rely "
+            "on the affected SVD-based operation."
+        )
diff --git a/aeon/utils/validation/tests/test_check_lapack_svd_safe.py b/aeon/utils/validation/tests/test_check_lapack_svd_safe.py
new file mode 100644
index 0000000000..9208bea1a5
--- /dev/null
+++ b/aeon/utils/validation/tests/test_check_lapack_svd_safe.py
@@ -0,0 +1,42 @@
+"""Tests for check_lapack_svd_safe."""
+
+import numpy as np
+import pytest
+
+from aeon.utils.validation import check_lapack_svd_safe
+
+
+def test_check_lapack_svd_safe_under_limit():
+    """Matrices under the 32-bit LAPACK element limit should not raise."""
+    limit = np.iinfo(np.int32).max
+    n_samples = 1000
+    n_features = limit // n_samples - 1
+
+    check_lapack_svd_safe(n_samples, n_features, "TestEstimator")
+
+
+def test_check_lapack_svd_safe_at_limit():
+    """Exactly at the limit should not raise."""
+    limit = np.iinfo(np.int32).max
+    n_samples = 1
+    n_features = limit
+
+    check_lapack_svd_safe(n_samples, n_features, "TestEstimator")
+
+
+def test_check_lapack_svd_safe_over_limit():
+    """Matrices exceeding the limit should raise an informative ValueError."""
+    n_samples = 112_186
+    n_features = 30_000
+
+    with pytest.raises(ValueError, match="TestEstimator"):
+        check_lapack_svd_safe(n_samples, n_features, "TestEstimator")
+
+
+def test_check_lapack_svd_safe_message_mentions_element_count():
+    """The raised error should surface sample/feature/element counts."""
+    n_samples = 200_000
+    n_features = 20_000
+
+    with pytest.raises(ValueError, match=str(n_samples * n_features)):
+        check_lapack_svd_safe(n_samples, n_features, "TestEstimator")
diff --git a/docs/api_reference/utils.md b/docs/api_reference/utils.md
index 2c6ad93ec4..05bedc7f56 100644
--- a/docs/api_reference/utils.md
+++ b/docs/api_reference/utils.md
@@ -176,6 +176,7 @@
     is_date_offset
     is_timedelta_or_date_offset
     check_n_jobs
+    check_lapack_svd_safe
     check_window_length
     get_n_cases
     get_type