diff --git a/docs/source/whats_new.rst b/docs/source/whats_new.rst
index 08418d41e..0e53aa045 100644
--- a/docs/source/whats_new.rst
+++ b/docs/source/whats_new.rst
@@ -39,6 +39,7 @@ Enhancements
 - Re-enable auto-execution of the Riemannian Artifact Rejection tutorial (``examples/advanced_examples/plot_riemannian_artifact_rejection.py``) now that pyRiemann 0.11 is on PyPI with per-potato metrics and ``method_combination`` support on ``PotatoField`` (by `Bruno Aristimunha`_)
 - Use NEMAR as the default download source for datasets with an assigned ``nemar_id``, while preserving existing dataset-specific downloaders as a fallback (by `Bruno Aristimunha`_).
 - Add :class:`moabb.datasets.preprocessing.EuclideanAlignment`, a trial-level Euclidean Alignment transformer (He & Wu 2020; Junqueira et al. 2024) that whitens each trial by the inverse square root of the Euclidean mean covariance to remove per-domain covariance shift before a (deep) model sees the data. Inductive and leakage-free by default (``fit`` learns the reference from training trials, ``transform`` re-applies it to unseen trials); ``fit_transform`` gives the transductive, per-recording form. Accepts an :class:`mne.BaseEpochs` or an ``(n_trials, n_channels, n_times)`` ndarray, uses a shrinkage covariance estimator (``"lwf"``) for robustness, and adds no new dependency (``pyriemann >= 0.11`` is already required). Distinct from :class:`pyriemann.transfer.TLCenter`, which recenters covariance *matrices* (:gh:`1108` by `Bruno Aristimunha`_).
+- Add :file:`examples/advanced_examples/plot_geometry_aware_recentering.py`, reproducing the within/cross double dissociation showing unsupervised test-time tangent-space recentering (``TangentSpace(tsupdate=True)``) drives the cross-session gain in EEG motor-imagery decoding, with no corresponding within-session effect (Rahimipour et al., in preparation) (by `Meysam Rahimipour`_).
 - Drive cross-validation folds with any stock scikit-learn cross-validator passed as ``cv_class``, controlled by a ``groups`` argument — a metadata column name, a list of column names (compound key, e.g. ``["subject", "session"]``), or a callable ``metadata -> array`` — together with callable ``cv_kwargs`` resolved against the metadata (e.g. ``cv_class=PredefinedSplit`` with a ``test_fold`` callable to target a single fold). ``groups`` is exposed on :class:`moabb.evaluations.WithinSessionEvaluation`, :class:`moabb.evaluations.WithinSubjectEvaluation`, :class:`moabb.evaluations.CrossSessionEvaluation` and :class:`moabb.evaluations.CrossSubjectEvaluation` and threaded to their splitters; each splitter keeps its default grouping (``"subject"`` / ``"session"`` / labels) when ``groups`` is ``None``. :class:`moabb.evaluations.splitters.CrossDatasetSplitter` gains ``groups`` (its ``group_column`` argument is now a deprecated alias) (:gh:`1104` by `Bruno Aristimunha`_).
 
 API changes
@@ -852,6 +853,7 @@ API changes
 .. _Anton Andreev: https://github.com/toncho11
 .. _Igor Carrara: https://github.com/carraraig
 .. _Bruno Aristimunha: https://github.com/bruAristimunha
+.. _Meysam Rahimipour: https://github.com/rahimipour-meysam-NeurIPS
 .. _Alexandre Barachant: https://github.com/alexandrebarachant
 .. _Quentin Barthelemy: https://github.com/qbarthelemy
 .. _Erik Bjäreholt: https://github.com/ErikBjare
diff --git a/examples/advanced_examples/plot_geometry_aware_recentering.py b/examples/advanced_examples/plot_geometry_aware_recentering.py
new file mode 100644
index 000000000..7fba36124
--- /dev/null
+++ b/examples/advanced_examples/plot_geometry_aware_recentering.py
@@ -0,0 +1,191 @@
+r"""
+=====================================================
+Geometry-Aware recentering for cross-session transfer
+=====================================================
+EEG covariance statistics drift from session to session (electrode
+repositioning, impedance changes, baseline arousal): the same mental task
+produces differently-shaped data on each recording. A classical Riemannian
+tangent-space pipeline (:class:`pyriemann.tangentspace.TangentSpace`) is
+already a strong baseline for motor-imagery decoding, but its tangent-space
+reference point is normally *frozen* at training time — so it does not
+correct for this drift. Setting ``tsupdate=True`` re-estimates that reference
+point, unsupervised, from each new (unlabelled) evaluation batch: a
+**single, label-free correction** cheap enough to put in front of any linear
+classifier [1]_.
+
+In a controlled, feature-matched benchmark across eight public MOABB
+motor-imagery datasets, Rahimipour, Yang & Van Hulle (in preparation) [1]_
+show that this recentering step accounts for a large, statistically decisive
+cross-session gain (Cohen's d = 1.06-1.50, all p_FDR < 1.1e-12) over its
+recentering-free twin, while the same two pipelines are statistically
+indistinguishable within-session (d ~ 0) — a double dissociation showing the
+gain is attributable to recentering specifically, not to the choice of final
+classifier. The same study found that substantially more complex deep
+sequence models (a bidirectional Mamba mixture-of-experts, an SPDNet-style
+network), given the *same* covariance features and a fair training budget,
+did not recover this gain and in fact underperformed the simple recentering
+pipeline in both protocols.
+
+This example reproduces the core comparison — recentering on vs. off — on
+the workhorse tangent-space + logistic-regression pipeline, following the
+within/cross double-dissociation design of [1]_.
+
+Note
+----
+Unlike :class:`moabb.datasets.preprocessing.EuclideanAlignment`, which
+whitens raw *trials* before any covariance step, this example acts on the
+tangent-space *reference point* used to linearise the SPD manifold — the
+mechanism is closely related to :class:`pyriemann.transfer.TLCenter`
+(matrix/tangent-vector recentering for transfer learning), but is expressed
+here directly via ``TangentSpace(tsupdate=True)`` on a single target session,
+matching how the study in [1]_ evaluates it under MOABB's
+:class:`~moabb.evaluations.CrossSessionEvaluation` /
+:class:`~moabb.evaluations.WithinSessionEvaluation` protocols, with no
+domain-encoding machinery required.
+"""
+
+# Authors: Meysam Rahimipour <rahimipour.2110739@studenti.uniroma1.it>
+#
+# License: BSD (3-clause)
+
+import matplotlib.pyplot as plt
+import mne
+import numpy as np
+from pyriemann.estimation import Covariances
+from pyriemann.tangentspace import TangentSpace
+from sklearn.linear_model import LogisticRegression
+from sklearn.pipeline import make_pipeline
+
+import moabb
+from moabb.datasets import BNCI2014_001
+from moabb.evaluations import CrossSessionEvaluation, WithinSessionEvaluation
+from moabb.paradigms import LeftRightImagery
+
+
+moabb.set_log_level("info")
+mne.set_log_level("WARNING")  # keep the gallery output readable
+
+###############################################################################
+# Build the two pipelines
+# ------------------------
+#
+# Both pipelines are identical except for one flag: whether the tangent-space
+# reference point is re-estimated at transform time (``tsupdate=True``,
+# "Geometry-Aware") or frozen from the training data ("TS + LR", the
+# recentering-free twin). Holding the classifier and covariance estimator
+# fixed isolates recentering as the only difference between the two.
+
+
+def make_geometry_aware(tsupdate):
+    return make_pipeline(
+        Covariances(estimator="oas"),
+        TangentSpace(metric="riemann", tsupdate=tsupdate),
+        LogisticRegression(max_iter=1000, C=1.0),
+    )
+
+
+pipelines = {
+    "Geometry-Aware (recenter)": make_geometry_aware(tsupdate=True),
+    "TS + LR (no recenter)": make_geometry_aware(tsupdate=False),
+}
+
+###############################################################################
+# Cross-session evaluation: where recentering should matter
+# ------------------------------------------------------------
+#
+# :class:`~moabb.evaluations.CrossSessionEvaluation` trains on one session and
+# tests on another (MOABB's standard leave-one-session-out protocol) — exactly
+# the setting where between-session covariance drift is present for
+# recentering to correct.
+
+dataset = BNCI2014_001()
+dataset.subject_list = dataset.subject_list[:4]  # keep the example fast
+paradigm = LeftRightImagery(fmin=8, fmax=32)
+
+cross_session_eval = CrossSessionEvaluation(
+    paradigm=paradigm, datasets=[dataset], overwrite=True, random_state=42
+)
+cross_results = cross_session_eval.process(pipelines)
+
+###############################################################################
+# Within-session evaluation: the control condition
+# ---------------------------------------------------
+#
+# :class:`~moabb.evaluations.WithinSessionEvaluation` trains and tests within
+# the *same* recording session, so there is no between-session shift for
+# recentering to correct. Per [1]_, recentering should therefore make little
+# to no difference here — the mechanism-isolating control for the
+# cross-session result above.
+
+within_session_eval = WithinSessionEvaluation(
+    paradigm=paradigm, datasets=[dataset], overwrite=True, random_state=42
+)
+within_results = within_session_eval.process(pipelines)
+
+###############################################################################
+# The double dissociation
+# -------------------------
+#
+# Plot the mean score per pipeline in both protocols side by side. Per [1]_,
+# the expected pattern is: a clear Geometry-Aware advantage cross-session,
+# and near-parity within-session.
+
+cross_means = cross_results.groupby("pipeline")["score"].mean()
+within_means = within_results.groupby("pipeline")["score"].mean()
+
+fig, ax = plt.subplots(figsize=(6, 4.5))
+x = np.arange(2)
+width = 0.35
+names = list(pipelines.keys())
+for i, name in enumerate(names):
+    vals = [within_means.get(name, np.nan), cross_means.get(name, np.nan)]
+    ax.bar(x + i * width, vals, width, label=name)
+ax.set_xticks(x + width / 2)
+ax.set_xticklabels(["Within-session\n(no drift)", "Cross-session\n(drift)"])
+ax.set_ylabel("Mean score")
+ax.set_title("Recentering helps specifically where there is drift to correct")
+ax.legend()
+fig.tight_layout()
+plt.show()
+
+print("Within-session means:\n", within_means)
+print("\nCross-session means:\n", cross_results.groupby("pipeline")["score"].mean())
+
+###############################################################################
+# Using it inside your own evaluation
+# --------------------------------------
+#
+# The recentering step is a single argument, no new dependency, and drops
+# into any tangent-space pipeline::
+#
+#     from pyriemann.estimation import Covariances
+#     from pyriemann.tangentspace import TangentSpace
+#     from sklearn.linear_model import LogisticRegression
+#     from sklearn.pipeline import make_pipeline
+#
+#     pipelines = {
+#         "Geometry-Aware": make_pipeline(
+#             Covariances(estimator="oas"),
+#             TangentSpace(metric="riemann", tsupdate=True),
+#             LogisticRegression(max_iter=1000),
+#         )
+#     }
+#
+# As in the note above, use ``tsupdate=True`` under
+# :class:`~moabb.evaluations.CrossSessionEvaluation` /
+# :class:`~moabb.evaluations.CrossSubjectEvaluation` (there is a shift to
+# correct), and ``tsupdate=False`` under
+# :class:`~moabb.evaluations.WithinSessionEvaluation` (there is not) — mixing
+# these up is exactly the confound the double-dissociation design in [1]_ is
+# built to rule out.
+#
+# For the full eight-dataset benchmark, deep-model comparison (bidirectional
+# Mamba mixture-of-experts, SPDNet), and complete statistical validation
+# (Friedman omnibus, FDR/Holm-corrected Wilcoxon, Cohen's d, bootstrap CIs,
+# Critical-Difference analysis), see [1]_.
+#
+# References
+# ----------
+# .. [1] Rahimipour, M., Yang, L., & Van Hulle, M. Simple Geometric
+#        Recentering Rivals Deep Sequence Models for Cross-Session EEG
+#        Motor-Imagery Decoding. In preparation, 2026.