feat(pi05): synthesize relative proprioceptive history

src/lerobot/datasets/compute_stats.py

@@ -682,6 +682,7 @@ def compute_relative_action_stats(
     chunk_size: int,
     exclude_joints: list[str] | None = None,
     num_workers: int = 0,
+    state_from_action: bool = False,
 ) -> dict[str, np.ndarray]:
     """Compute normalization statistics for relative actions over the full dataset.
 
@@ -700,6 +701,9 @@ def compute_relative_action_stats(
         num_workers: Number of parallel threads for computation. Values ≤1
             mean single-threaded. Numpy releases the GIL so threads give
             real parallelism here.
+        state_from_action: Use the current absolute action as state. This is
+            intended for state-less pose datasets where each action row is the
+            synchronized measured robot pose.
 
     Returns:
         Statistics dict with keys "mean", "std", "min", "max", "q01", …, "q99".
@@ -722,7 +726,7 @@ def compute_relative_action_stats(
 
     logging.info("Loading action/state data for relative action stats...")
     all_actions = np.array(hf_dataset[ACTION], dtype=np.float32)
-    all_states = np.array(hf_dataset[OBS_STATE], dtype=np.float32)
+    all_states = all_actions if state_from_action else np.array(hf_dataset[OBS_STATE], dtype=np.float32)
     episode_indices = np.array(hf_dataset["episode_index"])
 
     valid_starts = _get_valid_chunk_starts(episode_indices, chunk_size)
@@ -777,3 +781,50 @@ def compute_relative_action_stats(
     )
 
     return stats
+
+
+def compute_state_history_stats(
+    hf_dataset,
+    features: dict,
+    history_steps: int,
+    exclude_joints: list[str] | None = None,
+    relative: bool = False,
+) -> dict[str, np.ndarray]:
+    """Compute stats for flattened state history synthesized from absolute actions.
+
+    History is left-padded with the first action of each episode, matching dataset
+    boundary padding. When ``relative`` is enabled, every history pose is expressed
+    relative to its newest pose while excluded dimensions remain absolute.
+    """
+    if history_steps < 1:
+        raise ValueError("history_steps must be at least 1")
+    if exclude_joints is None:
+        exclude_joints = []
+
+    actions = np.asarray(hf_dataset[ACTION], dtype=np.float32)
+    episode_indices = np.asarray(hf_dataset["episode_index"])
+    sample_indices = np.arange(len(actions))
+    episode_starts = np.maximum.accumulate(
+        np.where(
+            np.concatenate(([True], episode_indices[1:] != episode_indices[:-1])),
+            sample_indices,
+            0,
+        )
+    )
+    offsets = np.arange(-(history_steps - 1), 1)
+    history_indices = np.maximum(sample_indices[:, None] + offsets[None, :], episode_starts[:, None])
+    history = actions[history_indices].copy()
+
+    if relative:
+        state_dim = actions.shape[-1]
+        names = features.get(ACTION, {}).get("names")
+        mask_step = RelativeActionsProcessorStep(
+            enabled=True,
+            exclude_joints=exclude_joints,
+            action_names=names,
+        )
+        mask = np.asarray(mask_step._build_mask(state_dim), dtype=np.float32)
+        history[..., : len(mask)] -= history[:, -1:, : len(mask)] * mask[None, None, :]
+
+    flattened = history.reshape(len(history), -1)
+    return get_feature_stats(flattened, axis=0, keepdims=False)

src/lerobot/datasets/dataset_tools.py

@@ -54,6 +54,7 @@ from .compute_stats import (
     aggregate_stats,
     compute_episode_stats,
     compute_relative_action_stats,
+    compute_state_history_stats,
 )
 from .dataset_metadata import LeRobotDatasetMetadata
 from .image_writer import write_image
@@ -1566,6 +1567,10 @@ def recompute_stats(
     relative_exclude_joints: list[str] | None = None,
     chunk_size: int = 50,
     num_workers: int = 0,
+    state_from_action: bool = False,
+    state_history_steps: int = 1,
+    relative_state_history: bool = False,
+    relative_state_exclude_joints: list[str] | None = None,
 ) -> LeRobotDataset:
     """Recompute stats.json from scratch by iterating all episodes.
 
@@ -1583,6 +1588,12 @@ def recompute_stats(
             ``policy.chunk_size``. Only used when ``relative_action=True``.
         num_workers: Number of parallel threads for relative action stats computation.
             Values ≤1 mean single-threaded. Only used when ``relative_action=True``.
+        state_from_action: Use absolute action rows as synthetic state while
+            computing relative-action stats, and write their absolute statistics
+            under ``observation.state``.
+        state_history_steps: Number of consecutive synthesized state samples.
+        relative_state_history: Express state history relative to its newest pose.
+        relative_state_exclude_joints: State dimensions to retain as absolute.
 
     Returns:
         The same dataset with updated stats.
@@ -1606,7 +1617,19 @@ def recompute_stats(
     # (matching what the model sees during training) and skip action in the
     # per-episode pass below.
     relative_action_stats = None
-    if relative_action and ACTION in features and OBS_STATE in features:
+    synthetic_state_stats = None
+    if state_from_action:
+        if ACTION not in features:
+            raise ValueError("state_from_action requires an action feature")
+        synthetic_state_stats = compute_state_history_stats(
+            dataset.hf_dataset,
+            features,
+            history_steps=state_history_steps,
+            exclude_joints=relative_state_exclude_joints,
+            relative=relative_state_history,
+        )
+
+    if relative_action and ACTION in features and (OBS_STATE in features or state_from_action):
         if relative_exclude_joints is None:
             relative_exclude_joints = ["gripper"]
         relative_action_stats = compute_relative_action_stats(
@@ -1615,6 +1638,7 @@ def recompute_stats(
             chunk_size=chunk_size,
             exclude_joints=relative_exclude_joints,
             num_workers=num_workers,
+            state_from_action=state_from_action,
         )
         features_to_compute.pop(ACTION, None)
 
@@ -1654,6 +1678,8 @@ def recompute_stats(
 
     if relative_action_stats is not None:
         new_stats[ACTION] = relative_action_stats
+    if synthetic_state_stats is not None:
+        new_stats[OBS_STATE] = synthetic_state_stats
 
     # Merge: keep existing stats for features we didn't recompute
     if dataset.meta.stats:

src/lerobot/policies/pi05/configuration_pi05.py

@@ -56,6 +56,14 @@ class PI05Config(PreTrainedConfig):
     # Populated at runtime from dataset metadata by make_policy.
     action_feature_names: list[str] | None = None
 
+    # Build proprioception from absolute action samples when the dataset has no
+    # observation.state. With history_steps=2, training samples request t-1 as
+    # well as the normal t..t+chunk_size-1 action targets.
+    state_from_action: bool = False
+    proprioception_history_steps: int = 1
+    use_relative_state_history: bool = False
+    relative_state_exclude_joints: list[str] = field(default_factory=lambda: ["gripper"])
+
     # Real-Time Chunking (RTC) configuration
     rtc_config: RTCConfig | None = None
 
@@ -121,6 +129,9 @@ class PI05Config(PreTrainedConfig):
         if self.dtype not in ["bfloat16", "float32"]:
             raise ValueError(f"Invalid dtype: {self.dtype}")
 
+        if self.proprioception_history_steps < 1:
+            raise ValueError("proprioception_history_steps must be at least 1")
+
     def validate_features(self) -> None:
         """Validate and set up input/output features."""
         for i in range(self.empty_cameras):
@@ -131,13 +142,6 @@ class PI05Config(PreTrainedConfig):
             )
             self.input_features[key] = empty_camera
 
-        if OBS_STATE not in self.input_features:
-            state_feature = PolicyFeature(
-                type=FeatureType.STATE,
-                shape=(self.max_state_dim,),  # Padded to max_state_dim
-            )
-            self.input_features[OBS_STATE] = state_feature
-
         if ACTION not in self.output_features:
             action_feature = PolicyFeature(
                 type=FeatureType.ACTION,
@@ -145,6 +149,25 @@ class PI05Config(PreTrainedConfig):
             )
             self.output_features[ACTION] = action_feature
 
+        if OBS_STATE not in self.input_features:
+            state_shape = (self.max_state_dim,)
+            if self.state_from_action and ACTION in self.output_features:
+                state_shape = self.output_features[ACTION].shape
+            state_feature = PolicyFeature(
+                type=FeatureType.STATE,
+                shape=state_shape,
+            )
+            self.input_features[OBS_STATE] = state_feature
+
+        state_dim = self.input_features[OBS_STATE].shape[-1]
+        history_state_dim = state_dim * self.proprioception_history_steps
+        if history_state_dim > self.max_state_dim:
+            raise ValueError(
+                "Flattened proprioception history exceeds max_state_dim: "
+                f"{state_dim} * {self.proprioception_history_steps} = {history_state_dim} > "
+                f"{self.max_state_dim}"
+            )
+
     def get_optimizer_preset(self) -> AdamWConfig:
         return AdamWConfig(
             lr=self.optimizer_lr,
@@ -168,7 +191,8 @@ class PI05Config(PreTrainedConfig):
 
     @property
     def action_delta_indices(self) -> list:
-        return list(range(self.chunk_size))
+        history_prefix = self.proprioception_history_steps - 1 if self.state_from_action else 0
+        return list(range(-history_prefix, self.chunk_size))
 
     @property
     def reward_delta_indices(self) -> None:

src/lerobot/policies/pi05/processor_pi05.py

@@ -15,7 +15,7 @@
 # limitations under the License.
 
 from copy import deepcopy
-from dataclasses import dataclass
+from dataclasses import dataclass, field
 from typing import Any
 
 import numpy as np
@@ -48,6 +48,144 @@ from lerobot.utils.constants import (
 from .configuration_pi05 import PI05Config
 
 
+@ProcessorStepRegistry.register(name="pi05_state_from_action_processor_step")
+@dataclass
+class Pi05StateFromActionProcessorStep(ProcessorStep):
+    """Synthesize proprioception from absolute actions in state-less datasets.
+
+    The dataset loader supplies ``history_steps - 1`` actions before the normal
+    target chunk. Those leading samples and action(t) become state history; only
+    the leading samples are then removed from the action targets.
+    """
+
+    enabled: bool = False
+    history_steps: int = 1
+    _inference_history: torch.Tensor | None = field(default=None, init=False, repr=False)
+
+    def __call__(self, transition: EnvTransition) -> EnvTransition:
+        if not self.enabled:
+            return transition
+
+        observation = transition.get(TransitionKey.OBSERVATION, {})
+        observed_state = observation.get(OBS_STATE)
+        if observed_state is not None:
+            # At inference the robot normally provides only the current state and
+            # there is no action target. Build a rolling history in the processor.
+            if transition.get(TransitionKey.ACTION) is None and observed_state.ndim == 2:
+                if self._inference_history is None:
+                    self._inference_history = observed_state.unsqueeze(1).repeat(1, self.history_steps, 1)
+                else:
+                    self._inference_history = torch.cat(
+                        [self._inference_history[:, 1:], observed_state.unsqueeze(1)], dim=1
+                    )
+                new_transition = transition.copy()
+                new_observation = dict(observation)
+                new_observation[OBS_STATE] = self._inference_history.clone()
+                new_transition[TransitionKey.OBSERVATION] = new_observation
+                return new_transition
+            return transition
+
+        action = transition.get(TransitionKey.ACTION)
+        if action is None:
+            raise ValueError("Cannot synthesize PI0.5 state without action")
+        if action.ndim != 3:
+            raise ValueError(f"Expected batched action chunks with shape (B, T, D), got {action.shape}")
+        if action.shape[1] < self.history_steps:
+            raise ValueError(
+                f"Action chunk has {action.shape[1]} steps, fewer than history_steps={self.history_steps}"
+            )
+
+        new_transition = transition.copy()
+        new_observation = dict(observation)
+        state = action[:, : self.history_steps].clone()
+        if self.history_steps == 1:
+            state = state[:, 0]
+        new_observation[OBS_STATE] = state
+        new_transition[TransitionKey.OBSERVATION] = new_observation
+        new_transition[TransitionKey.ACTION] = action[:, self.history_steps - 1 :]
+        return new_transition
+
+    def get_config(self) -> dict[str, Any]:
+        return {"enabled": self.enabled, "history_steps": self.history_steps}
+
+    def reset(self) -> None:
+        self._inference_history = None
+
+    def transform_features(
+        self, features: dict[PipelineFeatureType, dict[str, PolicyFeature]]
+    ) -> dict[PipelineFeatureType, dict[str, PolicyFeature]]:
+        return features
+
+
+@ProcessorStepRegistry.register(name="pi05_flatten_state_history_processor_step")
+@dataclass
+class Pi05FlattenStateHistoryProcessorStep(ProcessorStep):
+    """Optionally relativize raw state history, then flatten it for PI0.5."""
+
+    history_steps: int = 1
+    max_state_dim: int = 32
+    relative: bool = False
+    exclude_joints: list[str] = field(default_factory=list)
+    state_names: list[str] | None = None
+
+    def __call__(self, transition: EnvTransition) -> EnvTransition:
+        observation = transition.get(TransitionKey.OBSERVATION, {})
+        state = observation.get(OBS_STATE)
+        if state is None:
+            raise ValueError("State is required for PI05")
+        if self.history_steps == 1 and state.ndim == 2:
+            state = state.unsqueeze(1)
+        if state.ndim != 3 or state.shape[1] != self.history_steps:
+            raise ValueError(
+                f"Expected state history with shape (B, {self.history_steps}, D), got {state.shape}"
+            )
+
+        flattened_dim = state.shape[1] * state.shape[2]
+        if flattened_dim > self.max_state_dim:
+            raise ValueError(
+                f"Flattened state history has {flattened_dim} dimensions, above max_state_dim={self.max_state_dim}"
+            )
+
+        processed_state = state.clone()
+        if self.relative:
+            mask_step = RelativeActionsProcessorStep(
+                enabled=True,
+                exclude_joints=self.exclude_joints,
+                action_names=self.state_names,
+            )
+            mask = torch.tensor(
+                mask_step._build_mask(state.shape[-1]), dtype=state.dtype, device=state.device
+            )
+            reference = state[:, -1:, : mask.shape[0]]
+            processed_state[..., : mask.shape[0]] -= reference * mask
+
+        new_transition = transition.copy()
+        new_observation = dict(observation)
+        new_observation[OBS_STATE] = processed_state.flatten(start_dim=1)
+        new_transition[TransitionKey.OBSERVATION] = new_observation
+        return new_transition
+
+    def get_config(self) -> dict[str, Any]:
+        return {
+            "history_steps": self.history_steps,
+            "max_state_dim": self.max_state_dim,
+            "relative": self.relative,
+            "exclude_joints": self.exclude_joints,
+            "state_names": self.state_names,
+        }
+
+    def transform_features(
+        self, features: dict[PipelineFeatureType, dict[str, PolicyFeature]]
+    ) -> dict[PipelineFeatureType, dict[str, PolicyFeature]]:
+        transformed = deepcopy(features)
+        for feature_group in transformed.values():
+            state_feature = feature_group.get(OBS_STATE)
+            if state_feature is not None and self.history_steps > 1:
+                state_dim = state_feature.shape[-1] * self.history_steps
+                feature_group[OBS_STATE] = PolicyFeature(type=state_feature.type, shape=(state_dim,))
+        return transformed
+
+
 @ProcessorStepRegistry.register(name="pi05_prepare_state_tokenizer_processor_step")
 @dataclass
 class Pi05PrepareStateTokenizerProcessorStep(ProcessorStep):
@@ -139,7 +277,18 @@ def make_pi05_pre_post_processors(
     input_steps: list[ProcessorStep] = [
         RenameObservationsProcessorStep(rename_map={}),  # To mimic the same processor as pretrained one
         AddBatchDimensionProcessorStep(),
+        Pi05StateFromActionProcessorStep(
+            enabled=config.state_from_action,
+            history_steps=config.proprioception_history_steps,
+        ),
         relative_step,
+        Pi05FlattenStateHistoryProcessorStep(
+            history_steps=config.proprioception_history_steps,
+            max_state_dim=config.max_state_dim,
+            relative=config.use_relative_state_history,
+            exclude_joints=config.relative_state_exclude_joints,
+            state_names=config.action_feature_names,
+        ),
         # NOTE: NormalizerProcessorStep MUST come before Pi05PrepareStateTokenizerProcessorStep
         # because the tokenizer step expects normalized state in [-1, 1] range for discretization
         NormalizerProcessorStep(

src/lerobot/processor/relative_action_processor.py

@@ -126,20 +126,24 @@ class RelativeActionsProcessorStep(ProcessorStep):
         observation = transition.get(TransitionKey.OBSERVATION, {})
         state = observation.get(OBS_STATE) if observation else None
 
+        # State history has shape (B, H, D). Relative actions are referenced to
+        # the newest proprioceptive state, not the whole history tensor.
+        reference_state = state[:, -1] if state is not None and state.ndim == 3 else state
+
         # Always cache state for the paired AbsoluteActionsProcessorStep
-        if state is not None:
-            self._last_state = state
+        if reference_state is not None:
+            self._last_state = reference_state
 
         if not self.enabled:
             return transition
 
         new_transition = transition.copy()
         action = new_transition.get(TransitionKey.ACTION)
-        if action is None or state is None:
+        if action is None or reference_state is None:
             return new_transition
 
         mask = self._build_mask(action.shape[-1])
-        new_transition[TransitionKey.ACTION] = to_relative_actions(action, state, mask)
+        new_transition[TransitionKey.ACTION] = to_relative_actions(action, reference_state, mask)
         return new_transition
 
     def get_cached_state(self) -> torch.Tensor | None:

tests/processor/test_pi05_state_from_action.py

@@ -0,0 +1,175 @@
+#!/usr/bin/env python
+
+# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import numpy as np
+import pytest
+import torch
+
+pytest.importorskip("transformers")
+
+from lerobot.datasets.compute_stats import (  # noqa: E402
+    compute_relative_action_stats,
+    compute_state_history_stats,
+)
+from lerobot.policies.pi05.configuration_pi05 import PI05Config  # noqa: E402
+from lerobot.policies.pi05.processor_pi05 import (  # noqa: E402
+    Pi05FlattenStateHistoryProcessorStep,
+    Pi05StateFromActionProcessorStep,
+)
+from lerobot.processor.relative_action_processor import (  # noqa: E402
+    AbsoluteActionsProcessorStep,
+    RelativeActionsProcessorStep,
+)
+from lerobot.types import TransitionKey  # noqa: E402
+from lerobot.utils.constants import OBS_STATE  # noqa: E402
+
+
+def _transition(action: torch.Tensor | None, state: torch.Tensor | None = None) -> dict:
+    observation = {} if state is None else {OBS_STATE: state}
+    return {
+        TransitionKey.OBSERVATION: observation,
+        TransitionKey.ACTION: action,
+        TransitionKey.REWARD: None,
+        TransitionKey.DONE: None,
+        TransitionKey.TRUNCATED: None,
+        TransitionKey.COMPLEMENTARY_DATA: {},
+    }
+
+
+def test_pi05_config_requests_action_history_prefix():
+    config = PI05Config(
+        device="cpu",
+        chunk_size=4,
+        n_action_steps=4,
+        state_from_action=True,
+        proprioception_history_steps=2,
+    )
+
+    assert config.action_delta_indices == [-1, 0, 1, 2, 3]
+
+
+def test_state_from_action_extracts_history_and_preserves_target_horizon():
+    action = torch.arange(2 * 5 * 3, dtype=torch.float32).reshape(2, 5, 3)
+    step = Pi05StateFromActionProcessorStep(enabled=True, history_steps=2)
+
+    result = step(_transition(action))
+
+    torch.testing.assert_close(result[TransitionKey.OBSERVATION][OBS_STATE], action[:, :2])
+    torch.testing.assert_close(result[TransitionKey.ACTION], action[:, 1:])
+
+
+def test_relative_actions_use_newest_state_in_history_and_roundtrip():
+    state_history = torch.tensor([[[1.0, 10.0], [2.0, 20.0]]])
+    absolute = torch.tensor([[[3.0, 30.0], [4.0, 40.0]]])
+    relative_step = RelativeActionsProcessorStep(enabled=True)
+    absolute_step = AbsoluteActionsProcessorStep(enabled=True, relative_step=relative_step)
+
+    relative = relative_step(_transition(absolute, state_history))
+    expected = torch.tensor([[[1.0, 10.0], [2.0, 20.0]]])
+    torch.testing.assert_close(relative[TransitionKey.ACTION], expected)
+
+    recovered = absolute_step(_transition(relative[TransitionKey.ACTION]))
+    torch.testing.assert_close(recovered[TransitionKey.ACTION], absolute)
+
+
+def test_flatten_state_history_preserves_chronological_order():
+    state_history = torch.tensor([[[1.0, 2.0], [3.0, 4.0]]])
+    step = Pi05FlattenStateHistoryProcessorStep(history_steps=2, max_state_dim=4)
+
+    result = step(_transition(torch.zeros(1, 2, 2), state_history))
+
+    torch.testing.assert_close(
+        result[TransitionKey.OBSERVATION][OBS_STATE], torch.tensor([[1.0, 2.0, 3.0, 4.0]])
+    )
+
+
+def test_state_history_can_be_relative_with_absolute_gripper():
+    state_history = torch.tensor([[[1.0, 10.0, 0.2], [3.0, 20.0, 0.4]]])
+    step = Pi05FlattenStateHistoryProcessorStep(
+        history_steps=2,
+        max_state_dim=6,
+        relative=True,
+        exclude_joints=["gripper"],
+        state_names=["x", "y", "gripper_width"],
+    )
+
+    result = step(_transition(torch.zeros(1, 2, 3), state_history))
+
+    torch.testing.assert_close(
+        result[TransitionKey.OBSERVATION][OBS_STATE],
+        torch.tensor([[-2.0, -10.0, 0.2, 0.0, 0.0, 0.4]]),
+    )
+
+
+def test_inference_state_history_is_rolled_and_reset():
+    step = Pi05StateFromActionProcessorStep(enabled=True, history_steps=2)
+
+    first = step(_transition(None, torch.tensor([[1.0, 2.0]])))
+    second = step(_transition(None, torch.tensor([[3.0, 4.0]])))
+    torch.testing.assert_close(
+        first[TransitionKey.OBSERVATION][OBS_STATE], torch.tensor([[[1.0, 2.0], [1.0, 2.0]]])
+    )
+    torch.testing.assert_close(
+        second[TransitionKey.OBSERVATION][OBS_STATE], torch.tensor([[[1.0, 2.0], [3.0, 4.0]]])
+    )
+
+    step.reset()
+    reset = step(_transition(None, torch.tensor([[5.0, 6.0]])))
+    torch.testing.assert_close(
+        reset[TransitionKey.OBSERVATION][OBS_STATE], torch.tensor([[[5.0, 6.0], [5.0, 6.0]]])
+    )
+
+
+def test_flatten_state_history_checks_max_state_dim():
+    step = Pi05FlattenStateHistoryProcessorStep(history_steps=2, max_state_dim=3)
+
+    with pytest.raises(ValueError, match="above max_state_dim"):
+        step(_transition(torch.zeros(1, 2, 2), torch.zeros(1, 2, 2)))
+
+
+def test_relative_stats_can_use_absolute_action_as_state():
+    actions = np.asarray([[0.0, 0.0], [1.0, 2.0], [2.0, 4.0], [3.0, 6.0]], dtype=np.float32)
+    dataset = {"action": actions, "episode_index": np.zeros(4, dtype=np.int64)}
+    features = {"action": {"shape": [2], "names": ["x", "y"]}}
+
+    stats = compute_relative_action_stats(
+        dataset,
+        features,
+        chunk_size=2,
+        state_from_action=True,
+    )
+
+    np.testing.assert_allclose(stats["mean"], [0.5, 1.0])
+
+
+def test_relative_state_history_stats_match_processor_representation():
+    actions = np.asarray(
+        [[0.0, 0.1], [1.0, 0.2], [3.0, 0.3]],
+        dtype=np.float32,
+    )
+    dataset = {"action": actions, "episode_index": np.zeros(3, dtype=np.int64)}
+    features = {"action": {"shape": [2], "names": ["x", "gripper_width"]}}
+
+    stats = compute_state_history_stats(
+        dataset,
+        features,
+        history_steps=2,
+        exclude_joints=["gripper"],
+        relative=True,
+    )
+
+    expected = np.asarray([[0.0, 0.1, 0.0, 0.1], [-1.0, 0.1, 0.0, 0.2], [-2.0, 0.2, 0.0, 0.3]])
+    np.testing.assert_allclose(stats["mean"], expected.mean(axis=0))