Hierarchical Equivariant Policy via Frame Transfer
Authors: Haibo Zhao
Dian Wang
Yizhe Zhu
Xupeng Zhu
Owen Lewis Howell
Linfeng Zhao
Yaoyao Qian
Robin Walters
Robert Platt
Venue: ICML 2025 poster (2025)
Keywords: robot learning
imitation learning
robotic manipulation
equivariance
Primary area: applications->robotics
TL;DR: We propose a equivariant hierarchical policy learning framework for visuomotor policy learning

Abstract: Recent advances in hierarchical policy learning highlight the advantages of decomposing systems into high-level and low-level agents, enabling efficient long-horizon reasoning and precise fine-grained control. However, the interface between these hierarchy levels remains underexplored, and existing hierarchical methods often ignore domain symmetry, resulting in the need for extensive demonstrations to achieve robust performance. To address these issues, we propose Hierarchical Equivariant Policy (HEP), a novel hierarchical policy framework. We propose a frame transfer interface for hierarchical policy learning, which uses the high-level agent's output as a coordinate frame for the low-level agent, providing a strong inductive bias while retaining flexibility. Additionally, we integrate domain symmetries into both levels and theoretically demonstrate the system's overall equivariance. HEP achieves state-of-the-art performance in complex robotic manipulation tasks, demonstrating significant improvements in both simulation and real-world settings.

Hierarchical Equivariant Policy via Frame Transfer
Haibo Zhao"1
Dian Wang" x
Yizhe Zhu
Xupeng Zhu' Owen Howell Linfeng Zhao
Yaoyao Qian
Robin Walters Robert Platt
(zhao. haib, wang. dian, zhu xup, hwwell.w..ooooooooo... 1o, zhao. linf, qi gian an.aan r. r.walters, htt.::/aaeetteeer.otaaatttttttee
A Abstract
High Level
Recent advances in hicrarchical policy learning highlight the advantages of decomposing sys- tems into high-level and low-level agents, en- abling efficient long-houe mog-hhoizonn reasoning and pre- cise fine-grained control. However, the interface between these hierarchy levels remains underex- plored, and existing hierarchical methods often ignore domain symmetry, resulting in the need for extensive demonstrations to achieve robust performance. To address these issues, we pro- pose Hierarchical Equivariant Policy (HEP), a novel hierarchical policy framework. We pro- pose a frame transfer interface for hierarchical policy learning, which uses the high-level agent's output as a coordinate frame for the low-level agent, providing a strong inductive bias while retaining flexibility, Additionally, we integrate domain symmetries into both levels and theoret- ically demonstrate the system's 's overall equivari- ance. HEP achieves state-of-the-ar performance in complex robotic manipulation tasks, demon- strating significant improvements in both simula- tion and real-world settings. (Code and videos are available project page.)
Equi High-Lavel Agent
High-Lovl
Astion
Oba
Worl Framm
Frame Transfer
Level
Equil Low-Level Agent
Obs transfered
to Keypose Frame
Figure I. Hierarchical Equivariant Policy (HEP) composed of high-level agent that predicts coarse translation, low-level agent that predicts the fine-grained trajectory, and novel Frame Transfer interface that transfers the coordinate frame of the low- level to the predicted keypose frame from the high-level.
mapping raw sensory inputs to low-level actions such as end-effector trajectories. While these methods exhibit state- of-the-art performance when large amounts of training data are available, they struggle in scenarios with only limited data, due to the large function space required to parameter- ize complex end-to-end mappings.
1. Introduction
A promising alternative strategy to employ a hierarchical structural prior that decomposes the policy into different lev- els, e.g., high-level agent responsible for identifying goal pose and a low-level agent for trajectory refinement. Hier- archical methods can reduce the complexity of the policy function space by delegating morizoorzon reasoning to the high-level module and fine-grained control to the low-level module, enabling efficient learning and execution. Despite their promise, one underexplored question in hierarchical policy learning is what is the right interface between differ- ent levels. For example, in robotic manipulation, existing hierarchical methods (Ma et al., 2024; Xian et al., 2023) often impose rigid constraints on the interface between the high-level and low-level agents, where the high-level action is used as the last pose the low-level trajectory. This constraint limits flexibility and often requires both levels to
Learning-base based approaches have emerged as powerful paradigm for developing control policies in sequential decision-making tasks, such as robotic manipulation. By leveraging data-driven methods, policy learning provides scalable framework for addressing tasks with complex dynamics and high-dimensional observation spaces. Recent advancements in end-to-end policy learning (Zhao et al., 2023; Chi et al., 2023) have shown promising results in
'Equal contribution Northeastern University *Robotics Correspondence to: Dian Wang
and Ai Institute. <wang dian @ northeastem.ceuu..
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Hierarchical Equivariant Policy via Frame Transfer
perform fine-grained reasoning in high-dimensional spaces, negating some of the potential benefits of the hierarchical design. Moreover, prior hierarchical methods focus solely on the bierarchical decomposition and do not exploit the do- main symmetries often present in robotic tasks, missing an opportunity to further improve generalization and efficiency.
to unseen scenarios. One class of LfD learns abstracted keyframe actions (James & Davison, 2022; James al., 2022; Shridhar et al., 2023; Gervet et al., 2023; Goyal et al., 2023) in terms of the target pose of the gripper, then uses motion planning to interpolate between keyframes. This formulation enables learning with fewer decision steps, but is not suitable for non-prehensile actions like door opening or wiping (Xian et al., 2023; Ma al., 2024). Another class of LiD mimics the fine-grained trajectory directly (Song et al., 2020; Ye et al., 2022; Toyer et al., 2020; Zhang et al., 2018; Chi et al., 2023; Zhu et al., 2023; Mandlekar et al., 2021: Zhao et al., 2023; Wang et al., 2024), enabling broader task coverage but suffering from overloading the model with details (Zhao et al., 2023), covariant shift (Ke et al., 202 I), and poor performance in long-horizon tasks. To bridge these approaches, we introduce Frame Transfer, a novel interface that integrates keyframe-based and trajectory- based models, enhancing flexibility and task adaptability.
In this paper, we propose a novel hierarchical policy learning framework that overcomes these limitations by introducing more flexible and efficient interface between the high- level and low-level agents. Specifically, our high-level agent predicts a keypose in the form of coarse 3D location rep- resenting a subgoal of the task. This location is then used to construct the coordinate frame for the low-level policy, enabling it to predict trajectories relative to this keypose frame, as shown in Figure 1. This Frame Transfer inter- face maintains strong inductive bias (by anchoring the low-level policy to subgoal) yet offers structural flexibility (allowing the low-level policy to refine trajectories locally). Furthermore, Frame Transfer offers a natural fit for integrat- ing domain symmetry by decomposing it into the global symmetry of the subgoal (i.e., the subgoal should transform with the scene) and local symmetry of the low-level pol- icy (i.e., it should behave consistently in the local keypose frame). By incorporating equivariant structures at both lev- els, our entire hierarchical system becomes more robust to spatial variations, resulting in significantly improved sample efficiency. Lastly, to better encode 3D sensory information, we adopt a stacked voxel representation (Zhou & Tuzel, 2018), ensuring rich visual features and fast computation.
Hierarchical Policy has been explored for action refine- ment in a coarse-to- fine manner (Levy et al., 2018; Gualtieri & Platt, 2020; James et al., 2022) or through a two-stage hierarchy for translational and rotational actions (Sharma et al., 2017; Wang al., 2020; Zhu et al., 2022). While these approaches improve over end-to-end policies, they lack integration of keyframe and trajectory actions. Recent works (Xian et al., 2023; Ma et al., 2024) address this by hicrarchically combining a keyframe agent and a trajectory agent, but they fix the goal pose of the trajectory agent with the output from the keyfram agent, limiting flexibility in the low-level and demanding precise reasoning from the high-level agent. In contrast, our framework enables more adaptable interface between levels, allowing the low-level agent to refine high-level actions.
We summarize our contributions follows:
We propose Hierarchical Equivariant Policy (HEP), novel, sample-efficient hierarchical policy learning framework.
Equivariant Robot Learning leverages geometric sym- metries in 3-D Euclidean space, which has emerged as a powerful strategy for boosting the sample efficiency, robust- ness, and generalisation of ooboti-maniiuulation none-manipulaaann policies. An expanding line of research now demonstrates that en- coding SE(3) equivariance invariance in-plane rotations -iiaiion-dirretll into the perception-to-action pipeline can dramatically reduce the burden of data collec- tion and retraining when scenes or objects are repositioned. Recent works have explored this principle across a wide spectrum of tasks and architectures, from point-cloud net- works to conditiond diffusion models ( (Wang et al., 2022; 2021; Liu et al., 2023; Kim et al., 2023; Kohler et al., 2023; Nguyen et al., 2023; 2024; Eisner et al., 2024; Gao et al., 2024). A particularly active subfield studies bi- cquivariant tick-and-place policies that remain consistent under simultaneous transformations of both the target object and the robot gripper. Systems in this class-spanning neu- ral descriptors, transporters, and diffusion planners- have achieved ofte-of-the-ar art placement accuracy and transfer-
We introduce Frame Transfer as an interface for hierar- chical policy learning, providing effective and flexible policy decomposition.
We theoretically demonstrate the equivariance of HEP, showing its spatial generalizability. Although equivari- ance has been used in policy learning, our work is the first to study it in hierarchical policy.
-nneriince-nnariinnnee to translations and
We provide a thorough evaluation of our method in both simulation and the real-world. Among 30 RL- Bench (James et al., 2020) tasks, HEP outperforms state-of-the-as baselines by an average of 10% 23% in different settings, with particular improvement on tasks requiring fine control or long-horizon reasoning.
2. Related Work
Learning from Demonstrations (LfD) enables policies to be trained from human demonstrations and generalized
2

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Hierarchical Equivariant Policy via Frame Transfer
ability (Simeonov et al., 2022; Ryu et al., 2023b;a; Pan al., 2023; Huang et al., 2022; 2024a;c;b). Complementary research focuses on equivariant grasp synthesis, showing that symmetry-awar grasp networks can generalise to novel object poses with an order of magnitude fewer demonstra- tions (Zhu et al., 2022; Huang et al., 2023; Hu et al., 2024; Lim et al., 2024). At a finer temporal scale, several groups have begun embed equivariance into sereector--gnerattin modules for tasks such tool use, insertion, deformable manipulation, reporting sharper motion accuracy and im- proved long-horizon stability (Jia et al., 2023; Wang et al., 2024; Yang et al., 2024b;a). Unlike these independent appli- cations, we integrate equivariance into a hierarchical policy that unifies keyframe and trajectory-based learning.
and the action. let g (1, Ro) T(3) SO(2) where (fz, ly, 12) and Ro is the 2 x 2 rotation matrix, 9 acts on the action a by transforming the gripper pose command. Let R = R2
0 1]. ga {go1, go2. gam where
ga,- [Ro + l2 us + 1y); + L, Rg 9s. G))
g acts o through transforming the gripper pose in the same way as a, and transforming the point cloud P P= {ps Pi = (Zi, Gir Zi, fi) E B via gl = { where
gP: (Ro + lx Vi + by), 21 1.3 Jt)-
3.3. Voxel Maps as Function
In deep learning, voxel maps (3D volumetric data) are typ- ically expressed as tensors. However, it is sometimes con- venient to express volumetric data in the form of functions over the 3D space. Specifically, given one-channel voxel map V E RIIDDHXW we may equivalently express V as a continuous function V : R + R, where V(z, V2 describes the intensity value at the continuous world coor- dinate (x, y. 2). Notice that here the domain of V is the 3D world coordinate frame, not the discrete voxel indices. The relationship between the voxel indices and world coordi- nates is linear map defined by the spatial resolution and the origin of the voxel grid.
3. Background
3.1. Problem Definition
In this paper, we focus on visuomotor policy learning via Behavior Cloning (BC) in robotic manipulation. We aim to learn a policy : O + A to map from the observation space O to the action space A.
To define the observation and action spaces, let 8 (ar, 1/, 2, q. S R SO(3) x R be the space of gripper states where (z, y, 2) is a 3D position, q SO(3) is an orientation, is gripper aperature (open width). The observation space is 0 E O- = x3*kk+k)) x St including both a point cloud/ P- = {p: P = (r,, Mi, 2i, fc) E BR*+} with & dimensional point features (e.g., & = 3 for RGB) and t history steps of the gripper state. The action a = (ai, ( am E = 5 contains m control steps of
Similarly, if we have an m-channel voxel map V E RT x xxxxxx we can interpret it as V R2 - R", where each point (z, y, 2) in the volume maps to an m-dimmnsionall feature vector. The group g = (t E T(3) x SO(2) acts
voxel feature map as
the gripper state.
(gV) v. = ((O)V (x (x- yt ty): 2 tt),
tz), (1)
where t E (3)) acts on V by translating the voxel location, while 0 acts on V by both rotating the voxel location and transforming the feature vector via p(0) E GL(m), an m x m invertible matrix known as a group representation.
3.2. Equivariance
A function f is equivariant if it commutes with the transfor- mations of a symmetry group G, where Vgg G. f(x) (x(.). This is mathematical way of expressing that f is symmetric with respect to G: if we evaluate f for trans- formed versions of the same input, we should obtain trans- formed versions of the same output.
4. Hierarchical Equivariant Policy
The main contribution of our paper is a Hierarchical Equiv- ariant Policy that leverages equivariant learning in both the high-level and low-level agents and employs a novel frame transfer interface to connect them. In this section, we first introduce the overview of our hierarchical policy structure and the novel frame transfer interface. Then, we describe the high-level and low-level agents in detail.
Our objective to design policy that is symmetric (equiv- ariant) under the group g E T(3) x SO(2), where T(3) represents the group of 3D translations, and SO(2) rep- resents the group of planar rotations around the z-axis of the world coordinate system, (goo)= = (T))). This sym- metry captures the ground truth structure in many robotic tasks without enforcing unnecessary out-of-plane rotation equivariance (which is often invalid due to gravity and the canonical pose of objects).
The overview of our system is shown in Figure 2. We factor the policy learning problem into two-step action prediction using high-level agent Thigh and a low-level agent Tow.
To define a T(3 x SO(2) equivariant policy, we first need to define how the group element acts on the observation
i (() Too (o, (high) fhigh Thigh (o)
(2)
where hngh E T(3) is 3D translation predicted by Thigh-
3

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Hierarchical Equivariant Policy via Frame Transfer
High Level
Robot State
Equi Pointhlet
Down Black
Down Block
Up Block
Up Block
Point Cloud
Voxel Feature Map
Equivariant Unet
High-Level Action
Equi Stacked
Probability Map
Obs Frame
Voxel Enc
Frame Transfer
Low Level
Robot State
Equi PointNet
Equivarlant Diffusion Policy
Point Cloud
Voxel Feature Map
Equi Stacked Voxel Enc
Obs Keypose Frame
Low-Level Action
Figure 2. Overview of Hierarchical Equivariant Policy (HEP). In the highlevel (top), given point cloud input, we first use an equivariant stacked voxel encoder (green) process the point cloud and get voxel feature map. The voxel feature map is then sent to equivariant UNet (blue) to produce high-level action probability map. After taking the argmax of the action map as the high-level action, Frame Transfer (yellow) translate the coordinate frame of observation in the low-level (bottom). The translated observation sent to the stacked voxel encoder (green, same architecture as the one used in the high-level), followed by an equivariant diffusion policy (Wang et al., 2024) (blue) produce the low-level action.
4.1. Frame Transfer Interface
by the high-level agent, and a trajectory generator that produces a trajectory based on the transformed observation. Frame Transfer func-
The effectiveness on the design of the high-level action output and its integra- tion with the low-level agent. Prior approaches (Xian al., 2023; Ma al., 2024) often constrain the high-level agent to predict an SF(3) pose, which is then treated rigid con- straint for the low-level agent by enforcing as the endpoint of the low-level trajectory. While this design simplifies task decomposition, it restricts flexibility and imposes computa- tional burdens on the high-level agent, which must reason about precise pose constraints in high-dimensional spaces.
hierarchical policy depends largely
(OU A) x R O U A tion, which translates the (æ, y, component of the input observation action to the input keypose frame. Specif- ically, we define the +, operators between o or and hngh as addition and subtraction on the (ær, y, 2) component of o or a. For example, for = (x, y, 2, q, c), a + thigh = then /tihh-
((x, y, 2)+ fiigh q. c). The Frame Transfer function defined r(o, hngh))
(nigh, 7(a, hnghh)
The Frame Transfer interface offers several advantages. First, it provides an efficient mechanism that geometrically embeds the high-level action directly into the input of the low-level agent, ensuring seamless communication between the two levels. Second, by representing observations and tra- jectories in relative frame, introduces translation invari- ance to the low-level agent, simplifying its learning process and improving robustness. Third, unlike prior works (Xian et al., 2023; Ma et al., 2024) which treat the high-level pre- diction as a rigid motion planning constraint (thus forcing the high-level agent to generate accurate SE(3) poses and
To overcome these limitations, we propose flexible and efficient Frame Transfer interface (Figure 2 middle) between the high- and low-level agents by only passing a (3)) frame rather than constraining the pose. Specifically, our high- level agent predicts a 3D translation thigh. which used as canonical reference frame for the low-level agent,
Tio (o, tnigh)
(T, mnigh)) (nigh
(3)
where high the 3D translation (i.e., a keypose) predicted

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Hicrarchical Equivariant Policy via Frame Transfer
Equi PointNu
compression that reduces the fine details in the observation. To address this limitation, we adopt Stacked Voxels (Zhou & Tuzel, 2018) from the 3D vision literature, which preserve fine-grained spatial cues by replacing voxel downsampling with a PointNer (Qi et al., 2017) that aggregates information from all points within the spatial extent of each voxel.
Agg
Equi Stacked Voxel Enc
Specifically, given a point cloud P, we first partition it into H W D point sets, where each set P3 S P corresponds to the points contained within a voxel j in the H x W x D voxel grid. Each point set P3 is processed by an equívariant PointNet L: P3 + Jg. Js) to produce a c-dimensional aggregated feature vector for the voxel j. Repeating for all voxels results in a voxel grid feature map with dimensions c x H x W x D. This feature map then used as input to subsequent 3D convolutional networks.
Agg
Sub Paint Cloud in Voxal Region
Point Cloud
Standard Average Pooling
Figure 3. Equivariant Stacked Voxel Encoder. Compared with the standard average pooling in point cloud voxelization (bottom), stacked voxel representation (top) can provide a richer representa- tion of the points within the region of voxel.
limiting the policy in an open-loop manner), our approach interprets the high-level output flexible constraint. This flexibility reduces the computational burden on the high- level agent, as it only predicts a 3D translation, while pre- serving the system's capability to operate in both open-loop and closed-loop control settings.
This process, illustrated in Figure 3, retains more nuanced shape information compared to simple voxel downsampling. Moreover, we prove that the stacked voxel representation maintains equivariance. (See proof in Appendix C.)
Proposition 4.1. For g (t,0) E T(3) x SO(2), if the PointNet 1 is -Quui--quivarian and T(3)- i.e. 1(pP;)= = (())((P)), then the stucked voxel representation v P equivariant, i.e. v(gP) gv(P).
4.2. High-level Agent
To efficiently predict the high-level action dnigh E T33), we represent it as a voxel map discretizing Va : R - R where (a()) represents the probability of translation / (see subsec- tion 3.3). This provides a dense spatial representation and naturally handles translation multi-modalit modality (Shridhar et al., 2023). The center of the voxel with the highest predicted probability is then selected as the high-level agent's final output, fnigh arg max Va. Accordingly, the input obser- vation is voxelized to V. : R3 + R (where the output of Vo is RGB), and we use an SO())-equivariant 3D U-Net db Vo + Va to enforce g E T(3) x SO(2) symmetry, (gV.) (V.). The entire high-level structure is shown in Figure 2 top.
V s.t. v (e: I(P)) is T(3) SO(2)-
In practice, we implement the -i3v-inva in the Point- Net by using the relative position to the center of each voxel, and implement the SO(2) (2))---uivariiance using escnn (Cesa et al., 2022).
4.4. Low-level Agent
After predicting the high-level action high and using Frame Transfer to canonicalize the observation, our low-level tra- jectory generator & needs to create an SF(3) trajectory for the robot gripper. As shown in Figure bottom, we first process the observation with stacked voxel encoder, then leverage an equivariant diffusion policy (Wang al., 2024) to represent the policy á, which denoises the trajectory from randomly sampled noisy trajectory. Specifically, we model a conditional noise prediction function = o, a², k + et, where the observation o is the denoising conditioning. at is a noisy action, is the denoising step, and c* is the pre- dicted noise in a s.t. the noise-free action a = - The model is implemented as an (Qqu)-equivariint function, e (go., ga k) = (o, at, k), ensure the policy & it rep- resents is et al., 2024) for more details.
During training, the high-level agent's objective is to mini- mize the discrepancy between its predicted voxel heatmap V. and the ground truth one-hot heatmap V2 derived from expert demonstrations, using the cross-entropy loss,
Lnigh- - Σ 2)) log(Va v, 2,0.=
(4)
where V. (z, y, 2) is the probability for voxel (I, y, =) ob- tained by applying a softmax over the predicted heatmap.
4.3. Stacked Voxel Representation
Φ(go) = go))). See (Wang
As our high-level agent uses 3D voxel grids as the visual input, the voxel encoder plays a crucial role in the policy. Standard 3D convolutional encoders impose a heavy compu- tational burden, which often requires aggressive resolution
During training, given an expert observation trajectory pair (o, a). we first use the translation tn from the last step On as the keypose, then apply frame transfer to get
5

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Hierarchical Equivariant Policy via Frame Transfer
6' T (n) T(a, ln). The low-level loss
Liow = ||=(o", a + e²11"
(5)
U
where ex is a random noise conditioned on randomly sampled denoising step
Rolate& 1y
Rotate Translate
V
Rotate& + Translate
Translate
4.5. Symmetry of Policy
In this section, we describe the overall ((3)xS(( symme- try of our hierarchical architecture. As is shown in Figure 4, transformation the observation should lead the same transformation in both levels of HEP. Specifically, de- compose the symmetry into rotation and translation, and prove each separately.
High Level Action
Action
Figure 4. Equivariance HEP. When the observation rotated and translated, the high- and low- level actions are rotated and translated accordingly.
Let π be a hierarchical policy composed of a high-level agent Thigh. low-level agent Tlow: and frame-transfer func- tions (see section 4).
Proposition 4.2 (Hierarchical SO(2) Equivariance). a is -equivarara when the following assumptions hold for g E SO(2):
1. The high-level policy Thigh is -Qiii-eeqivaaiinn, Thigh (go)= - (Tiggh(()
(a) Open Microwave
(b) Stack Wine
(c) Shoes Out of
2. The low-level policy Nlw is -0()ieequivaiinn,, (go, (go, gtrigh) = g. Tlow (o, trigh)
Figure 5. The Simulation Tasks from RLBench (James et al., 2020). See Appendix all environments.
3. The Frame Transfer function T is -equiviaviaaii
In Appendix A we show that the entire hierarchical policy is (2)uqqquivarr so that rotating the observation results in an action rotated the same way.
with a parallel gripper, as well as four RGB-D cameras to provide the point cloud observation.
We evaluate our model on 30 RLBench tasks, among which 20 widely used in the prior works like (Xian al., 2023). The remaining 10 are challenging tasks that demand precise control, such as Lamp On, or oong-horizon planning. like Push Buttons. A subset of the 30 simulation tasks is shown in Figure 5. Each task trained using 100 demon- strations, more detailed task descriptions and visualizations are provided in Appendix F.
Proposition 4.3 (Hicrarchical T(3) Equivariance). ı is -egiiiaaaa when the following assumptions hold for t e T3)
1. Thigh -(uuivvauaar,an,, Thigh (0+ =t Thigh(
2. The Frame Transfer function is T(3)-invariant, and satisfies T(o, tnigh) = (( + t, tnigh +
We consider different control settings, open-loop and closed-loop control. In closed-loop, we use each control step in the dataset as the low-level's 's target, and next keyframe is used as the label for the high-level agent. In open-loop, we use the keyframe (i.e., some key actions in the entire trajec- tory like pick, place, etc.) defined by the prior work (Shrid- har et al., 2023) as the target for the high-level agent, then construct the low-level target by interpolating between the consecutive keyframes. In principle, the open-loop set- ting requires fewer prediction steps to finish task, while the closed-loop setting makes the policy more responsive. Thanks to the flexibility of our Frame Transfer interface, our policy can operate in both settings, while some prior works are limited in the open-loop setting.
Notably, even if the low-level policy is not T(3)- equivariant, the entire hierarchical policy æ is T(3)- equivariant. This is proven in Appendix B.
5. Simulation Experiment
5.1. Experimental Settings
To evaluate our policy, we first perform experiments in sim- ulated environments in the RLBench (James et al., 2020) benchmark implemented using CoppeliaSim (Rohmer et al., 2013) and PyRep (James et al., 2019). The simulated en- vironments contain a 7-joint Franka Panda robot equipped
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Hierarchical Equivariant Policy via Frame Transfer
Table Performance Different Models Across Various Tasks Simulation. Success rates (in percentages) are reported for each
task. Bolded values indicate the best performance for each task, and improvements are shown in blue where applicable.
Mothod (Open-loop)
Mean
Pick/Lift
Push Button
Knife Board
Put Moncy
Reach Target
Slide Block
Stack Wine
Take Money
Take Umbrella
up
Cup
Ours (HEP)
(8)+
+9(+1)
100++1)
96(+5)
98(-1)
100
100r-2)
100k+7)
90X-10)
100K+1)
+8(+4)
Chained Dilluser
78
98
96
91
99
100
98
93
100
96
94
Diffuser Actor
56
84
100
98
99
Method (Open-loop)
Unplug Charger
Close Door
Open Box
Open Fridge
Frame off
Open Oven
Books on Shelf
Wipe Desk
Cup in
Shoe out
Hanger
Cabinet
Box
Ours (HEP)
(9)
(0())4)
(00
13(+15)
93(+8)
87(+1)
99(+7)
77 12)
+6(+8)
90(+
Chained Diffuser
95
76
96
68
85
86
92
65
68
78
3D Dilluser Actor
49
15
41
71
3
36
5
21
Method (Open-loop)
Open Mi-
Turn on
Open Grill
Stack Blocks
Stack Cups
Push Buttons
USB in
Open
Put Item
Sort Shape
Lamp
Computer
Drawer
Drawer
Ours (HEP)
82(+26)
(5()
49))
54(-4)
32(44)
99(+12)
-
94..
95(+7)
22(+3)
Chained Diffuser
95
12
86
84
88
3D Dilliser Actor
46
20
70
28
87
42
71
70
19
Method (Closed-loop)
Mean
Turn On
Open Mi-
Push 3
Open
Put Item in
Slide Block
Stack
Take Money
Take
Pick up
Lamp
crowave
Battons
Drawer
Drawer
Umbrella
Cup
Ours (HLPP)
(9(+)2)) 57
60k 28
(4())
37(436)
95(+41)
76(+28) 48
+5(+ 75
89/+10) 79
94(+14) 8D
90(+9) 81
93(+15)
EquiDiff
42
78
Time
(a) Pot Cleaning
(b) Blocks to Drawer
(c) Blocks Stacking
Figure 6. Real-world Experiment Setting, Figure 6a: Pot cleaning, the robot needs to open the pot lid, pour detergent into the pot, and clean it with sponge. Figure 6b: Blocks to drawer, the robot needs to open the drawer, place two blocks inside, and close the drawer. Figure 6c: Blocks stacking, the robot needs to stack three blocks one by one.
5.2. Baseline
improvement of 10%. The task where HEP falls short of achieving the best results is Take Money. Further investi- gation reveals that HEP achieves 98% success rate earlier checkpoints but fails at the final checkpoint, likely due overfitting. Tasks involving precise actions or long-horizon trajectories e.g., Lamp-on on and Push 3 Buttons also exhibited consistently high success rates, demonstrating the adaptability of our method to diverse task requirements. We also compare our model with hierarchical diffusion pol- icy (Ma et al., 2024) in Appendix H
We compare our method against the following baselines. 3D Diffuser Actor: an open-loop agent that combines diffusion policies (Chi et al., 2023) with 3D scene representations. Chained Difffuser: an open-loop hierarchical agent that uses Act3D (Gervet et al., 2023) in the high-level and diffu- sion policy in the low-level. Equivariant Diffusion Policy (EquiDiff): an -quiierqui closed-loop policy that applies equivariant denoising.
5.3. Results
Closed-loop Results: Here consider 10 selected tasks that represent the full diversity and complexity of the com- plete task set. The closed-loop setting requires longer- horizon trajectories, making it harder to succeed in eval- uation. Despite this, our model consistently outperforms EquiDiff across all 10 tasks, achieving an average absolute
Table 1 presents the comparison in terms of the evaluation success rates of the last checkpoint across 100 trials.
Open-loop Results: Our model outperforms the baselines in 28 out of the 30 tasks, achieving an average absolute

---

Hierarchical Equivariant Policy via Frame Transfer
improvement of %. This improvement underscores the effectiveness of HEP in handling the increased complexity of long-horizon decision-making.
Table 3. Performance Different Models the Woal-World.
Task
Pot Cleaning
Blocks to Drawer
Blocks Stacking
Number Demo
30
5.4. Ablation Study
Chained Diffuser
0.3
0.2
0.4
Open HEP (Ouns)
0.8
0.85
0.9
To validate the impact of our contri- but perform ablation study in six tasks considering the follow- ing configurations: No Hierarchy: removes high-level agent and uses low-level agent only. No Equi: same architecture but removes all equivari- structure. No Stacked Voxel: re- moves the stacked voxel encoder. No FT: removes the Frame Transfer in- terface and uses the high-level action as an additional conditioning in the low-level. No Equi No FT: combination No Equi and No FT.
Closed-loop HEP (Ours)
Table Ablation Study Results.
Method
Target
No Hieranchy
0.51
No Equi No FT
0.60
No Equi
0,70
Demonstration
No FT
No Stacked Voxel
0.84
Complete Model
0.94
Location
Test location
Workspace
As is shown in Table 2, removing equivariance makes the most significant negative impact our model, reducing the mean success rate by 24%. The performance drop when removing Frame Transfer and stacked voxel encoder is 16% and 10%, respectively, demonstrating the importance of all three key pieces of our model. Moreover, the 10% perfor- mance difference between No Equi and No Equi No FT shows the potential of Frame Transfer beyond our model. See Table 7 in the Appendix for the full table.
Figure 7. One-Shot Test. The model is trained single demon- stration to evaluate its generalization capability.
contrast, the open-loop version follows single keypose for cleaning, facilitating smoother transition to the next stage.
One-Shot Generalization To evaluate the generalizabil- ity of our model, we perform a one-shot experiment where the model is trained to finish a pick-place task with only one demonstration. During testing, the object is placed in unseen poses, as shown in Figure 7. The results in Table 4 demonstrate the strong generalizability of our model, achiev- ing an 80% success rate over 20 trials. For comparison, we evaluate Chained Diffuser under the same setting, but only succeeded when the toy car was positioned exactly in the demonstration. This result highlights the superior general- ization ability of our approach, enabling robust execution of manipulation tasks from limited training data.
6. World Experiment
In this section, we evaluate our method on a real robot system comprised of a URS robot and Intel Realsense (Ke- selman et al., 2017) D455 RGBD sensors. Details on the experiment setting are given in Appendix G.
Baseline Comparison We experiment in three tasks as shown in Figure 6. These tasks are challenging due to their extreme long horizon (can be divided into 6 to sub-tasks) and the diverse types of manipulation involved. Evaluations conducted in 20 trials: 10 with object placements similar to the training dataset's is and 10 with unseen placements.
As shown in Table 3, our model successfully completes the tasks under open-loop control. Most failures occur due to the slight misalignment between the gripper and the object, likely caused by poor depth quality of the sensors. We further evaluate our model in a closed-loop setting, where it achieves similar performance to the open-loop version in two of the three tasks. However, in Pot Cleaning, while the agent progresses further in the task, it becomes stuck in a recurrent cleaning loop. This likely results from the lack of history information in the observations, preventing the agent from recognizing when to exit the cleaning phase. In
Figure 8, Environment Variations. Left shows the training envi- ronment. Middle and right are the test environment with variation.
Robust to Environment Variations In this experiment, we evaluate the robustness of our trained model under envi- ronmental variations. Specifically, we introduced modifica- tions to the Block Stacking task during test time by changing the color of the table (Color) and additionally adding un-
8

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Hierarchical Equivariant Policy via Frame Transfer
tion Graduate Research Fellowship Program (NSF-GREP) for financial support.
Table Results One-Shot Generalization Experiment.
Model
Success Rate
Impact Statement
Chained Diffuser
0.05
HEP (Ours)
0.80
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
Table 5. Results of Environmental Variation Experiment.
Method
No Variation
Color
Color+Objects
Chained Diffuser
References
НEP (Ours)
0.9
0,9
0.6
Cesa, G., Lang, L., and Weiler, M. A program build E(N)- equivariant steerable CNNs. In International Conference on Learning Representations, 2022. URL https:// openreview net forumr Age
related objects as distractors (Color+Objects), as shown in Figure 8. The result is shown in Table 5. Surprisingly, our model demonstrates exceptional adaptability, achieving 90% and 60% success rate under those two test-time variations, whereas the baseline fails to complete the task with those distractions.
Chi, C., Feng, S., Du, Y., Xu, Z., Cousineau, E., Burchfiel, B., and Song, S. Diffusion policy: Visuomotor policy learning via action diffusion. In Proceedings of Robotics: Science and Systems (RSS), 2023.
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7. Conclusion
In this work, we propose an Hierarchical Equívariant Pol- icy for visuomotor policy learning. By utilizing Frame Transfer, our architecture naturally has both translational and rotational equivariance. Experimentally, HEP achieves significantly higher performance than previous methods on behavior cloming tasks that require fine motor control. While our work provides a solid foundation for hierarchical policies with geometric structure, several future directions remain open for exploration. One key limitation is that our experiments focus on tabletop manipulation. Extend- ing HEP more complex robotic tasks, such as humanoid motion, is a promising direction. Another limitation is the lack of memory mechanisms, which can be critical for tasks requiring history information. Future work could explore in- tegrating Transformers (Vaswani, 2017) to enhance temporal reasoning. Finally, expanding Frame Transfer to incorporate both translational and rotational specification could further improve the effectiveness of hierarchical policies.
Eisner, B., Yang, Y., Davehev, T., Vecerik, M., Scholz, J., and Held, D. Deep SE(3)-equivariant geometric reasoning for precise placement tasks. In The Twelfth International Conference on Learning Representations, 2024. URL https: /pwprevveeweeeeeeeeeeeeeeeeooeee net forum? id=2inBuwIy12.
Gao, C., Xue, 7.,, Deng, S., Liang, T., Yang, S., Shao, L., and Xu, H. RiEMann: Near real-time SE(3)- equivariant robot manipulation without point cloud seg- mentation. In 8th Annual Conference on Robot Learning, 2024. URL :tthttps:///ppnreeeeeeee http//pppneeweeeeeeeeeee forum?
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Acknowledgment
Goyal, A., Xu. J., Guo, Y., Blukis, V., Chao, Y.-W., and Fox, D. Rvt: Robotic view transformer for 3d object manipulation. In Conference Robot Learning, pp. 694- 710. PMLR, 2023.
This work was supported in part by the National Science Foundation under Grant Ns. 1750649, 2107256, 2134178, 2314182. and 2409351, and by NASA under Grant No. 14774 The authors would like extend their gratitude to Boce Hu for designing the fin-ray gripper fin- gers and for proofreading the paper, to Heng Tian for design- ing and fabricating components for the robot experiments, and to Shaoming Li for collecting demonstrations for the robot experiments. We gratefully acknowledge their support. Owen L. Howell grateful to the National Science Founda-
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Hierarchical Equivariant Policy via Frame Transfer
A. Proof: The Full Policy is SO(2) Equivariant
Let us prove that the policy (2( Equivariant and satisfies
Vg E SO(2), =(g 2(g-0) x
(6)
We will prove this in two steps.
A.1. Low-level Equivariance
First, let us prove that the low-level agent is S0(2) equivariant. The low-level policy can written as
Tlow (o, lnigh)
((((TO, ) - -high))
The frame transfer functions satisfy
Vg E S0(2),
= -
and the diffusion policy satisfies
Vg E SO(2), o(g. = g. 6(0)
Thus, we have that
Vg E SO(2), Tiou (g 0,g [nigh) r(p(T(g o,g g. (nihh)) g -high))
Using the frame transfer function property T(g o.g 1) - T(,, 1)) we have that
Vg E S0()), Tlou (g 0,g (high) r(o(g T(o, (high)); 9 -- (night)
Using the SO()) equivariance of the diffusion policy and the properties of the frame transfer functions, we have that Vg E (0((00)),,))))) T(o(g- - T(o, thigh)) -tnihh) = T(g Φ(T(o, thiggh) )), g -trigh) = g T(O(T(O, thigh)). - -trigh)
Thus,
Vg E (0(()), Tlow 0. (nigh) = 9 (( (nigh)); (niggt)
And by definition,
(é((T(o, thigh)), thiggh) = -Tow (o, thigh)
Thus, we have that
Vg SO(2), Flow (g o.g. thigh) = 9 Nlow (o, thigh)
A.2. Full Policy Equivariance
Using the equivariance of the low-level policy, let us show that the full policy is SO(2) equivariant. The high-level, low-level and diffusion policies satisfy
Vg E SO(2), Thigh (g 0) = Thigh (o) Bg E S0(2), Toow (g o, 9 thigh) 9 Tlow (o, thigh)
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Hierarchical Equivariant Policy via Frame Transfer
Now, combining high-level and low-level policy together we got that:
[o) Toow (Thigh (o),
When g acting on both the input observation, we have that
Vgg E SO(2), [(g o) = Nlow (Thigh ( (g o).g.
Now, via the SO(2) equivariance of the high-level policy Thigh 0) = 9 Thigh (0) we have that Vg E S0(2), Tlow (Thigh (g o): o) Noo Thigh (o),9 .0) Thus, using the S0(2) equivariance of the low-level policy Tlow (g Thigh (0), g 0) g Toow (ToghThigh()))0) we have that Vg E 50(2), Tl 0) g Now (Tiggh (o).0)
Note that the Noo (Thigh (0),0) ) just the expression for x()). Thus, we must have that Ag E SO(2), x(g 0) x(0)
holds.
B. Proof: The Full Policy is T(3) Equivariant
As defined in subsection 4.1, +, as operators between o or and (nigh addition and subtraction on the (xr, U, 2) component of or a. Similarly, we can define the translation t E T(3) acting on o or a as an addition to the (x, y/ component as 0 + t or a +t.
First, suppose that the high-level policy Thigh (o) is (3))-qquivarian so that
Vt E T3), Thigh (o + f) + Thigh (o)
which is simply the statement that shifting scene shifts high-level policy the same way. Now, we will show that the full hierarchical policy satisfies the equivariance condition. The low-level policy is determined by
Tlow (Thigh (o), o) = T(é(T(o, Thigh Thigh (o))
How does the low-level policy transform under translation? Using T()) Toow (Tigg (Toigh (Thigh o), we have that
[(o + Too (o + L, Thigh (o t))
Using the definition of the low-level policy, we have that
(o + t) (o + Thigh + ()) = 7 ((((T( Whigh (o + f)), Thigh (o + ())
Now, using the equivariance of high-level policy, we have that Thigh (o = + Thigh (0) so that
<ép(To +, Trigh (o t)), Thigh (o + t)) = (0 + f, Thigh (0) + t), Thigh -
Now, we can simplify this expression via the fact that the frame transfer 7 function is T(3) invariant. We have that 7(O + t, (o) + +) T(o, thigh) which implies that
T(p(T(0 + f,, Thigh (0) + t), Thigh (0) + = (high()) -Thigh (0) - t)
Now, note that r(o+t, t, high (0) +t) = T(O, thigh) implies that r(o, - Thigh (o) - t) = T(o t, -highh (o)). Using the fact that 7(o + Thigh (0)) To, Thigh (o))
have that
T(O(T Thigh (o)), Thigh (o) t) = (()(T(o, Thigh (o)). - Thigh (o)) +
Thus, combining the above expressions and using the definition of the low-level policy, we have that
(o + t, Thigh (o + t)) (()(T(), (oigh (o) t) t + ((O(T(O, (o)), hhigh (0)) = t Tlow Thigh (0))
Thus, we have that
Too (o + f, Thigh (o + t)) t + Toow (o, Thigh (o))
This is just the expression for the full policy function as π (0) Flow (0, Thigh(()) Ergo, we must have that
T(O + t) = f (0)
and the full policy is T(3) Equivvaaaa..
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Hierarchical Equivariant Policy via Frame Transfer
C. Proof: Equivariance of the Stacked Voxel Representation
Proof. We aim to prove that stacked voxel representation is T(3) -Quuieaqunaa,,n,, i.e.,
(g gg
where E T(3) x S0(2) a group transformation.
Define a point set selection function m Ja: Jy: P + P, that selects the subset of points Pj S P within the voxel indexed by (y Jz). By the definition, m is equivariant function Jz) Jo
The stacked voxel representation for given voxel location ju. Jy: J2 can be written as:
(i = (m1(2, P)),
where:
mmje:Jys Jes P) selects the subset of points P3 S P within the voxel indexed by Jur
1(P)) maps the selected point subset Pj to a feature vector representing the voxel at (y: J2).
Substitute p gP into v(P). Using the definition, we have:
The point set selection function m is equivariant to group transformations, so we have:
m(jzajyyJe gg
P).
Substitute this into the expression for v(gP):
P(g Jyn = (gm(g Diz:)ys ( P)).
The PointNet / is
and
meaning:
l(gP)) p(0)((P)),
where P3 m(jn: jz, P), and p(0) is the linear representation of the rotation group action.
Applying this to (ggm(g (iz,
MgPP)inn p(0) (ier
From the definition of vPP), we know:
[mig (m (Jn.dy. P)) u(P((g ((nn)oo)z))
Substituting this into the equation:
MgP))ieshw..e) {(g))))) ( (jnrJnn)e))
Since = v(P) is voxel grid (in function representation). the group action v is defined as:
Thus, have:
((g)) gv(P).
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Hierarchical Equivariant Policy via Frame Transfer
D. Additional Background of Group Symmetry
The group T3) x SO(2) can be naturally decomposed into translation T(3), which is handled using methods like 3D convolution, and rotation S2),), which addressed via network design by introducing equivariant layers (Cesa et al., 2022) that respect (2) transformations through appropriate representations of (0(2) or its subgroups.
D.1. Group Action of (0())
We focus on three particular representations of g E SO(2) or its subgroup C₁ (containing u discrete rotations) that define how the group acts on different data. Specifically:
Trivial Representation po: The trivial representation Po characterizes the action of SO(2) or C₁, an invariant scalar E R such that (g)g = This means that every group element y leaves the scalar x unchanged.
Standard Representation P1: The standard representation P1 defines how SO(2) or C, acts on a vector e E R using a x 2 rotation matrix. The action is given by pw(g) y cos standard 2 x rotation matrix.
cos -
When 1, the representation Pr (g) corresponds to the sim
Regular Representation Pregi The regular representation Preg describes the action of C, on a vector x I via a u permu- tation matrices. Let g pTh be an element of the cyclic group C. {1,r), r"-1) and let x = (I1, .2..... I.) E IR Then the action is defined by (reg(g) (Zu-m- mn--mm------ +2 ................................ Zur 32, Tu-m). This operation cyclically permutes the coordinates of x in R
representation P can also be constructed as a combination of different representations. Specifically, P is de- fined as the direct sum p = Po p @ p2² which belongs the general linear group GL + 2n + 2m2)) In this case, p(g) is block diagonal matrix of size (no + 2m1 + 2n2) (no + 2n1 2n2) that acts vectors E
D.2. Group Action of T(3)
Follow the definition of The group (3) of 3D translations is an additive group, whose action is defined by shifting spatial coordinates. For example, for a point cloud P {pi, { P.,...) } where y; (Ir,, Vi, zi), the action of g E T(3) is t. P; = (z; + t.. 3/ + ty. y.y2 2 + tz). Similarly, for voxel-based representations, T(3) acts by shifting the spatial indices of the voxel grid. Convolutions are inherently translationally invariant. I would say this Translation symmetry is naturally handled by operations such as 3D convolutions, which are inherently translation -equaiion--qvvviiiat.
E. Training Detail
In the simulation experiments, we use batch size of 16 for training. Specifically, the observation contains one step of history observation, and steps of history action and the output of the denoising process is sequence of 18 action steps. In close-loop control we use all 18 steps for training and execute 18 steps, similar to prior work ((Xian et al., 2023)). In close-loop control 18 steps and 9 steps are used for training and execution, similar to setting of (Wang et al., 2024) a. We train our models with the AdamW (Loohcchiovv & Hutter, 2019)) optimizer (with a learning rate of 10-4 and weight decay of 5#10 4). We use DDPM ((Ho et al., 2020)) with 100 denoising steps for both training and evaluation. We training each tasks with 100000 iterates.
F. Detail of Simulation Tasks
Here are descriptions of 30 tasks, shown in Figure 9, mentioned in simulation experiment:
1. Pick/Lift: Grasp and lift a block from the table.
2. Push Button: Press a button.
3. Knife on Board: Place knife onto a cutting board.
4. Put Money: Put dollars in safe.
5. Reach Target: Move the gripper to a specified target location.
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Hierarchical Equivariant Policy via Frame Transfer
6. Slide Block: Slide block across the table certain
7. Stack Wine: Put wine bottles into a shelf.
8. Take Money: Take dollars from safe.
9. Take Umbrella: Retrieve an umbrella from stand.
10. Pick up Cup: Grasp and lift cup.
11. Unplug Charger: Disconnect charger from outlet.
12. Close Door: Shut door fully.
13. Open Box: Lift the lid of box.
14. Open Fridge: Pull the fridge door open.
15. Frame off Hanger: Remove a frame from hanger.
16. Open Oven: Open the oven door.
17. Books on Shelf: Put book on a shelf.
18. Wipe Desk: Wipe desk surface clean using cloth.
19. Cup in Cabinet: Place cup inside cabinet.
20. Shoe out of Box: Remove shoe from its box.
21. Open Microwave: Open microwave door.
22. Turn on Lamp: Activate a lamp using its switch.
23. Open Grill: Lift the lid of grill.
24. Stack Blocks: Stack blocks on top of each other.
25. Stack Cups: Arrange cups in stacked configuration.
26. Push 3 Buttons: Press three buttons in specific sequence.
27. Plug USB in Computer: Insert USB device into port.
28. Open Drawer: Pull drawer open.
29. Put Item in Drawer: Pull drawer open and place object inside drawer.
30. Sort Shape: Put shape in a shape sorter
G. World Experimental Settings
Our real-world experiments are conducted on a UR5e robotic arm equipped with a Robotiq 2F-85 gripper and three Intel RealSense D455 cameras as shown Figure Demonstrations are collected using 6-DoF 3DConnexion SpaceMouse at 10 Hz rate, logging both the visual observations (from all three cameras) and the robot's end-effector actions (position, orientation, and gripper states).
H. Comparison With Hierarchical Diffusion Policy(HDP)
We also compare our policy with another hierarchical baseline, HDP (Ma et al., 2024), by selecting seven tasks from the HDP paper that we evaluated. We then compare the success rates on these tasks, as shown Table Our approach achieves an absolute mean improvement of 20%, demonstrating superior sampling efficiency.
17

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Hierarchical Equivariant Policy via Frame Transfer
Table Performance of HDP and HEP on 7 Tasks.
MedhodiOpeen-ooo
Mean
Pick Up Cup
Open
Open Drawer
Open Microwave
Open Oven
Knife Bourd
Target
HDP
74 94(-20)
100
82 98(+16)
90 100(+10)
90 94(+4)
26 82(+56)
58 87(+29)
72 96(+24)
HEP (Ours)
100
Table 7. Performance of Different Ablations Various Tasks,
Method
Mean
Lamp
Open microw.
Push battons
Push button
Open box
Insert USB
No Hierarchy
0.51
0.28
0.42
0.01
0.96
0.99
0.38
Equi No FT
0.60
0.21
0.44
0.53
0.99
No Equi
0.70
0.41
0.53
0.67
0.98
0.99
0.64
No FT
0.78
0.75
0.56
0.73
0.98
0.99
0.68
No Stacked Voxel
0.84
0.77
0.65
0.87
0.99
Complete Model
0.94
0.95
0.82
0.99
1.00
1,00
0.90
Full Result of Ablation Study
We show the full result of ablation study (subsection 5.4) here at Table 7.
J. Voxelization Details
We build our voxelization function based on (Contributors, 2020). The size our voxel grid is 64*64*64 with maximum points within
K. Equivariance Error
We conducted an experiment measuring the equivariance error specifically on C4, subgroup of SO(2). This allowed us to quantify the difference between the rotated output and the output from a rotated input. The experimental results are summarized in the Table 8.
Table 8. Equivariance Error Under Different Rotations
Rotation
Equivariance Error
0"
0%
90"
0.013%
180
0.006%
270
0.009%
L. Performance Under Human Perturbation
We conducted an extra experiment evaluating the success rate of executing block stacking task under human perturbation mimicking a dynamic environment and include the results in Table 9,
18

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Hierarchical Equivariant Policy via Frame Transfer
Table Success Rate Under Human Perturbation
Task
Success Rate
Blocks stacking
0.8
Take Umbrella
Stack Wine
Open Microwave
Kntle Board
Open Box
Plug USB Computer
Slide Block
Take Money
Take Shoes Out Box
Push Buttons
Close Door
Money
Open Drawer
Open Fridge
Open Oven
Push Button
Shape Sorter
Books Shelf
Siide Cabinet Put
Stack Cupe
Take Frame off Hanger
Pick and Lift
Unplug Charger
Wipe Desk
Open Grill
Reach Targst
Lamp On
Pick Up Cup
Put Itmm Drawer
Stack Blocks
Figure 9, All simulation tasks we evaluate on
19

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Hierarchical Equivariant Policy via Frame Transfer
3 realsense
cameras
EALIENSE
Figure 10. Real-world Experiment Setting
20


Reviews:
[{"review_id": "KbdZdNici5", "reviewer": "Reviewer_Sk4u", "summary": "The paper introduces Hierarchical Equivariant Policy (HEP), a framework for hierarchical reinforcement learning that integrates equivariance (geometric symmetry) into a two-level policy architecture. The high-level policy outputs a coarse 3D subgoal (keypose), essentially a translation in space representing the next target location in the task. This subgoal is then used to “frame-shift” the low-level policy’s coordinate system via a Frame Transfer interface, meaning the low-level agent perceives the world relative to the high-level’s suggested frame.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their thoughtful feedback. We respond below:\n\n---\n \n> \"HEP addresses translational equivariance thoroughly... currently, the framework isn’t equipped to specify or leverage rotations... could limit performance on tasks where orientation is critical.\"\n\nThank you for bringing this up! We agree that predicting orientation subgoals at the high level could potentially further improve sample efficiency. However, we would like to clarify that our current low-level agent already predicts SE(3) actions, enabling it to handle tasks requiring complex end-effector orientations, such as door closing, fridge opening, and pot cleaning. That being said, we are actively working on an extension of this paper where the high-level explicitly predicts goal orientations. We will thoroughly investigate and compare the advantages and disadvantages of these two orientation-handling strategies in our follow-up work.\n\n> \"Experiments... confined to tabletop manipulation... scalability to other domains remains unclear.\"\n\nWe appreciate the reviewer's insightful suggestion. Extending HEP to more complex robots, such as humanoids, is indeed a valuable direction for future research. We recognize that the generality of HEP in cross-embodied scenarios remains to be fully established. Nonetheless, we firmly believe that HEP effectively demonstrates two fundamental principles essential for efficient policy learning: special Euclidean group symmetry and hierarchical policy decomposition. These principles are expected to inform and inspire future developments across various robotic domains.\n\n> \"HEP relies on demonstrations... could be a bottleneck... hyperparameter sensitivity was not thoroughly discussed.\"\n\nWe appreciate the reviewer's valuable insight. We agree that dependence on expert demonstrations can be a limiting factor, especially given the time-consuming nature of obtaining demonstrations. While this study primarily explores behavior cloning, we believe future research could effectively extend HEP into reinforcement learning frameworks, thus eliminating the necessity for human demonstrations.\nRegarding hyperparameter sensitivity, we would like to clarify that our approach did not involve any hyperparameter tuning. Specifically, we directly adopted the high-level hyperparameters from Act3D and the low-level hyperparameters from Equivariant Diffusion Policy without any finetuning. We believe this choice underscores the robustness of our method. We will also make this explicit in the final version of the manuscript.\n\n\n> \"Related work is comprehensive... recent hierarchical RL or imitation learning works outside diffusion models should be acknowledged.\"\n\nThanks for your valuable advice. We added following works as our related works:\n\n[1] Wang, C, et al. \"MimicPlay: Long-Horizon Imitation Learning by Watching Human Play.\" CoRL. PMLR, 2023.\n\n[2] Luo, J, et al. \"Multi-Stage Cable Routing through Hierarchical Imitation Learning.\" IEEE Transactions on Robotics, 2024.\n\n[3] Triantafyllidis, E, et al. \"Hybrid Hierarchical Learning for Solving Complex Sequential Tasks using the Robotic Manipulation Network (ROMAN).\" Nature Machine Intelligence, 2023.\n\n[4] Bagaria, A, et al. \"Effectively Learning Initiation Sets in Hierarchical Reinforcement Learning.\" NeurIPS, 2023.\n\n[5] Shao, J, et al. \"Pfrl: Pose-free reinforcement learning for 6d pose estimation.\" CVPR. 2020\n\n---\n\n### Reviewer’s Questions:\n\n> \"HEP showed strong one-shot generalization... Is it largely due to equivariant inductive bias?\"\n\nThank you for bring this up. We believe the reason is that we use a 3D Unet as our high level (which is T(3) equivariant), but most importantly, our frame transfer interface passes the equivariance and generalization ability to our low level, leading to an improved generalization ability of the whole policy.\n \n> \"Contribution of hierarchical decomposition alone (without equivariance) compared to flat equivariant policy?\"\n\nThis is a great question. We conducted an ablation study with hierarchical decomposition. And we put it into our response to Reviewer 3 cFSf due to character limitation. Please see Table 1 in our response to reviewer 3 cFSf for more details. As shown in the table, removing the hierarchical decomposition lead to a significant drop in performance, demonstrating importance of a hierarchical structure especially on long horizon task.\n\n> \"Improving robustness to depth sensor noise?\"\n\nWe thank the reviewer for raising this important point. While the high sample efficiency of our policy allows us to train directly on real-world data—enabling the policy to adapt to sensor noise to some degree—we agree that introducing additional noise during training (e.g., applying a dropout layer to randomly remove points) could further enhance the robustness of the system to sensor noise. We will explore this idea in future experiments.\n\nThank you again for your insightful feedback!", "claims_and_evidence": "The paper introduces a novel integration of equivariance into hierarchical policy learning. This is the first work to imbue a two-level (coarse-to-fine) policy with symmetry properties, theoretically proving that the combined high-low policy remains equivariant to translations and rotations. This theoretical contribution is non-trivial and extends prior equivariant RL approaches (which were single-level) to a hierarchical setting. By decomposing the symmetry into a global part (at the high level) and a local part (at the low level), the design cleverly ensures the overall policy is invariant to spatial transformations of the task, which is a new insight with potentially broad impact on how we design policies that generalize across space and orientation. Instead of the high-level simply commanding a fixed goal state for the low-level (as in prior two-stage approaches), it outputs a coordinate frame shift (a 3D translation) that serves as a context for the low-level. This provides a strong inductive bias (the low-level is “anchored” to work towards the subgoal) without rigidly constraining the low-level’s behavior. The low-level agent can thus refine the trajectory locally, handling details and adjustments that the high-level might miss. This hierarchical decomposition bridges the gap between keyframe-based and trajectory-based learning methods  – combining their advantages.", "methods_and_evaluation_criteria": "HEP demonstrates state-of-the-art results on a wide range of tasks. It consistently outperforms multiple baseline methods, including advanced diffusion-based policies, by a significant margin. A notable strength is the method’s demonstrated ability to generalize beyond its training conditions. The one-shot learning experiment, where HEP learned a task from a single demo and still succeeded 80% of the time on novel object configurations, is a compelling result. This level of generalization and robustness is a major practical strength, as real-world deployments often face variations that are not seen in training. The paper goes beyond simulation and validates the approach on a real robotic system, which strengthens the work significantly. Additionally, the authors include ablation studies that clearly quantify the contribution of each component: removing equivariance, Frame Transfer, or the voxel encoder each drops performance significantly (e.g. removing equivariance alone reduces success by 24%).", "theoretical_claims": "The low-level policy predicts a sequence of fine-grained actions (trajectory) relative to the subgoal frame instead of absolute coordinates. This design preserves a strong inductive bias (anchoring the low-level to an intermediate goal) while allowing flexibility for the low-level to adjust and refine the trajectory locally. Crucially, the authors incorporate domain symmetries into both levels of the policy: the high-level subgoal selection and the low-level trajectory generation are designed to be equivariant to translations and in-plane rotations (T(3) × SO(2) symmetry). This means if the environment or task is shifted or rotated, the HEP’s policy will produce a correspondingly shifted/rotated action sequence, greatly enhancing spatial generalization. Theoretical propositions (with proofs in the appendix) show that under the given design, the entire hierarchical policy is equivariant to those transformations.", "experimental_designs_or_analyses": "To efficiently handle visual input, HEP uses a stacked voxel grid representation of point clouds (from multi-view RGB-D cameras) processed by a 3D equivariant U-Net, enabling rich 3D features and fast inference. On the experimental side, the paper provides an extensive evaluation of HEP on 30 robotic manipulation tasks from RLBench and several real-world robot tasks.", "relation_to_broader_scientific_literature": "The paper is related to existing hierarchical methods in robotic manipulation such as Ma et al., 2024; Xian et al., 2023. This paper proposes an approach where the high-level agent predicts a keypose in the form of a coarse 3D location representing a subgoal of the task. This location is then used to construct the coordinate frame for the low-level policy.", "essential_references_not_discussed": "Shao, Jianzhun, et al. \"Pfrl: Pose-free reinforcement learning for 6d pose estimation.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.", "other_strengths_and_weaknesses": "•\tWhile HEP addresses translational equivariance thoroughly, the high-level Frame Transfer interface handles only translations (T(3)) and not rotations of the coordinate frame. The equivariance to rotations is incorporated in the network (policy) architecture for planar rotations (SO(2)), but the high-level does not explicitly output a desired orientation for the subgoal. This is noted by the authors as a limitation: currently the framework isn’t equipped to specify or leverage rotations in the subgoal, which could limit performance on tasks where orientation of the end-effector is critical. The paper suggests that extending Frame Transfer to include rotation is future work. Until that is realized, the method might struggle or require ad-hoc solutions in scenarios like screwing in a lightbulb or opening a door, where the goal orientation matters as much as position.\n\n•\tAnother limitation is that the experiments are confined to tabletop robotic manipulation tasks. All tasks in the paper involve a fixed robotic arm interacting with objects on a table or in a small workspace. This leaves open the question of how well the approach scales to other domains (e.g., legged locomotion, navigation, or deformable object manipulation). The authors explicitly note that extending HEP to more complex robots like humanoids is a promising direction, but it remains to be seen if the current design would directly apply or if significant modifications are needed. For example, a humanoid might require a deeper hierarchy or different equivariances. Thus, the generality of HEP beyond manipulation isn’t proven. \n\n•\tHEP is trained via behavior cloning on demonstration data. While the approach is more sample-efficient than prior methods it still fundamentally requires demonstration trajectories for each new task. This reliance on expert demos could be a bottleneck in scenarios where obtaining demonstrations is time-consuming or costly. As a minor point, hyperparameter sensitivity (e.g., how the choice of the interval m for high-level steps, or the number of diffusion steps, affects performance) is not deeply discussed – presumably these were tuned on a subset of tasks, but it’s not reported, leaving a bit of uncertainty on how robust the training setup is.\n\n•\tWhile the related work is thorough, there might be recent works on hierarchical RL or imitation (outside of diffusion models) that could be acknowledged for completeness. These are relatively minor and did not significantly hinder understanding or merit of the work.", "other_comments_or_suggestions": "No", "questions_for_authors": "1.\tHEP showed strong results even with very few demonstrations in some cases. Could the authors elaborate on what aspects of HEP enable such one-shot generalization? For example, is it largely the equivariant inductive bias that makes one demo cover many situations via symmetry? \n\n2.\thow much does the hierarchical decomposition alone (even without equivariance) contribute versus a flat equivariant policy? \n\n3.\tIn real-world tests some failures were due to misalignment from depth sensor noise. How might the system be made more robust to such errors?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "M2xJwSxCwC", "reviewer": "Reviewer_Vgsm", "summary": "The paper proposes a novel Hierarchical Equivariant Policy (HEP) framework for robotic manipulation tasks, combining hierarchical learning with translation and rotation equivariance via a flexible Frame Transfer interface. HEP decomposes tasks into high-level coarse predictions and low-level fine-grained trajectory generation, improving flexibility, sample efficiency, and spatial generalization. Experiments show HEP significantly outperforms existing approaches in simulation and real-world robotic tasks, especially those demanding precise control and long-horizon planning.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their response. We respond below:\n> “The theoretical claims seem correct under the assumptions stated, although they are impossible to verify due to the deep neural net.”\n\nWe thank the reviewer for raising this important point. While our theoretical claims appear valid under the stated assumptions, we acknowledge the difficulty of directly verifying these assumptions due to the complexity of deep neural networks. To address this concern empirically, we conducted an experiment measuring the equivariance error specifically on C4, a subgroup of SO(2). This allowed us to quantify the difference between the rotated output and the output from a rotated input. The experimental results are summarized in the table below:\n\n**Table 1. Equivariance Error Under Different Rotations**\n\n| Rotation | Equivariance Error |\n|----------|--------------------|\n| 0°   \t| 0%             \t|\n| 90°  \t| 0.013%         \t|\n| 180° \t| 0.006%         \t|\n| 270° \t| 0.009%         \t|\n\nAs you can see, the network is equivariant, modulo numerical error, to rotational transformation. Also, our network inherits the transnational equivariance through the Unet and frame transfer architecture.\n\n---\n\n> “In open-loop training, the low-level target is constructed by interpolating between the consecutive keyframes. This interpolation may fail in a clustered environment due to the need for obstacle avoidance. This also introduces one of the main limitations of the experimental setup: the method is tested only on a simple, unclustered table-top setting.”\n\nWe thank the reviewer for the question. In Section 6 **“Robust to Environment Variations”**, we demonstrate that the trained policy would be robust to some disturbance objects in the workspace. We conducted an extra experiment evaluating the success rate of executing a block stacking task under human perturbation mimicking a dynamic environment and include the results here:\n\n**Table 2. Success Rate Under Human Perturbation**\n\n| Task        \t| Success Rate |\n|------------------|--------------|\n| Blocks stacking  | 0.8      \t|\n\nHowever, the reviewer makes a good point that if the demonstration data does not contain obstacle avoidance while an obstacle is introduced at test time, the trained policy might fail. In future work, we propose to add an additional hierarchy of a trajectory optimization layer, which would refine the policy for obstacle avoidance.", "claims_and_evidence": "The experiments support the main claims. The main claims are:\n- HEP significantly improves robotic manipulation performance in both simulation (RLBench tasks) and real-world experiments compared to state-of-the-art methods.\n- Frame Transfer Interface effectively provides flexibility and efficiency in hierarchical policy learning.\n\nEmpirical evaluations across 30 diverse tasks demonstrate that HEP achieves higher success rates compared to baseline methods.", "methods_and_evaluation_criteria": "The proposed methods and simulation benchmark make sense for the problem. The inclusion of real-world experiments is also a plus. The ablations demonstrate the value of different components. One-shot generalization tests are also interesting.", "theoretical_claims": "The theoretical claims seem correct under the assumptions stated, although they are impossible to verify due to the deep neural net.", "experimental_designs_or_analyses": "In open-loop training, the low-level target is constructed by interpolating between the consecutive keyframes. This interpolation may fail in a clustered environment due to the need for obstacle avoidance. This also introduces one of the main limitations of the experimental setup: the method is tested only on a simple, unclustered table-top setting.", "relation_to_broader_scientific_literature": "The paper’s contributions are well-motivated, and address important limitations of existing approaches.", "essential_references_not_discussed": "Nothing I can think of.", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "t03JSbEKsd", "reviewer": "Reviewer_cFSf", "summary": "The paper proposes to develop SO(2)xT(3) equivariant hierarchical policy for imitation learning learnt policy. The high-level proposes the translation target in the canonical world frame. While the low-level policy uses the local frame to diffuse the action. The equivariance is achieved via frame transfer interface and voxel repr. Experiments show that the proposed hierarchical policy achieves ~10% performance when the number of demonstration is very limited.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their response. We respond below:\n\n> \"...related baselines are missing like equivariant policies, e.g., Equivariant Diffusion Policy. I would like understand the difference of having a hierarchical policy and more simple versions\"\n\n> \"There should be work on equivariant policies, e.g., Equivariant Diffusion Policy, Wang et al.\"\n\n\n> \"Could you show results of other equivariant policies?\"\n\nThank you for bringing this to our attention. We did provide comparisons with equivariant policies, specifically the Equivariant Diffusion Policy [1], labeled as **\"EDP\"** in Table 1. However, we acknowledge that this reference may not have been sufficiently clear. In our revised manuscript, we will explicitly clarify that **\"EDP\"** refers to the Equivariant Diffusion Policy and emphasize this comparison more clearly to avoid confusion.\n\nAdditionally, we've conducted an ablation study on the hierarchical architecture to better understand its benefits:\n\n### Table 1. Revised Ablation Experiment\n\n| **Method**     \t| **Mean** | **Lamp on** | **Open microw.** | **Push 3 buttons** | **Push button** | **Open box** | **Insert USB** |\n|--------------------|---------:|------------:|-----------------:|-------------------:|----------------:|-------------:|---------------:|\n| No Hierarchy   \t| 0.51 \t| 0.28    \t| 0.42         \t| 0.01           \t| 0.96        \t| 0.99     \t| 0.38       \t|\n| No Equi No FT  \t| 0.60 \t| 0.21    \t| 0.44         \t| 0.53           \t| 0.96        \t| 0.99     \t| 0.51       \t|\n| No Equi        \t| 0.70 \t| 0.41    \t| 0.53         \t| 0.67           \t| 0.98        \t| 0.99     \t| 0.64       \t|\n| No FT          \t| 0.78 \t| 0.75    \t| 0.56         \t| 0.73           \t| 0.98        \t| 0.99     \t| 0.68       \t|\n| No Stacked Voxel   | 0.84 \t| 0.77    \t| 0.65         \t| 0.87           \t| 0.99        \t| 0.99     \t| 0.79       \t|\n| **Complete Model** | **0.94** | **0.95**\t| **0.82**     \t| **0.99**       \t| **1.00**    \t| **1.00** \t| **0.90**   \t|\n\nOur findings demonstrate that incorporating a hierarchical structure notably enhances performance, particularly on long-horizon tasks.\n\n---\n\n**[1]** Wang, Dian, Stephen Hart, David Surovik, Tarik Kelestemur, Haojie Huang, Haibo Zhao, Mark Yeatman, Jiuguang Wang, Robin Walters, and Robert Platt. *\"Equivariant Diffusion Policy.\"* Conference on Robot Learning (CoRL). PMLR, 2024.", "claims_and_evidence": "The claim is well supported by the experiments. Furthermore, i agree that with these design choices, the policy is indeed equivariant.", "methods_and_evaluation_criteria": "As RL-Bench is the standard to test imitation learning algorithms, i believe the result is quite convincing on its capability to generalize well in the low data domain.", "theoretical_claims": "I agree that the theoretical claims on the equivariance property is correct.", "experimental_designs_or_analyses": "The experiment is comprehensive. However, i think related baselines are missing like equivariant policies, e.g., Equivariant Diffusion Policy. I would like understand the difference of having a hierarchical policy and more simple versions.", "relation_to_broader_scientific_literature": "The work studies methods that can allow the imitation policy works well in low data domain. This is an important problem for robot learning.", "essential_references_not_discussed": "There should be work on equivariant policies, e.g., Equivariant Diffusion Policy, Wang et al.", "other_strengths_and_weaknesses": "The design of the hierarchical policy is reasonable for the equivariant policy. However, i think evaluation is needed to show that a hierarchical policy is indeed needed for solving these imitation learning tasks.", "other_comments_or_suggestions": "None", "questions_for_authors": "1. Could you show results of other equivariant policies?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zLHOW9pn7Z", "reviewer": "Reviewer_1oMk", "summary": "Hierarchical Equivariant Policy (HEP) enhances hierarchical policy learning by introducing a frame transfer interface, where the high-level agent’s output serves as a coordinate frame for the low-level agent, improving flexibility and inductive bias. It also integrates domain symmetries at both levels, ensuring overall equivariance. HEP achieves state-of-the-art performance in complex robotic manipulation tasks, demonstrating improvements in both simulation and real-world settings.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their response. We respond below:\n\n---\n> “...The authors should provide more explanation to clarify the novelty of their approach.”\n\nWe agree with the reviewer that there exist various works on hierarchical policy learning. However, our method is the first to incorporate equivariant learning into hierarchical policy. This is both novel, and leads to sizable performance increases.  Additionally, our proposed frame transfer interface ensures translational equivariance and imposes soft constraints on the low-level agent.\n\nWe refer Reviewer 4 to Reviewer 1’s assessment of our method's novelty\n> “Can the method be applied in scenarios with only image input, without requiring RGB-D inputs?”\n\n\n\nCurrently, our approach requires a 3D understanding of the environment, which we obtain using RGB-D inputs. Given the expense and inherent noise associated with RGB-D sensors, an interesting direction for future work would be to extend our framework to scenarios that rely solely on RGB images. Recent advances in depth-estimation foundation models [1,2] may enable the generation of accurate 3D representations from pure image data. Additionally, in tabletop settings where a top-down camera is available, pixel coordinates can be directly mapped to spatial (x,y) positions without requiring explicit depth measurements, thus potentially enabling SE(2) equivariance in the policy.\n\n[1] Guo, Y, et al. \"Depth Anything: Unleashing the Power of Large-Scale Image-Text Pretraining for Zero-Shot Depth Estimation.\" arXiv preprint arXiv:2311.16502, 2023.  \n\n[2] Wen, B, et al. \"FoundationStereo: Zero-Shot Stereo Matching.\" arXiv preprint arXiv:2501.09898, 2025.  \n\n> “...separate policy trained for each task? ...does the policy incorporate language?”\n\nWe are evaluating our policy under a single-task setting following former work [3] for fair comparison. However, it should be straightforward to operate in a multitask setting by adding a language feature to the observation, as is done in [4,5]. Evaluating the performance in multi-task settings can be an interesting direction for future work.\n\n[3] Xian, Z et al \"ChainedDiffuser: Unifying Trajectory Diffusion and Keypose Prediction for Robotic Manipulation.\" CoRL. PMLR, 2023.\n\n[4] Ke, J, et al. \"3D Diffuser Actor: Policy Diffusion with 3D Scene Representations.\" CoRL. PMLR, 2024. \n\n[5] Shridhar, M, et al. \"Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation.\" CoRL. PMLR, 2023.  \n\n---\n\n> “How is the Equivariant Diffusion Policy used?...sampling procedure differ from that of a standard Diffusion Policy?”\n\nOur method improves upon standard diffusion policy in two key ways. Specifically, our policy is explicitly equivariant [6], meaning that it is automatically able to generalize to new problem instances related by symmetry. This is not inherent in Diffusion Policy [7]. Secondly, our method utilizes a hierarchical decomposition — namely, a high-level and low-level agent — not found in standard diffusion policy. As shown in our experiment result in Table 1 in our response to reviewer 3 cFSf (referenced here due to character limitations) and Table 1 here, these two changes enable our method to significantly outperform standard diffusion policy.\n\n[6] Weiler, M. et al. \"E(2)-Equivariant Neural Networks for Image Classification and Beyond.\" ICLR, 2019.  \n\n[7] Chi,C et al. \"Diffusion Policy: Visuomotor Policy Learning via Action Diffusion.\" RSS, 2023.  \n\n---\n\n> “...baselines use 3D scene representations; a comparison with state-of-the-art image-based visuomotor policies would provide a more comprehensive evaluation.”\n\nAs shown in the prior work [9], image-based Diffusion Policy [7] performs poorly in RLBench tasks, where the 3d representation of the workspace is essential. We also performed an extra experiment comparing the image-based diffusion policy against our method and we report the result here:\n\n### Table 1. Performance on 5 Tasks from RLBench\n| Method (Closed-loop) | Mean | Turn On Lamp | Open Microwave | Push 3 Buttons | Open Drawer | Put Item in Drawer |\n|-|-|-|-|-|-|-|\n| **Ours** | **79** (+23) | **60** (+32) | **64** (+22) | **37** (+36) | **95** (+41) | **76** (+28)  \t|\n| EquiDiff [8] | 57 | 28 | 42 | 1| 54|48|\n| DiffPo (Img) [7] | 2.8  | 4| 1 | 0  | 7| 2  |\n\nWe follow the hyperparameters from the original work, with the exception that we use RGB images from the same four cameras used in our setup (wrist, front, right shoulder, and left shoulder) and at the same resolution, to ensure a fair comparison.\n\n\n[8] Wang ,D ,et al \"Equivariant Diffusion Policy.\" CoRL. PMLR, 2024.\n\n[9] Shridhar, M et al \"Generative Image as Action Models.\" CoRL PMLR, 2024.", "claims_and_evidence": "The high-level policy outputs only x, y, z positions, while the low-level policy generates concrete actions. This approach is commonly used in hierarchical planning, where the high-level policy produces key points and the low-level policy generates trajectories. Additionally, the frame transfer mechanism resembles a coordinate transformation to a target-frame-centric representation. The authors should provide more explanation to clarify the novelty of their approach.", "methods_and_evaluation_criteria": "Can the method be applied in scenarios with only image input, without requiring RGB-D inputs?\n\nDuring the evaluation, is a separate policy trained for each task? Also, does the policy incorporate language inputs?\n\nHow is the Equivariant Diffusion Policy used? Does its sampling procedure differ from that of a standard Diffusion Policy?", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "All the baselines use 3D scene representations; a comparison with state-of-the-art image-based visuomotor policies would provide a more comprehensive evaluation.", "relation_to_broader_scientific_literature": "N/A", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This submission proposes the Hierarchical Equivariant Policy (HEP) framework, introducing equivariance into hierarchical imitation learning via a novel Frame Transfer interface. HEP demonstrates strong empirical performance across 30 RLBench tasks and real-world robotic manipulation scenarios, outperforming several baselines including diffusion-based and equivariant methods. The reviewers agreed that the submission presented the clear theoretical formulation, extensive experiments, one-shot generalization results, and real-robot deployment.

All reviewers agree that this submission is a well-executed contribution, particularly in integrating symmetry properties into multi-level policy structures. They also appreciated the robustness to data scarcity, the clean decomposition into high- and low-level behaviors, and strong empirical validation with meaningful ablations. While there were a few concerns (handling translational equivariance primarily and limited evaluation results), the rebuttal addressed most concerns (providing additional analysis, ablations, and clarification on experimental setups.) 

Overall, the submission is solid, and the AC recommends acceptance. It is well-positioned to inspire future research extending hierarchical equivariant control. I recommend a poster, only because of slightly limited coverage of experiments in terms of scaling.
Decision: Accept (poster)