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REVIEW 2 major objections 5 minor 27 references

Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects

T0 review · 2 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A heterogeneous graph policy whose actuator and object nodes are updated separately and constrained to be SE(3)-equivariant outperforms Transformer-based and homogeneous equivariant policies across seven rigid and deformable manipulation…

desk verdict Solid empirical RL paper with a new benchmark, but the scalar target-distance feature likely makes the tasks partially observable and needs clarification. read the letter →

arxiv 2502.07005 v6 pith:BKJ46OE3 submitted 2025-02-10 cs.LG cs.RO

Tai Hoang , Huy Le , Philipp Becker , Vien Anh Ngo , Gerhard Neumann This is my paper · ORCID
classification cs.LGcs.RO MSC 68T4068T0768T05
keywords heterogeneousgraphequivariantpolicySE(3)equivariancereinforcementlearningdeformableobjectmanipulationrigidinsertionneuralnetworktrustregion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to establish that robotic manipulation of varied rigid shapes and deformable objects—insertion, pushing, rope shaping, cloth hanging—is best learned by an explicitly heterogeneous, SE(3)-equivariant graph policy. It claims that its Heterogeneous Equivariant Policy (HEPi) outperforms Transformer-based and homogeneous equivariant policies on a new seven-task benchmark in final returns, sample efficiency, and generalization to unseen objects. The authors also argue, with a proof sketch, that treating actuator nodes as global virtual nodes connected to every object node lets any actuator and any object exchange information in a single message-passing layer, whereas k-nearest-neighbour local connections can make the actuator's output independent of distant object nodes. If the claim holds, geometry-aware inductive biases plus explicit role separation are a practical recipe for sample-efficient reinforcement learning in high-dimensional manipulation.

What carries the argument

The central object is HEPi's heterogeneous graph: nodes split into actuator nodes and object nodes, with intra-edges inside each set and directed fully connected inter-edges from objects to actuators, and with separate kernel parameters per edge type. The backbone is an efficient approximately SE(3)-equivariant message-passing network, based on lifting positions to position-orientation space and factorized kernels; the paper's Proposition 3.1 argues that because actuators connect to all object nodes, any actuator-object pair can exchange information in one layer, which the ablations link to avoiding oversquashing. Target information is absorbed into object-node features as a scalar distance to target, and the value function is a permutation-invariant DeepSets readout. Training uses a trust-region projection layer rather than clipped PPO to keep policy updates inside a KL constraint.

What would settle it

Train and evaluate HEPi on Rigid-Insertion-Two-Agents with object features restricted to the scalar distance to target (and no global target vector or orientation feature) and with target direction varied while distance is held fixed; if the policy's success tracks the unobserved direction, the observation is not Markovian and the reported returns would not reflect a policy that knows where the target is. The comparison that would settle it: add the full target vector to the object features and show the gap in success rate closes.

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Extended reading notes

Core claim

The paper claims that manipulation tasks with diverse geometries and deformable bodies can be cast as a single heterogeneous graph with disjoint actuator and object node sets, and that a policy built from that graph—HEPi—is more expressive than a homogeneous equivariant message-passing network and more sample-efficient than a Transformer. On its new GPU-simulated benchmark of seven tasks, HEPi reports higher average returns and better generalization to unseen objects, with the largest gains in tasks with large 3D search spaces: two-agent insertion, pushing, and cloth hanging. The authors attribute the gains to three design choices acting together: SE(3)-equivariant message passing, separate parameters for object-object, actuator-actuator, and object-actuator interactions, and a trust-region projection layer for stable on-policy updates. They support the graph design with Proposition 3.1, which shows that fully connected object-to-actuator edges let any actuator respond to any object node in one hop, while k-nearest-neighbour local connectivity can make that response independent of distant object nodes. They also report that adding attention to the graph does not improve performance and roughly doubles training time.

Load-bearing premise

The load-bearing premise is that the policy's observations fully specify the manipulation target: target information enters object nodes as a scalar distance to target, with absolute target coordinates only in the value function for cloth hanging, so for tasks with sampled target positions or orientations the agent must effectively have enough information elsewhere to reconstruct the target; if it does not, the benchmark results are not interpretable as solving the intended task.

Editorial extensions

If this is right

  • If the benchmark results hold, explicit heterogeneity—at least one parameter set per edge type—is a larger win than adding attention in on-policy graph RL; the paper's attention ablation shows no gain and about double training time.
  • The actuator-as-virtual-node design means one message-passing step suffices for global information flow, so deeper stacks are unnecessary and can hurt through oversquashing—a direct corollary of Proposition 3.1 supported by the paper's ablations.
  • SE(3) equivariance is the main driver of sample efficiency in large 3D search spaces; the cloth-hanging ablations show heterogeneous but non-equivariant GNNs need more samples to reach similar final performance.
  • The policy transfers across object resolutions: a model trained on roughly 20-node meshes evaluates on roughly 1200-node meshes with only mild degradation, and tolerates added position and velocity noise.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial: in the rigid-insertion and cloth-hanging tasks where the target pose is sampled, a scalar distance-to-target object feature is not Markovian by itself; the paper's reported performance implicitly requires target direction or orientation to be recoverable from other inputs or the scalar to be interpreted as a vector, and this should be stated explicitly when reusing the benchmark.
  • Editorial: the same heterogeneous-graph recipe could apply to multi-arm assembly or human-robot collaboration where each robot is an actuator sub-graph, since the paper's formulation already allows multiple actuators with complete intra-actuator edges.
  • Editorial: because the EMPN backbone is only approximately equivariant (orientations are sampled on a grid over the sphere), a direct test of the equivalence claim would be to compare performance as the orientation grid is refined; the paper reports gains up to 24 samples, so even finer grids are a natural stress test.
  • Editorial: the benchmark's use of keypoint coordinates as observations presumes a perception front-end; a testable extension is to plug learned keypoint extractors into the same policy to measure how much of the equivariance advantage survives visual noise.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper introduces HEPi, an SE(3)-equivariant heterogeneous graph policy for manipulation of rigid and deformable objects. It represents actuators and objects as disjoint node sets with separate message-passing kernels per edge type, uses a PONITA-style EMPN backbone, and Trust Region Projection Layers for stable on-policy RL. The authors propose a seven-task IsaacLab benchmark covering rigid insertion/sliding/pushing, rope closing/shaping, and cloth hanging, and report IQM returns with 95% confidence intervals over 10 seeds. They claim HEPi outperforms Transformer and homogeneous EMPN baselines in final return, sample efficiency, and generalization to unseen geometries, with ablations on attention, number of message-passing steps, k-NN connectivity, orientation discretization, sample-space size, and PPO vs. TRPL.

Significance. If the results hold, the benchmark and architecture are a useful contribution: the tasks address a real gap (geometry-aware RL for varying and deformable shapes), the evaluation is more careful than typical (10 seeds, IQM and confidence intervals, held-out objects, noise robustness, several ablations), and the heterogeneous graph design is a sensible way to combine equivariance with global information flow to actuators. However, the paper's central empirical claim is only interpretable if each task is a well-posed MDP; the scalar target feature problem discussed below casts doubt on this for orientation-dependent tasks. The relative ranking may survive because all policies see the same partial observations, but the benchmark's ability to support conclusions about precise orientation alignment is reduced.

major comments (2)
  1. [Section 3.2 and Appendix B] The observation for object nodes is stated to include 'the relative distance to the target, d_{v,target}' in Section 3.2, and Appendix B lists only the scalar 'distance to target dtarget' as the target-related feature for every task. For all rigid tasks, Rope-Shaping, and Cloth-Hanging, the target orientation is uniformly sampled and the reward explicitly depends on orientation (e.g., Rrotation, |cos(θalign)-1|, and the Dshape descriptor). A scalar distance from each object node to a target reference point is invariant under rotations of the target about that point, so distinct MDP states with different optimal actions and different rewards map to the same policy observation. Thus these tasks are partially observable as specified, and the reported returns cannot be interpreted as evidence that any method solves the intended orientation-sensitive manipulation problem. Please either include the target pose (e.g., a target vector or quaternion as a node or global feature) in the policy observation, restrict target sampling to position-only tasks, or explicitly reformulate the problem as a POMDP and make the memory and observation assumptions clear. This affects the benchmark's validity and should be addressed before the main comparative claim is accepted.
  2. [Appendix A, Proposition 3.1] The theoretical justification for the heterogeneous full-connectivity design is not fully established. The proof gives an explicit Jacobian for HEPi (Eq. 5) but only asserts, without derivation, that for MPNN+VNLocal the Jacobian becomes independent of u when u and v are 'more than 2 hops' apart. The notion of hop distance is not formalized for the mixed edge types (obj-obj, act-act, obj-act), and no equation is provided for the MPNN+VNLocal Jacobian. In a residual message-passing network, the Jacobian can depend on u through longer paths even when the direct connection is absent, so the claim needs a precise argument or a counterexample. Since Proposition 3.1 is presented as a contribution and used to justify the local-vs-global connection design, this gap should be closed.
minor comments (5)
  1. [Section 4.2, Figure 5 (right)] The generalization bar plots are reported without confidence intervals or an explicit number of seeds; please add error bars and seed counts for consistency with Figure 3.
  2. [Throughout] There are several typos, including 'NIVIDA IsaacLab' in Section 4.1 and 'rigid-slding' in Section 4.2; please proofread.
  3. [Section 3.2] The phrase 'one-hot scalar-vector' is ambiguous; clarify whether the node type is a scalar one-hot encoding or a concatenated vector.
  4. [Experimental evaluation] The paper reports only composite IQM returns, not task success rates. Adding a success-rate metric (e.g., thresholded on Rgoal/Rrotation or hole-hanger alignment) would make the benchmark more directly interpretable and strengthen the comparative claim.
  5. [Appendix B.7, Cloth-Hanging] The value function is given absolute target and initial coordinates while the policy receives only scalar distances; please explain why this asymmetry does not undermine the intended equivariance inductive bias or describe how the value function handles coordinate-frame dependence.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: HEPi's empirical claims rest on independent benchmark comparisons; the scalar target-distance issue is a correctness concern, not a circular one.

full rationale

The paper's central claims are empirical: HEPi outperforms Transformer and EMPN baselines in average return, sample efficiency, and generalization (Section 4, Figures 3-5, 7-8). These results come from independent evaluations on a newly built IsaacLab benchmark, with held-out objects and narrowed sample spaces, so they do not reduce to fitted parameters or to the architecture definition by construction. Proposition 3.1 is a mathematical statement proved from the update equations in Appendix A; although the HEPi half follows immediately from the full object-to-actuator aggregation in Eq. 2, proving a property of one's own architecture from its definitions is not circular reasoning about empirical performance. The paper adopts TRPL from Otto et al. (2021), whose authors overlap with the present paper, and cites Otto et al. (2023), Li et al. (2023), and Celik et al. (2024) in support; however, TRPL is a training component, not the central contribution, and the paper re-evaluates TRPL against PPO in Section 4.2, so these self-citations are not load-bearing. No equation fits a parameter and then renames that fit as a prediction. The potential issue flagged in the reader's take is a partial-observability risk: Section 3.2 and Appendix B list only a scalar 'distance to target dtarget' per object node, while rewards for rigid and cloth tasks depend on target orientation; this could make some benchmark tasks not fully observable, but that is a correctness/validity concern, not circularity. The Limitation paragraph in Section 6 acknowledges keypoint availability but does not mention this observability gap, which is a completeness gap rather than a circular step. Overall, the derivation chain is self-contained against external baselines and benchmarks.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central claims are empirical, so there are no fitted scientific constants. The hand-chosen architecture and training parameters below influence the results; the most consequential are the per-task trust region coefficients, the S2 orientation discretization, and the graph connectivity choices. The key domain assumptions are that the MDP is SE(3)-equivariant despite gravity, and that the target is fully encoded in node features.

free parameters (5)
  • trust region coefficient (per task) = 1.0 or 4.0 depending on task
    Chosen per task in Tables 5 and 6; controls the KL constraint strength and affects training stability and final return.
  • orientation discretization dimension (ori dim) = 16
    Controls sampling density on S2 for approximate equivariance; Appendix D shows higher values improve 3D performance at higher compute cost.
  • object graph KNN k = 3
    Number of object-object edges; chosen by hand, ablations in Appendix D show k=3 is competitive.
  • cloth hole boundary k = 10
    Policy observes only 10 keypoints around the hole; chosen by hand.
  • number of message passing steps per edge type = 1
    Default for HEPi; ablations show more steps do not help and can hurt due to oversquashing.
assumptions (3)
  • domain assumption The MDP transition and reward are SE(3)-equivariant under global transformations.
    Required for the equivariant policy to be a valid inductive bias. Fixed gravity and the sampling of pitch and roll in cloth hanging and insertion make full SE(3) equivariance only approximate; the paper does not discuss this mismatch.
  • domain assumption The target is fully specified by the node features, i.e., the observation is Markovian.
    Section 3.2 states target information is 'absorbed into the feature representation' as distance to target; if this is a scalar distance, direction to target is unobserved for sampled target positions (e.g., Cloth-Hanging), making the task partially observable.
  • standard math PONITA kernel factorizations preserve the universal approximation property for equivariant functions.
    Borrowed from Bekkers et al. (2024); the paper relies on it for expressiveness of the backbone.

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Cite this review

Pith. "Pith review of Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects." pith.science (2026). https://pith.science/paper/BKJ46OE3

@misc{pith2026250207005,
  author       = {Pith},
  title        = {Pith review of: Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BKJ46OE3}},
  note         = {Machine review of arXiv:2502.07005}
}
abstract

Manipulating objects with varying geometries and deformable objects is a major challenge in robotics. Tasks such as insertion with different objects or cloth hanging require precise control and effective modelling of complex dynamics. In this work, we frame this problem through the lens of a heterogeneous graph that comprises smaller sub-graphs, such as actuators and objects, accompanied by different edge types describing their interactions. This graph representation serves as a unified structure for both rigid and deformable objects tasks, and can be extended further to tasks comprising multiple actuators. To evaluate this setup, we present a novel and challenging reinforcement learning benchmark, including rigid insertion of diverse objects, as well as rope and cloth manipulation with multiple end-effectors. These tasks present a large search space, as both the initial and target configurations are uniformly sampled in 3D space. To address this issue, we propose a novel graph-based policy model, dubbed Heterogeneous Equivariant Policy (HEPi), utilizing $SE(3)$ equivariant message passing networks as the main backbone to exploit the geometric symmetry. In addition, by modeling explicit heterogeneity, HEPi can outperform Transformer-based and non-heterogeneous equivariant policies in terms of average returns, sample efficiency, and generalization to unseen objects. Our project page is available at https://thobotics.github.io/hepi.

Figures

Figures reproduced from arXiv: 2502.07005 by the authors.

Figure 1
Figure 1. Left: A Cloth-Hanging task represented by a heterogeneous graph that comprises two disjoint node sets, objects, and actuators, connected through directed, fully-connected inter-edges. Intra-edges occur within each set (both objects and actuators) to capture relationships within clus￾ters. Information is aggregated from objects to actuators via inter-edges. The target distance is ab￾sorbed into the feature representa… view at source ↗
Figure 2
Figure 2. Illustration of our diverse and challenging manipulation tasks, involving both rigid and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Evaluation curves for our seven manipulation tasks, comparing HEPi (ours), EMPN, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (21 more)
Figure 4
Figure 4. Figure 4: Performance of different models on the Cloth-Hanging task across varying sample spaces. Overall, performance improves as the sample space decreases. In terms of final performance, het￾erogeneous models outperform homogeneous baselines in most cases, demonstrating the b…
Figure 5
Figure 5. Figure 5: Left: Analysis of noise sensitivity and scalability to high-resolution objects in the Rigid￾Pushing task. Heatmaps show average returns under varying levels of artificial Gaussian noise in position and velocity inputs for both low-resolution and high-resolution objects…
Figure 7
Figure 7. Figure 7: Performance comparison on tasks with and without attention mechanisms over 10 seeds. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Performance comparison between HEPi and Transformer models with TRPL and PPO [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Demonstration of graph with overlapping and non-overlapping nodes. Actuator nodes are [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: Example trajectory of Rigid Sliding task. [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: Example trajectory of Rigid Pushing task. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: Example trajectory of Rigid Insertion task. [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: Example trajectory of Rigid Insertion with Two Agents task. [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]
Figure 14
Figure 14. Figure 14: Sample space of the Rigid-Insertion-Two-Agents task. [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: Example trajectory of Rope Closing task. [PITH_FULL_IMAGE:figures/full_fig_p020_15.png]
Figure 16
Figure 16. Figure 16: Example trajectory of Rope Shaping task. [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]
Figure 17
Figure 17. Figure 17: Example trajectory of Cloth Hanging task. [PITH_FULL_IMAGE:figures/full_fig_p022_17.png]
Figure 18
Figure 18. Figure 18: Sample space of the Cloth-Hanging task. Reward Function The total reward consists of the following sub-rewards: • Hole-hanger alignment reward: Rhole-hanger = ∥chole − changer∥ + 0.1 · | cos(θalign) − 1| where chole and changer represent the centroids of the cloth’s h…
Figure 19
Figure 19. Figure 19: Overview of all objects used in the rigid manipulation tasks. From left to right: [PITH_FULL_IMAGE:figures/full_fig_p024_19.png]
Figure 20
Figure 20. Figure 20: Performance of different models on the Cloth-Hanging task across various sample spaces. Assuming the global scene located at r = [0, 1, 0]T , then from left to right, we generate sample by rotating r by (a) θroll ∈ (−π/4, π/2), θyaw ∈ (−π, π), (b) θyaw ∈ (−π/2, π/2), …
Figure 21
Figure 21. Figure 21: Ablation on different k-nearest neighbors choices for obj-to-act edges in MPNN + VNLocal updates (in Section 3.3), evaluated across multiple tasks: rigid-insertion, rigid-insertion￾two-agents, and rope-shaping. Results are averaged over 8 seeds. message-passing steps …
Figure 22
Figure 22. Figure 22: Ablation on the number of message-passing steps (#MPs) for HEPi and EMPN models. [PITH_FULL_IMAGE:figures/full_fig_p026_22.png]
Figure 23
Figure 23. Figure 23: Ablation on different k-nearest neighbors for obj-to-act edges in MPNN + VNLocal (in Section 3.3) updates, evaluated on the Rigid-Insertion task with varying message passing steps m ∈ {1, 2, 3} for object nodes. Increasing the number of message passing steps degrades …
Figure 24
Figure 24. Figure 24: Ablation on the orientation discretization dimension ( [PITH_FULL_IMAGE:figures/full_fig_p027_24.png]
Figure 25
Figure 25. Figure 25: Ablation on the number of nearest neighbors ( [PITH_FULL_IMAGE:figures/full_fig_p027_25.png]

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Reference graph

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    (b) No overlapping node

    can be viewed as fully connected GNNs under the Message Passing Neural Network (MPNN) framework (Battaglia et al., 2018), since self-attention can be seen as a mechanism to aggregate 15 Published as a conference paper at ICLR 2025 (a) Overlapping node. (b) No overlapping node....

    2018

  15. [2019]

    Increasing ori dim improves performance in 3D tasks, such asrigid-insertion and cloth-hanging, by better approximat- ing full equivariance

    for han- 26 Published as a conference paper at ICLR 2025 O=24 O=16 O=8 HEPi EMPN -1.40 -1.20 -1.00IQM Return rigid-insertion-2D+z HEPi EMPN -1.40 -1.20 -1.00 rigid-insertion- two-agents-3D HEPi EMPN -1.40 -1.20 -1.00 cloth-hanging-3D Figure 24: Ablation on the orientation disc...

    2025

  16. [2020]

    Softgym: Benchmarking deep rein- forcement learning for deformable object manipulation

    Xingyu Lin, Yufei Wang, Jake Olkin, and David Held. Softgym: Benchmarking deep rein- forcement learning for deformable object manipulation. In Jens Kober, Fabio Ramos, and Claire Tomlin (eds.), Proceedings of the 2020 Conference on Robot Learning , volume 155 of Proceedings of...

    2020

  17. [2021]

    net/forum?id=WcY35wjmCBA

    URL https://openreview. net/forum?id=WcY35wjmCBA. Peter W. Battaglia, Jessica B. Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vin ´ıcius Flores Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, C ¸ aglar G¨ulc ¸ehre, H. Francis Song,...

    arXiv

  18. [2023]

    On over-squashing in message passing neural networks: the impact of width, depth, and topology

    11 Published as a conference paper at ICLR 2025 Francesco Di Giovanni, Lorenzo Giusti, Federico Barbero, Giulia Luise, Pietro Li `o, and Michael Bronstein. On over-squashing in message passing neural networks: the impact of width, depth, and topology. In Proceedings of the 40t...

    2025

  19. [2024]

    Diffusion-edfs: Bi-equivariant denoising generative modeling on se(3) for visual robotic manipulation

    Hyunwoo Ryu, Jiwoo Kim, Junwoo Chang, Hyun Seok Ahn, Joohwan Seo, Taehan Kim, Jongeun Choi, and Roberto Horowitz. Diffusion-edfs: Bi-equivariant denoising generative modeling on se(3) for visual robotic manipulation. arXiv preprint arXiv:2309.02685,

    arXiv

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Reviewed August 8, 2026 · model on record in the stance chip above.