reviews: 
Comments: The paper proposes a novel setting for representing robotic manipulation problems as heterogeneous graph learning problems. The authors introduce a graph-based policy model, *Heterogeneous Equivariant Policy (HEPi)*, featuring multiple *SE(3)* equivariant message-passing networks (EMPNs) to model smaller sub-graphs like actuators and objects. HEPi explicitly models heterogeneity by assigning distinct network parameters for each interaction type to reduce message mixing and improve expressiveness. HEPi is claimed to be the first study of equivariant policies on 3D space within a reinforcement learning setting for robotic manipulation.

The authors theoretically prove that, for HEPi any two actuator and object nodes can exchange information while the graph network with locally connected actuators and object nodes can not. This justifies their design of actuator nodes as global virtual nodes to connect all object nodes

The authors test the proposed heterogeneous graph representation with reinforcement learning for 6 rigid and deformable object tasks, including Rigid-Sliding, Rigid-Insertion, Rigid-Insertion-Two-Agents, Rope-Closing, Rope-Shaping, Cloth-Hanging. Empirical results show that the proposed approach is more sample efficient and less likely to converge on sub-optimal solutions compared with the state-of-the-art Transformer and non-heterogeneous EMPN methods.
Strengths: 1. The paper is well-written and presents its ideas clearly with solid formulation.
2. The proposed approach of modeling robotic manipulation problems as heterogeneous graph learning problems is well-motivated and clever to unify the structure for both rigid and deformable object tasks using sub-graphs for actuators and objects.
3. The adaptation of *SE(3)* equivariant message passing networks is reasonable and suitable to exploit the geometric symmetry for improving the sample efficiency in the large 3D search space of configurations. As far as I know, HEPi is one of the first studies of equivariant policies on 3D space within a reinforcement learning setting for robotic manipulation.
4. The empirical experiments are comprehensive and sound to support the arguments. Most results are averaged over 10 seeds using
interquartile mean with 95% confidence intervals, which is also statistically robust.
Weaknesses: 1. The experiments are limited to simple geometric shapes like ropes, triangles, and stars, which can be easily modeled using a few nodes (< 100 in all the experiments). However, the target objects in most 3D manipulation tasks are more complex and sophisticated, e.g., cabinets or dresses, which require significantly more nodes to model. I doubt whether HEPi can still generalize to all those complicated geometries, which brings much computational complexity to graph learning.
2. The current framework assumes that the object coordinates are readily available in the observation, which is basically a simulation setting. In real applications without coordinates, such coordinates can only be extracted from other CV models in the wild. As a graph policy model, HEPi is likely to suffer from the cumulated error in the observation and fail the tasks compared to non graph learning methods.
3. Some typos:
- L17: objects -> object.
- L182: “lifts”, the left quotation mark.
- L344: There should be a blank space before HEPi.

Nevertheless, the overall idea is novel, and empirical experiments are solid enough to support the proposed setting. I recommend that the paper should be accepted.
Recommendation: 8
Reviewer confidence: 3
Soundness/correctness: 4
Clarity: 3