Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper proposes a novel steerable convolution for 2D path planning, where the convolution operation benefits from incorporating symmetric constraints to reduce overall search space and improve planning performance. Specifically, by manipulating the input signal in a symmetric setting (e.g. rotation and flipping for 2D space) and enforcing consensus outputs, the symmetric convolution can learn to reduce ambiguous prediction and therefore have better potential in both efficiency and accuracy. 
strength_and_weaknesses: Pros:
- This paper provides a simplistic integration using VIN, which is easy to implement. 
- The motivation to use VIN and the effectiveness of symmetric constraint is discussed and proved (only in 2D grid case).
- The experiment shows substantial improvements over baselines: VIN & GPPN.

Additionally, although I don't have experience in path & agent planning, I found this paper easy to understand.

Cons:
- Differences should be highlighted compared to E(2)-CNN, as they also proposed a steerable convolution with kernel constraints. Can their steerable convolution be applied to the same task with a little modification?
- Defining the generalized symmetric operation is challenging. Although the paper demonstrates the 2D grid case where the input signal (\mathbb{Z}) is rotated 90 deg, extending to 3D or higher dimension might be more difficult. For example, if the Euler angle represents the rotation in 3D, rotating a 3D signal with multiple 90 deg will suffer the gimbal lock. 
clarity,_quality,_novelty_and_reproducibility: The overall quality is sound, as the motivation for integrating symmetric constraint into VIN (as a linear operator) is addressed and proved. Moreover, the effectiveness of the proposed module is validated in experiments. The author also provided complete supplementary material to make the paper self-contained, especially the implementation details of pseudo torch code, which I found easy to follow and reproduce.  
summary_of_the_review: I have several questions & concerns regarding the technique.
1. E(2)-CNN also proposed a transformation invariant representation yield by the steerable convolution. What is the difference compared to them? Can E(2)-CNN apply to the same task with slight modification?
2. Is the binary entropy loss applied to both raw and symmetric output?
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The paper proposes to build differentiable planning methods that are equivariant to translations, rotations, and reflection transforms. This is done by replacing standard convolutional layers (which are equivariant to translations) in differentiable planning algorithms like VINs and GPPNs with steerable convolutional layers (which are additionally equivariant to rotations and reflections). The authors also theoretically show that value operators and value iteration on 2D grids are equivariant, and this can be expressed as a steerable convolution. Experiments are performed on 2D grid / visual navigation and 2 DOF manipulation and demonstrate strong improvements over non-equivariant versions of the planning methods.
strength_and_weaknesses: # Strengths
* The paper focuses on an important problem and clearly motivates the need for equivariance for path planning (with good illustrative examples).
* The authors theoretically analyze the problem and provide key theorems to support the proposed algorithm
* The experiment setup is sensible and uses good baselines
* The results are strong and demonstrate consistent improvements over the baselines

# Weaknesses
* The results are only demonstrated only small and toyish maps (100 x 100 or smaller). In robotics planning, the maps can be significantly larger (e.g., 960 x 960 in Active Neural SLAM, Chaplot et al., ICLR 2020). It is unclear how the proposed method works on more complex scenarios.
* The metrics in Table 1, Figures 6 and 7 only capture success rate and not efficiency of the predicted plan relative to an optimal planner like A*. A common metric to measure this efficiency is SPL (Success weighted by Path Length) from Anderson et al., 2018: https://arxiv.org/pdf/1807.06757.pdf
clarity,_quality,_novelty_and_reproducibility: Clarity was good, the work appears to be novel and implementation details are provided for reproducibility.
summary_of_the_review: # Post-rebuttal update
The authors address the comments about the map sizes and optimality of paths for planning. I'm raising my rating to accept.

# Pre-rebuttal review
The paper tackles an important problem and proposes to incorporate equivariances in differentiable planning methods. It provides both theoretical and empirical analyses and demonstrates strong improvements over prior work. However, the results are demonstrated only in simplistic maps and do not capture closeness of planned paths to the optimal path.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper demonstrates one way to exploit the rotation and reflection symmetry structure in path planning problems. More specifically, the authors use Value Iteration Networks (VINs) to solve the path finding problem on the Z2 space. They show that the steerable convolution can incorporate the symmetry structure in the value iteration process. Experiments show that their proposed symmetry regularization can improve the training speed, training success rate, as well as generalizability.
strength_and_weaknesses: This paper flows very well and smoothly. The idea of exploiting the rotation and reflection symmetry in the path finding problem is simple but also elegant. And it is a good choice to start from Z2 space and VIN with steerable convolution. The authors formally build the connections among symmetries, value iterations, and steerable convolutions. Moreover, the experiment results further verify that this symmetry regularization does help.

Besides those strengths, I might have some questions in mind. 

First, although it is intuitive that symmetries could improve the performance and the experiments also demonstrate the effectiveness of such proposed inductive bias empirically, is it possible to prove or even compute quantitatively why symmetry can help the path finding problems? 

Second, it is also mentioned that the symmetry structure also exists in other higher-dimensional continuous Euclidean spaces or spatial graphs (of path finding problems), can the authors provide more clues on how to generalize their method to those cases? Since the current experiments are on small scales and those mentioned more general spaces could be more practical in some real-world problems. 

Third, in Section 6.3, why is iteration K set to be sqrt(2)M? And why is the iteration linear to the map size?

clarity,_quality,_novelty_and_reproducibility: The presentation of this paper looks clear to me. 

The quality of the definitions, proofs, and experiments is also fine. 

Although the ideas and techniques are not totally new, finding appropriate connections among those concepts should be appreciated. 

I think their method is reproducible. Moreover, they already promised that the code would be open-sourced. 

summary_of_the_review: This paper presents an elegant symmetry regularization to the VIN-based path finding pipeline. The methodology part reads very well and experiments are sufficient to back up their technical novelties. In summary, I think this paper looks good to me.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper introduces steerable convolutions into differentiable planning as an inductive bias. It received three expert reviews and quickly a consensus on acceptance emerged.

The reviewers appreciated the integration into VIN (differentiable planning) and the performance of the contribution, the theoretical formulation of equivariance. The weaknesses are the rather small toy problems, as it is unclear whether this contribution can generalize to realistic settings.

The AC agrees and estimates that these weaknesses are outweighted by the strong principled formulation of this problem.
justification_for_why_not_higher_score: The paper is interesting, but a better evaluation on realistic problems would have made it stronger.
justification_for_why_not_lower_score: -
Decision: Accept: poster