Differentiable and Learnable Wireless Simulation with Geometric Transformers

Thank you for your review and comments! In the following we discuss them in more detail and refer to relevant revised sections of our paper.

Why did we choose Adam?

Adam is indeed a robust and efficient optimizer for training deep learning models. As Wi-GATr is a transformer, thus a deep learning model as well, the benefits of Adam during training apply here as well regardless of the exact domain. Other optimizers might also apply and lead to good Wi-GATr performance.

Wi-GATr’s generalization capabilities come from the E(3)-equivariant design of the Geometric Algebra Transformer (GATr). It would be valuable for the authors to provide more justification or discussion regarding their contribution and novelty in implementing or improving such a design.

Thank you for this suggestion. We agree that GATr is a crucial component to this work. However, the architecture alone is not enough to solve practical wireless problems. We add both a novel tokenization scheme that allows us to represent 3D wireless problems in geometric algebra representations as well as inference algorithms, including a new approach to wireless inverse problems based on diffusion models. For practitioners, our release of two new datasets could be equally important. Beyond the technical contributions, we view our treatment of wireless channel modelling as a geometric deep learning problem as our novel key insight.

While the authors introduced their own datasets (Wi3R and WiPTR), the authors should provide a clearer justification for their choice of benchmarks, and using more widely recognized simulators such as WinProp or Wireless InSite could strengthen their work.

We did use Wireless InSite to obtain simulation measurements in the datasets we propose. We have made that reference more explicit in the manuscript. For clear justification and detailed simulation parameters, we would like to refer to Appendix D. Please let us know if you are missing specific details or explanations.

Thanks for the clarification. I am updating the score to 8.

Thank you for your review and comments! In the following we discuss them in more detail and refer to relevant revised sections of our paper.

The problem of this work is not well identified. The authors [...] do not give any introduction of the wireless channel model.

Thank you for pointing this out. We have added a background paragraph on channel models and signal propagation to our revised paper. In our experiments, we show examples of predicting non-coherent received power, band-limited received power, and delay spread.

The challenges [of model transfer] that need to be addressed are not clearly stated.

Applying transformers to modelling wireless signal propagation in 3D poses two challenges:

1. What is an adequate representation of the input data?
2. How can a transformer generalize to novel coordinate systems?

To address the first challenge, we show a comparison of a naive mesh representation to our tokenization scheme in Figure 3. To address the second challenge, we identified the symmetries of the problem and an adequate architecture, i.e. GATr. In order to apply GATr, one has to properly embed the mesh representation into the correct Geometric Algebra types (see Section 3.2). In our experiments, we show the significant impact using an equivariant architecture has on the problem, outperforming several baselines.

... the work consists only of two application experiments using the properties of the existing model.

It is true that we do not propose an entirely new architecture or algorithm in this work. However, we do show an entirely novel geometric deep learning approach to wireless simulation neural surrogates. We do think that our performant backbone with its new geometric tokenization scheme, a new approach to wireless inverse problems based on diffusion models and conditional sampling, the demonstration on several experiments, and the release of two new datasets to the community present enough useful innovation and insights at the intersection of wireless applications and geometric deep learning research. Beyond the technical contributions, we aim to impact both fields by highlighting the geometric nature of wireless channel modelling which represents a novel angle to this machine learning problem.

... Figure 1 shows the geometric surrogates for modeling wireless signal propagation. However, there is not enough explanation of this figure in the paper...

Thank you for bringing this to our attention! We have revised the caption of Figure 1 to improve clarity.

How were the two datasets generated? Were they extracted from other datasets or were they simulated themselves using other tools. Is this sufficient as one of the contributions of the paper?

The datasets were simulated using state-of-the-art wireless ray tracing software (Remcom Wireless InSite as noted by other reviewer). The diverse scenes and detailed wireless simulation makes the dataset compelling for data-driven channel modeling and the geometric deep learning community.

Edit: Fixed typo.

Thank you for your review and comments! In the following we discuss them in more detail and refer to relevant revised sections of our paper.

The most competitive baseline (SEGNN) is not evaluated on the WiPTR dataset.

We have implicitly mentioned in line 308 that training SEGNN runs out of memory on WiPTR. We have made this more explicit in our revision. Thank you for pointing this out! It is one of the advantages of our Wi-GATr approach that thanks to the transformer architecture, it scales much better to larger scenes than SEGNN.

Are the input coordinates of the transmitter/receiver 2D or 3D for the proposed model ?

We consider everything in 3D, including the input coordinates of the transmitter and receiver. In the synthetic datasets, the receiver and transmitter positions are randomly sampled in 3D, making it essential to take the height into account. This is one of the novelties of our approach.

Although the results on synthetic data are convincing regarding the contribution of the proposed architecture, the impact of the proposed architecture w.r.t. the transformer is not so clear on real data, although the authors explain this by the simplicity of the scene.

We argue that the main strength of our architecture is the generalization capabilities to new geometric layouts. Currently, real-world datasets are lacking variety in geometric layouts, collecting data on multiple scenes is challenging and time-consuming. Therefore, we show the generalization capabilities on simulated data. On the single real-world scene, where the geometry remains fixed throughout, the transformer performs competitively. However, as we evaluate on unseen scenarios, such as rotated or translated scenes (Table 1), Wi-GATr remains competitive and robust, while a baseline transformer fails.

Why does data augmentation lead to poorer results in some cases in table 2 for the transformer baseline ?

This is indeed surprising. We explain these results with the fact that the samples in the dataset have a lot of accidental shared structure, for instance that floor and ceiling are parallel to the x-y plane. E(3) augmentations remove this structure, so the network has to learn more from data. Given enough capacity and training steps, this should not be a problem, but within the fixed settings of our study this turned out to be more difficult to pick up for the transformer.

For Rx interpolation in in-distributions experiments (l. ~329) in table 1, have the floor layouts been seen by the model during training ? If so, this should be explained more clearly, and why this setting is relevant.

Yes, in the Rx interpolation setting, the floor layouts have been seen during training. However, receiver locations we evaluate on were not seen during training. This evaluation tests the generalization to unseen Rx positions, testing the capabilities as a wireless simulator. The real-world relevance is highlighted in Section 5.4, where the simulations tuned on sparse data are used to predict missing measurements.

We have rephrased the relevant parts in our revised paper to improve clarity. Thank you!

Minor remarks:

l. 297: |ap|^2 -> ap^2 ?

Thank you for pointing out the two typos. We have fixed them in the revision. Note that |a_p|^2 is more precise as a_p denotes the complex path gain. We have added a paragraph with background on channel modelling in Section 2 to clarify the notation.

I thank the authors for clarifying the points mentioned, I updated my score to 8.

Thank you for your review and comments! In the following we discuss them in more detail and refer to relevant revised sections of our paper.

The definitions of inverse problems lack clarity. For instance, the authors should provide a more detailed discussion and formulation for receiver localization. Additionally, the explanations of probabilistic inference with diffusion models on Page 5 are inconsistent with the discussion of diffusion models on Page 13...

Thank you for bringing this to our attention. In our revised paper, we have incorporated additional details on conditional sampling and receiver localization. Furthermore, we have extended the appendix with detailed descriptions of our masked training procedure, including pseudocode algorithms for training and sampling from our diffusion model. Overall, we use the DDPM formulation for the noise scheduler during training and we have adapted the notation in the appendix to clarify this.

This paper lacks of comparisons with public datasets for channel prediction and other state-of-the-art channel prediction models with NeRF and diffusion models.

We would like to highlight that the DICHASUS dataset is publicly available and contains real-world measurements. Could you provide more concrete pointers which aspects of other public datasets you are missing, please?

The novelty in the machine learning aspect of this paper is unclear. It appears that the work mainly leverages the equivariant Geometric Algebra Transformer for channel prediction.

You're right: the Geometric Algebra Transformer architecture is indeed a crucial component to our work. However, the architecture alone is not enough to solve practical wireless problems. We add both a novel tokenization scheme that allows us to represent 3D wireless problems in geometric algebra representations as well as inference algorithms, including a new approach to wireless inverse problems based on diffusion models. For practitioners, our release of two new datasets could be equally important. Beyond the technical contributions, we view our treatment of wireless channel modelling as a geometric deep learning problem as our novel key insight.

Regarding generalization, the authors primarily validate their approach on two different datasets. It would be helpful to consider cross-dataset scenarios to assess performance in unseen conditions. Additionally, the authors should discuss the impact of parameters, such as varying simulated frequencies and the number of paths, on prediction performance.

By pretraining on simulated data and fine-tuning on real-world data, we have shown cross-dataset benefits of our model and our generated dataset. Generalization with respect to other frequencies represents an interesting, but separate, orthogonal problem to the one that we tackled, namely generalization across geometries.

... correct typographical errors, such as “The The Tx and Rx locations are sampled uniformly within the bounds of the floor layouts.”

Thank you for pointing out this typo in our appendix. We have addressed it in our revision.

We thank the AC and the reviewers for the fruitful discussion and their decision.

We want to highlight that it is not our intention to generally replace ray tracing algorithms. We showed our method can solve problems that state-of-the-art ray tracing cannot solve. We invite interested researchers to try this out themselves using our open-source code. The links to the repositories can be found in the camera-ready version of the paper and the code will be published there by the time of the conference.