Score-based Source Separation with Applications to Digital Communication Signals

Summary

1. In this paper authors proposed a method for separating superimposed sources using diffusion based generative models. The proposed model derived a new objective function based on maximum a posterior and alpha posterior. 2. The application of the proposed work is clearly mentioned by considering the existing components in the system, The data driven score based single-channel source separation technique are proposed for signal septation which perform superior compared to the conventional methods. 3. The contribution of the proposed work are mainly. a. Bayesian method for single-channel source separation is used. b. Score Distillation Sampling (SDS) has got good results of local extrema loss. c. The proposed method performs well compared to the signal processing and annealed Langevin-dynamics-based approaches for RF source separation method and the results are encouraging. 4. The results presented in this paper are highly encouraging.

Strengths

Paper is very well organized.

Weaknesses

The experimental set set up should be clearly explained.

Questions

1. Justify randomizing across multiple noise levels, the local extrema of loss. 2. What is the value of k is chosen; relative scaling coefficient between the two signals 3. Explain the experimental set up used to derive results presented in Figure 1. 4. Increase the resolution of the Figure 2 and explain it in detail. 5. A detailed explanation of the diffusion model is required. papers related to diffusion model, and it can be applied to the proposed method need to be elaborated more. 6. Why the probabilities are converted to negative in the equation 6b justify it. 7. A Comparison is required how the computational complexity of the proposed work is reduced compared to the conventional methods. 8. Train and test ratio used for the implementation is 90:10 is there any specific reason for it.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The author need to address the questions and revise the paper and submit it back.

Summary

This paper proposed a new Bayesian method to separate a mixture of two signals $\mathbf{s}$ and $\mathbf{b}$ from the mixture signal $\mathbf{y}=\mathbf{s}+\kappa \mathbf{b}$ where $\kappa \in \mathbb{R}_+$ is known. The new method leverages the score from pre-trained diffusion models to extend MAP estimation using generalized Bayes' theorem with an $\alpha$-posterior across different levels of Gaussian smoothing. Experiments on RF sources demonstrate superior separation performance, with gains of up to $0.95$ in terms of both BER and MSE over classical and existing score-based source separation methods such as BASIS by Jayaram and Thickstun (ICML 2020).

Strengths

Using deep learning for source separation problems has appeared in much research literature. The key contribution of this paper is to provide a new separation method that works well for a superimposition of two discrete sources which produces a joint distribution with multiple equiprobable modes. This work can be considered a novel combination of well-known techniques.

Weaknesses

The main weak point of this work is a lack of theoretical analysis or intuitions behind the superior separation performance of the proposed method.

Questions

+ In your plots in Fig. 3, $\alpha$-RGS outperforms classical methods such that MF only or LMMSE +MF. Why can this fact hold? + Why can your method outperform BASIS for equiprobable multimodal distributions?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

This is a theoretical work. The authors already finished the checklist as well as stated the limitations of theorems and results.

Summary

This paper focuses on the problem of single-channel source separation (SCSS) for RF signals with discrete nature. The authors propose to solve the SCSS problem using MAP and use pre-trained diffusion models to approximate the scores for both the source signal and inference signal. To avoid being stuck in a local minimum, the proposed method uses an $\alpha$-posterior and optimizes across multiple noise levels. Experiments show that the proposed method significantly outperforms the baselines (both traditional and learned methods) in both MSE and BER.

Strengths

1) This paper is well-written and it is easy to follow. Given that it is the first work that explores score-based models in the SCSS problem of RF signals and it achieves significant improvement, this work could definitely point out a new direction in this domain and potentially influence other researchers. 2) The idea of using $\alpha$-posterior and randomizing across multiple noise levels could be potentially useful for other score-based optimization problems not limited to the scope of SCSS in RF signals.

Weaknesses

1) The proposed method requires to know the scale factor $\kappa$ (or SIR) and the distribution of the interference signal. However, the scaling factor is not available in real-world scenarios. Also, the interference signals could come from different sources such as WiFi, and Bluetooth. As a result, it may not be possible to train a diffusion model that models all kinds of interference signals in the real world. 2) I think this paper lacks theoretical analysis about: 1) how the proposed algorithm 1 could lead to the local extremum of equation (14), and 2) how minimizing the approximated loss in (9) and (14) could lead to the solution of the original MAP (6b) 3) It would be nice to have more ablation studies about: 1) optimizing across random noise levels vs fixed noise levels, 2) results with and without the zero mean noise in (12)

Questions

1) Could the authors describe more about the suitable conditions in line 205, page 6? 2) In Figure 3, seems like when the SIR is large (around -5dB), the trained SOI model could even outperform the analytical one. Could the authors explain more about that?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The authors have adequately addressed the limitations

Summary

A new method for separating superimposed sources using diffusion-based generative models is proposed (alpha-RGS). The method relies on separately trained statistical priors of independent sources and is guided by maximum a posteriori estimation with an α-posterior. Experimental results with RF mixtures demonstrate that the method results in a BER reduction of 95% over classical and existing learning-based methods.

Strengths

The authors propose a new method for source separation called α-RGS (α-posterior with Randomized Gaussian Smoothing). The method uses the (approximate) score from pre-trained diffusion models to extend maximum a posteriori (MAP) estimation using generalized Bayes' theorem with an α-posterior. α-RGS outperforms classical signal processing and annealed Langevin-dynamics-based approaches for RF source separation.

Weaknesses

.

Questions

1. It would be interesting to see how the model performs in different channel conditions, with different types of noise other than additive white Gaussian noise (AWGN). This would give us a better understanding of the model's robustness to different noise conditions. 2. The BER curve of the proposed model is noisy because it was generated using a small number of test examples. This noise will likely disappear if we sample more test examples, which will allow us to compute the exact improvement (in terms of dB) of the proposed model over the baseline.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

4 excellent

Limitations

.

Summary

This paper investigates a novel Bayesian approach for separating the superposition of two sources based on diffusion generative models. The problem is motivated by application to the spectrum of radio-frequency (RF) communication systems. Several experiments using real datasets on RF mixtures demonstrate that the proposed method reduces the bit error rate, which is the stared measure of performance for this application.

Strengths

The strengths of this paper are as follows: + It investigates a well-known problem, i.e., source separation, by using modern tools, i.e., diffusion generative models. In particular, the use of diffusion generative models to model the prior in the Bayesian source-separation framework is novel and appealing. + Several numerical results are provided by using real datasets. + The paper is well-written and the contribution is clearly stated.

Weaknesses

The weaknesses of this paper are as follows: + The paper introduces the problem of multi-source separation. However, it focus on the case of two sources and the methodology specializes very much on the presence of only two sources. + There is no theory or more specifically, there are no guarantees on performance of the proposed method to operate the underlaying sources. Notice that a lot have been done in this area and it would important to understand the limitations of the proposed method or at least to derive sufficient condition to ensure that the sources can be separated. + The applications to future wireless communication systems are interested but very much limited. In particular, those are applications are not the main focus of the ML community. it would have been beneficial to show the proposed can be used to other type of data since they are many practical cases (e.g. sounds and speech) for which source separation is requested.

Questions

+ The paper lacks of theoretical results showing the limitation of the proposed method and the assumptions on the data distribution to be able to perform source separation. + I strongly suggest the authors to further investigate other scenarios for which source separation is requested which could be of major interested for the ML community.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

2 fair

Presentation

3 good

Contribution

3 good

Limitations

The limitation are not well discussed; In particular, it is not clear the underlaying assumptions necessary to satisfy the source separation.

About the Rebuttal

I thank the authors for the detailed response. I think the majority of my concerns have been addressed.

Reply to authors' rebuttal

Thank you very much for your rebuttal. The answers are quite satisfactory. Hence, I raise my score.

Thank you for the rebuttal

Dear authors, thank you for providing a rebuttal. Some of the reviewers have already replied, so this is just to let you know that I am in contact with the remaining ones as well. Best, Your AC