Thank you for your helpful comments and questions. We present a “creative” (p3hC) and “novel approach” (pR5T) that attacks “an important physics problem” (x8ZD) with comparisons to baselines that “are well-presented, and highlight the advantage of the method in particular regimes” (pR5T). Reviewer x8ZD mentions that it is a “great paper” that is “exceptionally well-presented” so that “ even non-experts can understand the main scientific ideas.” As highlighted by reviewer pR5T, “presenting a paper like this while being faithful to the domain science [is] particularly challenging, and the authors do a good job in this respect.”
**Machine Learning Contributions (x8ZD, gGfb)**
We firmly believe that our work represents a significant contribution to the ML community. Below, we outline several reasons that we will clarify in the updated paper.
**Neural Fields for Science:** While neural field models with positional encoding have previously been applied to various problems, our work demonstrates how the framework can be incorporated with the underlying physics specific to our problem. We work with noisy measurements from a single viewpoint, and the cosmic web volumes we study have different statistical properties compared to natural scenes. As highlighted by pR5T, this unique context raises important ML questions: How does the implicit regularization in neural fields help estimate solutions to severely ill-posed, underconstrained inverse problems? And how well does positional encoding, effective in natural scenes, generalize to these new scientific contexts? Applications of neural fields was the topic of 2023 ICLR (https://sites.google.com/view/neural-fields) and 2024 ECCV (https://neural-fields-beyond-cams.github.io/) workshops, featuring invited talks that apply neural fields with positional encoding to different 3D reconstruction tasks. We believe that adapting neural fields to a new context with completely different physics represents a significant contribution, and gives value to the ML community.
**Introducing a New Problem to ML:** Additionally, one of the main challenges of interdisciplinary work is effective communication between fields, and we are glad to have expressed our results in a way that is understandable to the ML community (x8ZD, p3hC, pR5T), as this important problem could greatly benefit from their insights and contributions. We also wish to highlight that, to our knowledge, this is the first time that a comparison of 3D mass mapping methods has been done. We will make all code and datasets available so that this problem can be further studied by the ML community.
**A Stepping Stone to Future Work:** We believe our work is a necessary stepping stone to future work that would take advantage of the neural representation we’ve presented. One direction we are actively pursuing is leveraging the neural representation to obtain efficient uncertainty quantification, which, as pR5T notes, is important for downstream science. While probabilistic approaches to 2D mass mapping are an active field of study, to our knowledge none have yet been proposed for 3D mass mapping, possibly due to computational intractability arising from the extra dimension. Even in the simple case of the Wiener filter, which has an analytic posterior, computing this posterior with a full covariance becomes intractable in 3D. In future work, we plan to build on the theory from [1], which demonstrates how neural representations can play an essential role in enabling efficient posterior estimation. The method we present serves as a solid foundation for further progress in this important direction.
**Wiener Filter Baseline (p3hC, gGfb)**
As gGfb highlights through various references, there have been recent developments in the field of 2D mass mapping. However, these methods are not directly applicable to 3D. Currently, there are no publicly available 3D mass mapping codes in working condition. While one code exists, it is non-functional, and the authors were unable to provide a working version. To the best of the authors' knowledge, the Wiener filter remains the only 3D method that has been applied to real cosmic shear data, with its most recent usage documented in 2018 [2]. Although code for this method was also not publicly available, we implemented our own transverse Wiener filter to establish a baseline.
In regards to p3hC’s question about Gaussian priors: On scales much larger than those we are targeting, the overdensity field of the universe can be described as Gaussian [3]. This coupled with the simplicity of the Gaussian prior makes it a popular choice for reconstructions of this type. However, non-Gaussianity present on small cosmic scales motivates our more general ML-based approach.
[1] https://arxiv.org/abs/2007.05864
[2] https://academic.oup.com/pasj/article/70/SP1/S26/4097646
[3] https://ned.ipac.caltech.edu/level5/March01/Coles/Coles4.html