Additional Feedback: [After rebuttal] I appreciate the additional explanations in the rebuttal. I think the example (a more complete version) will go a long way in improving the paper, but as is presented I think not enough details is given for a proper evaluation, thus I look forward to reading a revised version of this work. Note that my tautology comment is not saying that the proof is trivial, but saying the way it is written masks the potential insights the proof may give, in particular, there should be a result that shows that such a limit in Cons 1 exists under some general conditions characterising the data and the model architecture. I believe the example provided in the rebuttal may potentially be useful for formalising this. On first reading, these conditions appear not well-motivated.

Before the author response, all the reviewers seem agree that the results were quite interesting (and I agree), but had a concern about the connection to ML. The author response included examples which mostly addressed this concern, so two reviewers recommended acceptance, while another (reviewer 1) recommended rejection, but was borderline. However, I feel the remaining concerns by reviewer 1 are rather minor.

Weaknesses: While the paper is written very clearly, there are several questions I'd like to raise. Firstly, in discussing the applicability of the results the paper mentions'some basic vision or sound recognition tasks' (line 33) - I'd like to ask about some examples of such tasks. Looking at the statement of the Theorem 1, seems that it should be applicable in finite-dimensional spaces with invertible covariance matrices. If it is so, then I do not understand the results. In particular, for X distributed with a finite support and has identity covariance matrix, the conditions (a) and (b) hold for arbitrarily large positive \alpha, however the theorem statement implies that the estimates will go to zero at an arbitrarily large polynomial rate, which is not true.

The submission considers noiseless (/low noise) linear regression with non-linear transformation of the input data, and show that under this setting, SGD achieves faster convergence rates. This is a very nice contribution with applicability to important problems as mentioned by the authors in their feedback. We urge the authors to incorporate the points they made in response to the reviews.

The paper concerns robust linear regression in the online setting, where the data follows a Gaussian linear model with corruptions. It is shown that the stochastic gradient descent on the absolute loss converges to the true parameter at a rate of order O(1/n). The paper received a universally positive evaluation from the reviewers, who acknowledged the novelty of the results, the theoretical justification of the proposed approach and the scalability of the algorithm. The main issue raised in the reviews is about quite restrictive assumptions on the data distribution (Gaussian linear model, and the centered data assumption).

After rebuttal: I have carefully read the comments from other reviewers and the feedback from the authors. My main concern was the generalization ability of NGD, but the experiments in the feedback are a bit confused to me because GD doesn't seem to achieve zero training loss but NGD converges to 0 very quickly in MNIST regression. I would suggest the authors provide more details about that experiment setting, e.g., how do you select the hyperparameter. Thus, I would like to keep my score unchanged. The framework for the proof follows the recent line of work about over-parametrization, e.g., the papers written by Du et al, Li and Liang, and Allen-Zhu et al., the core of which is the Gram matrix.

This paper proves fast convergence of natural gradient descent for over-parameterized neural networks, and its generalization error bound. This paper is on the borderline and was carefully discussed. The main concern is about the novelty of this paper, as well as lack of details in the experiments. The paper gathered some support from the reviewers to merit acceptance, after author response and reviewer discussion.

In recent years, artificial intelligence (AI) has become an integral part of daily life, serving as a transformative tool across various professional domains [1] and driving personal applications through advancements in transformer models that power large language models (LLMs) [2]. However, both training and inference of AI models demand substantial computational and energy resources, which are becoming increasingly challenging to access [3, 4]. While server-class GPUs are effective for training, their energy inefficiency [5] and high costs present significant barriers [6]. Additionally, the environmental impact of energy-intensive AI systems has raised critical concerns about their role in exacerbating climate change [4]. Amdahl's law predicts that performance and efficiency gains are best achieved through innovative application-specific accelerator architectures rather than scaling up multi-core general-purpose processors [7]. Consequently, applicationspecific integrated circuits (ASICs), both digital and analog, have emerged as critical solutions for enabling highefficiency training and inference of artificial neural networks [7, 8, 9]. Digital accelerators are widely adopted for training workloads. Notable examples include the Brainwave Neural Processing Unit (NPU) [10], Google's Tensor Processing Unit (TPU) [11], and low-precision inference accelerators such as YodaNN [5], the Unified Neural Processing Unit (UNPU) [12], and BRein Memory [13].

Delivering an immersive experience to virtual reality (VR) users through wireless connectivity offers the freedom to engage from anywhere at any time. Nevertheless, it is challenging to ensure seamless wireless connectivity that delivers real-time and high-quality videos to the VR users. This paper proposes a field of view (FoV) aware caching for mobile edge computing (MEC)-enabled wireless VR network. In particular, the FoV of each VR user is cached/prefetched at the base stations (BSs) based on the caching strategies tailored to each BS. Specifically, decentralized and personalized federated learning (DP-FL) based caching strategies with guarantees are presented. Considering VR systems composed of multiple VR devices and BSs, a DP-FL caching algorithm is implemented at each BS to personalize content delivery for VR users. The utilized DP-FL algorithm guarantees a probably approximately correct (PAC) bound on the conditional average cache hit. Further, to reduce the cost of communicating gradients, one-bit quantization of the stochastic gradient descent (OBSGD) is proposed, and a convergence guarantee of $\mathcal{O}(1/\sqrt{T})$ is obtained for the proposed algorithm, where $T$ is the number of iterations. Additionally, to better account for the wireless channel dynamics, the FoVs are grouped into multicast or unicast groups based on the number of requesting VR users. The performance of the proposed DP-FL algorithm is validated through realistic VR head-tracking dataset, and the proposed algorithm is shown to have better performance in terms of average delay and cache hit as compared to baseline algorithms.

Strengths: Preface I understand that reviews that claim that a method is not sufficiently novel or significant are often subjective and are difficult for authors to rebut. To make my review easier to engage with, I'm offering the following criteria along which I assess "significance" of a paper: (*i*) Does the paper offer a novel, non-obvious theoretical insight in the form of a proof or derivation? I will touch on these three criteria in my comments below and mark my comment accordingly. Relevance Bayesian inference applied to a variety of problems is an active area of research and the paper under review proposes a novel algorithm for fast convergence to a posterior distribution in Bayesian inference problems. While the proposed method is still limited in the parameter dimension, it improves on related methods and makes stein variational gradient descent more practically relevant.