We thank the reviewers for their comments and the largely positive feedback. Reviewers agree that " the paper clearly The improvement our approach provides " is demonstrated by experiments " The contribution was praised as " elegant ", Rigorous formulation and convergence properties of relative gradient: We will add more details on this. We will include these references in the paper. These architectures have several limitations, e.g. they We will include this discussion and reference in the paper. R6: T oo much emphasis on existing concepts, too little on the proposed approach: We will try to balance this.

There is a consensus among the knowledgeable reviewers that this work makes a significant contribution to the kernel community. It integrates several practical techniques and engineering efforts to further improve the scalability of the kernel machines. The techniques proposed in this work will permit the use of several GPUs in training kernel-based models with huge amount of data, which I also see as a significant contribution. Regardless of the overall score, I think this paper deserves an oral because it shows how to take full advantage of GPU hardware when solving learning problems with kernels methods. Scalability is one of the long-standing problems in kernel machines but has been largely neglected and under-appreciated in the past few years.

Additional Feedback: Major comments: 1) Smoothed analysis: Calling your analysis "smoothed analysis" is a bit confusing. Smoothed analysis would take worst-case over profiles, and then expectation over noise added. But as you say in your related work, you're taking worst-case over distributions coming from a family. Such analysis was already done in the past. For example, consider work that analyzed the probability of Condorcet's paradox under any distribution from the Mallows family.

Additional Feedback: I read all the reviews and the rebuttal. I agree with the authors that the proposed method is different from learned pseudo-exemplars in the embedding space as in VampVAE, and this work uses real exemplars in the image space. However, I am not convinced that randomly sampling exemplars in the data space with some heuristics based on LOO and trivial exemplar subsampling as regularizations on toy datasets is a significant contribution extending the exemplar-based prior in VampVAE. A possible limitation of the proposed Exemplar VAE is that, the generative model might not learn much beyond reconstruction, instead, it only produces some random samples that stay close to epsilon-ball of training data points. It's possible that Exemplar VAE even performs no better than a deterministic autoencoder with tiny Gaussian noise added to latent codes and k-means regularization in the latent space. VampVAE doesn't have this issue.

Self-consistency-based approaches, which involve repeatedly sampling multiple outputs and selecting the most consistent one as the final response, prove to be remarkably effective in improving the factual accuracy of large language models. Nonetheless, existing methods usually have strict constraints on the task format, largely limiting their applicability. In this paper, we present Integrative Decoding (ID), to unlock the potential of self-consistency in open-ended generation tasks. ID operates by constructing a set of inputs, each prepended with a previously sampled response, and then processes them concurrently, with the next token being selected by aggregating of all their corresponding predictions at each decoding step. In essence, this simple approach implicitly incorporates self-consistency in the decoding objective. Extensive evaluation shows that ID consistently enhances factuality over a wide range of language models, with substantial improvements on the TruthfulQA (+11.2%), Biographies (+15.4%) and LongFact (+8.5%) benchmarks. The performance gains amplify progressively as the number of sampled responses increases, indicating the potential of ID to scale up with repeated sampling.

While ChatGPT's primary purpose is to assist users in generating human-like text, it has also made significant contributions to the field of philosophy. This, in turn, has had a significant impact on educational assessment, enabling educators to evaluate students' critical thinking skills in new and exciting ways. The doomsayers, by contrast, are sceptical. Here at UCC, for example, I've heard more than a few colleagues echoing Socrates, who, in Plato's dialogue Phaedrus (370 BC), expresses similar worries about the invention of … wait for it … writing. "This invention will produce forgetfulness in the minds of those who learn to use it ... you offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with since they are not wise, but only appear wise."

OpenAI is an artificial intelligence research laboratory consisting of a team of researchers, engineers, and entrepreneurs working towards creating safe and beneficial AI. It was founded in 2015 by a group of entrepreneurs and researchers, including Elon Musk, Sam Altman, Greg Brockman, Ilya Sutskever, and Wojciech Zaremba. OpenAI conducts research in various fields of AI, including machine learning, natural language processing, robotics, and computer vision, and is also involved in developing AI technologies and applications that can benefit humanity. The organization aims to develop AI in a way that is safe, ethical, and beneficial for all, and promotes collaboration and open access to AI research and tools. Overall, OpenAI has been at the forefront of AI research and development, and has made significant contributions to the field.

Artificial intelligence (AI) has emerged as a revolutionary technology with the potential to transform virtually every industry, and the art world is no exception. AI has opened up new possibilities for artists to create unique and innovative works of art that were previously impossible. With the help of AI algorithms, artists can generate music, images, and even entire pieces of art, opening the door to a new era of creativity. This has given rise to the field of AI art, where artists are using this technology to push the boundaries of traditional art forms and create new ones altogether. In this context, it is essential to analyze the impact that AI art is having on the art world, both in terms of how it is being created and how it is being consumed.