We analyzed the multi-layer case beyond what is reported in the submitted paper. Equations to get the optimal error in the multi-layer case are in page 10-11 of the SM. The vertical lines show the PCA and the optimal threshold respectively. Our claims of optimality of AMP are indeed limited to the cases investigated numerically. We will make a statement collecting all the assumptions in the final version.

"Is Approval V oting Optimal Given Approval V otes?" NeurIPS-2015. The reviewer points to a paper about "threshold voting," but this is a very different idea.

With the exponential growth of research facilitated by modern technology and improved accessibility, scientific discoveries have become increasingly fragmented within and across fields. This makes it challenging to assess the significance, novelty, incremental findings, and equivalent ideas between related works, particularly those from different research communities. Large language models (LLMs) have recently demonstrated strong quantitative and qualitative reasoning abilities, and multi-agent LLM debates have shown promise in handling complex reasoning tasks by exploring diverse perspectives and reasoning paths. Inspired by this, we introduce Tree-of-Debate (ToD), a framework which converts scientific papers into LLM personas that debate their respective novelties. To emphasize structured, critical reasoning rather than focusing solely on outcomes, ToD dynamically constructs a debate tree, enabling fine-grained analysis of independent novelty arguments within scholarly articles. Through experiments on scientific literature across various domains, evaluated by expert researchers, we demonstrate that ToD generates informative arguments, effectively contrasts papers, and supports researchers in their literature review.

How do author perceptions match up to the outcomes of the peer-review process and perceptions of others? In a top-tier computer science conference (NeurIPS 2021) with more than 23,000 submitting authors and 9,000 submitted papers, we survey the authors on three questions: (i) their predicted probability of acceptance for each of their papers, (ii) their perceived ranking of their own papers based on scientific contribution, and (iii) the change in their perception about their own papers after seeing the reviews. The salient results are: (1) Authors have roughly a three-fold overestimate of the acceptance probability of their papers: The median prediction is 70% for an approximately 25% acceptance rate. (2) Female authors exhibit a marginally higher (statistically significant) miscalibration than male authors; predictions of authors invited to serve as meta-reviewers or reviewers are similarly calibrated, but better than authors who were not invited to review. (3) Authors' relative ranking of scientific contribution of two submissions they made generally agree (93%) with their predicted acceptance probabilities, but there is a notable 7% responses where authors think their better paper will face a worse outcome. (4) The author-provided rankings disagreed with the peer-review decisions about a third of the time; when co-authors ranked their jointly authored papers, co-authors disagreed at a similar rate -- about a third of the time. (5) At least 30% of respondents of both accepted and rejected papers said that their perception of their own paper improved after the review process. The stakeholders in peer review should take these findings into account in setting their expectations from peer review.

A recent report of Littmann [Commun. ACM '21] outlines the existence and the fatal impact of collusion rings in academic peer reviewing. We introduce and analyze the problem Cycle-Free Reviewing that aims at finding a review assignment without the following kind of collusion ring: A sequence of reviewers each reviewing a paper authored by the next reviewer in the sequence (with the last reviewer reviewing a paper of the first), thus creating a review cycle where each reviewer gives favorable reviews. As a result, all papers in that cycle have a high chance of acceptance independent of their respective scientific merit. We observe that review assignments computed using a standard Linear Programming approach typically admit many short review cycles. On the negative side, we show that Cycle-Free Reviewing is NP-hard in various restricted cases (i.e., when every author is qualified to review all papers and one wants to prevent that authors review each other's or their own papers or when every author has only one paper and is only qualified to review few papers). On the positive side, among others, we show that, in some realistic settings, an assignment without any review cycles of small length always exists. This result also gives rise to an efficient heuristic for computing (weighted) cycle-free review assignments, which we show to be of excellent quality in practice.

Given a pool of observations selected from a sensor stream, input data can be robustly represented, via a multiscale process, in terms of invariant concepts, and themes. Applying this to episodic natural language data, one may obtain a graph geometry associated with the decomposition, which is a direct encoding of spacetime relationships for the events. This study contributes to an ongoing application of the Semantic Spacetime Hypothesis, and demonstrates the unsupervised analysis of narrative texts using inexpensive computational methods without knowledge of linguistics. Data streams are parsed and fractionated into small constituents, by multiscale interferometry, in the manner of bioinformatic analysis. Fragments may then be recombined to construct original sensory episodes---or form new narratives by a chemistry of association and pattern reconstruction, based only on the four fundamental spacetime relationships. There is a straightforward correspondence between bioinformatic processes and this cognitive representation of natural language. Features identifiable as `concepts' and `narrative themes' span three main scales (micro, meso, and macro). Fragments of the input act as symbols in a hierarchy of alphabets that define new effective languages at each scale.

Technologies that can make a coherent summary take into account variables such as length, writing style and syntax.Automatic data summarization is part of machine learning and data mining. The main idea of summarization is to find a subset of data which contains the information of the entire set. Such techniques are widely used in industry today. Search engines are an example; others include summarization of documents, image collections and videos. Document summarization tries to create a representative summary or abstract of the entire document, by finding the most informative sentences, while in image summarization the system finds the most representative and important (i.e.