First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes an application of seriation algorithm for rank aggregation. They propose a similarity matrix based on pair-wise rankings. They consider two different scenarios for pair-wise rankings and show that seriation algorithm will recover the true ranking (by showing that the proposed similarity matrix is a strict R-matrix). They further provide results on robustness of their method to noise and errors in pairs.

In user-facing applications, displaying calibrated confidence measures-- probabilities that correspond to true frequency--can be as important as obtaining high accuracy. We are interested in calibration for structured prediction problems such as speech recognition, optical character recognition, and medical diagnosis. Structured prediction presents new challenges for calibration: the output space is large, and users may issue many types of probability queries (e.g., marginals) on the structured output. We extend the notion of calibration so as to handle various subtleties pertaining to the structured setting, and then provide a simple recalibra-tion method that trains a binary classifier to predict probabilities of interest. We explore a range of features appropriate for structured recalibration, and demonstrate their efficacy on three real-world datasets.

Rational decision-making under uncertainty requires coherent degrees of belief in events. However, event probabilities generated by Large Language Models (LLMs) have been shown to exhibit incoherence, violating the axioms of probability theory. This raises the question of whether coherent event probabilities can be recovered from the embeddings used by the models. If so, those derived probabilities could be used as more accurate estimates in events involving uncertainty. To explore this question, we propose enforcing axiomatic constraints, such as the additive rule of probability theory, in the latent space learned by an extended variational autoencoder (VAE) applied to LLM embeddings. This approach enables event probabilities to naturally emerge in the latent space as the VAE learns to both reconstruct the original embeddings and predict the embeddings of semantically related events. We evaluate our method on complementary events (i.e., event A and its complement, event not-A), where the true probabilities of the two events must sum to 1. Experiment results on open-weight language models demonstrate that probabilities recovered from embeddings exhibit greater coherence than those directly reported by the corresponding models and align closely with the true probabilities.

To mitigate risks from AI systems, we need to assess their capabilities accurately. This is especially difficult in cases where capabilities are only rarely displayed. Phuong et al. [12] propose two methods that aim to obtain better estimates of the probability of an AI agent successfully completing a given task. The milestone method decomposes tasks into subtasks, aiming to improve overall success rate estimation, while the expert best-of-N method leverages human guidance as a proxy for the model's independent performance. Our analysis of these methods as Monte Carlo estimators reveals that while both effectively reduce variance compared to naive Monte Carlo sampling, they also introduce bias. Experimental results demonstrate that the milestone method underestimates true solve rates for many real-world tasks due to its constraining assumptions. The expert best-of-N method exhibits even more severe underestimation across all tasks, attributed to an inherently flawed re-weighting factor. To enhance the accuracy of capability estimates of AI agents on difficult tasks, we suggest future work should leverage the rich literature on Monte Carlo Estimators.

Machine Learning research, as most of Statistics, heavily relies on the concept of a data-generating probability distribution. The standard presumption is that since data points are `sampled from' such a distribution, one can learn from observed data about this distribution and, thus, predict future data points which, it is presumed, are also drawn from it. Drawing on scholarship across disciplines, we here argue that this framework is not always a good model. Not only do such true probability distributions not exist; the framework can also be misleading and obscure both the choices made and the goals pursued in machine learning practice. We suggest an alternative framework that focuses on finite populations rather than abstract distributions; while classical learning theory can be left almost unchanged, it opens new opportunities, especially to model sampling. We compile these considerations into five reasons for modelling machine learning -- in some settings -- with finite populations rather than generative distributions, both to be more faithful to practice and to provide novel theoretical insights.

When there exists uncertainty, AI machines are The outline of the proof is as follows. After defining some designed to make decisions so as to reach the main concepts, we identify the Success Criterion and the best expected outcomes. Expectations are based necessary condition for any machine to learn the true objective on true facts about the objective environment the probabilities. From these conditions, we derive machines interact with, and those facts can be the theorem that learning implies the true guarantee of encoded into AI models in the form of true objective well-calibration. Roughly speaking, "truly guaranteed wellcalibration" probability functions.

We critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the statistical and the computational learning theories, for it implies that learning true probabilities is equivalent neither to obtaining a correct calculation of the true probabilities nor to obtaining an almost-sure convergence to them. We also briefly discuss some case studies from natural language processing and macroeconomics from the perspective of the new theory.

Motivated by the rapid ascent of Large Language Models (LLMs) and debates about the extent to which they possess human-level qualities, we propose a framework for testing whether any agent (be it a machine or a human) understands a subject matter. In Turing-test fashion, the framework is based solely on the agent's performance, and specifically on how well it answers questions. Elements of the framework include circumscribing the set of questions (the "scope of understanding"), requiring general competence ("passing grade"), avoiding "ridiculous answers", but still allowing wrong and "I don't know" answers to some questions. Reaching certainty about these conditions requires exhaustive testing of the questions which is impossible for nontrivial scopes, but we show how high confidence can be achieved via random sampling and the application of probabilistic confidence bounds. We also show that accompanying answers with explanations can improve the sample complexity required to achieve acceptable bounds, because an explanation of an answer implies the ability to answer many similar questions. According to our framework, current LLMs cannot be said to understand nontrivial domains, but as the framework provides a practical recipe for testing understanding, it thus also constitutes a tool for building AI agents that do understand.

In deep learning applications, robustness measures the ability of neural models that handle slight changes in input data, which could lead to potential safety hazards, especially in safety-critical applications. Pre-deployment assessment of model robustness is essential, but existing methods often suffer from either high costs or imprecise results. To enhance safety in real-world scenarios, metrics that effectively capture the model's robustness are needed. To address this issue, we compare the rigour and usage conditions of various assessment methods based on different definitions. Then, we propose a straightforward and practical metric utilizing hypothesis testing for probabilistic robustness and have integrated it into the TorchAttacks library. Through a comparative analysis of diverse robustness assessment methods, our approach contributes to a deeper understanding of model robustness in safety-critical applications.

In user-facing applications, displaying calibrated confidence measures-- probabilities that correspond to true frequency--can be as important as obtaining high accuracy. We are interested in calibration for structured prediction problems such as speech recognition, optical character recognition, and medical diagnosis. Structured prediction presents new challenges for calibration: the output space is large, and users may issue many types of probability queries (e.g., marginals) on the structured output. We extend the notion of calibration so as to handle various subtleties pertaining to the structured setting, and then provide a simple recalibration method that trains a binary classifier to predict probabilities of interest. We explore a range of features appropriate for structured recalibration, and demonstrate their efficacy on three real-world datasets.