While a similar phenomenon is known for estimators with i.i.d.

Equalized odds is a statistical notion of fairness in machine learning that ensures that classification algorithms do not discriminate against protected groups. We extend equalized odds to the setting of cardinality-constrained fair classification, where we have a bounded amount of a resource to distribute. This setting coincides with classic fair division problems, which allows us to apply concepts from that literature in parallel to equalized odds. In particular, we consider the axioms of resource monotonicity, consistency, and population monotonicity, all three of which relate different allocation instances to prevent paradoxes. Using a geometric characterization of equalized odds, we examine the compatibility of equalized odds with these axioms. We empirically evaluate the cost of allocation rules that satisfy both equalized odds and axioms of fair division on a dataset of FICO credit scores.

This work advances and substantiates the thesis that the resolution of this crisis lies in the domain of possibility theory, specifically in the axiomatic approach developed in Bychkovs article. Unlike numerous attempts to fix Dempster rule, this approach builds from scratch a logically consistent and mathematically rigorous foundation for working with uncertainty, using the dualistic apparatus of possibility and necessity measures. The aim of this work is to demonstrate that possibility theory is not merely an alternative, but provides a fundamental resolution to DST paradoxes. A comparative analysis of three paradigms will be conducted probabilistic, evidential, and possibilistic. Using a classic medical diagnostic dilemma as an example, it will be shown how possibility theory allows for correct processing of contradictory data, avoiding the logical traps of DST and bringing formal reasoning closer to the logic of natural intelligence.

Large-scale models are at the forefront of time series (TS) forecasting, dominated by two paradigms: fine-tuning text-based Large Language Models (LLM4TS) and training Time Series Foundation Models (TSFMs) from scratch. Both approaches share a foundational assumption that scaling up model capacity and data volume leads to improved performance. However, we observe a \textit{\textbf{scaling paradox}} in TS models, revealing a puzzling phenomenon that larger models do \emph{NOT} achieve better performance. Through extensive experiments on two model families across four scales (100M to 1.7B parameters) and diverse data (up to 6B observations), we rigorously confirm that the scaling paradox is a pervasive issue. We then diagnose its root cause by analyzing internal representations, identifying a phenomenon we call \textit{few-layer dominance}: only a small subset of layers are functionally important, while the majority are redundant, under-utilized, and can even distract training. Based on this discovery, we propose a practical method to automatically identify and retain only these dominant layers. In our models, retaining only 21\% of the parameters achieves up to a 12\% accuracy improvement and a 2.7$\times$ inference speedup. We validate the universality of our method on 8 prominent SOTA models (LLM4TS and TSFMs, 90M to 6B), showing that retaining less than 30\% of layers achieves comparable or superior accuracy in over 95\% of tasks.

In the late 19th century, Georg Cantor believed his new theory could help the Church understand the infinite nature of the divine. It might have escaped lay people at the time, but for some observers the ascension of Leo XIV as head of the Catholic Church this year was a reminder that the last time a Pope Leo sat in St. Peter's Chair in the Vatican, from 1878 to 1903, the modern view of infinity was born. Georg Cantor's completely original "naïve" set theory caused both revolution and revolt in mathematical circles, with some embracing his ideas and others rejecting them. Cantor was deeply disappointed with the negative reactions, of course, but never with his own ideas. Because he held firm to the belief that he had a main line to the absolute--that his ideas came direct from (the divine intellect).

It is often claimed that machine learning-based generative AI products will drastically streamline and reduce the cost of legal practice. This enthusiasm assumes lawyers can effectively manage AI's risks. Cases in Australia and elsewhere in which lawyers have been reprimanded for submitting inaccurate AI-generated content to courts suggest this paradigm must be revisited. This paper argues that a new paradigm is needed to evaluate AI use in practice, given (a) AI's disconnection from reality and its lack of transparency, and (b) lawyers' paramount duties like honesty, integrity, and not to mislead the court. It presents an alternative model of AI use in practice that more holistically reflects these features (the verification-value paradox). That paradox suggests increases in efficiency from AI use in legal practice will be met by a correspondingly greater imperative to manually verify any outputs of that use, rendering the net value of AI use often negligible to lawyers. The paper then sets out the paradox's implications for legal practice and legal education, including for AI use but also the values that the paradox suggests should undergird legal practice: fidelity to the truth and civic responsibility.

We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng [60] to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For Condrocet's paradox, we prove that the smoothed likelihood of the paradox either vanishes at an exponential rate as the number of agents increases, or does not vanish at all. For the ANR impossibility on the non-existence of voting rules that simultaneously satisfy anonymity, neutrality, and resolvability, we characterize the rate for the impossibility to vanish, to be either polynomially fast or exponentially fast. We also propose a novel easy-to-compute tie-breaking mechanism that optimally preserves anonymity and neutrality for even number of alternatives in natural settings. Our results illustrate the smoothed possibility of social choice--even though the paradox and the impossibility theorem hold in the worst case, they may not be a big concern in practice.

We initiate the work towards a comprehensive picture of the worst average-case satisfaction of voting axioms in semi-random models, to provide a finer and more realistic foundation for comparing voting rules. We adopt the semi-random model and formulation in [54], where an adversary chooses arbitrarily correlated "ground truth" preferences for the agents, on top of which random noises are added. We focus on characterizing the semi-random satisfaction of two well-studied voting axioms: Condorcet criterion and participation.