The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy. 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.

This investigation presents an empirical analysis of the incompatibility between human psychometric frameworks and Large Language Model evaluation. Through systematic assessment of nine frontier models including GPT-5, Claude Opus 4.1, and Gemini 3 Pro Preview using the Cattell-Horn-Carroll theory of intelligence, we identify a paradox that challenges the foundations of cross-substrate cognitive evaluation. Our results show that models achieving above-average human IQ scores ranging from 85.0 to 121.4 simultaneously exhibit binary accuracy rates approaching zero on crystallized knowledge tasks, with an overall judge-binary correlation of r = 0.175 (p = 0.001, n = 1800). This disconnect appears most strongly in the crystallized intelligence domain, where every evaluated model achieved perfect binary accuracy while judge scores ranged from 25 to 62 percent, which cannot occur under valid measurement conditions. Using statistical analyses including Item Response Theory modeling, cross-vendor judge validation, and paradox severity indexing, we argue that this disconnect reflects a category error in applying biological cognitive architectures to transformer-based systems. The implications extend beyond methodology to challenge assumptions about intelligence, measurement, and anthropomorphic biases in AI evaluation. We propose a framework for developing native machine cognition assessments that recognize the non-human nature of artificial 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).