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Confidence calibration is essential for making large language models (LLMs) reliable, yet existing training-free methods have been primarily studied under single-answer question answering. In this paper, we show that these methods break…
Which categories of explanation content are relevant for users of industrial AI systems, and how can those categories be organized for local, post-hoc explanations? To address these questions, a hybrid inductive-deductive qualitative…
Security aspects of the Index Coding with Side Information (ICSI) problem are investigated. Building on the results of Bar-Yossef et al. (2006), the properties of linear index codes are further explored. The notion of weak security,…
Leyva-V\'azquez and Smarandache (2025) demonstrated that neutrosophic T/I/F evaluation, where Truth, Indeterminacy, and Falsity are independent dimensions not constrained to sum to 1.0, which reveals "hyper-truth"' (T+I+F > 1.0) in 35% of…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
Confidence-weighted routing, selective abstention, and ensemble weighting all assume that a model's stated confidence is informative about its capability on the question being asked. They presume functional metacognition, the capacity to…
Modern machine learning models with high accuracy are often miscalibrated -- the predicted top probability does not reflect the actual accuracy, and tends to be over-confident. It is commonly believed that such over-confidence is mainly due…
Large Language Models (LLMs) show remarkable proficiency in natural language tasks, yet their frequent overconfidence-misalignment between predicted confidence and true correctness-poses significant risks in critical decision-making…
A multiclass classifier is said to be top-label calibrated if the reported probability for the predicted class -- the top-label -- is calibrated, conditioned on the top-label. This conditioning on the top-label is absent in the closely…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
We find that models report highest confidence precisely when they are fabricating. Across four model families (OLMo-3, Llama-3.1, Qwen3, Mistral), self-reported confidence inversely correlates with accuracy, with AUC ranging from 0.28 to…
For a regular uncountable cardinal kappa, we discuss the order relationship between the unbounding and dominating numbers on kappa and cardinal invariants of the higher meager ideal M_kappa. In particular, we obtain a complete…
For each countable ordinal $\alpha \ge 2$, the ideals $\mathsf{conv}_\alpha$ were introduced in ``Critical ideals for countable compact spaces'' (to appear in Fund. Math., see also arXiv:2503.12571) to characterize compact countable spaces…
We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of a log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a…
Pearl's causal hierarchy shows that observational, interventional, and counterfactual queries are qualitatively distinct. We ask a quantitative version of this question: how many additional bits are needed to specify higher-rung causal…
The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been…
A Monte Carlo simulation was used to determine which assumptions for ordered categorical data, continuity vs. discrete categories, most frequently identifies the underlying factor structure when a response variable has five ordered…
Increased availability of open-source software repositories and recent advances in code analysis using large language models (LLMs) has triggered a wave of new work to automate software engineering tasks that were previously very difficult…
In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…