相关论文: On the Tweety Penguin Triangle Problem

In line with the notion of probabilistic rough paths introduced in the previous contribution \cite{salkeld2021Probabilistic}, we address corresponding random controlled rough paths (first introduced in \cite{2019arXiv180205882.2B}), the…

In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Question answering tasks have shown remarkable progress with distributed vector representation. In this paper, we investigate the recently proposed Facebook bAbI tasks which consist of twenty different categories of questions that require…

Teaching how to derive minimax decision rules can be challenging because of the lack of examples that are simple enough to be used in the classroom. Motivated by this challenge, we provide a new example that illustrates the use of standard…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue…

We investigate the reverse mathematics strength of Martin's pointed tree theorem (MPT) and one of its variants, weak Martin's pointed tree theorem (wMPT).

The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…

The Sleeping Beauty problem is a probability riddle with no definite solution for more than two decades and its solution is of great interest in many fields of knowledge. There are two main competing solutions to the problem: the halfer…

The first direct observation of time-reversal (T) violation in the $B\bar{B}$ system has been reported by the BaBar collaboration, employing the method of Ba$\tilde {\rm n}\!$uls and Bernab\'eu. Given this, we generalize their analysis of…

In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically,…

Problems with majority voting over pairs as represented by Arrow's Theoremand those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected.…

In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by…

With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…

We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds…

This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…

In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical…

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by…

We study the question of what is computable by Turing machines equipped with time travel into the past; i.e., with Deutschian closed timelike curves (CTCs) having no bound on their width or length. An alternative viewpoint is that we study…