Related papers: The averaging trick and the Cerny conjecture
With Artificial Intelligence systems increasingly applied in consequential domains, researchers have begun to ask how these systems ought to act in ethically charged situations where even humans lack consensus. In the Moral Machine project,…
We introduce twin neural network (TNN) regression. This method predicts differences between the target values of two different data points rather than the targets themselves. The solution of a traditional regression problem is then obtained…
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
Algorithmic modeling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is…
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the…
Seymour conjectured that every oriented simple graph contains a vertex whose second neighborhood is at least as large as its first. Seymour's conjecture has been verified in several special cases, most notably for tournaments by Fisher. One…
This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…
In the field of artificial intelligence (AI) research, there seems to be a rapprochement between academics and industrial forces. The aim of this study is to assess whether and to what extent industrial domination in the field as well as…
Building reliable deception detectors for AI systems -- methods that could predict when an AI system is being strategically deceptive without necessarily requiring behavioural evidence -- would be valuable in mitigating risks from advanced…
It is often reported in forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the "forecast combination puzzle". Motivated…
We present several analytic theories and their relations to each other related to screw functions, taking the screw function of the simplest screw line as an example. Note that this article does not contain any new results.
We discuss the objectives of any endeavor in creating artificial intelligence, AI, and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant.…
The conjecture of Masser-Oesterl\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures.
A common assumption of political economy is that profit rates across firms or sectors tend to uniformity, and often models are formulated in which this tendency is assumed to have been realised. But in reality this tendency is never…
A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to…
Implicit arguments are not syntactically connected to their predicates, and are therefore hard to extract. Previous work has used models with large numbers of features, evaluated on very small datasets. We propose to train models for…
We examine the prime gaps using a statistical approach. It is first shown that the Andrica's conjecture is true for half or more cases. Using the arguments of averages, it is further shown that Andrica's conjecture is true. We further…
It is well known that models used in conventional regression analysis are commonly misspecified. A standard response is little more than a shrug. Data analysts invoke Box's maxim that all models are wrong and then proceed as if the results…
Good problems grab us. They invite us to find patterns, make conjectures, and prove-or perhaps disprove-a conjecture. When I first taught, I saw my work as tantalizing students with structures just beyond their reach, so that I could elicit…
We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…