Related papers: The Goebbellian Syndrome
LLMs can be unpredictable, as even slight alterations to the prompt can cause the output to change in unexpected ways. Thus, the ability of models to accurately explain their behavior is critical, especially in high-stakes settings. One…
We propose a novel training regime termed counterfactual training that leverages counterfactual explanations to increase the explanatory capacity of models. Counterfactual explanations have emerged as a popular post-hoc explanation method…
We prove a version of the Extra-zero conjecture formulated by the first named author for p-adic L-functions associated to Rankin-Selberg convolutions of modular forms of the same weight. The novelty of this result is to provide strong…
In his seminal paper from 1936, Alan Turing introduced the concept of non-computable real numbers and presented examples based on the algorithmically unsolvable Halting problem. We describe a different, analytically natural mechanism for…
The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet…
In 1977, Hugh Williams studied Lucas pseudoprimes to all Lucas sequences of a fixed discriminant. These are composite numbers analogous to Carmichael numbers and they satisfy a Korselt-like criterion: $n$ must be a product of distinct…
We show that the ability to consider counterfactual situations is a necessary assumption of Bell's theorem, and that, to allow Bell inequality violations while maintaining all other assumptions, we just require certain measurement choices…
This is revised version of my preprint: Max-Plank Institut fuer Mathematik, 2001, No 16.
It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context. The aim of this text is to show the converse is the case and invite the reader to…
By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low…
In this paper we concentrate on the nature of the liar paradox as a cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model [Aerts, Broekaert, Smets 1999] that has been…
In a recent paper, Enayat and Le lyk [2024] show that second order arithmetic and countable set theory are not definitionally equivalent. It is well known that these theories are biinterpretable. Thus, we have a pair of natural theories…
The adoption of increasingly complex deep models has fueled an urgent need for insight into how these models make predictions. Counterfactual explanations form a powerful tool for providing actionable explanations to practitioners.…
In this paper, we introduce and study a variant of Kummer's notion of (ir)regularity of primes which we call G-irregularity. It is based on Genocchi numbers $G_n$, rather than Bernoulli number $B_n.$ We say that an odd prime $p$ is…
All priors are not created equal. There are right and there are wrong priors. That is the main conclusion of this contribution. I use, a cooked-up example designed to create drama, and a typical textbook example to show the pervasiveness of…
This article discusses several erroneous claims which appear in textbooks on numerical methods and computational physics. These are not typos or mistakes an individual author has made, but widespread misconceptions. In an attempt to stop…
This paper has attracted interest around the world from the media (both TV and newspapers). In addition, we have received letters, emails and telephone calls. One of our favorites was a voicemail message asking us to return a call to…
Deviations from Bayesian updating are traditionally categorized as biases, errors, or fallacies, thus implying their inherent ``sub-optimality.'' We offer a more nuanced view. We demonstrate that, in learning problems with misspecified…
Many scholars have called for raising statistical hurdles to guard against false discoveries in academic publications. I show these calls may be difficult to justify empirically. Published data exhibit bias: results that fail to meet…
Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present…