Related papers: Intro To Logarithms After The Meltdown
We are at the dawn of a new era, where advances in computer power, broadband communication and digital sensor technologies have led to an unprecedented flood of data inundating our surrounding. It is generally believed that means such as…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge,…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
This paper revisits the conundrum faced when one attempts to understand the dynamics of black hole formation and evaporation without abandoning unitary evolution. Previous efforts to resolve this puzzle assume that information escapes in…
The process of black hole evaporation resulting from the Hawking effect has generated an intense controversy regarding its potential conflict with quantum mechanics' unitary evolution. In a recent couple of works of a collaboration…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
LLMs have shown promise in replicating human-like behavior in crowdsourcing tasks that were previously thought to be exclusive to human abilities. However, current efforts focus mainly on simple atomic tasks. We explore whether LLMs can…
One requirement of maintaining digital information is storage. With the latest advances in the digital world, new emerging media types have required even more storage space to be kept than before. In fact, in many cases it is required to…
This text argues for the potential of machine learning infused classification systems as vectors for a technically-engaged and constructive technology critique. The text describes this potential with several experiments in image data…
Recent advancements in Large Language Models (LLMs) have showcased striking results on existing logical reasoning benchmarks, with some models even surpassing human performance. However, the true depth of their competencies and robustness…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
Yes. Interval statistics have been used to conclude that major earthquakes are random events in time and cannot be anticipated or predicted. Machine learning is a powerful new technique that enhances our ability to understand the…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as non-global logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation of subleading…