Related papers: Spelling Rules for the Monster/Semple Tower
We describe computer calculations that were used in 2016 to classify subgroups of the Monster isomorphic to $PSL_2(8)$, containing $7B$-elements. It turns out that there is no such $PSL_2(8)$ in the Monster. These calculations confirm…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
In this paper we address a problem: How far can we iterate lower recursively Mahlo operations in higher reflecting universes? Or formally: How much can lower recursively Mahlo operations be iterated in set theories for higher reflecting…
Distributional semantics models are known to struggle with small data. It is generally accepted that in order to learn 'a good vector' for a word, a model must have sufficient examples of its usage. This contradicts the fact that humans can…
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about…
Recently, there has been interest in multiplicative recurrent neural networks for language modeling. Indeed, simple Recurrent Neural Networks (RNNs) encounter difficulties recovering from past mistakes when generating sequences due to high…
We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.)…
In recent years, the pen and paper RPG market has experienced significant growth. As a result, companies are increasingly exploring the integration of AI technologies to enhance player experience and gain a competitive edge. One of the key…
Contextual word-representations became a standard in modern natural language processing systems. These models use subword tokenization to handle large vocabularies and unknown words. Word-level usage of such systems requires a way of…
We introduce a recurrent neural network language model (RNN-LM) with long short-term memory (LSTM) units that utilizes both character-level and word-level inputs. Our model has a gate that adaptively finds the optimal mixture of the…
Measuring the quality of a generated sequence against a set of references is a central problem in many learning frameworks, be it to compute a score, to assign a reward, or to perform discrimination. Despite great advances in model…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…
We explore a family of nested recurrence relations with arbitrary levels of nesting, which have an interpretation in terms of fixed points of morphisms over a countably infinite alphabet. Recurrences in this family are related to a number…
We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images…
We introduce Many-Shot Regurgitation (MSR) prompting, a new black-box membership inference attack framework for examining verbatim content reproduction in large language models (LLMs). MSR prompting involves dividing the input text into…
The simplest theories where we can understand the origin of the baryon and lepton number violating interactions are discussed. We discuss the desert hypothesis in particle physics and the different scenarios where there is no need to assume…
Word embedding models such as GloVe rely on co-occurrence statistics from a large corpus to learn vector representations of word meaning. These vectors have proven to capture surprisingly fine-grained semantic and syntactic information.…
Riddles based on simple puns can be classified according to the patterns of word, syllable or phrase similarity they depend upon. We have devised a formal model of the semantic and syntactic regularities underlying some of the simpler types…
We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of elements of a ring labeled by any subset of indices, it is…
An overview of recent progress on searches for Lorentz- and CPT-violating signals with confined particles and antiparticles in Penning traps is presented. In the context of the Standard-Model Extension (SME), leading-order shifts in the…