Related papers: The Monster and black-box groups

We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.

In the present work we will present and analyze some basic processes at the local and global level in linguistic derivations that seem to go beyond the limits of Markovian or Turing-like computation, and require, in our opinion, a quantum…

The aim of this article is to understand the problem of "black box" algorithms, an issue inherent to the nascent field of Explainable Artificial Intelligence (XAI). While it is relatively easy to understand something someone explained to…

The ability to interpret machine learning models has become increasingly important now that machine learning is used to inform consequential decisions. We propose an approach called model extraction for interpreting complex, blackbox…

In recent literature, moonshine has been explored for some groups beyond the Monster, for example the sporadic O'Nan and Thompson groups. This collection of examples may suggest that moonshine is a rare phenomenon, but a fundamental and…

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in…

In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like…

Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…

As machine learning algorithms are increasingly applied to high impact yet high risk tasks, such as medical diagnosis or autonomous driving, it is critical that researchers can explain how such algorithms arrived at their predictions. In…

A hybrid model involves the cooperation of an interpretable model and a complex black box. At inference, any input of the hybrid model is assigned to either its interpretable or complex component based on a gating mechanism. The advantages…

In machine learning (ML), it is in general challenging to provide a detailed explanation on how a trained model arrives at its prediction. Thus, usually we are left with a black-box, which from a scientific standpoint is not satisfactory.…

With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…

We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these three groups, we…

The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a natural stratification of these spaces.

Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…

In recent years, machine learning (ML) has become a key enabling technology for the sciences and industry. Especially through improvements in methodology, the availability of large databases and increased computational power, today's ML…

We study fairness in Machine Learning (FairML) through the lens of attribute-based explanations generated for machine learning models. Our hypothesis is: Biased Models have Biased Explanations. To establish that, we first translate existing…

Our work serves as a framework for unifying the challenges of contemporary explainable AI (XAI). We demonstrate that while XAI methods provide supplementary and potentially useful output for machine learning models, researchers and…

In this work, we study the black-box targeted attack problem from the model discrepancy perspective. On the theoretical side, we present a generalization error bound for black-box targeted attacks, which gives a rigorous theoretical…