Related papers: The Monster and black-box groups

A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language…

While there are many machine learning methods to classify and cluster sequences, they fail to explain what are the differences in groups of sequences that make them distinguishable. Although in some cases having a black box model is…

A content-free expository article about the monster simple group.

Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and…

Adversarial attacks have threatened the application of deep neural networks in security-sensitive scenarios. Most existing black-box attacks fool the target model by interacting with it many times and producing global perturbations.…

We present a geometric approach to the Baum-Connes conjecture with coefficients for Gromov monster groups via a theorem of Khoskham and Skandalis. Secondly, we use recent results concerning the a-T-menability at infinity of large girth…

Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…

Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…

Computer models are widely used to study complex real world physical systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; and long evaluation times.…

Ensemble models are widely recognized in the ML community for their limited interpretability. For instance, while a single decision tree is considered interpretable, ensembles of trees (e.g., boosted trees) are often treated as black-boxes.…

A systematic study of maximal subgroups of the sporadic simple groups began in the 1960s. The work is now almost complete, only a few cases in the Monster remaining outstanding. We give a survey of results obtained, and methods used, over…

Artificial neural networks are often very complex and too deep for a human to understand. As a result, they are usually referred to as black boxes. For a lot of real-world problems, the underlying pattern itself is very complicated, such…

A random matrix model of black holes is given based on analysis of Gaussian complex ensembles, based on the generalization of chRMT of QCD. Spacetime freedoms are incorporated in terms of eigenvalues of the ensemble. Classical observables…

The types of constraints encountered in black-box and simulation-based optimization problems differ significantly from those treated in nonlinear programming. We introduce a characterization of constraints to address this situation. We…

Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of…

We review some of the possible models that are able to describe the current Universe which point out the future singularities that could appear. We show that the study of the dark energy accretion onto black- and worm-holes phenomena in…

Local explanation frameworks aim to rationalize particular decisions made by a black-box prediction model. Existing techniques are often restricted to a specific type of predictor or based on input saliency, which may be undesirably…

Let $\mathbb{M}$ be the Monster group, which is the largest sporadic finite simple group, and has first been constructed in 1982 by Griess. In 1985 Conway has constructed a 196884-dimensional rational epresentation $\rho$ of $\mathbb{M}$…

Recently, interpretable machine learning has re-explored concept bottleneck models (CBM). An advantage of this model class is the user's ability to intervene on predicted concept values, affecting the downstream output. In this work, we…

Adversarial examples, which are slightly perturbed inputs generated with the aim of fooling a neural network, are known to transfer between models; adversaries which are effective on one model will often fool another. This concept of…