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The paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. As the starting point of our programme, we construct Frobenius maps on black box groups of untwisted Lie type in odd…

Group Theory · Mathematics 2016-03-27 Alexandre Borovik , Şükrü Yalçınkaya

If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank $>1$, other than any $^2F_4(q)$, over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism.…

Group Theory · Mathematics 2011-12-14 W. M. Kantor , K. Magaard

This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…

Group Theory · Mathematics 2020-06-04 Alexandre Borovik , Şükrü Yalçınkaya

Given a global exponent $E$ for a black box group $\mathsf{Y}$ encrypting ${\rm SL}_2(\mathbb{F})$, where $\mathbb{F}$ is an unknown finite field of unknown odd characteristic, we construct, in probabilistic time polynomial in $\log E$, the…

Group Theory · Mathematics 2020-01-30 Alexandre Borovik , Şükrü Yalçınkaya

We propose a new randomized ensemble technique with a provable security guarantee against black-box transfer attacks. Our proof constructs a new security problem for random binary classifiers which is easier to empirically verify and a…

Machine Learning · Computer Science 2020-02-25 Kevin Shi , Daniel Hsu , Allison Bishop

Many deployed learned models are black boxes: given input, returns output. Internal information about the model, such as the architecture, optimisation procedure, or training data, is not disclosed explicitly as it might contain proprietary…

Machine Learning · Statistics 2018-02-15 Seong Joon Oh , Max Augustin , Bernt Schiele , Mario Fritz

Black box systems for automated decision making, often based on machine learning over (big) data, map a user's features into a class or a score without exposing the reasons why. This is problematic not only for lack of transparency, but…

Artificial Intelligence · Computer Science 2018-06-27 Dino Pedreschi , Fosca Giannotti , Riccardo Guidotti , Anna Monreale , Luca Pappalardo , Salvatore Ruggieri , Franco Turini

As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such…

Machine Learning · Computer Science 2020-02-04 Dylan Slack , Sophie Hilgard , Emily Jia , Sameer Singh , Himabindu Lakkaraju

We briefly explain how to implement the morphisms in our paper ``Natural representations of black box groups encrypting $SL_2(\mathbb{F})$" and provide some examples.

Group Theory · Mathematics 2025-10-17 Alexandre Borovik , Şükrü Yalçınkaya

Deep neural networks learn fragile "shortcut" features, rendering them difficult to interpret (black box) and vulnerable to adversarial attacks. This paper proposes semantic features as a general architectural solution to this problem. The…

Machine Learning · Computer Science 2024-04-18 Maciej Satkiewicz

In the literature on adversarial examples, white box and black box attacks have received the most attention. The adversary is assumed to have either full (white) or no (black) access to the defender's model. In this work, we focus on the…

Machine Learning · Computer Science 2022-03-22 Shi Hu , Eric Nalisnick , Max Welling

It has been demonstrated that adversarial graphs, i.e., graphs with imperceptible perturbations added, can cause deep graph models to fail on node/graph classification tasks. In this paper, we extend adversarial graphs to the problem of…

Social and Information Networks · Computer Science 2020-01-23 Jia Li , Honglei Zhang , Zhichao Han , Yu Rong , Hong Cheng , Junzhou Huang

For the black box groups $X$ encrypting ${\rm{PGL}}_2(q)$, $q$ odd, we propose an algorithm constructing a subgroup encrypting ${\rm{Sym}}_4$ and subfield subgroups of $X$. We also present the analogous algorithms for black box groups…

Group Theory · Mathematics 2014-03-11 Alexandre Borovik , Şükrü Yalçınkaya

We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the…

Group Theory · Mathematics 2007-05-23 Alexandre V. Borovik

We present an approach to explain the decisions of black box models for image classification. While using the black box to label images, our explanation method exploits the latent feature space learned through an adversarial autoencoder.…

Computer Vision and Pattern Recognition · Computer Science 2020-02-11 Riccardo Guidotti , Anna Monreale , Stan Matwin , Dino Pedreschi

In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…

Cryptography and Security · Computer Science 2023-01-18 Delaram Kahrobaei , Ramón Flores , Marialaura Noce

Given a black box group $\mathsf{Y}$ encrypting $\rm{PSL}_2(\mathbb{F})$ over an unknown field $\mathbb{F}$ of unknown odd characteristic $p$ and a global exponent $E$ for $\mathsf{Y}$ (that is, an integer $E$ such that $\mathsf{y}^E=1$ for…

Group Theory · Mathematics 2018-03-13 Alexandre Borovik , Şükrü Yalçınkaya

In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The…

Computers and Society · Computer Science 2018-06-22 Riccardo Guidotti , Anna Monreale , Salvatore Ruggieri , Franco Turini , Dino Pedreschi , Fosca Giannotti

Although counterfactual explanations are a popular approach to explain ML black-box classifiers, they are less widespread in NLP. Most methods find those explanations by iteratively perturbing the target document until it is classified…

Computation and Language · Computer Science 2024-04-24 Julien Delaunay , Luis Galárraga , Christine Largouët

Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…

Group Theory · Mathematics 2020-04-14 Barry Hurley , Ted Hurley
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