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We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

We develop new classifiers under group fairness in the attribute-aware setting for binary classification with multiple group fairness constraints (e.g., demographic parity (DP), equalized odds (EO), and predictive parity (PP)). We propose a…

A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…

Reliability measures associated with the prediction of the machine learning models are critical to strengthening user confidence in artificial intelligence. Therefore, those models that are able to provide not only predictions, but also…

We study a generalisation of the family of non-(virtually pro-$p$) hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in 2010. We prove that this family contains groups of finite lower rank. We also show that many…

We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…

The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific group classes, the best known algorithm for testing isomorphism…

Collaborative filtering is a rapidly advancing research area. Every year several new techniques are proposed and yet it is not clear which of the techniques work best and under what conditions. In this paper we conduct a study comparing…

We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite p-groups of nilpotency class less than p. This allows us to unify and generalize a number of existing enumerative results, and to…

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…

Lazard and Rouillier in [9], by introducing the concept of discriminant variety, have described a new and efficient algorithm for solving parametric polynomial systems. In this paper we modify this algorithm, and we show that with our…

Practical checkers based on refinement types use the combination of implicit semantic sub-typing and parametric polymorphism to simplify the specification and automate the verification of sophisticated properties of programs. However, a…

In convolutional neural networks (CNNs), the filter grouping in convolution layers is known to be useful to reduce the network parameter size. In this paper, we propose a new logarithmic filter grouping which can capture the nonlinearity of…

One main obstacle for the wide use of deep learning in medical and engineering sciences is its interpretability. While neural network models are strong tools for making predictions, they often provide little information about which features…

We aim to reduce the cost of the current bosonic randomized benchmarking proposal. To do this, we introduce two filter functions: one uses immanants, the other uses characters of the special unitary group. These filters avoid computing…

First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015. This paper considers the discrete case,…

In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…

Filter selection techniques are known for their simplicity and efficiency. However this kind of methods doesn't take into consideration the features inter-redundancy. Consequently the un-removed redundant features remain in the final…

In recent work, Rosenbaum and Wagner showed that isomorphism of explicitly listed $p$-groups of order $n$ could be tested in $n^{\frac{1}{2}\log_p n + O(p)}$ time, roughly a square root of the classical bound. The $O(p)$ term is entirely…

We introduce the Deep Edge Filter, a novel approach that applies high-pass filtering to deep neural network features to improve model generalizability. Our method is motivated by our hypothesis that neural networks encode task-relevant…