Related papers: Learning to be Simple

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…

We propose a simplification of the Theory-of-Mind Network architecture, which focuses on modeling complex, deterministic machines as a proxy for modeling nondeterministic, conscious entities. We then validate this architecture in the…

Humans surpass the cognitive abilities of most other animals in our ability to "chunk" concepts into words, and then combine the words to combine the concepts. In this process, we make "infinite use of finite means", enabling us to learn…

We show how to count and randomly generate finitely generated subgroups of the modular group $\textsf{PSL}(2,\mathbb{Z})$ of a given isomorphism type. We also prove that almost malnormality and non-parabolicity are negligible properties for…

Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable…

This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple groups with a variety of interesting properties. Most…

The ability of deep neural networks to generalise well even when they interpolate their training data has been explained using various "simplicity biases". These theories postulate that neural networks avoid overfitting by first learning…

Uhlenbeck proved that a set of simple elements generates the group of rational loops in GL(n,C) that satisfy the U(n)-reality condition. For an arbitrary complex reductive group, a choice of representation defines a notion of rationality…

We present a differentiable framework capable of learning a wide variety of compositions of simple policies that we call skills. By recursively composing skills with themselves, we can create hierarchies that display complex behavior. Skill…

Obtaining compositional mappings is important for the model to generalize well compositionally. To better understand when and how to encourage the model to learn such mappings, we study their uniqueness through different perspectives.…

The last decade has shed some light on theoretical properties such as their consistency for regression tasks. In the current paper, we propose a new class of very simple learners based on so-called naive trees. These naive trees partition…

Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or…

The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertices are the generating k-tuples of the group (for a fixed…

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

In this paper we define Ordered Generating System for finite non-abelian groups, which is a generalization of the basis theorem for finite abelian groups. We prove the following: If each composition factor of a group G has Ordered…

The tremendous potential exhibited by deep learning is often offset by architectural and computational complexity, making widespread deployment a challenge for edge scenarios such as mobile and other consumer devices. To tackle this…

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the…

This article proves a version of the Feit-Thompson theorem for simple groups of finite Morley rank: a connected groups of finite Morley rank with a finite Sylow 2-subgroup has a trivial Sylow 2-subgroups.