Related papers: Lessons I learned from Richard Stanley
We introduce a control-tutored reinforcement learning (CTRL) algorithm. The idea is to enhance tabular learning algorithms by means of a control strategy with limited knowledge of the system model. By tutoring the learning process, the…
In this note we introduce several instructive examples of bijections found between several different combinatorially defined sequences of sets. Each sequence has cardinalities given by the Catalan numbers. Our results answer some questions…
Learning algorithms are often used in conjunction with expert decision makers in practical scenarios, however this fact is largely ignored when designing these algorithms. In this paper we explore how to learn predictors that can either…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by…
This paper proposes a new approach to training recommender systems called deviation-based learning. The recommender and rational users have different knowledge. The recommender learns user knowledge by observing what action users take upon…
For Boris Zilber on his 75th birthday. I trace the roots of my collaboration with Boris Zilber, which combines categoricity theory, finite model theory, algorithmics, and combinatorics.
Unsupervised learning of compact and relevant state representations has been proved very useful at solving complex reinforcement learning tasks. In this paper, we propose a recurrent capsule network that learns such representations by…
Knowledge distillation is a technique for improving the performance of a simple "student" model by replacing its one-hot training labels with a distribution over labels obtained from a complex "teacher" model. While this simple approach has…
This is an introduction to algebraic combinatorics, written for a quarter-long graduate course. It starts with a rigorous introduction to formal power series with some combinatorial applications, then discusses integer partitions (proving…
The author describes some of his experiences as a mathematician cooperating with diabetes specialists.
We give a short appreciation of Robin Milner's seminal contributions to the theory of concurrency.
The authors have been using a largely algebraic form of ``computational discovery'' in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational…
For many years, researchers in psychology, education, statistics, and machine learning have been developing practical methods to improve learning speed, retention, and generalizability, and this work has been successful. Many of these…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of…
Recommender systems research is concerned with many aspects of recommender system behavior and effects than simply its effectiveness, and simulation can be a powerful tool for uncovering these effects. In this brief position paper, I…
As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…
This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial…
This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…