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The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…

This paper proves a representation theorem regarding sequences of random elements that take values in a Borel space and are measurable with respect to the sigma algebra generated by an arbitrary union of sigma algebras. This, together with…

Let $G$ be a simple graph whose vertices are partitioned into two subsets, called filled vertices and empty vertices. A vertex $v$ is said to be forced by a filled vertex $u$ if $v$ is a unique empty neighbor of $u$. If we can fill all the…

Tokenization is a hardcoded compression step which remains in the training pipeline of Large Language Models (LLMs), despite a general trend towards architectures becoming increasingly end-to-end. Prior work has shown promising results at…

Resolving the exploration-exploitation trade-off remains a fundamental problem in the design and implementation of reinforcement learning (RL) algorithms. In this paper, we focus on model-free RL using the epsilon-greedy exploration policy,…

Model-based reinforcement learning (MBRL) has shown its advantages in sample-efficiency over model-free reinforcement learning (MFRL). Despite the impressive results it achieves, it still faces a trade-off between the ease of data…

Applying deep learning to solve real-life instances of hard combinatorial problems has tremendous potential. Research in this direction has focused on the Boolean satisfiability (SAT) problem, both because of its theoretical centrality and…

Let $\mathcal{N}$ be the $\sigma$-ideal of the null sets of reals. We introduce a new property of forcing notions that enable control of the additivity of $\mathcal{N}$ after finite support iterations. This is applied to answer some open…

Traditional parametric econometric models often rely on rigid functional forms, while nonparametric techniques, despite their flexibility, frequently lack interpretability. This paper proposes a parsimonious alternative by modeling the…

The goal is to show that an edge-reinforced random walk on a graph of bounded degree, with reinforcement weight function $W$ taken from a general class of reciprocally summable reinforcement weight functions, traverses a random attracting…

Assuming that there is no inner model with a strong cardinal, the following is shown: any subset of \omega_1 can be made \Delta^1_3 (in the codes) by a reasonable set-forcing; there is a reasonable set-generic extension with a \Delta^1_3…

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…

A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and has a strong forcing axiom of higher order than usual. Instead of "for every suitable forcing…

The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…

Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…

In this short note, we shall prove some observations regarding the connection between indestructible $\omega_1$-guessing models and the $\omega_1$-approximation property of forcing notions.

Generalization is one of the most important issues in machine learning problems. In this study, we consider generalization in restricted Boltzmann machines (RBMs). We propose an RBM with multivalued hidden variables, which is a simple…

A subset $S$ of initially infected vertices of a graph $G$ is called forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbour, infects…

Almost 10 years ago, Impagliazzo and Kabanets (2010) gave a new combinatorial proof of Chernoff's bound for sums of bounded independent random variables. Unlike previous methods, their proof is constructive. This means that it provides an…

We introduce a new and natural stationary set preserving forcing $\mathbb P^{c-c}({\lambda},{\mu})$ that (under $\mathsf{NS}_{\omega_1}$ precipitous + existence of $H_{\theta}^#$ for a sufficiently large regular ${\theta}$) increases the…