Related papers: Lattice-Theoretic Progress Measures and Coalgebrai…

The problems of enumerating lattice walks, with an arbitrary finite set of allowed steps, both in one and two dimensions, where one must always stay in the non-negative half-line and quarter-plane respectively, are used, as case studies, to…

In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

With growing applications of Machine Learning (ML) techniques in the real world, it is highly important to ensure that these models work in an equitable manner. One main step in ensuring fairness is to effectively measure fairness, and to…

In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a…

Fair predictive algorithms hinge on both equality and trust, yet inherent uncertainty in real-world data challenges our ability to make consistent, fair, and calibrated decisions. While fairly managing predictive error has been extensively…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

Explaining why aggregated measures change is a critical challenge in data analytics that existing systems struggle to address. While current attribution methods exist, they lack a unified solution that is simultaneously general for…

Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…

We approximate $d$-variate periodic functions in weighted Korobov spaces with general weight parameters using $n$ function values at lattice points. We do not limit $n$ to be a prime number, as in currently available literature, but allow…

Negotiations, a model of concurrency with multi party negotiation as primitive, have been recently introduced in arXiv:1307.2145, arXiv:1403.4958. We initiate the study of games for this model. We study coalition problems: can a given…

Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of…

This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…

Aligning large language models (LLMs) with human preferences is inherently multi-objective: different users and evaluation criteria impose heterogeneous and often conflicting requirements on model outputs. We propose CAGE (Common-Agency…

We propose an extension of the classical dichotomous categorization of research programmes into progress and degeneration according to Lakatos in the form of a neutral third category: the stagnant research programme. First, a critical…

In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness.…

Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…

Reliable evaluation is fundamental to the progress of Large Language Models (LLMs), yet the evaluation process during pre-training is plagued by significant instability that obscures true learning dynamics. In this work, we systematically…