Related papers: Mutual Conversion Between Preference Maps And Cook…
To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an ``optimal'' subset of alternatives. In this paper, we provide a quantitative analysis of…
In classic reinforcement learning (RL) and decision making problems, policies are evaluated with respect to a scalar reward function, and all optimal policies are the same with regards to their expected return. However, many real-world…
Considering a group of users, each specifying individual preferences over categorical attributes, the problem of determining a set of objects that are objectively preferable by all users is challenging on two levels. First, we need to…
We introduce a natural generalization of twisted maps, called \emph{warped maps}. While twisted maps play an important role in the study of Deligne--Mumford stacks, warped maps are better suited for studying Artin stacks. Heuristically,…
Transformers have emerged as the prevailing standard solution for various AI tasks, including computer vision and natural language processing. The widely adopted Query, Key, and Value formulation (QKV) has played a significant role in this.…
Parallel coordinate plots (PCPs) are a prevalent method to interpret the relationship between the control parameters and metrics. PCPs deliver such an interpretation by color gradation based on a single metric. However, it is challenging to…
Tournaments are graphs obtained by assigning a direction for every edge in an undirected complete graph. We give a formula for the number of isomorphism classes of vertex-transitive tournaments with prime order. For that, we introduce…
The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X…
In complex K-theory, the Fourier-Mukai transform is an isomorphism between K-theory groups of a torus and its dual torus which is defined by pullback, tensoring by the Poincar\'e line bundle and pushforward. The Fourier-Mukai transform…
A particular orthogonal map on a finite dimensional real quadratic vector space (V,Q) with a non-degenerate quadratic form Q of any signature (p,q) is considered. It can be viewed as a correlation of the vector space that leads to a dual…
We develop a qualitative theory of Markov Decision Processes (MDPs) and Partially Observable MDPs that can be used to model sequential decision making tasks when only qualitative information is available. Our approach is based upon an…
The word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly…
Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum…
We often try to predict others' actions by obtaining supporting information that shows a preference index of surrounding people. In order to reproduce these situations, we propose a game named "One-sided Preference Game with Reference…
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…
It is tempting to assume that because effectiveness metrics have free choice to assign scores to search engine result pages (SERPs) there must thus be a similar degree of freedom as to the relative order that SERP pairs can be put into. In…
Given a set of agents with approval preferences over each other, we study the task of finding $k$ matchings fairly representing everyone's preferences. We model the problem as an approval-based multiwinner election where the set of…
In this paper we discuss the relationships between conditional and preferential logics and neural network models, based on a multi-preferential semantics. We propose a concept-wise multipreference semantics, recently introduced for…
An important aspect of AI design and ethics is to create systems that reflect aggregate preferences of the society. To this end, the techniques of social choice theory are often utilized. We propose a new social choice function motivated by…
We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete derivative is taken. We show that the maps of finite…