Related papers: Interval-Valued Rank in Finite Ordered Sets
Learning to rank -- producing a ranked list of items specific to a query and with respect to a set of supervisory items -- is a problem of general interest. The setting we consider is one in which no analytic description of what constitutes…
Motivated by applications to information retrieval, we study the lattice of antichains of finite intervals of a locally finite, totally ordered set. Intervals are ordered by reverse inclusion; the order between antichains is induced by the…
We introduce the finite-horizon first-order rank profile of a language $L \subseteq \Sigma^*$: the least quantifier rank needed by an $\mathrm{FO}[<]$ sentence to classify membership in $L$ correctly on all words of length at most $n$. The…
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
We introduce a partial order structure on the set of interval orders of a given size, and prove that such a structure is in fact a lattice. We also provide a way to compute meet and join inside this lattice. Finally, we show that, if we…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main drivers of geometric deep learning, and paradigms that were…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
We describe a data structure that can maintain a dynamic set of points given by their Cartesian coordinates, and maintain the point whose product of ranks within the two coordinate orderings is minimum or maximum, in time $O(\sqrt{n\log…
This paper primarily demonstrates a method to quantitatively assess the alignment between multi-step, structured reasoning in large language models and human preferences. We introduce the Alignment Score, a semantic-level metric that…
We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. The algorithm shows a very competitive performance on…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
We study two constructions related to the intervals of finite posets. The first one is a poset. The second one is more complicated. Loosely speaking it can be seen as a poset with some extra zero-relations. As main result, we show that…
Object ranking is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects, which are typically represented as feature vectors, the goal is to learn a ranking…
In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
We propose a theoretical framework under which preference profiles can be meaningfully compared. Specifically, given a finite set of feasible allocations and a preference profile, we first define a ranking vector of an allocation as the…