Related papers: Valuations and Metrics on Partially Ordered Sets
Current evaluation metrics for language modeling and generation rely heavily on the accuracy of predicted (or generated) words as compared to a reference ground truth. While important, token-level accuracy only captures one aspect of a…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
The distributed and continuous representations used by neural networks are at odds with representations employed in linguistics, which are typically symbolic. Vector quantization has been proposed as a way to induce discrete neural…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
The automatic ranking of word pairs as per their semantic relatedness and ability to mimic human notions of semantic relatedness has widespread applications. Measures that rely on raw data (distributional measures) and those that use…
I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…
In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as…
In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…
Contemporary undertakings provide limitless opportunities for widespread application of machine reasoning and artificial intelligence in situations characterised by uncertainty, hostility and sheer volume of data. The paper develops a…
Considering voting rules based on evaluation inputs rather than preference rankings modifies the paradigm of probabilistic studies of voting procedures. This article proposes several simulation models for generating evaluation-based voting…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
In an effort to regulate Machine Learning-driven (ML) systems, current auditing processes mostly focus on detecting harmful algorithmic biases. While these strategies have proven to be impactful, some values outlined in documents dealing…
This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of…
A common problem in LLM evaluation is how to choose a subset of metrics from a full suite of possible metrics. Subset selection is usually done for efficiency or interpretability reasons, and the goal is often to select a ``representative''…
Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on one of the most…
Probing experiments investigate the extent to which neural representations make properties -- like part-of-speech -- predictable. One suggests that a representation encodes a property if probing that representation produces higher accuracy…
Partial evaluation (PE) is a powerful and general program optimization technique with many successful applications. However, it has never been investigated in the context of expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF,…
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the linear-time/branching-time…
The amount of information in the form of features and variables avail- able to machine learning algorithms is ever increasing. This can lead to classifiers that are prone to overfitting in high dimensions, high di- mensional models do not…
In this paper we present different ways to parametrize subsets of the space of valuations on $K[x]$ extending a given valuation on $K$. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here…