Related papers: On multidimensional item response theory -- a coor…
Item response theory (IRT) is a popular modeling paradigm for measuring subject latent traits and item properties according to discrete responses in tests or questionnaires. There are very limited discussions on heterogeneity pattern…
Response-free item difficulty modelling promises to reduce reliance on response-based calibration but is intrinsically difficult on reading-comprehension multiple-choice items, where difficulty depends on inferential demands across wording…
The majority of contemporary object-tracking approaches do not model interactions between objects. This contrasts with the fact that objects' paths are not independent: a cyclist might abruptly deviate from a previously planned trajectory…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…
Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
We present an unbiased theory of symmetric multicategories, where sequences are replaced by families. To be effective, this approach requires an explicit consideration of indexing and reindexing of objects and arrows, handled by the double…
Within the educational context, students' assessment tests are routinely validated through Item Response Theory (IRT) models which assume unidimensionality and absence of Differential Item Functioning (DIF). In this paper, we investigate if…
The proliferation of Large Language Models (LLMs) necessitates valid evaluation methods to guide downstream applications and actionable future improvements. The Item Response Theory (IRT) has recently emerged as a promising framework for…
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…
Item (question) difficulties play a crucial role in educational assessments, enabling accurate and efficient assessment of student abilities and personalization to maximize learning outcomes. Traditionally, estimating item difficulties can…
Motivated by the study of meromorphic vector fields, a model theory of "compact complex manifolds equipped with a generic derivation" is here proposed. This is made precise by the notion of a differential CCM-structure. A first-order…
Zero-Shot Composed Image Retrieval (ZS-CIR) aims to retrieve target images by integrating information from a composed query (reference image and modification text) without training samples. Existing methods primarily combine caption models…
Dynamics of a free point particle on a multi world-line is presented and shown to reduce to that of a bosonic string theory at the appropriate limit. Other higher dimensional extended objects are argued to appear at other regions of the…
Although foundation models (FMs) claim to be powerful, their generalization ability significantly decreases when faced with distribution shifts, weak supervision, or malicious attacks in the open world. On the other hand, most domain…
We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the…
We consider families of geometries of D--dimensional space, described by a finite number of parameters. Starting from the De Witt metric we extract a unique integration measure which turns out to be a geometric invariant, i.e. independent…
In this article ideas from Kit Fine's theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generic mathematical structures can be viewed as generic systems of mathematical objects,…
We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…