Related papers: Scaling Dimension
Generating a huge number of association rules reduces their utility in the decision making process, done by domain experts. In this context, based on the theory of Formal Concept Analysis, we propose to extend the notion of Formal Concept…
In computer science, combinatorics, and model theory, the VC dimension is a central notion underlying far-reaching topics such as error rate for decision rules, combinatorial measurements of classes of finite structures, and neo-stability…
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…
Text-guided diffusion models have revolutionized generative tasks by producing high-fidelity content from text descriptions. They have also enabled an editing paradigm where concepts can be replaced through text conditioning (e.g., a dog to…
Teaching dimension is a learning theoretic quantity that specifies the minimum training set size to teach a target model to a learner. Previous studies on teaching dimension focused on version-space learners which maintain all hypotheses…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of…
Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…
In this chapter we discuss soft concept analysis, a study which identifies an enriched notion of "conceptual scale" as developed in formal concept analysis with an enriched notion of "linguistic variable" as discussed in fuzzy logic. The…
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…
Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such "VC dimensions" exist for models taking…
In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Motivated by distinct, though related, criteria, a growing number of attribution methods have been developed tointerprete deep learning. While each relies on the interpretability of the concept of "importance" and our ability to visualize…
This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose…
Distributivity is a well-established and extensively studied notion in lattice theory. In the context of data analysis, particularly within Formal Concept Analysis (FCA), lattices are often observed to exhibit a high degree of…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Semantic data and knowledge infrastructures must reconcile two fundamentally different forms of representation: natural language, in which most knowledge is created and communicated, and formal semantic models, which enable…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has…