Related papers: The No-Clash Teaching Dimension is Bounded by VC D…
Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. Among all valid confidence sets for…
We study the VC-dimension of the set system on the vertex set of some graph which is induced by the family of its $k$-connected subgraphs. In particular, we give tight upper and lower bounds for the VC-dimension. Moreover, we show that…
This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on VC_ind-density, and…
For the semantic segmentation of images, state-of-the-art deep neural networks (DNNs) achieve high segmentation accuracy if that task is restricted to a closed set of classes. However, as of now DNNs have limited ability to operate in an…
Recently, the authors introduced the theory of high-arity PAC learning, which is well-suited for learning graphs, hypergraphs and relational structures. In the same initial work, the authors proved a high-arity analogue of the Fundamental…
This work studies embedding of arbitrary VC classes in well-behaved VC classes, focusing particularly on extremal classes. Our main result expresses an impossibility: such embeddings necessarily require a significant increase in dimension.…
The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
In statistical setting of the pattern recognition problem the number of examples required to approximate an unknown labelling function is linear in the VC dimension of the target learning class. In this work we consider the question whether…
Embedding-based representations in Euclidean space $\mathbb{R}^d$ are a cornerstone of modern machine learning, where a major goal is to use the \emph{smallest dimension} that faithfully captures data relations. In this work, we prove sharp…
In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…
We solve exactly the general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical…
We introduce a new model of teaching named "preference-based teaching" and a corresponding complexity parameter---the preference-based teaching dimension (PBTD)---representing the worst-case number of examples needed to teach any concept in…
Given a raw knowledge in the form of a data table/a decision system, one is facing two possible venues. One, to treat the system as closed, i.e., its universe does not admit new objects, or, to the contrary, its universe is open on…
Understanding the self-directed learning complexity has been an important problem that has captured the attention of the online learning theory community since the early 1990s. Within this framework, the learner is allowed to adaptively…
In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue…
Categorical attributes with qualitative values are ubiquitous in cluster analysis of real datasets. Unlike the Euclidean distance of numerical attributes, the categorical attributes lack well-defined relationships of their possible values…
Imbalance in classification tasks is commonly quantified by the cardinalities of examples across classes. This, however, disregards the presence of redundant examples and inherent differences in the learning difficulties of classes.…
As large language models (LLMs) advance toward expert-level performance in engineering domains, reliable reasoning under user-specified constraints becomes critical. In circuit analysis, for example, a numerically correct solution is…
Contradictory multimodal inputs are common in real-world settings, yet existing benchmarks typically assume input consistency and fail to evaluate cross-modal contradiction detection - a fundamental capability for preventing hallucinations…