Related papers: Model Theory of Scattered Piecewise Interpretable …

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…

The paper is aimed to establish the interdependence between linear expand-contract plasticity of an ellipsoid in a separable Hilbert spaces and properties of the set of its semi-axes.

To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs…

The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…

We summarize recent progress on the theory and applications of structural identifiability of compartmental models. On the applications side, we review identifiability analyses undertaken recently for models arising in epidemiology,…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

Despite the growing body of work in interpretable machine learning, it remains unclear how to evaluate different explainability methods without resorting to qualitative assessment and user-studies. While interpretability is an inherently…

Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…

We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…

We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral…

Text embeddings are a fundamental component in many NLP tasks, including classification, regression, clustering, and semantic search. However, despite their ubiquitous application, challenges persist in interpreting embeddings and…

We present a novel technique for learning semantic representations, which extends the distributional hypothesis to multilingual data and joint-space embeddings. Our models leverage parallel data and learn to strongly align the embeddings of…

We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states.

Interpretable rationales for model predictions are crucial in practical applications. We develop neural models that possess an interpretable inference process for dependency parsing. Our models adopt instance-based inference, where…

Foundations of the theory of Hilbert spaces with reproducing kernels are discussed. It is demonstrated that the claims in the papers of S.Saitoh and in his book "Theory of reproducing kernels and applications, Pitman research notes, 189,…

We explore the structure of the moduli space of vacua of Improved Bifundamentals, a recently introduced class of superconformal field theories. Utilizing the Hilbert Series, computed as a specific limit of the Superconformal Index, we…

We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in terms of the underlying noise level is known in many cases.…