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We extend the concept of a partial group action to non-associative algebras in a variety \(\mathcal{V}(I)\), solve the globalization problem within \(\mathcal{V}(I)\) and examine its universal property. It is achieved using what we call the…
Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have…
This paper generalizes the changes-in-changes (CIC) model to handle discrete treatments with more than two categories, extending the binary case of Athey and Imbens (2006). While the original CIC model is well-suited for binary treatments,…
Given a partial action $\theta$ of a group on a set with an algebraic structure, we construct a reflector of $\theta$ in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In…
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
In this paper we present a formal computational framework for modeling manipulation actions. The introduced formalism leads to semantics of manipulation action and has applications to both observing and understanding human manipulation…
We observe that the Reedy model structure on a diagram category can be constructed by iterating an operation of "bigluing" model structures along a pair of functors and a natural transformation. This yields a new explanation of the…
We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements…
We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential algebra is of Colombeau type in the sense that it contains…
Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical…
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…
The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…
In many applications, there is a need to predict the effect of an intervention on different individuals from data. For example, which customers are persuadable by a product promotion? which patients should be treated with a certain type of…
We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an alternative construction of the universal…
We introduce some algebraic structures such as singularity, commutators and central extension in modified categories of interest. Additionally, we introduce the cat$^{1}$-objects with their connection to crossed modules in these categories…
This paper presents a deep neural-network-based hierarchical graphical model for individual and group activity recognition in surveillance scenes. Deep networks are used to recognize the actions of individual people in a scene. Next, a…
We introduce deep neural networks for the analysis of anatomical shapes that learn a low-dimensional shape representation from the given task, instead of relying on hand-engineered representations. Our framework is modular and consists of…
We study actions of linear algebraic groups on central simple algebras using algebro-geometric techniques. Suppose an algebraic group G acts on a central simple algebra A of degree n. We are interested in questions of the following type:…