Related papers: Some contributions to presheaf model theory, II --…
This is the second part of the paper which proves the compatibility of pushforward along a proper morphism of an \'{e}tale constructible sheaf and the pushforward of its characteristic cycle up to $p$-torsion. In this second part, we show a…
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…
We formulate coherence modeling as a regression task and propose two novel methods to combine techniques from our setup with pairwise approaches. The first of our methods is a model that we call "first-next," which operates similarly to…
We give an analysis and generalizations of some long-established constructive completeness results in terms of categorical logic and pre-sheaf and sheaf semantics. The purpose is in no small part conceptual and organizational: from a few…
The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be…
This paper introduces cellular sheaf theory to graphical methods and reciprocal constructions in structural engineering. The elementary mechanics and statics of trusses are derived from the linear algebra of sheaves and cosheaves. Further,…
We study fairness in Machine Learning (FairML) through the lens of attribute-based explanations generated for machine learning models. Our hypothesis is: Biased Models have Biased Explanations. To establish that, we first translate existing…
Human social behavior is structured by relationships. We form teams, groups, tribes, and alliances at all scales of human life. These structures guide multi-agent cooperation and competition, but when we observe others these underlying…
The objective of this article is to introduce a fairness interpretability framework for measuring and explaining the bias in classification and regression models at the level of a distribution. In our work, we measure the model bias across…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
The purpose of this paper is to develop a theory of $(\infty, 1)$-stacks, in the sense of Hirschowitz-Simpson's `Descent Pour Les n-Champs', using the language of quasi-category theory and the author's local Joyal model structure. The main…
Attribution methods explain which input features drive a model's prediction, making them central to model debugging and mechanistic interpretability. Yet backward attribution methods, including gradients, LRP, and transformer-specific…
The ubiquity of machine learning based predictive models in modern society naturally leads people to ask how trustworthy those models are? In predictive modeling, it is quite common to induce a trade-off between accuracy and…
A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…
A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fra\"iss\'e…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
We define a version of the Ehrenfeucht-Fra\"iss\'e game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length $n$ exactly corresponds to being…
A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the…