Related papers: Localized Transfunctions
In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic…
Grokking -- the abrupt transition from memorization to generalization long after near-zero training loss -- has been studied mainly in single-task settings. We extend geometric analysis to multi-task modular arithmetic, training…
We introduce the concept of F-decomposable systems, well-ordered inverse systems of Hausdorff compacta with fully closed bonding mappings. A continuous mapping between Hausdorff compacta is called fully closed if the intersection of the…
Multiple object tracking (MOT) is the task containing detection and association. Plenty of trackers have achieved competitive performance. Unfortunately, for the lack of informative exchange on these subtasks, they are often biased toward…
Motion prediction, recently popularized as world models, refers to the anticipation of future agent states or scene evolution, which is rooted in human cognition, bridging perception and decision-making. It enables intelligent systems, such…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…
Sets of invariant measures are considered for continuous maps of a metric compact set. We take Kantorovich metric to calculate distance between measures and Hausdorff metrics to calculate distance between compact sets. Consider the function…
By means of the idea of measurements on the crossed space-time nonlocal observables, we extend the mechanism for the two-way quantum teleportation to the chain teleportation among N spatially separated spin-1/2 systems. Since in the process…
A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence…
Functional transductions realized by two-way transducers (or, equally, by streaming transducers or MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown in 2013 that it is decidable…
Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…
Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We prove a version of the implicit function theorem for Lipschitz mappings $f:\mathbb{R}^{n+m}\supset A \to X$ into arbitrary metric spaces. As long as the pull-back of the Hausdorff content $\mathcal{H}_{\infty}^n$ by $f$ has positive…
Localization, that is the estimation of a robot's location from sensor data, is a fundamental problem in mobile robotics. This papers presents a version of Markov localization which provides accurate position estimates and which is tailored…
The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modeling. While…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…