Related papers: A parameterization process, functorially

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

This paper proposes a methodology for generating and perturbing detailed derivations of equations at scale, aided by a symbolic engine, to evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems.…

We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…

Neural processes are a family of models which use neural networks to directly parametrise a map from data sets to predictions. Directly parametrising this map enables the use of expressive neural networks in small-data problems where neural…

Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…

Automatic gesture generation from speech generally relies on implicit modelling of the nondeterministic speech-gesture relationship and can result in averaged motion lacking defined form. Here, we propose a database-driven approach of…

We propose a method to write and check a specification including quantifiers using behaviors, i.e., input-output pairs. Our method requires the following input from the user: (1) answers to a finite number of queries, each of which presents…

We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…

Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many…

This study aims to provide a data-driven approach for empirically tuning and validating rating systems, focusing on the Elo system. Well-known rating frameworks, such as Elo, Glicko, TrueSkill systems, rely on parameters that are usually…

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is…

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

Recommender system is the most successful commercial technology in the past decade. Technical mammoth such as Temu, TikTok and Amazon utilize the technology to generate enormous revenues each year. Although there have been enough research…

We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…

This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…

The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…

Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at…

In the framework of Event Enhanced Quantum Theory (EEQT) a probabilistic construction of the piecewise deterministic process associated with a dynamical semigroup is presented. The process generates sample histories of individual systems…

In general, providing an axiomatization for an arbitrary logic is a task that may require some ingenuity. In the case of logics defined by a finite logical matrix (three-valued logics being a particularly simple example), the generation of…

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…