相关论文: On the Mathematical Impossibility of Safe Universa…
We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…
This work applies universal adaptive control to control barrier functions to achieve forward invariance of a safe set despite the presence of unmatched parametric uncertainties. The approach combines two ideas. The first is to construct a…
We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly geometric H\"older continuous rough paths can be approximated…
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…
We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random $\{0,1\}$-valued filter, that have two modes of operation: in the first each…
The Universal Approximation Theorem posits that neural networks can theoretically possess unlimited approximation capacity with a suitable activation function and a freely chosen or trained set of parameters. However, a more practical…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
We consider models of quantum computation that involve operations performed on some fixed resourceful quantum state. Examples that fit this paradigm include magic state injection and measurement-based approaches. We introduce a framework…
By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…
The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…
In this paper, we study the robustness of safety properties of a linear dynamical system with respect to model uncertainties. Our paper involves three parts. In the first part, we provide symbolic (analytical) and numerical (representation…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential…
Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
The universal approximation property (UAP) holds a fundamental position in deep learning, as it provides a theoretical foundation for the expressive power of neural networks. It is widely recognized that a composition of linear and…
We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…