Related papers: Collapsing Catalytic Classes
This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying…
We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
At higher altitudes, for high temperature gases, for instance near space shuttles moving at hypersonic speed, not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In…
Conformal prediction (CP) offers distribution-free uncertainty quantification for machine learning models, yet its interplay with fairness in downstream decision-making remains underexplored. Moving beyond CP as a standalone operation…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
In this work, we provide a refinement of the selective CLT result of Tian and Taylor (2015), which allows for selective inference in non-parametric settings by adjusting for the asymptotic Gaussian limit for selection. Under some regularity…
We study the computational power of randomized computations on infinite objects, such as real numbers. In particular, we introduce the concept of a Las Vegas computable multi-valued function, which is a function that can be computed on a…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable…
Stochastic Computing (SC) is a computing paradigm that allows for the low-cost and low-power computation of various arithmetic operations using stochastic bit streams and digital logic. In contrast to conventional representation schemes…
In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
Quantum catalysis, the ability to enable previously impossible transformations by using auxiliary systems without degrading them, has emerged as a powerful tool in various resource theories. Although catalytically enabled state…
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$…
A conformal restriction system is a commutative, associative, unital algebra equipped with a representation of the groupoid of univalent conformal maps on connected open sets of the Riemann sphere, and a family of linear functionals on…
Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…
Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which allows the ITTM to compute through ordinal stages. This…
Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice,…