相关论文: The Asymptotic Cost of Complexity

We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the…

Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the…

We consider the issue of multiple agents learning to communicate through reinforcement learning within partially observable environments, with a focus on information asymmetry in the second part of our work. We provide a review of the…

In this paper, we investigate how to measure the intelligence of systems under specific structures. Two indicators are adopted to characterize the intelligence of a given structure, namely the function diversity of the structure, and the…

Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…

Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…

This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with…

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…

Shannon's information entropy measures of the uncertainty of an event's outcome. If learning about a system reflects a decrease in uncertainty, then a plausible intuition is that learning should be accompanied by a decrease in the entropy…

We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second,…

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

Reinforcement learning (RL) methods have been shown to be capable of learning intelligent behavior in rich domains. However, this has largely been done in simulated domains without adequate focus on the process of building the simulator. In…

In order to find out the limiting speed of solving a specific problem using computer, this essay provides a method based on information entropy. The relationship between the minimum computational complexity and information entropy change is…

Effective and intelligent exploration has been an unresolved problem for reinforcement learning. Most contemporary reinforcement learning relies on simple heuristic strategies such as $\epsilon$-greedy exploration or adding Gaussian noise…

Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…

In many practical applications of learning algorithms, unlabeled data is cheap and abundant whereas labeled data is expensive. Active learning algorithms developed to achieve better performance with lower cost. Usually Representativeness…

In this paper we examine the concept of complexity as it applies to generative art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic measures of…

Maximizing long-term rewards is the primary goal in sequential decision-making problems. The majority of existing methods assume that side information is freely available, enabling the learning agent to observe all features' states before…