Related papers: State-space fading memory
State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…
A computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion…
This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractional integral inequalities of Gr\"onwall--Wendroff type that…
Dynamic state and parameter estimation methods for dynamic security assessment in power systems are becoming increasingly important for system operators. Usually, the data used for this type of applications stems from phasor measurement…
Modeling long-range dependencies in sequential data remains a central challenge in machine learning. Transformers address this challenge through attention mechanisms, but their quadratic complexity with respect to sequence length limits…
We study safe policy improvement (SPI) for partially observable Markov decision processes (POMDPs). SPI is an offline reinforcement learning (RL) problem that assumes access to (1) historical data about an environment, and (2) the so-called…
Dynamic functional connectivity (DFC) analysis involves measuring correlated neural activity over time across multiple brain regions. Significant regional correlations among neural signals, such as those obtained from resting-state…
The field of Machine Learning has changed significantly since the 1970s. However, its most basic principle, Empirical Risk Minimization (ERM), remains unchanged. We propose Functional Risk Minimization~(FRM), a general framework where…
This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case.…
The capacity of non-coherent stationary Gaussian fading channels with memory under a peak-power constraint is studied in the asymptotic weak-signal regime. It is assumed that the fading law is known to both transmitter and receiver but that…
We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on…
Working within the quantum filtering framework, we establish a dynamic programming principle in an infinite-dimensional setting by embedding the state space into the Hilbert-Schmidt space. We then study a stabilization problem for…
Smoothing is a technique for estimating the state of an imperfectly monitored open system by combining both prior and posterior measurement information. In the quantum regime, current approaches to smoothing either give unphysical outcomes,…
We study a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbations via an additive Gaussian noise. We show that for a broad…
Inference is a versatile tool that underlies scientific discovery, machine learning, and everyday decision-making: it describes how an agent updates a probability distribution as partial information is acquired from multiple measurements,…
In this paper, we address the problem of computing maximal state-control invariant sets using failing trajectories. We introduce the concept of state-control invariance, which extends control invariance from the state space to the joint…
The performance of supervised semantic segmentation methods highly relies on the availability of large-scale training data. To alleviate this dependence, few-shot semantic segmentation (FSS) is introduced to leverage the model trained on…
It is argued using a Gedankenexperiment that a scalable quantum memory could be used as a perpetuum mobile of the second kind and hence cannot be realized in Nature. The reasoning is based on the assumption that the Landauer's principle for…
We analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We…
Representation learning is a fundamental but challenging problem, especially when the distribution of data is unknown. We propose a new representation learning method, termed Structure Transfer Machine (STM), which enables feature learning…