相关论文: Regularity and Stability Properties of Selective S…

This paper deals with the analysis of input/output-to-state stability (IOSS) and construction of state-norm estimators for continuous-time switched nonlinear systems under restricted switching. Our contributions are twofold. First, given a…

Uniform-noise discrete diffusion and flow models (e.g., D3PM, SEDD, UDLM, DFM) generate sequences non-autoregressively by iteratively refining randomly initialized vocabulary tokens through multiple context-dependent replacements. These…

This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under…

This paper presents versions of integral input-to-state stability and integral input-to-integral-state stability for nonlinear sampled-data systems, under the low measurement rate constraint. In particular, we compensate the lack of…

We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant because the boundary conditions can be…

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…

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a ``passively protected quantum memory,'' defined as an encoded qubit coupled to an environment that naturally wants to correct…

While port-Hamiltonian descriptor systems are known to be stable and passive, they may not be asymptotically stable or strictly passive. Necessary and sufficient conditions are presented when these properties as well as the regularity and…

Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…

We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability~$1$. Our approach is based on the novel notion…

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF…

Structured State Space Models (SSMs) have emerged as alternatives to transformers. While SSMs are often regarded as effective in capturing long-sequence dependencies, we rigorously demonstrate that they are inherently limited by strong…

Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic…

We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and…

Consider the symmetric exclusion process evolving on an interval and weakly interacting at the end-points with reservoirs. Denote by $I_{[0,T]} (\cdot)$ its dynamical large deviations functional and by $V(\cdot)$ the associated…

Autonomous experimental systems are increasingly used in materials research to accelerate scientific discovery, but their performance is often limited by low-quality, noisy data. This issue is especially problematic in data-intensive…

Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from…

Long Short-Term Memory (LSTM) Recurrent Neural networks (RNNs) rely on gating signals, each driven by a function of a weighted sum of at least 3 components: (i) one of an adaptive weight matrix multiplied by the incoming external input…

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…