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Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
Reinforcement learning with function approximation can be unstable and even divergent, especially when combined with off-policy learning and Bellman updates. In deep reinforcement learning, these issues have been dealt with empirically by…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of…
Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates {q} satisfying Hamilton's motion equations will likewise satisfy them when played "backwards", with the corresponding momenta changing signs :…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the…
Feature selection, as a vital dimension reduction technique, reduces data dimension by identifying an essential subset of input features, which can facilitate interpretable insights into learning and inference processes. Algorithmic…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
The reliability of a learning model is key to the successful deployment of machine learning in various applications. However, it is difficult to describe the phenomenon due to the complicated nature of the problems in machine learning. It…
Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before…
We consider a nonlinear non-autonomous system with time-varying delays $$ \dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t))) $$ which has a large number of applications in the theory of artificial neural networks. Via…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
Estimation and inference on causal parameters is typically reduced to a generalized method of moments problem, which involves auxiliary functions that correspond to solutions to a regression or classification problem. Recent line of work on…
The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We…
A primary goal of class-incremental learning is to strike a balance between stability and plasticity, where models should be both stable enough to retain knowledge learned from previously seen classes, and plastic enough to learn concepts…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
Algorithm evaluation and comparison are fundamental questions in machine learning and statistics -- how well does an algorithm perform at a given modeling task, and which algorithm performs best? Many methods have been developed to assess…
We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum…