Related papers: Recurrent Equilibrium Networks: Flexible Dynamic M…

This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate nonlinear systems -- that satisfy a Lipschitz property and…

We introduce Harmonic Robustness, a powerful and intuitive method to test the robustness of any machine-learning model either during training or in black-box real-time inference monitoring without ground-truth labels. It is based on…

Traditional artificial neural networks consist of nodes with non-oscillatory dynamics. Biological neural networks, on the other hand, consist of oscillatory components embedded in an oscillatory environment. Motivated by this feature of…

The stability-plasticity dilemma is a major challenge in continual learning, as it involves balancing the conflicting objectives of maintaining performance on previous tasks while learning new tasks. In this paper, we propose the…

We introduce robust learning equilibrium. The idea of learning equilibrium is that learning algorithms in multi-agent systems should themselves be in equilibrium rather than only lead to equilibrium. That is, learning equilibrium is immune…

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…

Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…

Recurrent neural networks (RNNs) have been used extensively and with increasing success to model various types of sequential data. Much of this progress has been achieved through devising recurrent units and architectures with the…

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…

Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive…

Implicit Neural Representations (INRs) encode discrete signals in a continuous manner using neural networks, demonstrating significant value across various multimedia applications. However, the vulnerability of INRs presents a critical…

Forecasting complex system dynamics, particularly for long-term predictions, is persistently hindered by error accumulation and computational burdens. This study presents RefreshNet, a multiscale framework developed to overcome these…

To foster trust in machine learning models, explanations must be faithful and stable for consistent insights. Existing relevant works rely on the $\ell_p$ distance for stability assessment, which diverges from human perception. Besides,…

After a more than decade-long period of relatively little research activity in the area of recurrent neural networks, several new developments will be reviewed here that have allowed substantial progress both in understanding and in…

Vision-based locomotion in outdoor environments presents significant challenges for quadruped robots. Accurate environmental prediction and effective handling of depth sensor noise during real-world deployment remain difficult, severely…

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…

Spiking neural networks (SNNs) are gaining popularity in deep learning due to their low energy budget on neuromorphic hardware. However, they still face challenges in lacking sufficient robustness to guard safety-critical applications such…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

The resilience of convolutional neural networks against input variations and adversarial attacks remains a significant challenge in image recognition tasks. Motivated by the need for more robust and reliable image recognition systems, we…

Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…