Related papers: On Stability of Sampling-Reconstruction Models
The rapid development of machine learning (ML) and artificial intelligence (AI) applications requires the training of large numbers of models. This growing demand highlights the importance of training models without human supervision, while…
We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…
For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…
Trusting machine learning algorithms requires having confidence in their outputs. Confidence is typically interpreted in terms of model reliability, where a model is reliable if it produces a high proportion of correct outputs. However,…
We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and…
Learning-based and data-driven techniques have recently become a subject of primary interest in the field of reconstruction and regularization of inverse problems. Besides the development of novel methods, yielding excellent results in…
In many settings, robust data analysis involves computational methods for uncertainty quantification and statistical inference. To design frequentist studies that leverage robust analysis methods, suitable sample sizes to achieve desired…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
In this work, we provide an analytical proof of the robustness of topological entanglement under a model of random local perturbations. We define a notion of average topological subsystem purity and show that, in the context of quantum…
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x,y\in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rangle|)_{j\in J}$ and $(|\langle y, x_j\rangle|)_{j\in J}$…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Recent strides in pretrained transformer-based language models have propelled state-of-the-art performance in numerous NLP tasks. Yet, as these models grow in size and deployment, their robustness under input perturbations becomes an…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
Assessing small-signal stability of power systems composed of thousands of interacting generators is a computationally challenging task. To reduce the computational burden, this paper introduces a novel condition to assess and certify…
The literature on provable robustness in machine learning has primarily focused on static prediction problems, such as image classification, in which input samples are assumed to be independent and model performance is measured as an…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…