Related papers: Error Propagation in the Hypercycle

Supervisory control theory provides means to synthesize supervisors for systems with discrete-event behavior from models of the uncontrolled plant and of the control requirements. The applicability of supervisory control theory often fails…

We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system…

We consider the robust linear regression model $\boldsymbol{y} = X\beta^* + \boldsymbol{\eta}$, where an adversary oblivious to the design $X \in \mathbb{R}^{n \times d}$ may choose $\boldsymbol{\eta}$ to corrupt all but a (possibly…

The widespread use of generative models has created a feedback loop, in which each generation of models is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation…

We study how idiosyncratic firm-level shocks generate aggregate volatility and tail risk when they propagate through a production network under overlapping adjustment: new productivity draws arrive before the economy reaches the static…

Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light…

We consider autoregressive sequences $X_n=aX_{n-1}+\xi_n$ and $M_n=\max\{aM_{n-1},\xi_n\}$ with a constant $a\in(0,1)$ and with positive, independent and identically distributed innovations $\{\xi_k\}$. It is known that if $\mathbf…

Ensemble learning is a popular technique to improve the accuracy of machine learning models. It traditionally hinges on the rationale that aggregating multiple weak models can lead to better models with lower variance and hence higher…

In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection…

Models with nonlinear architectures/parameterizations such as deep neural networks (DNNs) are well known for their mysteriously good generalization performance at overparameterization. In this work, we tackle this mystery from a novel…

The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the interface between the two fluids is improving the stability. The multi-layer Hele -…

We consider a propagation of transition fronts in one-dimensional chains with bi-stable nondegenerate on-site potential. If one adopts linear coupling in the chain and piecewise linear on-site force, then it is possible to develop…

We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these subcomplexes capture many important structural properties of…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

Obtaining enough labeled data to robustly train complex discriminative models is a major bottleneck in the machine learning pipeline. A popular solution is combining multiple sources of weak supervision using generative models. The…

Given graphs $G_1,\ldots,G_s$ all on a common vertex set and a graph $H$ with $e(H) = s$, a copy of $H$ is \emph{transversal} or \emph{rainbow} if it contains one edge from each $G_i$. We establish a stability result for transversal…

Genetic systems with multiple loci can have complex dynamics. For example, mean fitness need not always increase and stable cycling is possible. Here, we study the dynamics of a genetic system inspired by the molecular biology of…

One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have…

We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the…

Let $N$ be the number of triangles in an Erd\H{o}s-R\'enyi graph $\mathcal{G}(n,p)$ on $n$ vertices with edge density $p=d/n,$ where $d>0$ is a fixed constant. It is well known that $N$ weakly converges to the Poisson distribution with mean…