相关论文: Asymptotic Frame Theory for Analog Coding

In the classic wiretap model, Alice wishes to reliably communicate to Bob without being overheard by Eve who is eavesdropping over a degraded channel. Systems for achieving that physical layer security often rely on an error correction code…

Localization of normal modes is used in recent microelectromechanical systems (MEMS) technologies with orders of magnitude improvements in sensitivity. A pair of eigenvalues veer, or avoid crossing each other, as a single parameter of a…

Detecting or classifying already known sparse signals contaminated by Gaussian noise from compressive measurements is different from reconstructing sparse signals, as its objective is to minimize the error probability which describes…

Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or…

Bipartite networks are a natural representation of the interactions between entities from two different types. The organization (or topology) of such networks gives insight to understand the systems they describe as a whole. Here, we rely…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted…

An equiangular tight frame (ETF) yields a type of optimal packing of lines in a Euclidean space. ETFs seem to be rare, and all known infinite families of them arise from some type of combinatorial design. In this paper, we introduce a new…

Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…

We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show…

Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…

The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…

The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly…

Graph Neural Networks (GNNs) have shown great power in various domains. However, their predictions may inherit societal biases on sensitive attributes, limiting their adoption in real-world applications. Although many efforts have been…

This paper explores semi-supervised anomaly detection, a more practical setting for anomaly detection where a small additional set of labeled samples are provided. We propose a new KL-divergence based objective function for semi-supervised…

This is the fourth in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. In this…

Maximum eigenvalue detection (MED) is an important application of random matrix theory in spectrum sensing and signal detection. However, in small signal-to-noise ratio environment, the maximum eigenvalue of the representative signal is at…

Considering the constrained stochastic optimization problem over a time-varying random network, where the agents are to collectively minimize a sum of objective functions subject to a common constraint set, we investigate asymptotic…

Standard statistical learning theory predicts that Large Language Models (LLMs) should overfit because their parameter counts vastly exceed the number of training tokens. Yet, in practice, they generalize robustly. We propose that the…