Related papers: The Random Subsequence Model and Uniform Codes for…

Recently, Hopfield and Krotov introduced the concept of {\em dense associative memories} [DAM] (close to spin-glasses with $P$-wise interactions in a disordered statistical mechanical jargon): they proved a number of remarkable features…

We study the problem of strong coordination of the actions of two nodes $X$ and $Y$ that communicate over a discrete memoryless channel (DMC) such that the actions follow a prescribed joint probability distribution. We propose two novel…

Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight…

The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a…

In this work, we present a variant of the multilayer random sequential adsorption (RSA) process that is inspired by orthogonal resource sharing in wireless communication networks. In the one-dimensional (1D) version of this variant, the…

We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A of pairs (a_i,w_i) for i = 1,..,n and w_i>0, a segment A(i,j) is a consecutive subsequence of A starting with index i and ending with…

In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected…

We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…

A major bottleneck of standard auto-regressive large language models is that their inference process is inherently sequential, resulting in very long and costly inference times. To circumvent this, practitioners proposed a class of language…

Neural networks with random weights appear in a variety of machine learning applications, most prominently as the initialization of many deep learning algorithms and as a computationally cheap alternative to fully learned neural networks.…

The problem of reconstructing a source sequence with the presence of decoder side-information that is mis-synchronized to the source due to deletions is studied in a distributed source coding framework. Motivated by practical applications,…

We introduce the following natural generalization of trace reconstruction, parameterized by a deletion probability $\delta \in (0,1)$ and length $n$: There is a length $n$ string of probabilities, $S=p_1,\ldots,p_n,$ and each "trace" is…

We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…

This paper presents a neural network filter method based on contraction operators to address model collapse in recursive training of generative models. Unlike \cite{xu2024probabilistic}, which requires superlinear sample growth…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

The continuous random energy model (CREM) is a toy model of spin glasses on $\{0,1\}^N$ that, in the limit, exhibits an infinitely hierarchical correlation structure. We give two polynomial-time algorithms to approximately sample from the…

We consider a channel-independent decoder which is for i.i.d. random codes what the maximum mutual-information decoder is for constant composition codes. We show that this decoder results in exactly the same i.i.d. random coding error…

Using historical data to predict future events has many applications in the real world, such as stock price prediction; the robot localization. In the past decades, the Convolutional long short-term memory (LSTM) networks have achieved…

We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours…

The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required…