相关论文: Strong data processing constant is achieved by bin…

We introduce a protocol called ENCORE which simultaneously compresses and encrypts data in a one-pass process that can be implemented efficiently and possesses a number of desirable features as a streaming encoder/decoder. Motivated by the…

Given a stochastic matrix $P$ partitioned in four blocks $P_{ij}$, $i,j=1,2$, Kemeny's constant $\kappa(P)$ is expressed in terms of Kemeny's constants of the stochastic complements $P_1=P_{11}+P_{12}(I-P_{22})^{-1}P_{21}$, and…

The strong-coupling constant is determined from the low-momentum region of the transverse-momentum distribution of $Z$ bosons produced through the Drell-Yan process, using predictions at third order in perturbative QCD. The analysis employs…

A $t$-spanner of a point set $X$ in a metric space $(\mathcal{X}, \delta)$ is a graph $G$ with vertex set $P$ such that, for any pair of points $u,v \in X$, the distance between $u$ and $v$ in $G$ is at most $t$ times $\delta(u,v)$. We…

Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the…

We present a new determination of the strong coupling constant $\alpha_s$ from a global QCD analysis CT25 of parton distribution functions (PDFs) that incorporates high-precision experimental measurements from the Run-2 of the Large Hadron…

We study the robustness of quantum computers under the influence of errors modelled by strictly contractive channels. A channel $T$ is defined to be strictly contractive if, for any pair of density operators $\rho,\sigma$ in its domain, $\|…

In 1952, von Neumann gave a series of groundbreaking lectures that proved it was possible for circuits consisting of 3-input majority gates that have a sufficiently small independent probability $\delta > 0$ of malfunctioning to reliably…

The principal inertia components of the joint distribution of two random variables $X$ and $Y$ are inherently connected to how an observation of $Y$ is statistically related to a hidden variable $X$. In this paper, we explore this…

For several communication models, the dispersive part of a communication channel is described by a bilinear operation $T$ between the possible sets of input signals and channel parameters. The received channel output has then to be…

We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory…

Synthetically-generated data plays an increasingly larger role in training large language models. However, while synthetic data has been found to be useful, studies have also shown that without proper curation it can cause LLM performance…

Scaling laws in language modeling traditionally quantify training loss as a function of dataset size and model parameters, providing compute-optimal estimates but often neglecting the impact of data quality on model generalization. In this…

In this paper, we study the averaging principle for a class of stochastic differential equations driven by $\alpha$-stable processes with slow and fast time-scales, where $\alpha\in(1,2)$. We prove that the strong and weak convergence order…

Data-processing is a desired property of classical and quantum divergences and information measures. In information theory, the contraction coefficient measures how much the distinguishability of quantum states decreases when they are…

Modern compression methods can summarize a target distribution $\mathbb{P}$ more succinctly than i.i.d. sampling but require access to a low-bias input sequence like a Markov chain converging quickly to $\mathbb{P}$. We introduce a new…

Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

This work studies the problem of constructing capacity-achieving codes from an algorithmic perspective. Specifically, we prove that there exists a Turing machine which, given a discrete memoryless channel $p_{Y|X}$, a target rate $R$ less…