Related papers: On empirical cumulant generating functions of code…
It was recently shown that the lossless compression of a single source $X^n$ is achievable with a notion of strong locality; any $X_i$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error.…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
To guarantee that an LLM's outputs conform to a specified structure, context-free grammar (CFG) decoding engines force the selection of next tokens that produce strings that conform to a given CFG. While current CFG-constrained decoding…
In this paper, we present an extension to the recursive Gaussian Process (RGP) regression that enables the satisfaction of inequality constraints and is well suited for a real-time execution in control applications. The soft inequality…
We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE)…
We prove that all R\'enyi entanglement entropies of spin-chains described by generic (gapped), translational invariant matrix product states (MPS) are extensive for disconnected sub-systems: All R\'enyi entanglement entropy densities of the…
We propose a general-purpose approximation to the Ferguson-Klass algorithm for generating samples from L\'evy processes without Gaussian components. We show that the proposed method is more than 1000 times faster than the standard…
In this paper, we use the replica approach to study the R\'enyi entropy $S_L$ of generic locally excited states in (1+1)D CFTs, which are constructed from the insertion of multiple product of local primary operators on vacuum.…
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…
In this letter we study the weak-convergence properties of random variables generated by unsharp quantum measurements. More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit…
We propose a framework for joint entropy coding and encryption using Chaotic maps. We begin by observing that the message symbols can be treated as the symbolic sequence of a discrete dynamical system. For an appropriate choice of the…
Classifier-Free Guidance (CFG) has been a default technique in various visual generative models, yet it requires inference from both conditional and unconditional models during sampling. We propose to build visual models that are free from…
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…
Understanding the computational complexity of learning efficient classical programs in various learning models has been a fundamental and important question in classical computational learning theory. In this work, we study the…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…
The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for…
Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of single-user memoryless channels. Recently Polyanskiy et al. studied the benefit of variable-length feedback with termination (VLFT)…
We propose a method to study the secrecy constraints in key generation problems where side information might be present at untrusted users. Our method is inspired by a recent work of Hayashi and Tan who used the R\'enyi divergence as the…
We introduce a generic presentation of 'syntactic objects built by mixed induction and coinduction' encompassing all standard kinds of infinitary terms, as well as derivation trees in non-wellfounded proof systems. We then define a notion…
The proliferation of deep learning-based machine vision applications has given rise to a new type of compression, so called video coding for machine (VCM). VCM differs from traditional video coding in that it is optimized for machine vision…