Related papers: Multihead Finite-State Compression
A binary string of length $2^k$ induces the Boolean function of $k$ variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The…
We present two examples of finite-alphabet, infinite excess entropy processes generated by invariant hidden Markov models (HMMs) with countable state sets. The first, simpler example is not ergodic, but the second is. It appears these are…
As a fundamental data format representing spatial information, depth map is widely used in signal processing and computer vision fields. Massive amount of high precision depth maps are produced with the rapid development of equipment like…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
This paper studies a singular limit problem for a reduced model for compressible non-resistive MHD which was first introduced in \cite{Li-Sun_JDE, Li-Sun} in a two-dimensional setting. This system can also be related to a certain class of…
This work studies the joint design of precoding and backhaul compression strategies for the downlink of cloud radio access networks. In these systems, a central encoder is connected to multiple multi-antenna base stations (BSs) via…
Magic state distillation is a crucial yet resource-intensive process in fault-tolerant quantum computation. The protocol's overhead, defined as the number of input magic states required per output magic state with an error rate below…
Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to…
Computing problems that handle large amounts of data necessitate the use of lossless data compression for efficient storage and transmission. We present a novel lossless universal data compression algorithm that uses parallel computational…
The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…
Neural data compression has been shown to outperform classical methods in terms of $RD$ performance, with results still improving rapidly. At a high level, neural compression is based on an autoencoder that tries to reconstruct the input…
Learning-based lossless image compression employs pixel-based or subimage-based auto-regression for probability estimation, which achieves desirable performances. However, the existing works only consider context dependencies in one…
A hypothesis class admits a sample compression scheme, if for every sample labeled by a hypothesis from the class, it is possible to retain only a small subsample, using which the labels on the entire sample can be inferred. The size of the…
We describe lossless quantum compression of unknown mixtures (of non-orthogonal states) and give an expression of the optimal rate of compression.
Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize…
A new compression method called difference-Huffman coding (DHC) is introduced in this paper. It is verified empirically that DHC results in a smaller multidimensional physical representation than those for other previously published…
While neural lossy compression techniques have markedly advanced the efficiency of Channel State Information (CSI) compression and reconstruction for feedback in MIMO communications, efficient algorithms for more challenging and practical…
Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…