Related papers: Multihead Finite-State Compression
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…
Consider the problem of predicting the next symbol given a sample path of length n, whose joint distribution belongs to a distribution class that may have long-term memory. The goal is to compete with the conditional predictor that knows…
The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and…
Omni-modal Large Language Models (Omni-LLMs) have demonstrated strong capabilities in audio-video understanding tasks. However, their reliance on long multimodal token sequences leads to substantial computational overhead. Despite this…
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number…
Suppose there is a large file which should be transmitted (or stored) and there are several (say, m) admissible data-compressors. It seems natural to try all the compressors and then choose the best, i.e. the one that gives the shortest…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
This paper describes the conversion of a Hidden Markov Model into a finite state transducer that closely approximates the behavior of the stochastic model. In some cases the transducer is equivalent to the HMM. This conversion is especially…
This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…
Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find…
This paper focuses on reducing memory usage in enumerative model checking, while maintaining the multi-core scalability obtained in earlier work. We present a tree-based multi-core compression method, which works by leveraging sharing among…
Existing compression methods typically focus on the removal of signal-level redundancies, while the potential and versatility of decomposing visual data into compact conceptual components still lack further study. To this end, we propose a…
We consider a variation of the Wyner-Ziv problem pertaining to lossy compression of individual sequences using finite-state encoders and decoders. There are two main results in this paper. The first characterizes the relationship between…
The Run Length Encoding (RLE) compression method is a long standing simple lossless compression scheme which is easy to implement and achieves a good compression on input data which contains repeating consecutive symbols. In its pure form…
Modern language models are trained almost exclusively on token sequences produced by a fixed tokenizer, an external lossless compressor often over UTF-8 byte sequences, thereby coupling the model to that compressor. This work introduces…
Human mathematics (HM), the mathematics humans discover and value, is a vanishingly small subset of formal mathematics (FM), the totality of all valid deductions. We argue that HM is distinguished by its compressibility through…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…