Related papers: Properties of maximum Lempel-Ziv complexity string…
We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization,…
The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…
We put robust upper limits on the average cosmological density \Omega_s of cosmic strings based on the variability properties of a large homogeneous sample of SDSS quasars. We search for an excess of characteristic variations of quasar…
This paper studies the limits of language models' statistical learning in the context of Zipf's law. First, we demonstrate that Zipf-law token distribution emerges irrespective of the chosen tokenization. Second, we show that Zipf…
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
We present an algorithm which computes the Lempel-Ziv factorization of a word $W$ of length $n$ on an alphabet $\Sigma$ of size $\sigma$ online in the following sense: it reads $W$ starting from the left, and, after reading each $r =…
We propose a new representation of the offsets of the Lempel-Ziv (LZ) factorization based on the co-lexicographic order of the processed prefixes. The selected offsets tend to approach the k-th order empirical entropy. Our evaluations show…
We propose a new approach for calculating the Lempel-Ziv factorization of a string, based on run length encoding (RLE). We present a conceptually simple off-line algorithm based on a variant of suffix arrays, as well as an on-line algorithm…
Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and…
Large extra dimensions, of size of order of TeV^{-1} ~= 10^{-16} cm, arise naturally in the context of supersymmetry breaking in string theory, while strings at a TeV scale offer a solution to the gauge hierarchy problem, as an alternative…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
Leptoquarks extending the Standard Model (SM) are attracting an increasing attention in the recent literature. Hence, the identification of 4D SM-like models and the classification of allowed leptoquarks from strings is an important step in…
In this article we examine the appearance of tensionless strings in M-Theory. We subsequently interpret these tensionless strings in a String Theory context. In particular, we examine tensionless strings appearing in M-Theory on $S^{1}$,…
We propose and study a family of universal sequential probability assignments on individual sequences, based on the incremental parsing procedure of the Lempel-Ziv (LZ78) compression algorithm. We show that the normalized log loss under any…
This work investigates the resilience of contemporary large language models (LLMs) against frequent character-level perturbations. We examine three types of character-level perturbations including introducing numerous typos within words,…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
Lossless data compression has been widely studied in computer science. One of the most widely used lossless data compressions is Lempel-Zip(LZ) 77 parsing, which achieves a high compression ratio. Bidirectional (a.k.a. macro) parsing is a…