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Packing and shuffling tokens is a common practice in training auto-regressive language models (LMs) to prevent overfitting and improve efficiency. Typically documents are concatenated to chunks of maximum sequence length (MSL) and then…

We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild…

A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…

Code Large Language Models (CLLMs) have exhibited outstanding performance in program synthesis, attracting the focus of the research community. The evaluation of CLLM's program synthesis capability has generally relied on manually curated…

The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order $k$ have a particularly simple structure.…

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space $\mathbb{R}^d$ across length scales is an outstanding challenge in physics, chemistry, and…

Spectral variability significantly impacts the accuracy and convergence of hyperspectral unmixing algorithms. Many methods address complex spectral variability; yet large-scale distortions to the scale of the observed pixel signatures due…

Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this…

We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…

We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…

Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…

This study investigates Hermitian rank-metric codes, a special class of rank-metric codes, focusing on perfect codes and on the analysis of their covering properties. Firstly, we establish bounds on the size of spheres in the space of…

In this work we study the list-decoding size of Reed-Muller codes. Given a received word and a distance parameter, we are interested in bounding the size of the list of Reed-Muller codewords that are within that distance from the received…

Transferring the optimal learning rate from small to large neural networks can enable efficient training at scales where hyperparameter tuning is otherwise prohibitively expensive. To this end, the Maximal Update Parameterization (muP)…

We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of…

Metamorphic testing (TM) examines the relations between inputs and outputs of test runs. These relations are known as metamorphic relations (MR). Currently, MRs are handpicked and require in-depth knowledge of the System Under Test (SUT),…

Local rank modulation scheme was suggested recently for representing information in flash memories in order to overcome drawbacks of rank modulation. For $0 < s\leq t\leq n$ with $s$ divides $n$, an $(s,t,n)$-LRM scheme is a local rank…

Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…

Large language models (LLMs) exhibit remarkable multilingual capabilities despite the extreme language imbalance in the pre-training data. In this paper, we closely examine the reasons behind this phenomenon, focusing on the pre-training…

A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…