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The practicality of reinforcement learning algorithms has been limited due to poor scaling with respect to the problem size, as the sample complexity of learning an $\epsilon$-optimal policy is $\tilde{\Omega}\left(|S||A|H^3 /…

Machine Learning · Computer Science 2023-06-12 Tyler Sam , Yudong Chen , Christina Lee Yu

We study the problem of extracting random bits from weak sources that are sampled by algorithms with limited memory. This model of small-space sources was introduced by Kamp, Rao, Vadhan and Zuckerman (STOC'06), and falls into a line of…

Computational Complexity · Computer Science 2021-08-25 Eshan Chattopadhyay , Jesse Goodman

In coding theory, a common question is to understand the threshold rates of various local properties of codes, such as their list decodability and list recoverability. A recent work Levi, Mosheiff, and Shagrithaya (FOCS 2025) gave a novel…

Information Theory · Computer Science 2025-10-16 Joshua Brakensiek , Yeyuan Chen , Manik Dhar , Zihan Zhang

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…

Methodology · Statistics 2022-05-04 Paris V. Giampouras , Athanasios A. Rontogiannis , Eleftherios Kofidis

Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as…

Machine Learning · Computer Science 2026-02-02 Pingzhi Tang , Ruijie Zhou , Fanxu Meng , Wenjie Pei , Muhan Zhang

It is well known that constructing codes with good parameters is one of the most important and fundamental problems in coding theory. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes…

Information Theory · Computer Science 2019-12-23 Lingfei Jin , Liming Ma , Chaoping Xing

In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…

Combinatorics · Mathematics 2021-02-23 Ran Tao , Tao Feng , Weicong Li

Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this…

Combinatorics · Mathematics 2023-09-22 Daniele Bartoli , Martino Borello , Giuseppe Marino

A combinatorial design is a family of sets that are almost disjoint, which is applied in pseudo random number generations and randomness extractions. The parameter, $\rho$, quantifying the overlap between the sets within the family, is…

Combinatorics · Mathematics 2013-01-11 Xiongfeng Ma , Zhen Zhang , Xiaoqing Tan

Large language models (LLM) have achieved remarkable performance across a wide range of tasks. However, their substantial parameter sizes pose significant challenges for deployment on edge devices with limited computational and memory…

Computation and Language · Computer Science 2025-12-16 Yu-Chen Lu , Sheng-Feng Yu , Hui-Hsien Weng , Pei-Shuo Wang , Yu-Fang Hu , Liang Hung-Chun , Hung-Yueh Chiang , Kai-Chiang Wu

Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide…

Combinatorics · Mathematics 2023-01-24 Daniele Bartoli , Martino Borello

Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…

Numerical Analysis · Mathematics 2020-11-30 Paul B. Rohrbach , Sergey Dolgov , Lars Grasedyck , Robert Scheichl

Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and…

Chemical Physics · Physics 2017-08-23 Cannada A. Lewis , Justus A. Calvin , Edward F. Valeev

The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and quantum-resistant cryptography. Linearized Reed-Solomon (LRS)…

Information Theory · Computer Science 2026-02-10 Kuo Shang , Chen Yuan , Ruiqi Zhu

We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…

Computational Complexity · Computer Science 2020-11-17 Venkatesan Guruswami , Chaoping Xing

The recent work of \cite{CRT,DonohoPol} rigorously proved (in a large dimensional and statistical context) that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of…

Information Theory · Computer Science 2013-04-02 Mihailo Stojnic

In [Frobenius1896] it was shown that many important properties of a finite group could be examined using formulas involving the character ratios of group elements, i.e., the trace of the element acting in a given irreducible representation,…

Representation Theory · Mathematics 2021-07-07 Shamgar Gurevich , Roger Howe

We study deterministic extractors for oblivious bit-fixing sources (a.k.a. resilient functions) and exposure-resilient functions with small min-entropy: of the function's n input bits, k << n bits are uniformly random and unknown to the…

Computational Complexity · Computer Science 2010-12-14 Yakir Reshef , Salil Vadhan

We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…

Numerical Analysis · Mathematics 2016-08-02 Glenn Byrenheid , Lutz Kämmerer , Tino Ullrich , Toni Volkmer

This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension…

Information Theory · Computer Science 2019-04-30 Jared Antrobus , Heide Gluesing-Luerssen