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We present a novel lossless universal source coding algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other…
Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximum-likelihood (ML) performance of short length $(\leq 256)$ RM codes. Recursive decoding employs the Plotkin construction to split the…
Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size $L$. Two asymptotic regimes are considered, the fixed list-size regime, where $L$ is fixed…
The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the…
Out-of-distribution (OOD) detection is essential for ensuring the reliability of deep learning models operating in open-world scenarios. Current OOD detectors mainly rely on statistical models to identify unusual patterns in the latent…
Why do larger language models generalize better? To investigate this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla…
Large Language Models (LLMs) are nowadays extensively used for various types of software engineering tasks, primarily code generation. Previous research has shown how suitable prompt engineering could help developers in improving their code…
This paper shows that the normalized maximum likelihood~(NML) code-length calculated in [1] is an upper bound on the NML code-length strictly calculated for the Gaussian Mixture Model. When we use this upper bound on the NML code-length, we…
Memorization in large language models poses critical risks for privacy and fairness as these systems scale to billions of parameters. While previous studies established correlations between memorization and factors like token frequency and…
Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…
This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $\epsilon$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The…
We prove the existence of codebooks for d-semifaithful lossy compression that are simultaneously universal with respect to both the class of finite-alphabet memoryless sources and the class of all bounded additive distortion measures. By…
Log-linear models are typically fitted to contingency table data to describe and identify the relationship between different categorical variables. However, the data may include observed zero cell entries. The presence of zero cell entries…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
The recent line of study on randomness extractors has been a great success, resulting in exciting new techniques, new connections, and breakthroughs to long standing open problems in several seemingly different topics. These include seeded…
A classic result in algorithmic information theory is that every infinite binary sequence is computable from a Martin-Loef random infinite binary sequence. Proved independently by Kucera and Gacs, this result answered a question by Charles…
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We…
Machine learning (ML) models for electronic structure typically rely on large datasets generated by computationally expensive Kohn-Sham density functional theory calculations, as it is not known a priori which portions of the data are…
We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…
Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel…