Related papers: Coding over Core Models
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
We survey recent generalizations and improvements of the linear programming method that involve semidefinite programming. A general framework using group representations and tools from graph theory is provided.
In the first paper of this two part communication, we solved in a unified framework a variety of two terminal source coding problems with noncooperative encoders, thereby consolidating works of Shannon, Slepian-Wolf, Wyner,…
Positional Encodings (PEs) are used to inject word-order information into transformer-based language models. While they can significantly enhance the quality of sentence representations, their specific contribution to language models is not…
Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can…
The notion of a KU-valued function on a set is introduced and related properties are investigated. Codes generated by KU-valued functions are established. Moreover, we will provide an algorithm which allows us to find a KU-algebra starting…
In this article we extend the theory of the binary codes (the strict code $\mathcal{K}$ and the extended code $\mathcal{K}'$), associated to a projective nodal surface, to a coding theory for normal surfaces, with special consideration of…
We investigate techniques for designing modulation/coding schemes for the wireless two-way relaying channel. The relay is assumed to have perfect channel state information, but the transmitters are assumed to have no channel state…
We investigate a few aspects of the notion of Levi core, introduced by the authors in a previous work: a basic finiteness question, the connections with Kohn's algorithm and with Catlin's property (P).
Pre-trained models of code built on the transformer architecture have performed well on software engineering (SE) tasks such as predictive code generation, code summarization, among others. However, whether the vector representations from…
In this paper we collect some open set-theoretic problems that appear in the large-scale topology (called also Asymptology). In particular we ask problems about critical cardinalities of some special (large, indiscrete, inseparated) coarse…
The foundations of mathematics have long been considered settled by the Zermelo-Fraenkel-Choice axioms. But set theory abounds in models with different truths and even classical questions such as the measurability of projective sets can…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…
For language models to generalize correctly to novel expressions, it is critical that they exploit access compositional meanings when this is justified. Even if we don't know what a "pelp" is, we can use our knowledge of numbers to…
These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory,…
In this paper, we investigate a novel family of polar codes based on multi-kernel constructions, proving that this construction actually polarizes. To this end, we derive a new and more general proof of polarization, which gives sufficient…
We observe that the notion of two sets being equal up to finitely many elements is a homotopy equivalence relation in a model category, and suggest a homotopy-invariant variant of Generalised Continuum Hypothesis about which more can be…
Large language models (LLMs) have shown impressive performance in \emph{code} understanding and generation, making coding tasks a key focus for researchers due to their practical applications and value as a testbed for LLM evaluation. Data…
The notion of source polarization is introduced and investigated. This complements the earlier work on channel polarization. An application to Slepian-Wolf coding is also considered. The paper is restricted to the case of binary alphabets.…
In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar…