Related papers: A Survey on the Local Divisor Technique

Diffusion large language models (dLLMs) represent a significant advancement in text generation, offering parallel token decoding capabilities. However, existing open-source implementations suffer from quality-speed trade-offs that impede…

The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…

A k-query Locally Decodable Code (LDC) encodes an n-bit message x as an N-bit codeword C(x), such that one can probabilistically recover any bit x_i of the message by querying only k bits of the codeword C(x), even after some constant…

A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…

Time series forecasting is critical across multiple domains, where time series data exhibit both local patterns and global dependencies. While Transformer-based methods effectively capture global dependencies, they often overlook short-term…

In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…

Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms…

We present a locality preserving loss (LPL) that improves the alignment between vector space embeddings while separating uncorrelated representations. Given two pretrained embedding manifolds, LPL optimizes a model to project an embedding…

This write-up contains some minor results and notes related to our work [HQ15] (some of them already known in the literature). In particular, it shows the following: - We show that a graph with polynomial expansion have sublinear…

Large language models (LLMs) have shown great promise for capturing contextual information in natural language processing tasks. We propose a novel approach to speaker diarization that incorporates the prowess of LLMs to exploit contextual…

Concurrent Kleene Algebra is an elegant tool for equational reasoning about concurrent programs. An important feature of concurrent programs that is missing from CKA is the ability to restrict legal interleavings. To remedy this we extend…

This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…

This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…

We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed…

Ben-Sasson and Sudan (RSA 2006) showed that repeated tensor products of linear codes with a very large distance are locally testable. Due to the requirement of a very large distance the associated tensor products could be applied only over…

Trickle-down is a phenomenon in high-dimensional expanders with many important applications -- for example, it is a key ingredient in various constructions of high-dimensional expanders or the proof of rapid mixing for the basis exchange…

In this paper, we propose a semi-supervised dictionary learning method that uses both the information in labelled and unlabelled data and jointly trains a linear classifier embedded on the sparse codes. The manifold structure of the data in…

The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with…

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…

We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that…