Related papers: Generalized Straight-Line Programs
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
Large Language Models (LLMs) have demonstrated impressive abilities in symbol processing through in-context learning (ICL). This success flies in the face of decades of critiques asserting that artificial neural networks cannot master…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
We examine the speech modeling potential of generative spoken language modeling (GSLM), which involves using learned symbols derived from data rather than phonemes for speech analysis and synthesis. Since GSLM facilitates textless spoken…
Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved…
In this paper we develop efficient first-order algorithms for the generalized trust-region subproblem (GTRS), which has applications in signal processing, compressed sensing, and engineering. Although the GTRS, as stated, is nonlinear and…
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…
Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…
The performance of Large Language Models (LLMs) relies heavily on the quality of prompts, which are often manually engineered and task-specific, making them costly and non-scalable. We propose a novel approach, Supervisory Prompt Training…
While Large Language Models (LLMs) have achieved remarkable performance in many tasks, much about their inner workings remains unclear. In this study, we present novel experimental insights into the resilience of LLMs, particularly GPT-4,…
The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…
Given a sequence $S$ of length $n$, a letter-duplicated subsequence is a subsequence of $S$ in the form of $x_1^{d_1}x_2^{d_2}\cdots x_k^{d_k}$ with $x_i\in\Sigma$, $x_j\neq x_{j+1}$ and $d_i\geq 2$ for all $i$ in $[k]$ and $j$ in $[k-1]$.…
We demonstrate the ability of large language models (LLMs) to perform iterative self-improvement of robot policies. An important insight of this paper is that LLMs have a built-in ability to perform (stochastic) numerical optimization and…
In 2009, a lossless compression algorithm based on 1D chaotic maps known as Generalized Lur\"{o}th Series (or GLS) has been proposed. This algorithm (GLS-coding) encodes the input message as a symbolic sequence on an appropriate 1D chaotic…
Explicit chain-of-thought (CoT) reasoning substantially improves the reasoning ability of large language models (LLMs), but incurs high inference cost due to lengthy autoregressive traces. Existing latent reasoning methods offer a promising…
We initiate the study of sub-linear sketching and streaming techniques for estimating the output size of common dictionary compressors such as Lempel-Ziv '77, the run-length Burrows-Wheeler transform, and grammar compression. To this end,…
We investigate the generalization properties of dense text embeddings when the embedding backbone is a large language model (LLM) versus when it is a non-LLM encoder, and we study the extent to which spherical linear interpolation (SLERP)…
A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…
Sign Language Production (SLP) is a challenging task, given the limited resources available and the inherent diversity within sign data. As a result, previous works have suffered from the problem of regression to the mean, leading to…
We prove that for any $\varepsilon>0$, a non-deterministic Turing machine $\mathcal{T}$ with time complexity $T(n)$ can be emulated by an $S$-machine with time and space complexities at most $T(n)^{1+\varepsilon}$ and $T(n)$, respectively.…