Related papers: Iterated Straight-Line Programs
Large language models (LLMs) iteratively generate text token by token, with memory usage increasing with the length of generated token sequences. Since the request generation length is generally unpredictable, it is difficult to estimate…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Binary Integer Programming (BIP) problems are of interest due in part to the difficulty they pose and because of their various applications, including those in graph theory, combinatorial optimization and network optimization. In this note,…
Large language models (LLMs) enable strong text generation, and in general there is a practical tradeoff between fine-tuning and prompt engineering. We introduce Simplify-This, a comparative study evaluating both paradigms for text…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
Long prompt leads to huge hardware costs when using transformer-based Large Language Models (LLMs). Unfortunately, many tasks, such as summarization, inevitably introduce long documents, and the wide application of in-context learning…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…
Automating string transformations has been one of the killer applications of program synthesis. Existing synthesizers that solve this problem produce programs in domain-specific languages (DSL) that are engineered to help the synthesizer,…
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 propose a timed and soft extension of Concurrent Constraint Programming. The time extension is based on the hypothesis of bounded asynchrony: the computation takes a bounded period of time and is measured by a discrete global clock.…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We describe a technique to obtain linear descriptions for polytopes from extended formulations. The simple idea is to first define a suitable lifting function and then to find linear constraints that are valid for the polytope and guarantee…
Recent advancements in large language models (LLMs) have enabled their successful application to a broad range of tasks. However, in information-intensive tasks, the prompt length can grow fast, leading to increased computational…
Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…
Large language models (LLMs) are now used in multi-turn workflows, but we still lack a clear way to measure when iteration helps and when it hurts. We present an evaluation framework for iterative refinement that spans ideation, code, and…
The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…