LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important applications in machine learning applications such as classification, bioinformatics, and noisy learning. We study LP-type problems in several streaming and distributed big data models, giving ε-approximation linear sketching algorithms with a focus on the high accuracy regime with low dimensionality d, that is, when d < (1/ε)^0.999. Our main result is an O(ds) pass algorithm with O(s(√d/ε)^{3d/s}) ⋅ poly(d, log (1/ε)) space complexity in words, for any parameter s ∈ [1, d log (1/ε)], to solve ε-approximate LP-type problems of O(d) combinatorial and VC dimension. Notably, by taking s = d log (1/ε), we achieve space complexity polynomial in d and polylogarithmic in 1/ε, presenting exponential improvements in 1/ε over current algorithms. We complement our results by showing lower bounds of (1/ε)^Ω(d) for any 1-pass algorithm solving the (1 + ε)-approximation MEB and linear SVM problems, further motivating our multi-pass approach.

An emerging area of research in situated and multimodal interactive conversations (SIMMC) includes interactions in scientific papers. Since scientific papers are primarily composed of text, equations, figures, and tables, SIMMC methods must be developed specifically for each component to support the depth of inquiry and interactions required by research scientists. This work introduces $Conversational Papers$ (cPAPERS), a dataset of conversational question-answer pairs from reviews of academic papers grounded in these paper components and their associated references from scientific documents available on arXiv. We present a data collection strategy to collect these question-answer pairs from OpenReview and associate them with contextual information from $LaTeX$ source files. Additionally, we present a series of baseline approaches utilizing Large Language Models (LLMs) in both zero-shot and fine-tuned configurations to address the cPAPERS dataset.