Related papers: Machine Learning meets Algebraic Combinatorics: A …
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
Model combination, often regarded as a key sub-field of ensemble learning, has been widely used in both academic research and industry applications. To facilitate this process, we propose and implement an easy-to-use Python toolkit, combo,…
Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset. As the size of datasets contemporary machine learning models rely on becomes…
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…
The evaluation of Large Language Models (LLMs) on mathematical reasoning has largely focused on elementary problems, competition-style questions, or formal theorem proving, leaving graduate-level and computational mathematics relatively…
The acquisition and performance of arithmetic skills and basic operations such as addition, subtraction, multiplication, and division are essential for daily functioning, and reflect complex cognitive processes. This paper explores the…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
While a real-world research program in mathematics may be guided by a motivating question, the process of mathematical discovery is typically open-ended. Ideally, exploration needed to answer the original question will reveal new…
With the recent rise of generative Artificial Intelligence (AI), the need of selecting high-quality dataset to improve machine learning models has garnered increasing attention. However, some part of this topic remains underexplored, even…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
The task of developing a machine learning (ML) model for a particular problem is inherently open-ended, and there is an unbounded set of possible solutions. Steps of the ML development pipeline, such as feature engineering, loss function…
A challenge in creating a dataset for machine reading comprehension (MRC) is to collect questions that require a sophisticated understanding of language to answer beyond using superficial cues. In this work, we investigate what makes…
Machine-learning from a disparate set of tables, a data lake, requires assembling features by merging and aggregating tables. Data discovery can extend autoML to data tables by automating these steps. We present an in-depth analysis of such…
Active learning is a practical field of machine learning that automates the process of selecting which data to label. Current methods are effective in reducing the burden of data labeling but are heavily model-reliant. This has led to the…
The Graph Brain Project is an experiment in how the use of automated mathematical discovery software, databases, large collaboration, and systematic investigation provide a model for how mathematical research might proceed in the future.…
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
Answer set programming is a leading declarative constraint programming paradigm with wide use for complex knowledge-intensive applications. Modern answer set programming languages support many equivalent ways to model constraints and…
Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors…