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One of the fundamental limitations of Deep Neural Networks (DNN) is its inability to acquire and accumulate new cognitive capabilities. When some new data appears, such as new object classes that are not in the prescribed set of objects…
Some aspects of Computer Algebra (notably Computation Group Theory and Computational Number Theory) have some good databases of examples, typically of the form "all the X up to size n". But most of the others, especially on the polynomial…
This paper reviews past and ongoing efforts in using high-throughput ab-inito calculations in combination with machine learning models for materials design. The primary focus is on bulk materials, i.e., materials with fixed, ordered,…
For many use cases, combining information from different datasets can be of interest to improve a machine learning model's performance, especially when the number of samples from at least one of the datasets is small. However, a potential…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…
Recent advances in data science, machine learning, and artificial intelligence, such as the emergence of large language models, are leading to an increasing demand for data that can be processed by such models. While data sources are…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
Big data have the characteristics of enormous volume, high velocity, diversity, value-sparsity, and uncertainty, which lead the knowledge learning from them full of challenges. With the emergence of crowdsourcing, versatile information can…
Data-centric AI is at the center of a fundamental shift in software engineering where machine learning becomes the new software, powered by big data and computing infrastructure. Here software engineering needs to be re-thought where data…
Scientific datasets play a crucial role in contemporary data-driven research, as they allow for the progress of science by facilitating the discovery of new patterns and phenomena. This mounting demand for empirical research raises…
Despite the advancements in large language models (LLMs) for mathematical reasoning, solving competition-level math problems remains a significant challenge, especially for open-source LLMs without external tools. We introduce the MMIQC…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
The rapid expansion of data from diverse sources has made anomaly detection (AD) increasingly essential for identifying unexpected observations that may signal system failures, security breaches, or fraud. As datasets become more complex…
General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…
We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…