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The grounding bottleneck poses one of the key challenges that hinders the widespread adoption of Answer Set Programming in industry. Hybrid Grounding is a step in alleviating the bottleneck by combining the strength of standard bottom-up…
Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which…
Student repetition in secondary education imposes significant resource burdens, particularly in resource-constrained contexts. Addressing this challenge, this study introduces a unified machine learning framework that simultaneously…
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…
Geometric morphometrics (GMM) is widely used to quantify shape variation, more recently serving as input for machine learning (ML) analyses. Standard practice aligns all specimens via Generalized Procrustes Analysis (GPA) prior to splitting…
"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…
Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large…
We present a method for generating possible proofs of a query with respect to a given Answer Set Programming (ASP) rule set using an abductive process where the space of abducibles is automatically constructed just from the input rules…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
This study aims to determine a predictive model to learn students probability to pass their courses taken at the earliest stage of the semester. To successfully discover a good predictive model with high acceptability, accurate, and…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the…
We present the Theorem Prover Museum, and initiative to conserve -- and make publicly available -- the sources and source-related artefacts of automated reasoning systems. Theorem provers have been at the forefront of Artificial…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
Student performance prediction is one of the most important subjects in educational data mining. As a modern technology, machine learning offers powerful capabilities in feature extraction and data modeling, providing essential support for…