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Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
The key to success in machine learning (ML) is the use of effective data representations. Traditionally, data representations were hand-crafted. Recently it has been demonstrated that, given sufficient data, deep neural networks can learn…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
Machine learning (ML) is believed to be an effective and efficient tool to build reliable prediction model or extract useful structure from an avalanche of data. However, ML is also criticized by its difficulty in interpretation and…
Deep learning models are favored in many research and industry areas and have reached the accuracy of approximating or even surpassing human level. However they've long been considered by researchers as black-box models for their…
Lample and Charton (2019) describe a system that uses deep learning technology to compute symbolic, indefinite integrals, and to find symbolic solutions to first- and second-order ordinary differential equations, when the solutions are…
The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their…
Can Machine Learning (ML) autonomously recover interpretable mathematical structure from raw numerical data? We aim to answer this question using the classification of real-root configurations of polynomials up to degree five as a…
Tree-structured multi-task architectures have been employed to jointly tackle multiple vision tasks in the context of multi-task learning (MTL). The major challenge is to determine where to branch out for each task given a backbone model to…
Recently, deep neural networks have expanded the state-of-art in various scientific fields and provided solutions to long standing problems across multiple application domains. Nevertheless, they also suffer from weaknesses since their…
Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…
We propose a hybrid architecture that integrates decision tree-based symbolic reasoning with the generative capabilities of large language models (LLMs) within a coordinated multi-agent framework. Unlike prior approaches that loosely couple…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
We propose a novel method for automatic program synthesis. P-Tree Programming represents the program search space through a single probabilistic prototype tree. From this prototype tree we form program instances which we evaluate on a given…
Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…
Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic…
Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical…