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We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
Symbolic Regression (SR) offers an interpretable alternative to conventional Machine-Learning (ML) approaches, which are often criticized as ``black boxes''. In contrast to standard regression models that require a prescribed functional…
Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…
Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step"…
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Symbolic regression has recently gained traction in AI-driven scientific discovery, aiming to recover explicit closed-form expressions from data that reveal underlying physical laws. Despite recent advances, existing methods remain…
Probabilistic Regression Trees (PRTrees) generalize traditional decision trees by incorporating probability functions that associate each data point with different regions of the tree, providing smooth decisions and continuous responses.…
Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of…
Symbolic learning represents the most straightforward approach to interpretable modeling, but its applications have been hampered by a single structural design choice: the adoption of propositional logic as the underlying language.…
Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…
The field of Statistical Relational Learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which make them considerably…
Symbolic regression corresponds to an ensemble of techniques that allow to uncover an analytical equation from data. Through a closed form formula, these techniques provide great advantages such as potential scientific discovery of new…
Symbolic Regression (SR) plays a central role in scientific knowledge discovery by distilling mathematical equations from observational data. Most existing SR methods function within a bi-level optimization framework: an outer loop that…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
Symbolic Regression (SR) is a well-established framework for generating interpretable or white-box predictive models. Although SR has been successfully applied to create interpretable estimates of the average of the outcome, it is currently…
The goal in Symbolic Regression (SR) is to discover expressions that accurately map input to output data. Because often the intent is to understand these expressions, there is a trade-off between accuracy and the interpretability of…
Modern language models address complex questions through chain-of-thought (CoT) reasoning (Wei et al., 2023) and retrieval augmentation (Lewis et al., 2021), yet struggle with error propagation and knowledge integration. Tree-structured…
Recursive neural networks (RvNN) have been shown useful for learning sentence representations and helped achieve competitive performance on several natural language inference tasks. However, recent RvNN-based models fail to learn simple…