相关论文: Additive Atomic Forests for Symbolic Function and …

Standard dense retrievers lack a native calculus for multi-atom logical constraints. We introduce Neuro-Symbolic Fuzzy Logic (NSFL), a framework that adapts formal t-norms and t-conorms to neural embedding spaces without requiring…

Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…

This article is concerned with a data-driven divide-and-conquer strategy to construct symbolic abstractions for interconnected control networks with unknown mathematical models. We employ a notion of alternating bisimulation functions (ABF)…

Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is…

Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is…

Large Language Models (LLMs) have shown remarkable reasoning performance but struggle with multi-step deductive reasoning involving a series of rule application steps, especially when rules are presented non-sequentially. Our preliminary…

We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search…

A new ensemble framework for interpretable model called Linear Iterative Feature Embedding (LIFE) has been developed to achieve high prediction accuracy, easy interpretation and efficient computation simultaneously. The LIFE algorithm is…

Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…

We demonstrate a library for the integration of domain knowledge in deep learning architectures. Using this library, the structure of the data is expressed symbolically via graph declarations and the logical constraints over outputs or…

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…

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…

This paper extends the classical Ostrogradsky-Hermite reduction for rational functions to more general functions in primitive extensions of certain types. For an element $f$ in such an extension $K$, the extended reduction decomposes $f$ as…

This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the disagreement coefficient for…

Neural-symbolic approaches to machine learning incorporate the advantages from both connectionist and symbolic methods. Typically, these models employ a first module based on a neural architecture to extract features from complex data.…

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression…

In multi-label learning, each instance is associated with multiple labels and the crucial task is how to leverage label correlations in building models. Deep neural network methods usually jointly embed the feature and label information…

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…

Retrieval-augmented generation (RAG) has been widely adopted to ground large language models (LLMs) in external knowledge, yet it remains largely underexplored for improving reasoning. Existing methods either rely on online exploration…

Meadows are a sort of commutative rings with a multiplicative identity element and a total multiplicative inverse operation. In this paper we study algebraic properties of common meadows, which are meadows that introduce, as the inverse of…