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

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…

In the paper, we present the ADD-Lib, our efficient and easy to use framework for Algebraic Decision Diagrams (ADDs). The focus of the ADD-Lib is not so much on its efficient implementation of individual operations, which are taken by other…

We introduce Exhaustive Symbolic Integration (ESI), a method that enumerates all symbolic functions up to a given complexity $k$ within a specified operator basis and determines which admit closed-form antiderivatives within the same class.…

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…

We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein…

Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and programs with high complexity or on…

The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high…

Simon's factorization theorem is a celebrated tool in algebraic automata theory, providing bounded-depth decompositions of words with respect to morphisms into finite semigroups. We develop an analogue of Simon's theorem for \emph{forests}…

Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models. We introduce Latent Grammar Flow (LGF), a…

We consider the additive decomposition problem in primitive towers and present an algorithm to decompose a function in an S-primitive tower as a sum of a derivative in the tower and a remainder which is minimal in some sense. Special…

We are interested in neurosymbolic systems consisting of a high-level symbolic layer for explainable prediction in terms of human-intelligible concepts; and a low-level neural layer for extracting symbols required to generate the symbolic…

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…

Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite the emerging application of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain…

In this study, we present an incremental machine learning framework called Adaptive Decision Forest (ADF), which produces a decision forest to classify new records. Based on our two novel theorems, we introduce a new splitting strategy…

Feature transformation enhances data representation by deriving new features from the original data. Generative AI offers potential for this task, but faces challenges in stable generation (consistent outputs) and valid generation…

We introduce Functional Group-Aware Representations for Small Molecules (FARM), a novel foundation model designed to bridge the gap between SMILES, natural language, and molecular graphs. The key idea behind FARM is the incorporation of…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

Modern neural networks rely on generic activation functions (ReLU, GELU, SiLU) that ignore the mathematical structure inherent in scientific data. We propose Neuro-Symbolic Activation Discovery, a framework that uses Genetic Programming to…