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This paper presents an artificial intelligence algorithm that can be used to derive formulas from various scientific disciplines called automatic derivation machine. First, the formula is abstractly expressed as a multiway tree model, and…
Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…
A tree functional is called additive if it satisfies a recursion of the form $F(T) = \sum_{j=1}^k F(B_j) + f(T)$, where $B_1,\ldots,B_k$ are the branches of the tree $T$ and $f(T)$ is a toll function. We prove a general central limit…
We propose a symbolic generative task description language and a corresponding inference engine capable of representing arbitrary multimodal tasks as structured symbolic flows. Unlike conventional generative models that rely on large-scale…
We consider the formulation of a symbolic execution (SE) procedure for functional programs that interact with effectful, opaque libraries. Our procedure allows specifications of libraries and abstract data type (ADT) methods that are…
Artificial intelligence (AI) has emerged as a transformative force across industries, driven by advances in deep learning and natural language processing, and fueled by large-scale data and computing resources. Despite its rapid adoption,…
Manuscript symbols can be stored, recognized and retrieved from an entropic digital memory that is associative and distributed but yet declarative; memory retrieval is a constructive operation, memory cues to objects not contained in the…
We investigate notions of complete representation by partial functions, where the operations in the signature include antidomain restriction and may include composition, intersection, update, preferential union, domain, antidomain, and set…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
Growing interest in modelling complex systems from brains to societies to cities using networks has led to increased efforts to describe generative processes that explain those networks. Recent successes in machine learning have prompted…
Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to…
Deep code generation is a topic of deep learning for software engineering (DL4SE), which adopts neural models to generate code for the intended functions. Since end-to-end neural methods lack domain knowledge and software hierarchy…
There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…
Despite significant progress in the development of neural-symbolic frameworks, the question of how to integrate a neural and a symbolic system in a \emph{compositional} manner remains open. Our work seeks to fill this gap by treating these…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Search trees are fundamental data structures in computer science. We study functionals on random search trees that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal…
This paper introduces a novel supervised classification strategy that integrates functional data analysis (FDA) with tree-based methods, addressing the challenges of high-dimensional data and enhancing the classification performance of…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
We propose an unsupervised tree boosting algorithm for inferring the underlying sampling distribution of an i.i.d. sample based on fitting additive tree ensembles in a fashion analogous to supervised tree boosting. Integral to the algorithm…
Tree ensemble models like random forests and gradient boosting machines are widely used in machine learning due to their excellent predictive performance. However, a high-performance ensemble consisting of a large number of decision trees…