Related papers: Efficient Symbolic Computation via Hash Consing
Current tabling systems suffer from an increase in space complexity, time complexity or both when dealing with sequences due to the use of data structures for tabled subgoals and answers and the need to copy terms into and from the table…
As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge…
We introduce Metatheory.jl: a lightweight and performant general purpose symbolics and metaprogramming framework meant to simplify the act of writing complex Julia metaprograms and to significantly enhance Julia with a native term rewriting…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable…
The remarkable advancements in artificial intelligence (AI), primarily driven by deep neural networks, are facing challenges surrounding unsustainable computational trajectories, limited robustness, and a lack of explainability. To develop…
This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the…
Neurosymbolic AI is an emerging compositional paradigm that fuses neural learning with symbolic reasoning to enhance the transparency, interpretability, and trustworthiness of AI. It also exhibits higher data efficiency making it promising…
Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to…
Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques…
We consider convex underestimators that are used in the global optimization {\alpha}BB method and its variants. The method is based by augmenting the original nonconvex function by a relaxation term that is derived from an interval…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
Neuro-symbolic AI systems integrate neural perception with symbolic reasoning to enable data-efficient, interpretable, and robust intelligence beyond purely neural models. Although this compositional paradigm has shown superior performance…
Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like…
Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
Neuro-symbolic artificial intelligence is a novel area of AI research which seeks to combine traditional rules-based AI approaches with modern deep learning techniques. Neuro-symbolic models have already demonstrated the capability to…
This paper compares Julia reduction and hyperbolic reduction with the aim of finding equivalent binary forms with minimal coefficients. We demonstrate that hyperbolic reduction generally outperforms Julia reduction, particularly in the…