LLMs have demonstrated highly effective learning, human-like response generation,and decision-making capabilities in high-risk sectors. However, these models remain black boxes because they struggle to ensure transparency in responses. The literature has explored numerous approaches to address transparency challenges in LLMs, including Neurosymbolic AI (NeSy AI). NeSy AI approaches were primarily developed for conventional neural networks and are not well-suited to the unique features of LLMs. Consequently, there is a limited systematic understanding of how symbolic AI can be effectively integrated into LLMs. This paper aims to address this gap by first reviewing established NeSy AI methods and then proposing a novel taxonomy of symbolic integration in LLMs, along with a roadmap to merge symbolic techniques with LLMs. The roadmap introduces a new categorisation framework across four dimensions by organising existing literature within these categories. These include symbolic integration across various stages of LLM, coupling mechanisms, architectural paradigms, as well as algorithmic and application-level perspectives. The paper thoroughly identifies current benchmarks, cutting-edge advancements, and critical gaps within the field to propose a roadmap for future research. By highlighting the latest developments and notable gaps in the literature, it offers practical insights for implementing frameworks for symbolic integration into LLMs to enhance transparency.

Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method will be successful, and compare against the existing human-made heuristics (called guards) that perform this task in a leading CAS. We find the transformer can outperform these guards, gaining up to 30% accuracy and 70% precision. We further show that the inference time of the transformer is inconsequential which shows that it is well-suited to include as a guard in a CAS. Furthermore, we use Layer Integrated Gradients to interpret the decisions that the transformer is making. If guided by a subject-matter expert, the technique can explain some of the predictions based on the input tokens, which can lead to further optimisations.

Computer systems could also be smarter than people at some issues, however are they clever? The ultimate in our Computing turns 60 collection, to mark the sixtieth anniversary of the primary pc in an Australian college, seems at how clever the expertise has turn into. The time period "synthetic intelligence" (AI) was first used again in 1956 to explain the title of a workshop of scientists at Dartmouth, an Ivy League school in the US. At that pioneering workshop, attendees mentioned how computer systems would quickly carry out all human actions requiring intelligence, together with taking part in chess and different video games, composing nice music and translating textual content from one language to a different language. These pioneers had been wildly optimistic, although their aspirations had been unsurprising.

In this article, we describe some recent results and trends concerning hybrid neural symbolic systems based on a recent workshop on hybrid neural symbolic integration. The Neural Information Processing Systems (NIPS) workshop on hybrid neural symbolic integration, organized by Stefan Wermter and Ron Sun, was held on 4 to 5 December 1998 in Breckenridge, Colorado.

Three approaches to symbolic integration in the 1960's are described. The first, from artificial intelligence, led to Slagle's SAINT and to a large degree to Moses' SIN. The second, from algebraic manipulation, led to Manove's implementation and to Horowitz' and Tobey's reexamination of the Hermite algorithm for integrating rational functions. The third, from mathematics, led to Richardson's proof of the unsolvability of the problem for a class of functions and for Risch's decision procedure for the elementary functions. Generalizations of Risch's algorithm to a class of special functions and programs for solving differential equations and for finding the definite integral are also described.