One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with the ability of deep learning to learn from raw data. However, most current approaches require manually engineered symbolic knowledge, and where end-to-end training is considered, such approaches are either restricted to learning definite programs, or are restricted to training binary neural networks. In this paper, we introduce Neuro-Symbolic Inductive Learner (NSIL), an approach that trains a general neural network to extract latent concepts from raw data, whilst learning symbolic knowledge that maps latent concepts to target labels. The novelty of our approach is a method for biasing the learning of symbolic knowledge, based on the in-training performance of both neural and symbolic components. We evaluate NSIL on three problem domains of different complexity, including an NP-complete problem. Our results demonstrate that NSIL learns expressive knowledge, solves computationally complex problems, and achieves state-of-the-art performance in terms of accuracy and data efficiency. Code and technical appendix: https://github.com/DanCunnington/NSIL

The application of Artificial Intelligence (AI) to synthetic biology will provide the foundation for the creation of a high throughput automated platform for genetic design, in which a learning machine is used to iteratively optimise the system through a design-build-test-learn (DBTL) cycle. However, mainstream machine learning techniques represented by deep learning lacks the capability to represent relational knowledge and requires prodigious amounts of annotated training data. These drawbacks strongly restrict AI's role in synthetic biology in which experimentation is inherently resource and time intensive. In this work, we propose an automated biodesign engineering framework empowered by Abductive Meta-Interpretive Learning ($Meta_{Abd}$), a novel machine learning approach that combines symbolic and sub-symbolic machine learning, to further enhance the DBTL cycle by enabling the learning machine to 1) exploit domain knowledge and learn human-interpretable models that are expressed by formal languages such as first-order logic; 2) simultaneously optimise the structure and parameters of the models to make accurate numerical predictions; 3) reduce the cost of experiments and effort on data annotation by actively generating hypotheses and examples. To verify the effectiveness of $Meta_{Abd}$, we have modelled a synthetic dataset for the production of proteins from a three gene operon in a microbial host, which represents a common synthetic biology problem.

For many reasoning-heavy tasks, it is challenging to find an appropriate end-to-end differentiable approximation to domain-specific inference mechanisms. Neural-Symbolic (NeSy) AI divides the end-to-end pipeline into neural perception and symbolic reasoning, which can directly exploit general domain knowledge such as algorithms and logic rules. However, it suffers from the exponential computational complexity caused by the interface between the two components, where the neural model lacks direct supervision, and the symbolic model lacks accurate input facts. As a result, they usually focus on learning the neural model with a sound and complete symbolic knowledge base while avoiding a crucial problem: where does the knowledge come from? In this paper, we present Abductive Meta-Interpretive Learning ($Meta_{Abd}$), which unites abduction and induction to learn perceptual neural network and first-order logic theories simultaneously from raw data. Given the same amount of domain knowledge, we demonstrate that $Meta_{Abd}$ not only outperforms the compared end-to-end models in predictive accuracy and data efficiency but also induces logic programs that can be re-used as background knowledge in subsequent learning tasks. To the best of our knowledge, $Meta_{Abd}$ is the first system that can jointly learn neural networks and recursive first-order logic theories with predicate invention.