Visual generative abductive learning studies jointly training symbol-grounded neural visual generator and inducing logic rules from data, such that after learning, the visual generation process is guided by the induced logic rules. A major challenge for this task is to reduce the time cost of logic abduction during learning, an essential step when the logic symbol set is large and the logic rule to induce is complicated. To address this challenge, we propose a pre-training method for obtaining meta-rule selection policy for the recently proposed visual generative learning approach AbdGen [Peng et al., 2023], aiming at significantly reducing the candidate meta-rule set and pruning the search space. The selection model is built based on the embedding representation of both symbol grounding of cases and meta-rules, which can be effectively integrated with both neural model and logic reasoning system. The pre-training process is done on pure symbol data, not involving symbol grounding learning of raw visual inputs, making the entire learning process low-cost. An additional interesting observation is that the selection policy can rectify symbol grounding errors unseen during pre-training, which is resulted from the memorization ability of attention mechanism and the relative stability of symbolic patterns. Experimental results show that our method is able to effectively address the meta-rule selection problem for visual abduction, boosting the efficiency of visual generative abductive learning.

Neuro-Symbolic (NeSy) AI could be regarded as an analogy to human dual-process cognition, modeling the intuitive System 1 with neural networks and the algorithmic System 2 with symbolic reasoning. However, for complex learning targets, NeSy systems often generate outputs inconsistent with domain knowledge and it is challenging to rectify them. Inspired by the human Cognitive Reflection, which promptly detects errors in our intuitive response and revises them by invoking the System 2 reasoning, we propose to improve NeSy systems by introducing Abductive Reflection (ABL-Refl) based on the Abductive Learning (ABL) framework. ABL-Refl leverages domain knowledge to abduce a reflection vector during training, which can then flag potential errors in the neural network outputs and invoke abduction to rectify them and generate consistent outputs during inference. ABL-Refl is highly efficient in contrast to previous ABL implementations. Experiments show that ABL-Refl outperforms state-of-the-art NeSy methods, achieving excellent accuracy with fewer training resources and enhanced efficiency.

Despite the great success of neural visual generative models in recent years, integrating them with strong symbolic reasoning systems remains a challenging task. There are two levels of symbol grounding problems among the core challenges: the first is symbol assignment, i.e. mapping latent factors of neural visual generators to semantic-meaningful symbolic factors from the reasoning systems by learning from limited labeled data. The second is rule learning, i.e. learning new rules that govern the generative process to enhance the symbolic reasoning systems. To deal with these two problems, we propose a neurosymbolic learning approach, Abductive visual Generation (AbdGen), for integrating logic programming systems with neural visual generative models based on the abductive learning framework. To achieve reliable and efficient symbol grounding, the quantized abduction method is introduced for generating abduction proposals by the nearest-neighbor lookup within semantic codebooks. To achieve precise rule learning, the contrastive meta-abduction method is proposed to eliminate wrong rules with positive cases and avoid less informative rules with negative cases simultaneously. Experimental results show that compared to the baseline approaches, AbdGen requires significantly less labeled data for symbol assignment. Furthermore, AbdGen can effectively learn underlying logical generative rules from data, which is out of the capability of existing approaches.

An important application of Synthetic Biology is the engineering of the host cell system to yield useful products. However, an increase in the scale of the host system leads to huge design space and requires a large number of validation trials with high experimental costs. A comprehensible machine learning approach that efficiently explores the hypothesis space and guides experimental design is urgently needed for the Design-Build-Test-Learn (DBTL) cycle of the host cell system. We introduce a novel machine learning framework ILP-iML1515 based on Inductive Logic Programming (ILP) that performs abductive logical reasoning and actively learns from training examples. In contrast to numerical models, ILP-iML1515 is built on comprehensible logical representations of a genome-scale metabolic model and can update the model by learning new logical structures from auxotrophic mutant trials. The ILP-iML1515 framework 1) allows high-throughput simulations and 2) actively selects experiments that reduce the experimental cost of learning gene functions in comparison to randomly selected experiments.

Neuro-symbolic hybrid systems are promising for integrating machine learning and symbolic reasoning, where perception models are facilitated with information inferred from a symbolic knowledge base through logical reasoning. Despite empirical evidence showing the ability of hybrid systems to learn accurate perception models, the theoretical understanding of learnability is still lacking. Hence, it remains unclear why a hybrid system succeeds for a specific task and when it may fail given a different knowledge base. In this paper, we introduce a novel way of characterising supervision signals from a knowledge base, and establish a criterion for determining the knowledge's efficacy in facilitating successful learning. This, for the first time, allows us to address the two questions above by inspecting the knowledge base under investigation. Our analysis suggests that many knowledge bases satisfy the criterion, thus enabling effective learning, while some fail to satisfy it, indicating potential failures. Comprehensive experiments confirm the utility of our criterion on benchmark tasks.

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.

In many real tasks there are human knowledge expressed in logic formulae as well as data samples described by raw features (e.g., pixels, strings). It is popular to apply SRL or PILPtechniques to exploit human knowledge through learning of symbolic data, or statistical learning techniques to learn from the raw data samples; however, it is often desired to directly exploit these logic formulae on raw data processing, like human beings utilizing knowledge to guide perception. In this paper, we propose an approach, LASIN, which combines Logical Abduction and Statistical Induction. The LASIN approach generates candidate hypotheses based on the abduction of first-order formulae, and then, the hypotheses are exploited as constraints for statistical induction. We apply theLASIN approach to the learning of representation of written primitives, where a primitive is a basic component in human writing. Our results show that the discovered primitives are reasonable for human perception, and these primitives, if used in learning tasks such as classification and domain adaptation, lead to better performances than simply applying feature learning based on raw data only.