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.

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.