When Is Prior Knowledge Helpful? Exploring the Evaluation and Selection of Unsupervised Pretext Tasks from a Neuro-Symbolic Perspective

Neuro-symbolic (Nesy) learning improves the target task performance of models by enabling them to satisfy knowledge, while semi/self-supervised learning (SSL) improves the target task performance by designing unsupervised pretext tasks for unlabeled data to make models satisfy corresponding assumptions. We extend the Nesy theory based on reliable knowledge to the scenario of unreliable knowledge (i.e., assumptions), thereby unifying the theoretical frameworks of SSL and Nesy. Through rigorous theoretical analysis, we demonstrate that, in theory, the impact of pretext tasks on target performance hinges on three factors: knowledge learnability with respect to the model, knowledge reliability with respect to the data, and knowledge completeness with respect to the target. We further propose schemes to operationalize these theoretical metrics, and thereby develop a method that can predict the effectiveness of pretext tasks in advance. This will change the current status quo in practical applications, where the selections of unsupervised tasks are heuristic-based rather than theory-based, and it is difficult to evaluate the rationality of unsupervised pretext task selection before testing the model on the target task. In experiments, we verify a high correlation between the predicted performance-estimated using minimal data-and the actual performance achieved after large-scale semi-supervised or self-supervised learning, thus confirming the validity of the theory and the effectiveness of the evaluation method.

Curriculum Abductive Learning

Abductive Learning (ABL) integrates machine learning with logical reasoning in a loop: a learning model predicts symbolic concept labels from raw inputs, which are revised through abduction using domain knowledge and then fed back for retraining. However, due to the nondeterminism of abduction, the training process often suffers from instability, especially when the knowledge base is large and complex, resulting in a prohibitively large abduction space. While prior works focus on improving candidate selection within this space, they typically treat the knowledge base as a static black box. In this work, we propose Curriculum Abductive Learning (C-ABL), a method that explicitly leverages the internal structure of the knowledge base to address the ABL training challenges. C-ABL partitions the knowledge base into a sequence of sub-bases, progressively introduced during training. This reduces the abduction space throughout training and enables the model to incorporate logic in a stepwise, smooth way. Experiments across multiple tasks show that C-ABL outperforms previous ABL implementations, significantly improves training stability, convergence speed, and final accuracy, especially under complex knowledge setting.

Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible

The current Neuro-Symbolic (NeSy) Learning paradigm suffers from an over-reliance on labeled data. If we completely disregard labels, it leads to less symbol information, a larger solution space, and more shortcuts-issues that current Nesy systems cannot resolve. This paper introduces a novel learning paradigm, Verification Learning (VL), which addresses this challenge by transforming the label-based reasoning process in Nesy into a label-free verification process. VL achieves excellent learning results solely by relying on unlabeled data and a function that verifies whether the current predictions conform to the rules. We formalize this problem as a Constraint Optimization Problem (COP) and propose a Dynamic combinatorial Sorting (DCS) algorithm that accelerates the solution by reducing verification attempts, effectively lowering computational costs to the level of a Constraint Satisfaction Problem (CSP). To further enhance performance, we introduce a prior alignment method to address potential shortcuts. Our theoretical analysis points out which tasks in Nesy systems can be completed without labels and explains why rules can replace infinite labels, such as in addition, for some tasks, while for others, like Sudoku, the rules have no effect. We validate the proposed framework through several fully unsupervised tasks including addition, sort, match, and chess, each showing significant performance and efficiency improvements.

Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection

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.