Hao-Yuan He

Abductive Learning (ABL) is a promising framework for integrating sub-symbolic perception and logical reasoning through abduction. In this case, the abduction process provides supervision for the perception model from the background knowledge. Nevertheless, this process naturally contains uncertainty, since the knowledge base may be satisfied by numerous potential candidates. This implies that the result of the abduction process, i.e., a set of candidates, is ambiguous; both correct and incorrect candidates are mixed in this set. The prior art of abductive learning selects the candidate that has the minimal inconsistency of the knowledge base. However, this method overlooks the ambiguity in the abduction process and is prone to error when it fails to identify the correct candidates. To address this, we propose Ambiguity-Aware Abductive Learning (A3BL), which evaluates all potential candidates and their probabilities, thus preventing the model from falling into sub-optimal solutions. Both experimental results and theoretical analyses prove that A3BL markedly enhances ABL by efficiently exploiting the ambiguous abduced supervision.

Integrating logical reasoning and machine learning by approximating logical inference with differentiable operators is a widely used technique in the field of Neuro-Symbolic Learning. However, some differentiable operators could introduce significant biases during backpropagation, which can degrade the performance of Neuro-Symbolic systems. In this paper, we demonstrate that the loss functions derived from fuzzy logic operators commonly exhibit a bias, referred to as Implication Bias. To mitigate this bias, we propose a simple yet efficient method to transform the biased loss functions into Reduced Implication-bias Logic Loss (RILL). Empirical studies demonstrate that RILL outperforms the biased logic loss functions, especially when the knowledge base is incomplete or the supervised training data is insufficient.

Since acquiring perfect supervision is usually difficult, real-world machine learning tasks often confront inaccurate, incomplete, or inexact supervision, collectively referred to as weak supervision. In this work, we present WSAUC, a unified framework for weakly supervised AUC optimization problems, which covers noisy label learning, positive-unlabeled learning, multi-instance learning, and semi-supervised learning scenarios. Within the WSAUC framework, we first frame the AUC optimization problems in various weakly supervised scenarios as a common formulation of minimizing the AUC risk on contaminated sets, and demonstrate that the empirical risk minimization problems are consistent with the true AUC. Then, we introduce a new type of partial AUC, specifically, the reversed partial AUC (rpAUC), which serves as a robust training objective for AUC maximization in the presence of contaminated labels. WSAUC offers a universal solution for AUC optimization in various weakly supervised scenarios by maximizing the empirical rpAUC. Theoretical and experimental results under multiple settings support the effectiveness of WSAUC on a range of weakly supervised AUC optimization tasks.