Association Rule Mining (ARM) is the task of mining patterns among data features in the form of logical rules, with applications across a myriad of domains. However, high-dimensional datasets often result in an excessive number of rules, increasing execution time and negatively impacting downstream task performance. Managing this rule explosion remains a central challenge in ARM research. To address this, we introduce Aerial+, a novel neurosymbolic ARM method. Aerial+ leverages an under-complete autoencoder to create a neural representation of the data, capturing associations between features. It extracts rules from this neural representation by exploiting the model's reconstruction mechanism. Extensive evaluations on five datasets against seven baselines demonstrate that Aerial+ achieves state-of-the-art results by learning more concise, high-quality rule sets with full data coverage. When integrated into rule-based interpretable machine learning models, Aerial+ significantly reduces execution time while maintaining or improving accuracy.