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Drug addiction or drug overdose is a global public health crisis, and the design of anti-addiction drugs remains a major challenge due to intricate mechanisms. Since experimental drug screening and optimization are too time-consuming and expensive, there is urgent need to develop innovative artificial intelligence (AI) methods for addressing the challenge. We tackle this challenge by topology-inferred drug addiction learning (TIDAL) built from integrating topological Laplacian, deep bidirectional transformer, and ensemble-assisted neural networks (EANNs). The topological Laplacian is a novel algebraic topology tool that embeds molecular topological invariants and algebraic invariants into its harmonic spectra and non-harmonic spectra, respectively. These invariants complement sequence information extracted from a bidirectional transformer. We validate the proposed TIDAL framework on 22 drug addiction related, 4 hERG, and 12 DAT datasets, showing that TIDAL is a state-of-the-art framework for the modeling and analysis of drug addiction data. We carry out cross-target analysis of the current drug addiction candidates to alert their side effects and identify their repurposing potentials, revealing drugmediated linear and bilinear target correlations. Finally, TIDAL is applied to shed light on relative efficacy, repurposing potential, and potential side effects of 12 existing anti-addiction medications. Our results suggest that TIDAL provides a new computational strategy for pressingly-needed anti-substance addiction drug development.