Deep learning neural networks, constructed for the prediction of chemical binding at 79 pharmacologically important human biological targets, show extremely high performance on test data (accuracy 92.2 ± 4.2%, MCC 0.814 ± 0.093 and ROC-AUC 0.96 ± 0.04). A new molecular similarity measure, Neural Network Activation Similarity, has been developed, based on signal propagation through the network. This is complementary to standard Tanimoto similarity, and the combined use increases confidence in the computer's prediction of activity for new chemicals by providing a greater understanding of the underlying justification. The in silico prediction of these human molecular initiating events is central to the future of chemical safety risk assessment and improves the efficiency of safety decision making.