Multi-species acute toxicity assessment forms the basis for chemical classification, labelling and risk management. Existing deep learning methods struggle with diverse experimental conditions, imbalanced data, and scarce target data, hindering their ability to reveal endpoint associations and accurately predict data-scarce endpoints. Here we propose a machine learning paradigm, Adjoint Correlation Learning, for multi-condition acute toxicity assessment (ToxACoL) to address these challenges. ToxACoL models endpoint associations via graph topology and achieves knowledge transfer via graph convolution. The adjoint correlation mechanism encodes compounds and endpoints synchronously, yielding endpoint-aware and task-focused representations. Comprehensive analyses demonstrate that ToxACoL yields 43%-87% improvements for data-scarce human endpoints, while reducing training data by 70% to 80%. Visualization of the learned top-level representation interprets structural alert mechanisms. Filled-in toxicity values highlight potential for extrapolating animal results to humans. Finally, we deploy ToxACoL as a free web platform for rapid prediction of multi-condition acute toxicities.