LOTUS: Evolving Multimodal Unlearning via Hyperbolic Entailment and Lorentz Transport

AbstractMultimodal Large Language Models (MLLMs) face critical privacy challenges due to the indiscriminate memorization of sensitive data. Existing unlearning methods, largely adapted from Euclidean paradigms, suffer from a geometric mismatch: they fail to disentangle specific instances from general concepts, causing catastrophic forgetting or unsafe substitution. We introduce LOTUS (Lorentz Transport for Unlearning Strategies), a framework for surgical semantic pruning within the Lorentz manifold. Leveraging hyperbolic geometry’s hierarchical nature, LOTUS employs an Inverted Entailment Cone Loss to sever the inheritance of sensitive concepts and a Lorentz Transport mechanism to align pruned features within the tangent space, ensuring compatibility with Euclidean backbones via a safety refusal prior. Experiments on MLLMU-Bench with LLaVA and Qwen show that LOTUS significantly outperforms baselines, effectively erasing targeted visual data while preserving general utility.