LOTUS: Evolving Multimodal Unlearning via Hyperbolic Entailment and Lorentz Transport

Multimodal Large Language Models (MLLMs) face critical privacy challenges arising from the indiscriminate memorization of sensitive data. Existing unlearning methods often fail to precisely disentangle specific instances from general concepts, leading to either catastrophic forgetting of useful knowledge or unsafe content substitution. We attribute these failures to a fundamental geometric mismatch: these approaches primarily operate in Euclidean space, which lacks the capacity to model the hierarchical entailment inherent in visual-linguistic concepts. To address this, we introduce LOTUS (LOrentz Transport for Unlearning Strategies), a framework that performs surgical semantic pruning within the Lorentz manifold. LOTUS employs an Inverted Entailment Cone Loss to sever the semantic inheritance of sensitive concepts and a Lorentz Transport mechanism to align pruned features with a safety refusal prior in the tangent space. Extensive experiments on MLLMU-Bench demonstrate that LOTUS significantly outperforms baselines, improving unlearning efficacy by over 9% on LLaVA compared to state-of-the-art constraint-based methods. Crucially, LOTUS achieves this precision while maintaining general utility, effectively resolving the dilemma between thorough erasure and model stability.