Recovering a Missing Modality in Multimodal QA via Low-Rank Completion

Multimodal question answering (MMQA) systems assume every modality is present at inference, yet in practice a modality is often missing—an imaging study is unavailable or a record is incomplete. We study counterfactual MMQA: answering as if the missing modality were present. We show this is a low-rank recovery problem and propose a pipeline organized around one principle, keep everything low rank: (i) the vision backbone is adapted with LoRA rather than fully finetuned; (ii) the missing modality is reconstructed by Robust-PCA matrix completion over the joint feature matrix; and (iii) a locality-sensitive hashing (LSH) twin index with a doubly-robust head gives sublinear, bias-corrected retrieval. On VQA-RAD, with all images missing our completion module retains 0.448 accuracy on image dependent questions, versus 0.045 for mean imputation and 0.000 for naive masking; on the full set it matches or exceeds the full-modality oracle. The effect hinges on a synergy: LoRA produces low-rank-structured features that are exactly what low-rank completion needs—under full fine-tuning the same completion does not help. We close with an explicit account of when cross modal completion can, and cannot, recover the missing signal.