FerVA: Faithful Expert Reconstruction and Visual Alignment

A compact space can represent every expert update yet exclude their best shared reconstruction. Task-specific input correlations reorient expert contributions, so storing every update need not preserve that optimum. For fixed statistics and expert supports, we establish when an input restriction is lossless and identify the unique minimal faithful space. The restriction loss lower-bounds every merge confined to that input span under the same reconstruction objective. Faithful Expert Reconstruction and Visual Alignment (FerVA) turns this distinction into a two-component method: a static language solve retains full input features in compact output coordinates, while a supervised visual calibrator learns through an auxiliary decoder and transfers a valid visual mixture to the constructed model. In a controlled six-task UCIT study, recovering the omitted component raises final average score (FAA) from 69.54 to 76.04. At correction rank 16, objective-guided recovery reaches 75.54 versus 71.18–71.33 for three random bases. The separate complete method leads reproduced merged baselines in FAA across four UCIT/DCL–backbone settings, reaching 76.20 on UCIT–LLaVA, 4.05 points above the strongest comparator. These results link reconstruction-faithful coordinates to task value in multimodal consolidation.