The Geometry of Compromise: Unlocking Generative Capabilities via Controllable Modality Alignment

The modality gap is intrinsic to multimodal alignment, where embeddings from different modalities remain partially separated in a shared representation space. In continual learning, CLIP-based vision-language models (VLMs) not only suffer catastrophic forgetting but also experience modality gap drift that disrupts the shared embedding geometry. Such drift degrades cross-modal alignment and generalization. We propose FPCD, an efficient framework combining Fast Null-space Projection (FNP) and Contrastive Distillation (CD). FNP accumulates compact Gram matrices of previous tasks' activations and projects gradients onto layer-adaptive approximate null spaces to reduce interference with learned representations. By replacing singular value decomposition with symmetric eigendecomposition, FNP accelerates projection-basis construction by a factor of 5-9. CD uses a small reference set to align the bidirectional image-to-text and text-to-image similarity distributions of the fine-tuned model with CLIP, thereby preserving pretrained cross-modal relations. On the 11-task MTIL benchmark, FPCD achieves 87.6% Last, 76.4% Average, and 65.2% Transfer. It also maintains more stable modality gaps and stronger zero-shot retrieval performance on COCO Captions and Flickr30k than competing methods. These results highlight the importance of controlling modality gap drift during continual adaptation of VLMs.

Contrastive vision-language models learn shared embedding spaces by aligning matched image-text pairs, yet their representations remain separated by a modality gap. Prior work reports divergent effects of modifying this gap: reducing it can improve zero-shot classification and cross-modal alignment, whereas removing gap-related structure can degrade image-text retrieval. In this paper, we provide a unified geometric explanation for these task-dependent effects. Across CLIP and SigLIP encoders, we find that a single dominant direction captures 94.4-99.9% of the squared norm of the image-text mean separation, revealing that the mean-separation component is approximately rank-one. A decomposition of the similarity score then identifies three task-specific roles. In zero-shot classification, query-side fixed gap-offset subtraction is exactly equivalent to an additive class bias. In standard cross-modal retrieval, projecting out the gap direction and renormalising residuals discards candidate-specific norm information, inducing a multiplicative ranking distortion; a geometry-derived exponent tracks the grid-search optimum (Spearman rho = 0.93) and restores performance in some settings, although the gains transfer unevenly. In mixed-modal retrieval, the gap direction sorts candidates by modality; its removal can improve cross-modal ranking, unlike random or non-gap controls. Residual semantic structure after removal defines the limits of the rank-one account. Together, these results explain why gap modification can improve, degrade, or restore performance across downstream settings. By clarifying when and why gap modification changes model behavior, this account provides a principled basis for selecting gap interventions in similarity-based vision-language systems across evaluated downstream tasks.

Vision-language models such as CLIP embed images and text in a shared space, where modality-specific distributions often remain separated. Existing accounts connect this modality gap to initialization, contrastive dynamics, and information imbalance, while its distributional and pairwise contributions to retrieval remain unresolved. We introduce UOT-Gap, a training-free variational diagnostic that models frozen image and text embeddings with unbalanced entropic optimal transport (UOT). The UOT optimum separates transport, coupling complexity, and marginal mass variation; a complementary pair-aware residual compares observed image-caption pairs with the UOT soft matching. On Flickr8K and COCO-1K with frozen CLIP, OpenCLIP, and SigLIP encoders, caption degradation reduces Flickr8K Recall@1 from 0.559 to 0.003. Across six dataset-model conditions, the pair-aware residual tracks retrieval degradation with mean absolute Spearman 0.973, compared with 0.392 for the mean gap. The association remains stable across five random COCO-1K subsets at $0.954\pm0.026$, with a minimum of 0.943. UOT barycentric updates reduce the transport objective while degrading retrieval, distinguishing geometric objective descent from task improvement. These results establish UOT-Gap as a diagnostic for caption quality, modality alignment, and retrieval robustness.