RE-TRIANGLE: Does TRIANGLE Enable Multimodal Alignment Beyond Cosine Similarity in Retrieval?

Different machine learning models can represent the same underlying concept in different ways. This variability is particularly valuable for in-the-wild multimodal retrieval, where the objective is to identify the corresponding representation in one modality given another modality as input. This challenge can be effectively framed as a representation alignment problem. For example, given a sentence encoded by a language model, retrieve the most semantically aligned image based on representations produced by an image encoder, or vice versa. To gain insights into the performance impact of different metrics, embedding spaces, and representation alignment for retrieval tasks, we first empirically investigate the geometric relationships between visual and textual embeddings derived from both vision-language models and combined unimodal models. We then align these representations using four standard similarity metrics as well as two learned ones, implemented via neural networks of different architectures with varying losses across multiple benchmarks. Our experimental findings indicate that cosine similarity consistently outperforms all the investigated metrics in representation alignment tasks, and that Wasserstein distance provides a complementary perspective on cross-modal distributional differences. We also observe that our proposed custom contrastive loss is advantageous over the MSE loss for aligning image and text representations, for both multilayer perceptrons and transformer-based models. Taken together, our findings offer novel insights and practical considerations for researchers working in multimodal information retrieval, particularly in real-world, cross-modal applications. Our code is publicly available.

Multimodal retrieval integrates video, audio, subtitles, and text; however, recent geometric aggregators, such as Gramian volumes, hyperbolic volumes, and spectral objectives, treat all modalities symmetrically. Under a unified evaluation protocol, their joint scores frequently lag behind the strongest single-modality pathway by 1.9 to 27.6 R@1. Controlled analyses attribute this outcome to uniform modality influence. This work introduces Spherical Centroid Aggregation with Learned Adaptive Relevance (SCALAR), a query-conditioned aggregator that assigns relevance-based weights to each available modality before computing a spherical centroid. SCALAR accommodates arbitrary modality subsets and is trained on masked, reduced-arity views using rank-8 LoRA adapters. Across five benchmarks, SCALAR achieves positive aggregation gain on four, reaching +4.0 R@1, while none of the evaluated prior aggregators is positive on more than one. A uniform-weight ablation reproduces the degradation observed with symmetric aggregation. With only 4.8 million trainable parameters, SCALAR attains the highest text-to-video R@1 on three and performs within seed variation of the best result on a fourth. Under test-time modality dropout, SCALAR's representation-stage score surpasses the released GRAM checkpoint at every evaluated masking rate and benchmark by 3.2 to 10.9 R@1. Finally, as modalities are removed, rerankers trained exclusively on complete modality sets increasingly converge toward their video-only pathways, diminishing these representation-level gains and underscoring a limitation of standard two-stage retrieval pipelines.

Training multimodal large language models has long been limited by the scarcity of high-quality paired multimodal data. Recent studies show that the shared representation space of pretrained multimodal contrastive models can serve as a bridge, enabling models to perform multimodal training with unimodal data. However, the key premise of this paradigm remains insufficiently understood: can representations from different modalities be reliably interchanged? The core obstacle lies in the persistent Modality Gap in the shared space. In this work, we revisit the geometric nature of the modality gap. We find that modality representations already share compatible dominant semantic geometry. What truly hinders modality interchangeability is not a simple global shift, but an anisotropic residual structure concentrated along a small number of dominant directions. Based on this finding, we further propose the principle of anisotropic modality gap alignment: effective modality alignment should align with the target-modality distribution while preserving the semantic structure of the source modality. Guided by this principle, we propose an anisotropic geometric correction framework, AnisoAlign, for unpaired modality alignment. This framework leverages the internal geometric prior of the target modality and performs bounded correction on source-modality representations, thereby constructing substitute representations in the target modality. Experiments confirm its benefits in both geometric diagnostics and text-only MLLM training. Overall, this work recasts the modality gap from an empirical observation into a correctable, structured geometric phenomenon and provides a new representation alignment perspective for training multimodal models with unimodal data.