Abstract
In self-supervised learning, a third modality should improve, or at least preserve, performance. Across nine image-text-tabular datasets, we show that it instead harms performance: the trimodal model underperforms its own best bimodal subset in 55.6% of paired runs under VICReg. The same failure occurs in 51.1% of paired runs under SimSiam. We call this failure multimodal saturation. We propose that the failure lies in the alignment geometry. Riemannian VICReg (R-VICReg) generalizes classical VICReg: it aligns views by squared geodesic distance on learnable negative-curvature product factors and recovers VICReg exactly as curvature vanishes. Over the same 45 paired runs, R-VICReg raises the probability that the third modality helps from 44.4% to 64.4%, with gains concentrated where VICReg saturates.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Ben Abbes, N., Le, D. H., Mtibaa, S., & Nguyen, V. T. (2026). On the Geometry of Multimodal Saturation: Riemannian VICReg. https://omanscience.com/en/articles/on-the-geometry-of-multimodal-saturation-riemannian-vicreg
MLA 9
Ben Abbes, Nessim, et al. "On the Geometry of Multimodal Saturation: Riemannian VICReg." https://omanscience.com/en/articles/on-the-geometry-of-multimodal-saturation-riemannian-vicreg.
Chicago (author–date)
Ben Abbes, Nessim, Duc Han Le, Sabri Mtibaa, and Van-Tam Nguyen. 2026. "On the Geometry of Multimodal Saturation: Riemannian VICReg." https://omanscience.com/en/articles/on-the-geometry-of-multimodal-saturation-riemannian-vicreg.
Harvard
Ben Abbes, N., Le, D. H., Mtibaa, S. and Nguyen, V. T. (2026) 'On the Geometry of Multimodal Saturation: Riemannian VICReg', Available at: https://omanscience.com/en/articles/on-the-geometry-of-multimodal-saturation-riemannian-vicreg.
Vancouver
Ben Abbes N, Le DH, Mtibaa S, Nguyen VT. On the Geometry of Multimodal Saturation: Riemannian VICReg. https://omanscience.com/en/articles/on-the-geometry-of-multimodal-saturation-riemannian-vicreg
IEEE
N. Ben Abbes, D. H. Le, S. Mtibaa, and V. T. Nguyen, "On the Geometry of Multimodal Saturation: Riemannian VICReg," https://omanscience.com/en/articles/on-the-geometry-of-multimodal-saturation-riemannian-vicreg.