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arXiv · 2605.06477

GeoStack: A Framework for Quasi-Abelian Knowledge Composition in VLMs

Pranav Mantini·Shishir K. Shah
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Abstract

We address the challenge of knowledge composition in Vision-Language Models (VLMs), where accumulating expertise across multiple domains or tasks typically leads to catastrophic forgetting. We introduce GeoStack (Geometric Stacking), a modular framework that allows independently trained domain experts to be composed into a unified model. By imposing geometric and structural constraints on the adapter manifold, GeoStack ensures the foundational knowledge of the base model is preserved. Furthermore, we mathematically demonstrate a weight-folding property that achieves constant-time inference complexity ($O(1)$), regardless of the number of integrated experts. Experimental results across multi-domain adaptation and class-incremental learning show that GeoStack provides an efficient mechanism for long-term knowledge composition while significantly mitigating catastrophic forgetting. Code is available at https://github.com/QuantitativeImagingLaboratory/GeoStack.

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Pranav Mantini, Shishir K. Shah. 2026-05-07. GeoStack: A Framework for Quasi-Abelian Knowledge Composition in VLMs. https://arxiv.org/abs/2605.06477

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