Modern foundation models such as large language models (LLMs) and large multi-modal models (LMMs) require a massive amount of computational and memory resources. We propose a new framework to convert such LLMs/LMMs into a reduced-dimension latent structure. Our method extends a local activation-aware tensor decomposition to a global attention-aware joint tensor de-composition. Our framework can significantly improve the model accuracy over the existing model compression methods when reducing the latent dimension to realize computationally/memory-efficient LLMs/LLMs. We show the benefit on several benchmark including multi-modal reasoning tasks.