CS-VLM: Compressed Sensing Attention for Efficient Vision-Language Representation Learning

Vision-Language Models (vLLMs) have emerged as powerful architectures for joint reasoning over visual and textual inputs, enabling breakthroughs in image captioning, cross modal retrieval, and multimodal dialogue. However, as these models scale to longer video sequences and richer language descriptions, the quadratic complexity of the standard attention mechanism presents a fundamental computational bottleneck. This challenge is exacerbated in vLLMs, where attention must be computed not only within modalities but also across them, leading to prohibitive memory and latency costs. In this work, we introduce the Compressed Sensing Attention Transformer (CSAT), a novel architecture that reimagines attention computation through the lens of compressed sensing. By projecting high dimensional key and value representations into a lower-dimensional subspace via random measurement matrices and reconstructing the attention outputs using sparse recovery algorithms, CSAT significantly reduces attention complexity while maintaining semantic fidelity. Applied to vLLMs, CSAT exploits the inherent compressibility of both visual and textual representations especially evident in video, where temporal redundancy is high, and in language, where cross-modal grounding is often sparse. In contrast to LLMs, which must often model entangled symbolic dependencies, vLLMs benefit from structured sparsity in alignment and scene composition, making them particularly well-suited to compressed attention. We provide a formal mathematical treatment of CSAT, demonstrate its integration into vision language pipelines, and validate its performance on standard benchmarks, highlighting its promise as a scalable, interpretable, and resource efficient solution for next generation multimodal transformers.