Bandwidth constraints during signal acquisition frequently impede real-time detection applications. Hyperspectral data is a notable example, whose vast volume compromises real-time hyperspectral detection. To tackle this hurdle, we introduce a novel approach leveraging pre-acquisition modulation to reduce the acquisition volume. This modulation process is governed by a deep learning model, utilizing prior information. Central to our approach is LUM-ViT, a Vision Transformer variant. Uniquely, LUM-ViT incorporates a learnable under-sampling mask tailored for pre-acquisition modulation. To further optimize for optical calculations, we propose a kernel-level weight binarization technique and a three-stage fine-tuning strategy. Our evaluations reveal that, by sampling a mere 10\% of the original image pixels, LUM-ViT maintains the accuracy loss within 1.8\% on the ImageNet classification task. The method sustains near-original accuracy when implemented on real-world optical hardware, demonstrating its practicality. Code will be available at https://github.com/MaxLLF/LUM-ViT.