Decoder-only models generate tokens autoregressively by caching key/value vectors, but as the cache grows, inference becomes memory-bound. To address this issue, we introduce CLOVER (Cross-Layer Orthogonal Vectors), a novel approach that treats pairs of attention layers as a set of low-rank decompositions. CLOVER applies Singular Value Decomposition (SVD) to the ( Q )-( K ) and ( V )-( O ) pairs within each attention head. The resulting singular values can either guide pruning or serve as trainable parameters for efficient fine-tuning of all orthogonal vectors. After pruning or fine-tuning, these values are reintegrated into the model without increasing its parameter count. We apply CLOVER to various models, including GPT-2 XL, DeepSeek-V2-Lite, Whisper-Large-v3, Stable Diffusion XL, and LLaMA-3.2-11B-Vision. Our results demonstrate that CLOVER significantly improves pruning efficiency. For instance, the perplexity of pruning 70% of the ( Q )-( K ) pairs in GPT-2 XL is similar to that of pruning just 8% with vanilla methods. Fine-tuning the singular values further results in a full-rank update, outperforming state-of-the-art methods (LoRA, DoRA, HiRA, and PiSSA) by 7.6%, 5.5%, 3.8%, and 0.7%, respectively, on eight commonsense tasks for LLaMA-2 7B.