Autoregressive decoding in large Transformer language models is frequently memory-bandwidth bound: each generated token reads and updates an ever-growing key--value (KV) cache. As context length and batch size increase, KV-cache storage and traffic can dominate inference cost, limiting throughput and deployment scalability. A common mitigation is to compress the KV cache by projecting per-head key and value matrices to a lower rank and storing only the projections. However, many post-training projection methods optimize proxy objectives such as variance preservation or reconstruction fidelity, which do not explicitly account for the end-to-end behavior of the decoder during generation. This thesis studies KV-cache compression from a functional perspective: can projection bases optimized to preserve decoder-layer outputs yield better memory--performance trade-offs than proxy-driven approximations? We propose a post-training framework in which lightweight predictors, trained offline on a calibration set while keeping the language model frozen, output orthonormal projection bases for keys and values.