Rotated Tucker residual for outlier-resistant KV quantization

Integrate this into the KV-cache write path for every layer and separately for K and V. Maintain Tucker factors for the selected backbone, compute the reconstructed block X_tilde, and form R=X-X_tilde for each incoming token block. Use a fixed fast orthogonal transform on the residual feature dimension: a normalized Hadamard transform is suitable when the feature width is a power of two, while a randomized orthogonal matrix can be used for an offline prototype. Partition the rotated residual into blocks of 64 or 128 values. For each block, compute s=max(abs(Y))/(2^(b-1)-1), store the scale s and integer codes clip(round(Y/s), -2^(b-1), 2^(b-1)-1). Decode by multiplying codes by s, applying the inverse orthogonal transform, and adding X_tilde. For b=0, skip residual storage and return only the Tucker reconstruction. Log block maxima, scale variance, residual MSE, and attention-output error before and after rotation; norm preservation is guaranteed mathematically, whereas quantization improvement must be measured. Start with a small one-layer test and then full Mistral-7B inference at equal residual bit-width and equal total bytes. Compare direct residual quantization, rotated residual quantization, direct 4-bit KV, and FP16 KV on perplexity, long-context retrieval, decode throughput, transform overhead, and peak memory. Success is lower cache reconstruction error and smaller perplexity degradation at 2- or 4-bit residual precision without making the transform bandwidth dominate attention.