Don't be so Stief! Learning KV Cache low-rank approximation over the Stiefel manifold

Luca Benfenati; Matteo Risso; Andrea Vannozzi; Ahmet Caner Yüzügüler; Lukas Cavigelli; Enrico Macii; Daniele Jahier Pagliari; Alessio Burrello

arXiv · 2601.21686

Don't be so Stief! Learning KV Cache low-rank approximation over the Stiefel manifold

Luca Benfenati·Matteo Risso·Andrea Vannozzi·Ahmet Caner Yüzügüler·Lukas Cavigelli·Enrico Macii·Daniele Jahier Pagliari·Alessio Burrello

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Abstract

Key-value (KV) caching enables fast autoregressive decoding but at long contexts becomes a dominant bottleneck in High Bandwidth Memory (HBM) capacity and bandwidth. A common mitigation is to compress cached keys and values by projecting per-head matrices to a lower rank, storing only the projections in the HBM. However, existing post-training approaches typically fit these projections using SVD-style proxy objectives, which may poorly reflect end-to-end reconstruction after softmax, value mixing, and subsequent decoder-layer transformations. For these reasons, we introduce StiefAttention, a post-training KV-cache compression method that learns orthonormal projection bases by directly minimizing decoder-layer output reconstruction error. StiefAttention additionally constructs layer-wise error-rank profiles over candidate ranks, enabling sequential rank allocation under a user-specified KV cache budget. Notably, on Llama3-8B under the same conditions, StiefAttention outperforms EigenAttention by $4.2$ points on C4 perplexity and $8.9$ points on 0-shot MMLU accuracy at iso-compression, yielding lower relative error and higher cosine similarity with respect to the original decoder-layer outputs.

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Luca Benfenati, Matteo Risso, Andrea Vannozzi, Ahmet Caner Yüzügüler, Lukas Cavigelli, Enrico Macii, Daniele Jahier Pagliari, Alessio Burrello. 2026-01-29. Don't be so Stief! Learning KV Cache low-rank approximation over the Stiefel manifold. https://arxiv.org/abs/2601.21686

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