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

• URL: http://arxiv.org/abs/2601.21686v1
• Date: Thu, 29 Jan 2026 13:19:24 GMT
• Title: Don't be so Stief! Learning KV Cache low-rank approximation over the Stiefel manifold
• Authors: Luca Benfenati, Matteo Risso, Andrea Vannozzi, Ahmet Caner Yüzügüler, Lukas Cavigelli, Enrico Macii, Daniele Jahier Pagliari, Alessio Burrello,
• Abstract summary: StiefAttention is a KV-cache compression method that learns emphorthonormal projection bases by directly minimizing output reconstruction error.<n>It outperforms EigenAttention by $11.9$ points on C4 perplexity and $5.4%$ on 0-shot MMLU accuracy at iso-compression, lower relative error and higher cosine similarity with respect to the original decoder-layer outputs.
• Score: 7.162701793686856
• License: http://creativecommons.org/licenses/by/4.0/
• 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 matrixes 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 \emph{orthonormal} projection bases by directly minimizing \emph{decoder-layer output reconstruction error}. StiefAttention additionally precomputes, for each layer, an error-rank profile over candidate ranks, enabling flexible layer-wise rank allocation under a user-specified error budget. Noteworthy, on Llama3-8B under the same conditions, StiefAttention outperforms EigenAttention by $11.9$ points on C4 perplexity and $5.4\%$ 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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