Tensor Decomposition of Transformer Key-Value Caches: Spectral Structure and Format Comparison
The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers. We measure the singular-value spectra of all four mode unfoldings on Mistral-7B-v0.3 and LLaMA-2-13B and compare four standard tensor decompositions: Tucker, CP, tensor train, and t-SVD, at matched storage. The spectra partition the four axes into two classes. The token and feature modes carry low-rank structure, particularly for keys. The head and layer modes are nearly full-rank and resist compression at any practical error level. Among the four decompositions, Tucker achieves the lowest reconstruction error at every compression r...
| Authors | Rahul Krishnan, Volker Schulz |
|---|---|
| Primary category | math.NA |
| Published | 23 September 2026 |
| Last updated at source | 23 September 2026 |
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