# Spectral-LSH: Sub-Quadratic Prompt Compression via Krylov-Projected Locality-Sensitive Hashing

> Source: <https://arxiv.org/abs/2607.19368>
> Published: 2026-07-23 04:00:00+00:00

arXiv:2607.19368v1 Announce Type: new
Abstract: Long-prompt inference remains expensive because prefill attention scales quadratically with sequence length. We propose Spectral-LSH, a training-free prompt compression method that operates before the prompt enters the language model. Spectral-LSH approximates the dominant components of an implicit attention-kernel operator using a Krylov subspace method together with random features, avoiding explicit $O(N^2)$ attention-kernel materialization. It then applies SimHash in the resulting attention eigenspace to group similar tokens and aggregate them into macro-tokens with causal positional assignments.
We evaluate Mistral-7B-Instruct-v0.3, Qwen2.5-7B-Instruct, and Qwen2.5-14B-Instruct on C4. Our experiments reveal a compression-ratio phase transition. Below $\rho = 4 \times$, local token redundancy is low enough that lightweight chunking typically provides the best latency--quality trade-off. Above $\rho = 8 \times$, the spectral path preserves quality that chunking loses. At $\rho = 16 \times$, Qwen2.5-7B (adaptive) reduces the PPL ratio from 353.409 to 196.963, while Qwen2.5-14B (adaptive) reduces it from 9.533 to 3.427.
On a small long-context structured stress test containing JSON-like, code-like, and table-like inputs, local LSH also improves every metric over chunking at $8 \times$. The adaptive backend captures both regimes by using the chunk path at low compression and spectral clustering at high compression, although chunking remains the fastest backend in total latency.