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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.\n  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 pr","title":"Spectral-LSH: Sub-Quadratic Prompt Compression via Krylov-Projected Locality-Sensitive Hashing","url":"https://arxiv.org/abs/2607.19368","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.19368v1 Announce Type: new \nAbstract: 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.\n  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. 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