SPICY-KV: SPectral Invariant Coarse-graining with dYadic KV Renormalization for 28.6x–50.0x LLM Context Compression

PATENT PENDING (United States USPTO & Canada CIPO Patent Applications Filed — Claims 1–20; International PCT Priority Reserved). Author: Yuge Y (Elithia Technologies — Commercial Licensing, IP Acquisition & Independent R&D Inquiries: [email protected]).Code & Benchmarks: https://github.com/Yuge-Y/SPICY-KV | https://huggingface.co/ElithiaTechnologies/SPICY-KV Abstract: We introduce SPICY-KV (SPectral Invariant Coarse-graining with dYadic KV renormalization, also disclosed as AMG-KV), a thermodynamic and spectral multigrid framework for variable-resolution compression of Large Language Model (LLM) Key-Value (KV) caches. Existing KV compression methods rely either on discrete token eviction (SnapKV, PyramidKV, H2O, StreamingLLM)—which suffers from observation-window blindness and Softmax partition function collapse—or on post-RoPE token merging (KVMerger, CaM)—which triggers destructive trigonometric phase interference across sequence indices. SPICY-KV resolves both limitations by: (1) lifting cached keys into a phase-decoupled (pre-RoPE), two-level step-moderated mean-centered conceptual manifold; (2) detecting Inter-Block Harmonic Bridge Hubs and shielding contiguous bound-value token spans via a causal 1D dilation filter; (3) executing Hybrid Algebraic Multigrid (C/F) Splitting into exact fine-resolution landmark tokens (C-points) and mass-conserving coarse macro-nodes (F-aggregates); and (4) calibrating multi-scale attention via a first-order logarithmic mass offset log(m_m) and a second-order subgrid variance cumulant closure that analytically closes the Softmax Jensen Inequality Gap. Across 8 experimental phases on DeepSeek-R1-Distill-Qwen-1.5B and DeepSeek-R1-Distill-Qwen-7B—including the NVIDIA RULER benchmark suite—SPICY-KV achieves 100.0% (1.5B) and 91.7% (7B) RULER recall at 28.6x compression (3.5% KV), and 87.5% (1.5B) and 66.7% (7B) recall at 50.0x compression (2.0% KV).