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This paper explores the storage and retrieval of quantized key-value (KV) states in long-context autoregressive inference, proposing a novel archive format using contractive iterated-map codes. The method achieves lossless storage with linear time complexity, enabling O(1) random access and amortized appending, while significantly reducing the memory footprint of the KV cache by 36-54x compared to traditional fp16 caches. A key finding reveals that quantizing keys is approximately four times more detrimental than quantizing values, guiding a hybrid bit allocation strategy that optimizes performance while maintaining context integrity.
Archiving quantized KV states can shrink memory usage by up to 54x without sacrificing retrieval speed or accuracy.
The key-value (KV) cache dominates the memory cost of long-context autoregressive inference, and a growing body of work compresses it through quantization, eviction, or offloading. We study a complementary question: once a position's KV state has been quantized to codebook indices, how should the resulting symbol stream be stored, and can the storage layer do more than store? A family of contractive iterated-map codes that serialize a symbol sequence into a sequence of low-dimensional real vectors is revisited, and it is shown that they form a natural archive format for a quantized KV cache with the following features. The method provides exactly the access pattern a growing cache requires. It is lossless, it runs in linear time, and supports O(1) random access and O(1) amortized append. A controlled study of the quantizer feeding this archive is conducted on GPT-2 with 1024-token contexts. Keeping a small exact window (4 attention sinks + 32 recent tokens) and archiving the rest, per-head residual vector quantization reduces the archived cache by 36-54x relative to an fp16 cache at a perplexity cost of 11-15%, and we quantify a sharp key/value asymmetry -- quantizing keys is roughly 4x more damaging than quantizing values, consistent with prior low-bit KV work -- and use it to allocate bits in a hybrid scheme. Finally, we show the archive is simultaneously a search index: approximate substring queries execute directly on the stored vectors, and matched context is decoded from the matched vector without ever materializing the surrounding text. We release all code; every number reproduces from a single command on a laptop CPU.
