We propose \textbf{Hurwitz Quaternion Multiplicative Quantization (HQMQ)}, a \textbf{calibration-free} method for KV cache compression of large language models. HQMQ treats each 4-element chunk of K or V as a quaternion and quantizes its unit direction to the \emph{product} qp⋅qs, where qp ranges over the 24-element Hurwitz group 2T (the 24 vertices of the 24-cell on S3, pairwise angle 60∘) and qs ranges over a per-(layer, head) secondary codebook of S \emph{random} unit quaternions. The multiplicative composition yields 24S effective codewords at S stored parameters; random initialization suffices because left-multiplication is an S3 isometry, so seeded codebooks vary in end-task ppl by <1.5%. A per-batch median-multiplier outlier extraction step (C=3, no calibration) handles modern outlier-heavy architectures. We evaluate on five modern open models: Mistral-7B (dense MHA), Llama-3-8B and Qwen2.5-7B and Qwen3-8B (dense GQA), and gpt-oss-20b (sparse MoE). On Mistral-7B and Qwen3-8B, HQMQ matches fp16 within 0.02--0.03 ppl points at ∼5 bits. On Qwen2.5-7B and Qwen3-8B, where naive int4 collapses to 104+ ppl, HQMQ + Med3× recovers fp16 quality within 0.02--0.10 ppl points at ∼5 bits. HQMQ Pareto-dominates naive int by 3--1900× at matched bits across all five models, and downstream zero-shot accuracy matches fp16 at 3.79 bits on Mistral. Against the strongest calibrated KV-quantization baseline, HQMQ at 3.79 bits matches KIVI-4 (∼4.5 bits) within ∼1 pt on CoQA, 0.6 pts on TruthfulQA, and 2.3 pts on GSM8K, at 16% fewer bits and without a calibration pass. At the storage level, HQMQ delivers up to 5.05× KV compression, shrinking a Llama-3-70B 128k-context cache from 43 GB to 8.5 GB.
Large language models cache all previously computed key-value (KV) pairs during generation, and this KV cache grows linearly with sequence length, making it a primary memory bottleneck for serving. Quantizing the KV cache to fewer bits reduces this cost, yet all current quantizers assign the same bit-width to every attention head, ignoring the large variation in head importance. A natural idea is to allocate more bits to important heads and fewer to the rest. We show, however, that such mixed-precision allocation has a hidden pitfall: each quantizer follows a different distortion curve D(b)=alpha*beta^{-b}, and the decay rate beta varies from 3.6 to 5.3 across quantizer designs. Applying one quantizer's distortion model to another inverts the allocation order and makes performance worse than uniform quantization. We call this failure mode distortion model mismatch and propose RateQuant to resolve it. RateQuant fits a per-quantizer distortion model from a small calibration set, then solves the resulting bit-allocation problem in closed form via reverse waterfilling from rate-distortion theory. On Qwen3-8B at 2.5 average bits, calibrated RateQuant reduces KIVI's perplexity from 49.3 to 14.9 (70% reduction) and improves QuaRot by 6.6 PPL. The entire calibration takes 1.6 s on a single GPU and adds zero overhead at inference time.
KV-cache memory is a major bottleneck in real-world LLM serving, where systems must simultaneously support latency-sensitive small-batch requests and high-throughput concurrent workloads. Although many KV-cache compression methods improve offline accuracy or compression ratio, they often violate practical serving constraints such as paged memory layouts, regular memory access, and fused attention execution, limiting their effectiveness in deployment. In this work, we identify the minimal set of 4-bit KV-cache quantization methods that remain viable under these constraints. Our central finding is that a simple design--token-wise INT4 quantization with block-diagonal Hadamard rotation--consistently achieves the best accuracy-efficiency trade-off. Across multiple models and benchmarks, this approach recovers nearly all of the accuracy lost by naive INT4, while more complex methods such as vector quantization and Hessian-aware quantization provide only marginal additional gains once serving compatibility is taken into account. To make this practical, we implement a fused rotation-quantization kernel that integrates directly into paged KV-cache layouts and introduces zero measurable end-to-end overhead, matching plain INT4 throughput across concurrency levels. Our results show that effective KV-cache compression is fundamentally a systems co-design problem: under real serving constraints, lightweight block-diagonal Hadamard rotation is a viable method that delivers near-lossless accuracy without sacrificing serving efficiency.
KV-cache quantizers usually optimize storage-space reconstruction, even though attention reads keys through logits and values through attention-weighted readout. We argue that persistent cache error should be measured in model-visible coordinates. For keys, the visible object is score error modulo constant shifts; this yields HeadQ, a key-side method that stores a low-rank residual side code in a calibration-learned query basis and applies it as an additive logit correction. For values, fixed-attention readout gives an A2-weighted token-distortion surrogate. Across six models, Fisher/score-space error predicts attention KL far better than raw key MSE; same-budget counterexamples, null-space interventions, query-PCA controls, and wrong-sign HeadQ falsify storage-MSE alternatives. Matched Pythia checkpoints localize the main anomaly to a small-model low-entropy route-flip boundary. In K-only WikiText-103 decode experiments with dense values, HeadQ removes roughly 84--94% of the excess perplexity on the strongest 2-bit rows; in an auxiliary full-KV 2-bit composition, HeadQ plus an A2 value policy improves all six models.