Paper detail

When Quantization Is Free: An int4 KV Cache That Outruns fp16 on Apple Silicon

KV-cache quantization is framed as a quality--latency trade-off. We show it is \emph{inverted} on Apple Silicon's unified memory: a single fused Metal kernel (sign-randomized FFT $+$ per-channel $λ$ $+$ per-group abs-max $+$ int4 nibble pack), exposed as a HuggingFace \texttt{Cache} subclass, runs \emph{faster than fp16} across $256$--$4096$-token prefixes on Gemma-3 1B ($-3$ to $-8\%$ ms/tok) and at short context on Qwen2.5-1.5B ($-0.7$ to $-2.6\%$ through $1$K), with $3\times$ persistent memory compression and quality preserved ($\dPPL = 0.000$ Qwen short-prompt; $+3.6$ hook $\dPPL$ Gemma). The kernel's $\sim\!25$\,ns/vec overhead is below the bandwidth savings from $3\times$ compression. The fused kernel also closes Qwen's 4-bit per-token catastrophe ($\dPPL = +7975 \to +638.6$, $12.5\times$ reduction) at $182$\,GFLOPS / $D{=}128$. Supporting findings: $\SRFT$ and $\SRHT$ are statistically indistinguishable for KV quality (we pick $\SRFT$ for mixed-radix and matrix-multiply alignment); a learned-rotation ablation surfaces a regularization role for the fixed random SRFT base (learning $R+λ$ without SRFT lowers calibration MSE $84.9\%$ vs $50.3\%$ but yields worse PPL); Householder rotations at $k{=}d/2$ reflectors are effectively lossless at $d{=}256$.