P-Cast Precision in FP8 Attention: Sink-Induced Collapse and the Optimality of S=2^8
FP8 (E4M3) acceleration for attention computation offers significant throughput gains, but the 3-bit mantissa introduces precision challenges when the softmax probability matrix~$P$ is cast to FP8 before the $P \cdot V$ matrix multiplication. We analyze two implementation choices that affect output precision under the \emph{Attention Sink} phenomenon: (1)~the KV block iteration order, and (2) the static scaling factor applied to $P$ before casting. We show that forward KV iteration causes \emph{P-collapse} -- to leading order a fraction $Φ(Δ+ δ_k - 6.93 - \ln S)$ of non-sink $P$ values underflow to zero, where the small shift $δ_k \approx 1$ (for $k_{\text{sink}}{=}4$) is the expected wit...
| Authors | Reed Lau |
|---|---|
| Primary category | cs.AR |
| Published | 2 June 2026 |
| Last updated at source | 2 June 2026 |
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