What the Loss Curve Misses: FP4 Pretraining Slows the Acquisition of Rare Facts

Low-precision pretraining is usually judged by validation loss. We ask whether matching loss also means learning rare facts as efficiently. We train transformers from scratch with emulated 4-bit matrix multiplications on synthetic biographies with controlled exposure counts, on their own and mixed into web text. NVFP4 needs 1.32$\times$ and 1.52$\times$ as many exposures as BF16 to match its recall while validation loss differs by only 0.5% and 2%, and 1.26$\times$ and 1.30$\times$ when both models are evaluated with BF16 matrix multiplications. Under our primary readout, the exposure cost is about 1.2$\times$ at matched loss. Zero-mean gradient noise reproduces the cost of quantizing only the backward pass, which barely moves the loss. In a controlled experiment at twice the NVFP4 error, noise fed only to Adam's second-moment estimate acts like a lower learning rate and its cost fades,…