[2607.09800]
Zekai Shang
Master weights and stochastic rounding bypass invisible stored-weight updates but do not locate lost direct-storage proposals or parameters worth protecting. We ask what one matched high-precision pilot trace can audit before a low-precision run. The exact target-code event is distinct from projected-code and archived symmetric-spacing aggregate proxies; neither proxy is a pathwise certificate. In the principal controlled two-layer grid, the archived symmetric-spacing proxy tracks nondegenerate crossings spanning 384x in time with median predicted/measured ratio 1.000 and 94.5% within 15%. In analytic-grid GPT-2-124M/OpenWebText runs with common initial target codes, changing only post-optimizer write-back from round-to-nearest to stochastic rounding recovers 89.2-92.2% of the loss gap through 10,000 steps. The same policy contrast recovers 92.9-93.6% at 3,000 E5M2 steps in one fixed 162.2M-parameter decoder configuration, but its visibility trajectories are not informative enough to establish diagnostic transfer. At exactly 10% of the eligible-2-D blanket fp32-master payload, mean recoveries across three fixed seeds are 71.4% for clipped signed leverage, 69.4% for absolute proposal contribution, and 2.1% for freeze-only; the latter comparison does not establish leverage superiority. In a post-selection fixed-target check, one seed-2031 absolute-proposal-contribution mask, reused unchanged across fixed target seeds 2035-2037, recovers 67.8-69.0% (mean 68.5%) at the same exact 10% eligible-2-D fp32-master payload and 1000-step horizon; target-specific masks recover 67.1-70.6% (mean 68.7%). A reference trace therefore supports separate aggregate-visibility and first-order-importance analyses, with failed transfer and superiority tests delimiting both.