ULPack: Reference-Conditioned Lossless Compression of Checkpoint Trajectories

Studying model training requires checkpoint trajectories, whose storage cost limits temporal resolution. Although adjacent checkpoints are numerically close, existing lossless codecs either operate on XOR bit patterns or ignore trajectory-specific conditional structure. We show that a reference weight's exponent predicts the bit length of its displacement in ordered floating-point space without side information. We introduce \textbf{ULPack}, a lossless codec which exploits this dependence by conditioning entropy models of ordered-integer residuals on the reference exponent. Across bfloat16, float16, and float32 trajectories, ULPack reduces storage by up to 27\% against ZipNN, 21\% against zstd-19, and 11.5\% against FM-Delta. Across two dense trajectories, compression improves as updates shrink and reference conditioning strengthens, while near-uniform low-order bits set the remaining compression floor and earlier checkpoints add little information.