Delta-Matching: Closing the Final Gap of Native 8-bit Training for LLMs

Abstract:Reliable FP8 attention remains a barrier to fully native 8-bit large language model training. We derive how forward-backward inconsistencies produce stale delta and empirically show how it distorts training dynamics. Our stale-delta hybrid runs show a modest loss gap at 569M parameters but substantial loss increases and downstream degradation at 1.67B and 5.29B. QK normalization, NoPE (no positional encoding), and lower-learning-rate context extension mitigate or delay degradation without eliminating it. This pattern suggests accumulated optimization error that smaller models and short runs can conceal. We propose Delta-Matching, proving that it restores the softmax gradient's zero-row-sum invariant under the stated numerical assumptions. It enables native block-scaled FP8 in every forward and backward attention-core matmul without architectural changes, smaller global batches, or auxiliary forward outputs. Across tested architectures, scales, and training stages, Delta-Matching matches BF16/FP32 mixed-precision training loss and overall downstream performance. We will release our implementation, trained models, and data recipes.

Machine Learning (cs.LG)

arXiv:2609.37852 [cs.LG]

(or arXiv:2609.37852v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.37852 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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