  Distributed machine learning enables parallel training of extensive datasets
by delegating computing tasks across multiple workers. Despite the cost
reduction benefits of distributed machine learning, the dissemination of final
model weights often leads to potential conflicts over model ownership as
workers struggle to substantiate their involvement in the training computation.
To address the above ownership issues and prevent accidental failures and
malicious attacks, verifying the computational integrity and effectiveness of
workers becomes particularly crucial in distributed machine learning. In this
paper, we proposed a novel binary linear tree commitment-based ownership
protection model to ensure computational integrity with limited overhead and
concise proof. Due to the frequent updates of parameters during training, our
commitment scheme introduces a maintainable tree structure to reduce the costs
of updating proofs. Distinguished from SNARK-based verifiable computation, our
model achieves efficient proof aggregation by leveraging inner product
arguments. Furthermore, proofs of model weights are watermarked by worker
identity keys to prevent commitments from being forged or duplicated. The
performance analysis and comparison with SNARK-based hash commitments validate
the efficacy of our model in preserving computational integrity within
distributed machine learning.
