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PoGO: A Scalable Proof of Useful Work via Quantized Gradient Descent and Merkle Proofs

We present a design called \emph{Proof of Gradient Optimization} (PoGO) for blockchain consensus, where miners produce verifiable evidence of training large-scale machine-learning models. Building on previous work, we incorporate \emph{quantized gradients} (4-bit precision) to reduce storage and computation requirements, while still preserving the ability of verifiers to check that real progress has been made on lowering the model's loss. Additionally, we employ Merkle proofs over the full 32-bit model to handle large parameter sets and to enable random leaf checks with minimal on-chain data. We illustrate these ideas using GPT-3 (175B parameters) as a reference example and also refer to smaller but high-performance models (e.g., \emph{Gemma~3} with 27B parameters). We provide an empirical cost analysis showing that verification is significantly cheaper than training, thanks in part to quantization and sampling. We also discuss the necessity of longer block times (potentially hours) when incorporating meaningful training steps, the trade-offs when using specialized GPU hardware, and how binary diffs may incrementally optimize updates. Finally, we note that fine-tuning can be handled in a similar manner, merely changing the dataset and the manner of sampling but preserving the overall verification flow. Our protocol allows verifiers to issue either \emph{positive} or \emph{negative} attestations; these are aggregated at finalization to either confirm the update or slash the miner.

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