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

We present a design called Proof of Gradient Optimization (PoGO) for blockchain consensus, where miners produce veri fiable evidence of training large-scale machine-learning models. Bu ilding on previous work [1,2,3], we incorporate quantized gradients (4-bit precision [7] [8][9]) to reduce storage and computation requirements, wh ile still preserving the ability of verifiers to check that real progress h as been made on lowering the model's loss. Additionally, we employ Merkl e 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) [5] as a reference example and also r efer to smaller but high-performance models (e.g., Gemma 3 with 27B parameters). We provide an empirical cost analysis showing that ve rification is significantly cheaper than training, thanks in part to quant ization and sampling. We also discuss the necessity of longer block time s (potentially hours) when incorporating meaningful training steps, the t rade-offs when using specialized GPU hardware, and how binary diffs may incr ementally optimize updates. Finally, we note that fine-tuning can be ha ndled in a similar manner, merely changing the dataset and the manner o f sampling but preserving the overall verification flow. Our protocol al lows verifiers to issue either positive or negative attestations; these are aggregated at finalization to either confirm the update or slash the miner.