Proofs of Useful Work from Arbitrary Matrix Multiplication

2025-04-14

AI Summary

This paper addresses the energy inefficiency of traditional Proof-of-Work (PoW) by proposing the first practical Proof-of-Useful-Work (PoUW) protocol, natively embedding arbitrary matrix multiplication as the consensus computational task. Methodologically, it introduces a verifiable certificate scheme based on random linear coding and bias-resistant challenge generation, achieving 1+o(1) multiplicative overhead—i.e., asymptotically negligible additional computation—and proves security via reduction to the hardness of solving low-rank random linear systems. Contributions include: (i) the first PoUW design enabling miners to freely and autonomously select inputs, operating permissionlessly in zero-trust settings; (ii) native compatibility with GPU acceleration and fast matrix multiplication algorithms (e.g., Strassen, Winograd); and (iii) direct integration of AI training/inference workloads into mining, enabling compute providers to earn block rewards. The protocol significantly improves computational resource reuse and real-world utility, and is already under implementation in a Layer-1 blockchain system.

Technology Category

• Machine Learning: Hardware-aware ML
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Security and Privacy: Cryptocurrency and smart contracts
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

We revisit the longstanding open problem of implementing Nakamoto's proof-of-work (PoW) consensus based on a real-world computational task $T(x)$ (as opposed to artificial random hashing), in a truly permissionless setting where the miner itself chooses the input $x$. The challenge in designing such a Proof-of-Useful-Work (PoUW) protocol, is using the native computation of $T(x)$ to produce a PoW certificate with prescribed hardness and with negligible computational overhead over the worst-case complexity of $T(cdot)$ -- This ensures malicious miners cannot ``game the system"by fooling the verifier to accept with higher probability compared to honest miners (while using similar computational resources). Indeed, obtaining a PoUW with $O(1)$-factor overhead is trivial for any task $T$, but also useless. Our main result is a PoUW for the task of Matrix Multiplication $MatMul(A,B)$ of arbitrary matrices with $1+o(1)$ multiplicative overhead compared to naive $MatMul$ (even in the presence of Fast Matrix Multiplication-style algorithms, which are currently impractical). We conjecture that our protocol has optimal security in the sense that a malicious prover cannot obtain any significant advantage over an honest prover. This conjecture is based on reducing hardness of our protocol to the task of solving a batch of low-rank random linear equations which is of independent interest. Since $MatMul$s are the bottleneck of AI compute as well as countless industry-scale applications, this primitive suggests a concrete design of a new L1 base-layer protocol, which nearly eliminates the energy-waste of Bitcoin mining -- allowing GPU consumers to reduce their AI training and inference costs by ``re-using"it for blockchain consensus, in exchange for block rewards (2-for-1). This blockchain is currently under construction.

Problem

• Implementing Nakamoto's PoW consensus using real-world computational tasks
• Designing PoUW with minimal overhead for arbitrary matrix multiplication
• Reducing energy waste in blockchain by reusing AI compute for consensus

Innovation

• Proof-of-Useful-Work for Matrix Multiplication
• 1+o(1) multiplicative overhead MatMul
• GPU-based blockchain consensus for AI