International Association
for Cryptologic Research

Recent advancements in machine learning accuracy and utility have been driven by the effective combination of sophisticated models with high-performance computational scaling. As the development of large-scale models shifts away from commodity hardware to outsourced computation, it becomes paramount to ensure that the training process is executed with integrity and transparency. This encompasses verifying that adequate computational resources were expended and that the resulting model is accurate, rather than the product of skipped steps or resource-saving shortcuts by the external provider. Building on our previous efforts, which demonstrated the computational feasibility of using this system to argue correctness for differentially-private linear regression, we extend those results to achieve fully provable back-propagation—a cornerstone operation in modern machine learning training. Our system achieves complete zero-knowledge, revealing nothing about the input data during training, and ensures quantum security by relying on no weak cryptographic primitives. Efficiency is substantially increased through the use of a fixed-point decimal representation, reducing the computational overhead typically associated with floating-point arithmetic. Notably, our solution is doubly efficient, achieving a logarithmic-time verifier and a linear-time prover. Implemented entirely in Rust without reliance on external machine learning libraries, and executed within a cryptographically secure virtual machine, this work represents a significant advancement toward verifiable, secure, and efficient outsourced machine learning computations.