LuminAIR leverages the strengths of two powerful frameworks: Luminal and Stwo.
  • Luminal provides the foundation for our machine learning framework, expertly handling computational graphs and compilers.
  • Stwo serves as the constraint framework, enabling us to design an Algebraic Intermediate Representation (AIR) that is provable using Stwo’s compatible prover and verifier.

​
Luminal: A Minimalist Machine Learning Framework

Luminal is a Rust-based machine learning framework, drawing inspiration from Tinygrad. Its key feature is the use of composable compilers, which simplify the process of adding support for new backends. Luminal’s design philosophy centers around a minimal core, ensuring maintainability. At its heart, Luminal operates with just 11 primitive operators:
  • Unary: Log2, Exp2, Sin, Sqrt, Recip
  • Binary: Add, Mul, Mod, LessThan
  • Other: SumReduce, MaxReduce, Contiguous
These ops are enough to support linear regression, convnets, transformers, etc. You might think that such a small set of operations would severely limit the library’s capabilities. However, Luminal overcomes this limitation through the strategic use of composable compilers. These compilers allow us to extend the functionality of the core by adding new operations and optimizations in a modular and isolated manner. For example, because the core library doesn’t handle specific devices, we can create compilers that replace the core operations with equivalent operations optimized for different hardware, such as CUDA GPUs or TPUs. In the context of LuminAIR, we use compilers to target ZK circuits. The beauty of this approach is that with only 11 core operations, the process of creating these specialized compilers becomes remarkably straightforward. Therefore, our work with LuminAIR involves leveraging Luminal’s composable compilers to develop efficient compilers specifically tailored for proving computational graphs using Zero Knowledge proofs.

​
AIR: A Custom Algebraic Intermediate Representation Proved with Stwo

Stwo, developed by Starkware, represents the next generation of STARK provers. It incorporates the innovative Circle STARK protocol, along with a variety of other optimizations. Stwo unlocks the potential of the highly efficient prime field M31, benefiting the entire ZK-proof ecosystem. We are leveraging Stwo framework to define constraints for our AIR. LuminAIR designs a compiler that swaps each operation in the graph with its corresponding component in our AIR, enabling the generation of C-STARK proofs for the computational graph. While, in theory, we could support other ZK backends in the future by developing new compilers, our primary focus for now is on Stwo.