Announcing Yarrow

I’ve recently been funded to work on my project yarrow, which is a datastructure and data-parallel (read: GPU-accelerated) algorithms for string diagrams. A key feature of yarrow is to do with differentiability. More on that shortly.

Quick note: yarrow is still early in development, and the API is not likely to be stable for a few weeks. That aside, so far I’ve released:

• A paper describing the datastructures and algorithms of yarrow
• The yarrow library in Python (still in development!)
• Documentation for the library
• A homepage for the project.

Within a week or so I’ll also be finishing up a more in-depth blog post about yarrow, but for now the documentation is the best place to understand what it’s about.

Differentiable Circuits and Zero-Knowledge Machine Learning

So how does yarrow relate to Zero-Knowledge ML? Well, to describe a zero-knowledge computation, you need an arithmetic circuit, and these can be represented as string diagrams.

In fact, we wrote a paper doing not just that, but also showing how the gradients of such circuits can computed efficiently via “reverse derivatives”¹.

Ultimately, this means that yarrow will² be able to:

• Represent a ZK computation as an arithmetic circuit \(c\)
• Transform the circuit \(c\) into a circuit \(d\) which computes a single step of gradient descent

The idea is to allow for zero-knowledge training of models.

This is made possible by a key feature of yarrow: it natively handles a certain kind of hypergraph structure. This means that, given a circuit \(f\), we can compute an “optic” diagram:

Roughly speaking, in the specific case of machine learning with neural networks, the “backwards” arrows in these diagrams carry the gradients of the model. For a more formal description of this process, see Section 10 of the paper.

That’s it for now! If you’d like to keep updated follow me on twitter or check back later!