This post was written by George Wiese and Artem Grigor. After Zero Gravity's 1st place finish at ZK Hack Lisbon in April, PSE recognized the potential of the Zero Gravity project and provided a grant for further research in the ZKML area.

It's been an incredible journey since our team first ventured into the world of zero-knowledge proofs for Weightless Neural Networks (WNNs) at the ZK Hack Lisbon event. For an in-depth look at where we started, we recommend checking out Ben's insightful post.

Since then, we have improved the implementation from a python script that generates Aleo code to a Halo2 CLI that anyone can use. Check out our previous blogpost to understand how you can prove and verify WNN evaluation on Ethereum.

Fast-forward to today, and we're excited to share our latest research findings, revealing the progress we've made in the fields of cryptography and weightless neural network. We believe that the best way to describe our work is through the exciting discoveries we've uncovered.

Our journey started with a deep dive into optimizing the Rust Prover, a crucial component in cryptographic protocols. Our goal was clear: find ways to significantly enhance the efficiency of lookups, a task that consumes a substantial portion of constraints in these protocols.

One of our paths of exploration led us to investigate folding schemes like Sangria and Origami. These schemes showed promise in reducing constraints associated with lookups in cryptographic proofs. However, to fully leverage their potential, they require further development and integration into the Halo2 library.

As we were determined to improve the performance despite all the wonderful technology like Sangria and Lasso still being unavailable, we introduced our own compression scheme for optimizing lookups. It compresses several binary lookup rows into a single field lookup, which significantly raises the performance for sparse lookup tables, such as ones we have in WNN Bloom Filter.

The result has been 14 fold theoretical lookup table compression, though we are sure we could get it to 30 fold, making it twice as efficient as our current optimised version.

Our research extended to improving data preprocessing and feature selection for Weightless Neural Networks (WNNs), with the aim of taking their performance to new heights.

Our exploration uncovered the value of data augmentation as a powerful tool to combat overfitting and enhance the generalization of WNNs. However, we learned that caution must be exercised when applying data augmentation to smaller models, as it may lead to performance degradation. Larger models, on the other hand, excel at handling the increased variety of patterns introduced by data augmentation.

One of our standout achievements was the development of a feature selection algorithm that proved highly effective in reducing model size while maintaining commendable accuracy. Even for smaller models, we achieved remarkable reductions in size, sometimes up to 50%, with only a modest drop in accuracy.

We delved into the world of feature selection algorithms and introduced the greedy algorithm. Though computationally demanding, it offers a means to construct models with precisely selected features. The impact of this approach varies depending on the dataset's complexity, making it a valuable tool for larger and more intricate datasets.

As we conclude this phase of our journey, we look ahead with eagerness to what lies beyond. We have identified crucial areas for further exploration and development that will shape the future of zero-knowledge proofs for Weightless Neural Networks.

Our efforts will continue to focus on enhancing lookup compression algorithms, such as Lasso, and ensuring their seamless integration with existing cryptographic libraries like Halo2. The quest for novel compression techniques that reduce constraints in lookup operations remains a central research area.

The application of feature selection algorithms to larger and more complex datasets is on our horizon. Evaluating their performance and scalability on datasets beyond MNIST will provide valuable insights into their practical utility.

Our journey has been filled with challenges, breakthroughs, and innovative solutions. We've taken steps forward, fueled by the belief that our work contributes to a collective understanding of these complex fields.

• Research Repository

• Detailed Research Writeup

• Implementation of Lookup Compression

For a deeper dive into our research findings, we invite you to explore our research repository, read our detailed research writeup, and examine the implementation of lookup compression. Join us on this exciting journey of exploration, where innovation and privacy-preserving technologies intersect.

To revisit where our journey began, take a look at our Initial Blog Post from the Hackathon.