Illia Dovhopolyi, Artem Sdobnov, Dmytro Zakharov Acknowledgement The UltraGroth proving system explained here is an adapted for real use cases version of the protocol initially described in Merlin404's article on HackMD. Huge credit to their work, which inspired much of what follows. Prerequisites We assume you already understand the basics of modern zero-knowledge (ZK) constructions. This article aims to build intuition around the UltraGroth proving system, and deep, formal knowledge of Groth16 isn't strictly necessary. However, familiarity with our previous blogs on the Bionetta framework will be beneficial, as examples here utilize Bionetta circuits. Activation Functions are too expensive During the development of Bionetta, one of our most significant challenges was optimizing the constraint cost of activation functions like ReLU. Each ReLU operation costs at least $253$ constraints due to the bit decomposition of input signals. Considering neural networks rely heavily on non-linear activations, this quickly becomes prohibitively expensive. As an example, consider our LeakyReLU implementation:

Illia Dovhopolyi, Dmytro Zakharov Linear operations, like those commonly used in neural networks, are very fast when calculated on a CPU. However, in ZK systems, they typically result in a large number of constraints, making them prohibitively expensive. In this article, we'll introduce a simple yet powerful optimization used in Bionetta that removes constraint costs for linear operations in R1CS circuits, making them absolutely free! Linear Regression example To illustrate this clearly, consider a simple linear regression circuit. We have two input vectors: x with length n, and w with length n+1. We want to constraint the following linear regression formula: $$ y = \sum_{i=0}^{n-1} (x_i \cdot w_{i+1}) + w_0 $$

Introduction Dmytro Zakharov, Lasha Antadze, Oleksandr Kurbatov Note. The basic ZK is required. The security of current neutral networks is comparable to the security of the Internet in its early days. While all major companies are focused on performance, there is a massive gap in AI safety. We can't trust that there are no hundreds of low-paid workers behind the model. We can't be sure the model doesn't lie. We can't verify the model output. We can't be sure it doesn't collect (actually it does) any personal data about clients and doesn't share it with anyone. While AI is expanding the world, we need a fundamentally different approach to how it must operate. We introduce Bionetta🌿 -- a zkML framework that is designed to resolve some security concerns and allow achieving the following set of properties: Provability. The verifier can check the correctness of the model execution.