0x0 Introduction zkp Alice wants to prove that she knows some private information and public information which passes given computations or constraints. And Bob can verify the proof provided by Alice without revealing any private information. So in such scenario, we need zero knowledge proof (ZKP). The key properties of ZKP are two things.One is the computation could be hard or expensive, and the verification is very cheap. We call it succinctness. For blockchain, it’s really useful for verifying an expensive computation in smart contract. This is what zkEVM does in Layer-2 blockchain as we can run a program in off-chain zkEVM and also generate the proof off-chain. And then we only need a cheap gas fee for verifying it on-chain. Another property of ZKP is the zero knowledge. Because the verifier does not need to know the private. It’s useful in user-privacy preserving scenario. Take ZK version of Kaggle as an example, a user can use ZKP to prove that he has a machine learning model which gets 99% accuracy on an image classification task but he does not want to public his valuable model to the verifier. It’s also note that the public includes input, output, and any intermediate variable in computation. So it’s useful for public some important results along with the proof. With the rapid development of various AI technologies and their amazing capabilities, how to combine them with cutting-edge cryptography and blockchain technologies to improve their security and transparency is a much-needed and promising direction. Leveraging zero knowledge to proetct private information while keeping it's verifiability for machine learning algorithms is what ZKML does. Daniel Kang's blog [9] privdes us a good example to verify the algorithmic integrity of Twitter’s recommendation results with zkml. Although Twitter open-sourced their algorithm, if Twitter generates "For You" timeline with other models instead of the public version they guaranteed, they are able to manipulate bias and content censorship. We were able to ensure via ZKP that Twitter was not secretly using a malicious alternative recommendation model. All operations in machine learning models are related to float numbers. But all the operations in Halo2's ZK circuit are natively in BN254 field which is a finite unsigned integer type. Implementing fixed/float point arithmetic is an important basic for any type of ML or numerical algorithm. Because the ZK proof system only accept ZK circuit which consists of many constraints that only support +, -, *, and = operations over BN254. So if we want to use ZK proof system to proof our computation, we must find a way (arithmetization) to transform the computation to ZK circuit with ZK language. The transformation is what this project does. This project provides an easy-to-use fixed point arithmetic chip based on Halo2. Fixed point numbers will be automatically represented with BN254 numbers. It provides basic operations (multiplication, addition, subtraction, division) and also implements a large number of commonly used nonlinear functions (e.g., log, sin) using the ZK primitive. To show the power of the implemented fixed point arithmetic, this project leverages it to implement the most representative machine learning algorithms, including linear regression, logistic regression, and decision tree. In addition to the inference of these algorithms, this project also implements the more challenging and ambitious training process.