This project demonstrates the implementation of both Linear Regression and a Multi-Layer Perceptron (MLP) using the o1js library. The Linear Regression model serves as a fundamental building block, while the MLP is designed to take five input values and predict an output through two hidden layers. Additionally, we provide a Jupyter Notebook implemented in PyTorch that mimics the structure of the MLP defined in o1js.

• Node.js (v20.11.1)
• Python 3.x (for the Jupyter Notebook)

1. Build the project: This step compiles TypeScript code (mlp.ts) into JavaScript (mlp.js).

   npm run build

2. Run the project: Execute the compiled JavaScript file.

   node dist/mlp.js

3. Benchmarking: To benchmark the performance of the Linear Regression and MLP implementations, you can use gtime to measure execution time.

   Run the script to install gtime:

   sh install_gtime.sh

   Run the benchmarks: After installing gtime, you can benchmark the two models by running the following commands:

   sh bench.sh

4. Jupyter Notebook: The project includes a Jupyter Notebook (src/notebook/mlp_comparison.ipynb) that implements the same MLP model in PyTorch as defined in the o1js TypeScript code. This notebook allows you to compare the outputs of both models.

   To run the notebook:

   1. Navigate to the models/mlp directory.

      cd models/mlp

   2. Open the notebook using Jupyter:

      jupyter notebook ./mlp.ipynb

   3. Execute the cells to see the PyTorch implementation of the MLP and compare it with the o1js version.

The MLP (Multi-Layer Perceptron) implemented in this project consists of the following components:

• Input Layer: Takes 5 input values.
• Hidden Layer 1: Applies linear transformation followed by a ReLU activation function.
• Hidden Layer 2: Takes the output of the first hidden layer, applies another linear transformation, and passes it through another ReLU activation.
• Output Layer: Produces the final output value using a linear transformation.

To better understand the MLP structure, refer to the following diagram, which represents the data flow and operations within the network:

Input Layer (5 inputs)
  |
  v
+------------------------+
|  Hidden Layer 1        |  (Linear Regression + ReLU)
|  Weighted Sum (z1)     | -> ReLU(z1) -> a1
+------------------------+
  |
  v
+------------------------+
|  Hidden Layer 2        |  (Linear Regression + ReLU)
|  Weighted Sum (z2)     | -> ReLU(z2) -> a2
+------------------------+
  |
  v
+------------------------+
|  Output Layer          |  (Linear Regression)
|  Weighted Sum (z3)     | -> Output (z3)
+------------------------+
  |
  v
Output

model,exp_num,proving_time,memory_usage,cpu_usage
ezkl,1,67.66,1344276,757%
o1js,1,165.54,1090636,841%
ezkl,2,70.15,1343040,748%
o1js,2,208.12,1168216,864%
ezkl,3,69.18,1360868,688%
o1js,3,201.29,1166896,849%
ezkl,4,69.08,1319804,711%
o1js,4,198.60,1147124,862%
ezkl,5,68.62,1355372,770%
o1js,5,223.88,1216168,881%