ZKP Neural Networks

Prototype of evalutation of neural networks inside zero knowledge proofs using the plonky2 proof system.

ZKML

To find out more about zero-knowledge machine learning, check out the awesome-zkml repository we have created. It aggregates scientific research papers, codebases, articles, and use cases in the field of ZKML.

Potential Worldcoin use cases

Worldcoin is a Privacy-Preserving Proof-of-Personhood Protocol. ZKML could help us make our protocol more trustless, and make it more easily upgradeable and auditabie.

• Verifying that a user has created a valid and unique WorldID locally by running the IrisCode model on self-hosted biometric data and is calling _addMember(uint256 groupId, uint256 identityCommitment) function on the WorldID Semaphore identity group with a valid identityCommitment. -> Makes protocol more permissionless
• Making the Orb trustless, provide proof that fraud filters on the hardware and firmware are applied
• Enable IrisCode upgradeability

Technological stack

• Python, numpy - Flexible dynamic programming language and the fundamental package for scientific computing in Python -> used to create a vanilla implementation of a CNN
• Rust - A performant, memory safe, systems-level programming language.
• plonky2: Powerful zero-knowledge proving system developed by the Polygon Zero team -> to create zero knowledge circuits of the inference step of a neural network
• serde - Serialization/Deserialization library for Rust

Build and run

cargo +nightly run --release -- -vvv --input-size 1000 --output-size 1000

Validate equality of Rust and Python CNN implementations

# open Python CNN implementation directory
cd ref_cnn
# run CNN model and check result
python3 vanilla_cnn.py
# generate JSON files for the random number generated matrices in the model 
python3 generate_cnn_json.py
cd ../
# run Rust CNN implementation and compare results against your previous results
cargo test serialize::tests::deserialize_nn_json -- --show-output  

• This will run the vanilla CNN Python implementation and generate JSON files for the random matrices generated by numpy, these will be deserealized by serde in the Rust implementation and turned into an ndarray ArcArray<f32, IxDyn>.
• With this approach we can get rid of any randomness in matrix generation and verify that we are using the same data.
• It also creates a standardized intermediary format that can be understood by Rust to import and export ML models easily from other languages (Python in our case).

Example output

• Python

> python ref_cnn/vanilla_cnn.py
               layer |    output shape |     #parameters |            #ops 
-------------------- | --------------- | --------------- | --------------- 
       conv 32x5x5x3 |   (116, 76, 32) |            2400 |        21158400 
            max-pool |    (58, 38, 32) |               0 |               0 
                relu |    (58, 38, 32) |               0 |               0 
      conv 32x5x5x32 |    (54, 34, 32) |           25600 |        47001600 
            max-pool |    (27, 17, 32) |               0 |               0 
                relu |    (27, 17, 32) |               0 |               0 
             flatten |        (14688,) |               0 |               0 
     conv 1000x14688 |         (1000,) |        14689000 |        14688000 
                relu |         (1000,) |               0 |               0 
         conv 5x1000 |            (5,) |            5005 |            5000 
           normalize |            (5,) |               0 |               6 

final output: [-0.11425511 -0.13403508 -0.41759714 -0.24778798  0.85626755]

• Rust

---- serialize::tests::deserialize_nn_json stdout ----
layer                | output shape    | #parameters     | #ops           
-----------------------------------------------------------------------------
conv 32x5x5x3        | [116, 76, 32]      | 2400  | 7052800
max-pool             | [38, 58, 32]      | 0     | 282112
relu                 | [58, 38, 32]      | 70528 | 0    
conv 32x5x5x32       | [54, 34, 32]      | 25600 | 1468800
max-pool             | [17, 27, 32]      | 0     | 58752
relu                 | [27, 17, 32]      | 14688 | 0    
flatten              | [14688]      | 0     | 0    
full                 | [1000]      | 14689000 | 14688000
relu                 | [1000]      | 1000  | 0    
full                 | [5]      | 5005  | 5000 
normalize            | [5]      | 0     | 6    
final output (normalized):
[-0.11425512, -0.13403504, -0.41759717, -0.24778795, 0.8562675]

Benchmark Python vs Rust CNN implementations

cd ref_cnn
python benchmark_cnn.py
# generates matrices for the Rust implementation to use 
python generate_cnn_json.py
cargo bench bench_neural_net

Example output

Machine: M1 Max Macbook Pro

• Python: 0.830s

The average time is 0.8297840171150046 seconds for 1000 runs

• Rust: 0.151s

test nn::bench_neural_net ... bench: 151,632,316 ns/iter (+/- 1,469,992)

In this benchmark the Rust implementation is 5.5x faster!

Run tests

Verify that all components of the rust codebase are working fine and that no breaking changes were introduced.

cargo test 

In order to see output use cargo test -- --output, i.e.:

cargo test nn::tests::neural_net -- --show-output 

Serialize/Deserialize CNN model

Python to JSON -> JSON to Rust

Serializing the vanilla CNN model created with numpy into JSON and desearilizing the model into a NeuralNetwork Rust object

# change directory to cnn folder
cd ref_cnn
# generate json file for the model
python generate_cnn_json.py

cargo test serialize::tests::deserialize_model_json -- --show-output  

Rust to JSON

# serializes a CNN model with random weights into src/json/nn.json
cargo test serialize::tests::serialize_model_json -- --show-output  

Full circle

Create a NeuralNetwork object with random weights in Rust, serialize it into JSON and deserialize back into a NeuralNetwork Rust object

# serializes a CNN model with random weights into src/json/nn.json
cargo test serialize::tests::serde_full_circle -- --show-output  

Serialization/Deserialization benchmarks

Benchmarks for serializing and deserializing the reference CNN (Rust/JSON) using serde.

# full serialization benchmark times (M1 Max Macbook Pro)
# cargo bench - 579,057,637 ns/iter (+/- 20,202,535)
cargo bench bench_serialize_neural_net

# full deserialization benchmark times (M1 Max Macbook Pro)
# cargo bench - 565,564,850 ns/iter (+/- 61,387,641)
cargo bench bench_deserialize_neural_net