This document discusses zero-knowledge proofs and their application to machine learning models through a technique called Zero-Knowledge Machine Learning (ZKML). ZKML allows machine learning models to generate cryptographic proofs that verify computations on private inputs without revealing the inputs or model. This could enable applications like a machine learning marketplace with verifiable predictions on sensitive data or training models privately. Some challenges to ZKML include the expensive computation of zero-knowledge proofs and representing models with arithmetic circuits. The author's company, Attic 42, is working on tools to address these challenges and enable practical applications of zero-knowledge techniques like ZKML.

1. ZKML
Zero-Knowledge Machine Learning
Aleksandar Veljković
Senior researcher @ Attic 42, 3327 R&D

2. Machine Learning
Model
X1
X2
Xn
Inputs Outputs
Y2
Y1
Yk

3. Deep Neural Networks
Black box model
- Private training data
- Private model parameters
Large number of parameters
Expensive model training
- Hardware costs
- Time costs

4. Deep Neural Networks
Market potential!
Model
X1
X2
Xn
Inputs Outputs
Y2
Y1
Yk
Large number of parameters
Black box model
- Private training data
- Private model parameters
Expensive model training
- Hardware costs
- Time costs

5. ML Marketplace
Train models
- Acquire data
- Acquire hardware
Sell model predictions
- API access

6. ML Marketplace
Train models
- Acquire data
- Acquire hardware
Sell model predictions
- API access
How can a user trust the results?
- Is that the correct model?
- Are the predictions correct?
- Is the model same for every user?

7. Zero-knowledge Proofs
Verification of computation
- Convert algorithm to arithmetic circuit
- Generate proof of execution
Privacy preserving
- Hidden circuit inputs

8. Zero-knowledge Proofs
Verification of computation
- Convert algorithm to arithmetic circuit
- Generate proof of execution
Privacy preserving
- Hidden circuit inputs
ZK Circuit
X1
X2
Xn
Private Inputs Public Outputs
Y2
Y1
Yk

9. Arithmetic Circuits
X1
X3
X2 Y

10. Proof Generation
X1
X3
X2 Y
ZK Proof system
Private
Inputs
Public
Outputs
Proof of
Execution
+
Verification Key

11. Proof Verification
Y
Public
Outputs
Proof of
Execution
ZK Verifier
+
Verification Key

12. Proof Verification
Y
Public
Outputs
Proof of
Execution
ZK Verifier
+
Verification Key
Verifiable in smart contracts!

13. ZKML
X1
X3
X2 Y
Model
X1
X2
Xn
Inp
uts
Out
puts
Y2
Y1
Yk
Convert Model to Arithmetic Circuit

14. ZKML Use Cases
Public inputs – Private model
- ML Marketplace
- Predictions based on sensitive data
Private inputs – Public model
- Training models on sensitive data
Public inputs – Public model
- Offloading computation

15. ZKML Use Cases

16. ZKML Challenges
Expensive proof generation
- Hardware requirements
- Time complexity
Arithmetization
- Only integer values allowed
Trusted vs no trusted setup
- Toxic waste values
. . .

17. ZK @ 3327
Model to circuit
- Arithmetization library (ZKFloat)
- SK model to circuit library (SKProof)
Noir + Cairo
Low level constraint optimizations
- Rust + Arkworks
Grants
- Anonymyzation in MACI (Ethereum Foundation)
Experimental domain
- ZK Applications

18. ZK @ 3327
Consultancy services
ZK software architecture design
Education
Looking forward to collaborate with you!

19. Thank you!