Circuit 1: Training Certification

The training certification circuit proves that a model was trained fairly on a committed dataset.

Purpose

When a model provider registers their model, they must prove:

1. Weights match commitment - The model weights hash to the committed weightsHash
2. Dataset is valid - Each training row exists in the committed dataset Merkle tree
3. Model is fair - Predictions satisfy the fairness threshold (demographic parity)

Public Inputs

Input	Type	Description
weights_hash	Field	Poseidon hash of model weights
dataset_merkle_root	Field	Root of committed dataset tree
fairness_threshold	u32	Max allowed disparity (e.g., 10 = 10%)

Private Inputs

Input	Type	Description
weights	[Field; N]	Model weights
dataset	[[Field; F]; D]	Training data rows
merkle_proofs	[MerkleProof; D]	Proofs for each row
predictions	[u1; D]	Model predictions
sensitive_attrs	[u1; D]	Protected attribute values

Verification Logic

// 1. Verify weights hash
let computed_hash = poseidon_hash(weights);
assert(computed_hash == weights_hash);

// 2. Verify each dataset row is in committed tree
for i in 0..DATASET_SIZE {
    let leaf = compute_leaf_hash(dataset[i]);
    assert(verify_merkle_proof(leaf, merkle_proofs[i], dataset_merkle_root));
}

// 3. Compute demographic parity
let group_0_positive = count(predictions where sensitive_attr == 0 && pred == 1);
let group_1_positive = count(predictions where sensitive_attr == 1 && pred == 1);
let group_0_total = count(sensitive_attr == 0);
let group_1_total = count(sensitive_attr == 1);

let rate_0 = group_0_positive * 100 / group_0_total;
let rate_1 = group_1_positive * 100 / group_1_total;

// 4. Check fairness threshold
let disparity = abs(rate_0 - rate_1);
assert(disparity <= fairness_threshold);

Fairness Metric

The circuit uses demographic parity:

$$ \text{Disparity} = \left| P(\hat{Y}=1 \mid A=0) - P(\hat{Y}=1 \mid A=1) \right| $$

Where:

• $\hat{Y}$ = model prediction
• $A$ = sensitive attribute (e.g., gender, race)

Usage

# Generate proof via CLI
zkfair proof generate --weights-hash 0x...

# Submit to contract
zkfair proof submit --proof ./proof.json