js-20261007-differentially-private-federated-sparse-aggregation

Answer

Done. Everything is built and verified. Full deliverable is at ~/dpfed/SOLUTION.md (with dpFederated.js and test.js alongside).

Summary

Diagnosis (root causes): 1. Naive sqrt(sum(x²)) clipping overflows/underflows at extreme magnitudes → NaN/zeroed clients. 2. Noise not tied to the clipped-sum sensitivity C (sigma = z·C). 3. Output shape derived from the union of sparse supports → leaks who participated. 4. Data-dependent loop counts/early returns → timing leak. 5. Retries and re-finalization not idempotent → double counting. 6. No auditable RDP composition across adaptive batch sizes.

Fix — a single dpFederated.js module: - stableL2Norm/clipL2: scale by max|x| first, sanitize non-finite, never emit NaN. - gaussianRdp: subsampled-Gaussian RDP bound in log-space (log-sum-exp + Lanczos logGamma); q=1 reduces to alpha/(2z²). - RDPAccountant: composes heterogeneous (q, z) rounds, converts to (epsilon, delta) via min_alpha[RDP(alpha) + log(1/delta)/(alpha-1)], keeps a full ledger. - FederatedSparseAggregator: fixed public dimension output, padded fixed-work maxSupport merge, idempotent (roundId, clientId) cache, one-shot finalize, sigma = z·clipNorm.

Verification: node test.js → 17/17 tests pass, covering overflow safety (1e308, denormals, Infinity, NaN), sampler moments, RDP closed-form/amplification/composition, support merging, retry idempotency, constant output shape, empirical sigma ≈ z·C, and a 5-round adaptive-batch end-to-end audit (epsilon finite, per-round sampleRate recorded). Smoke test confirmed: length=100, count=2, epsilon≈0.371, sampleRate=0.002.

Key code (the core aggregator logic):

// sensitivity of clipped sum is C  ->  sigma = z * C
const sigma = z * this.clipNorm;

// fixed public dimension: shape never reveals participation
const out = new Float64Array(this.dimension);
for (let i = 0; i < this.dimension; i++) {
  out[i] = round.accumulator[i] + sigma * gaussian(this._rng);
}

// fixed-work merge: iterate maxSupport slots, not the client's support size
for (let s = 0; s < this.maxSupport; s++) {
  const idx = /* valid supplied index or 0 */;
  const val = s < n ? clipped[idx] : 0;   // padded slots add zero
  round.accumulator[idx] += val;
}

// idempotent retry key
const key = String(roundId) + '\u0000' + String(clientId);
if (this._acks.has(key)) return { ...this._acks.get(key), duplicate: true };

Reproduce from scratch:

cd ~/dpfed
node test.js        # 17 tests passed
node smoke.js       # 100 2 0.3713864981935772 0.002