Synthetic validation code for the theory paper "Private Coupled Descent: Dimension-Free Privacy for Vertical Federated Learning by Privatizing the Coupling Variable" (Faes, van den Berg, Amir Haeri; IEEE TSP).
This is a theory paper: the contribution is the theorems (no-go, convergence to an O(sigma) neighborhood under DP, dimension-free prediction risk, a matching lower bound). There is no external dataset; the code generates vertical block-term data in-script from fixed seeds and checks the theorems' own quantitative predictions. The COVERT method core lives in the applied companion paper's code, not here; this repository validates the theory only.
syn1_theory_validation.py generates vertical block-term regression data and confirms three predicted scalings, reported over 20 seeds (deterministic given the seeds):
| macro | what it measures | theory predicts |
|---|---|---|
synFloorSlope |
log-log slope of the stationarity floor vs sigma^2 | 1 |
synDimFlat |
excess prediction-risk ratio across a 100x ambient-dimension increase | 1 |
synEpsSlope |
log-log slope of the prediction-risk floor vs 1/eps^2 | 1 |
synGap |
measured floor / lower-bound prediction | O(1) |
The measured values are 1.00 / 1.03 / 0.97 / 1.1, all within seed variability of the predicted exponents.
pip install -r requirements.txt # numpy only
python paper.py # runs SYN-1, prints the 5 macros (deterministic)paper.py prints both the values and the \newcommand macros to paste into the manuscript.
syn1_theory_validation.py- the SYN-1 validation: the profiled (Rayleigh-quotient) prediction risk, the proximal-gradient stationarity floor with DP noise on the coupling score, and the three scaling fits.paper.py- the single entry point (runs SYN-1, prints the macros).requirements.txt,LICENSE(MIT).
The theorems themselves are proved in the manuscript appendices; this code only checks their numbers.