  Imagine training a machine learning model with Differentially Private
Stochastic Gradient Descent (DP-SGD), only to discover post-training that the
noise level was either too high, crippling your model's utility, or too low,
compromising privacy. The dreaded realization hits: you must start the lengthy
training process from scratch. But what if you could avoid this retraining
nightmare? In this study, we introduce a groundbreaking approach (to our
knowledge) that applies differential privacy noise to the model's weights after
training. We offer a comprehensive mathematical proof for this novel approach's
privacy bounds, use formal methods to validate its privacy guarantees, and
empirically evaluate its effectiveness using membership inference attacks and
performance evaluations. This method allows for a single training run, followed
by post-hoc noise adjustments to achieve optimal privacy-utility trade-offs. We
compare this novel fine-tuned model (DP-Weights model) to a traditional DP-SGD
model, demonstrating that our approach yields statistically similar performance
and privacy guarantees. Our results validate the efficacy of post-training
noise application, promising significant time savings and flexibility in
fine-tuning differential privacy parameters, making it a practical alternative
for deploying differentially private models in real-world scenarios.
