Losing Less: A Loss for Differentially Private Deep Learning
Bibliographic record
Abstract
Differentially Private Stochastic Gradient Descent, DP-SGD, is the canonical approach to training deep neural networks with guarantees of Differential Privacy (DP). However, the modifications DP-SGD introduces to vanilla gradient descent negatively impact the accuracy of deep neural networks. In this paper, we are the first to observe that some of this performance can be recovered when training with a loss tailored to DP-SGD; we challenge cross-entropy as the de facto loss for deep learning with DP. Specifically, we introduce a loss combining three terms: the summed squared error, the focal loss, and a regularization penalty. The first term encourages learning with faster convergence. The second term emphasizes hard-to-learn examples in the later stages of training. Both are beneficial because the privacy cost of learning increases with every step of DP-SGD. The third term helps control the sensitivity of learning, decreasing the bias introduced by gradient clipping in DP-SGD. Using our loss function, we achieve new state-of-the-art tradeoffs between privacy and accuracy on MNIST, FashionMNIST, and CIFAR10. Most importantly, we improve the accuracy of DP-SGD on CIFAR10 by 4% for a DP guarantee of 𝜀 = 3.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.026 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".