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Leave-one-out Distinguishability in Machine Learning
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Proposes leave-one-out distinguishability (LOOD), an analytical KL/mean-distance measure of output-distribution change from adding one training point, computed via NNGP Gaussian-process posteriors to quantify memorization, influence, and leakage.
Problem
Measuring data memorization, information leakage, and influence of training points requires costly leave-one-out retraining and approximate influence functions that are inaccurate for deep networks.
Approach
Define LOOD as the statistical distance between prediction distributions of models trained with and without a differing data point, and compute it analytically by modeling the randomness of training with Gaussian processes (NNGP), unifying influence, memorization and MIA-based leakage under one measure.
Key results
- LOOD under NNGP correlates strongly with leave-one-out MIA AUC on CIFAR-10 subsets of size 1000.
- Mean distance LOOD achieves the highest correlation with actual prediction difference from leave-one-out retraining, outperforming influence functions and TracIn.
- Analytical LOOD gives over 140x speedup versus retraining (40 GPU minutes vs 100 GPU hours).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Estimate leakage and influence analytically with LOOD instead of evaluating retrained models | Neural-network leakage and influence estimation · Leave-one-out setting | speedup: 140× speed up | Helped |
| Use ReLU instead of GeLU | Fully connected NNGP · CIFAR-10 car and plane images | LOOD: 1.1× | Mixed |
| Use KL divergence LOOD instead of mean distance LOOD | LOOD leakage measurement · CIFAR-10 leave-one-out membership inference | correlation with MIA AUC | Helped |
| Use NNGP mean distance LOOD to estimate prediction differences | Influence estimation for deep neural networks · Leave-one-out retraining | correlation with prediction difference | Helped |
Surprising findings
- Mean distance LOOD is poorly correlated with MIA success, and the query maximizing mean distance can differ from the differing point, so KL LOOD is preferred.
- Under ReLU, leakage is lower than under GeLU; smooth activations induce higher LOOD, implying a privacy-accuracy trade-off.
Limitations
- NNGP is an idealized infinite-width model; performance gap to trained networks remains.
- Mean distance LOOD is first-order only and not well correlated with MIA success.
- KL LOOD is asymmetric; analysis restricted to one direction.
Experimental setup
Datasets: CIFAR-10
Benchmarks: CIFAR-10
Metrics: KL divergence LOOD mean distance LOOD AUC of membership inference attack Pearson correlation speedup
Baselines: influence function TracIn leave-one-out retraining of neural networks
Builds on: NNGP influence functions memorization (Feldman and Zhang) Rényi differential privacy
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