Eric Gan

Lauren Watson, Eric Gan, Mohan Dantam et al.

Differentially private stochastic gradient descent (DP-SGD) is known to have poorer training and test performance on large neural networks, compared to ordinary stochastic gradient descent (SGD). In this paper, we perform a detailed study and comparison of the two processes and unveil several new insights. By comparing the behavior of the two processes separately in early and late epochs, we find that while DP-SGD makes slower progress in early stages, it is the behavior in the later stages that determines the end result. This separate analysis of the clipping and noise addition steps of DP-SGD shows that while noise introduces errors to the process, gradient descent can recover from these errors when it is not clipped, and clipping appears to have a larger impact than noise. These effects are amplified in higher dimensions (large neural networks), where the loss basin occupies a lower dimensional space. We argue theoretically and using extensive experiments that magnitude pruning can be a suitable dimension reduction technique in this regard, and find that heavy pruning can improve the test accuracy of DPSGD.

Eric Gan

Empirically, modern deep learning training often occurs at the Edge of Stability (EoS), where the sharpness of the loss exceeds the threshold below which classical convergence analysis applies. Despite recent progress, existing theoretical explanations of EoS either rely on restrictive assumptions or focus on specific squared-loss-type objectives. In this work, we introduce and study a structural property of loss functions that we term product-stability. We show that for losses with product-stable minima, gradient descent applied to objectives of the form $(x,y) \mapsto l(xy)$ can provably converge to the local minimum even when training in the EoS regime. This framework substantially generalizes prior results and applies to a broad class of losses, including binary cross entropy. Using bifurcation diagrams, we characterize the resulting training dynamics, explain the emergence of stable oscillations, and precisely quantify the sharpness at convergence. Together, our results offer a principled explanation for stable EoS training for a wider class of loss functions.

Yu Yang, Eric Gan, Gintare Karolina Dziugaite et al.

Neural networks trained with (stochastic) gradient descent have an inductive bias towards learning simpler solutions. This makes them highly prone to learning spurious correlations in the training data, that may not hold at test time. In this work, we provide the first theoretical analysis of the effect of simplicity bias on learning spurious correlations. Notably, we show that examples with spurious features are provably separable based on the model's output early in training. We further illustrate that if spurious features have a small enough noise-to-signal ratio, the network's output on the majority of examples is almost exclusively determined by the spurious features, leading to poor worst-group test accuracy. Finally, we propose SPARE, which identifies spurious correlations early in training and utilizes importance sampling to alleviate their effect. Empirically, we demonstrate that SPARE outperforms state-of-the-art methods by up to 21.1% in worst-group accuracy, while being up to 12x faster. We also show that SPARE is a highly effective but lightweight method to discover spurious correlations.