Liron Mor-Yosef

Neta Shoham, Liron Mor-Yosef, Haim Avron

Recent literature generalization in deep learning has examined the relationship between the curvature of the loss function at minima and generalization, mainly in the context of overparameterized neural networks. A key observation is that "flat" minima tend to generalize better than "sharp" minima. While this idea is supported by empirical evidence, it has also been shown that deep networks can generalize even with arbitrary sharpness, as measured by either the trace or the spectral norm of the Hessian. In this paper, we argue that generalization could be assessed by measuring flatness using a soft rank measure of the Hessian. We show that when an exponential family neural network model is exactly calibrated, and its prediction error and its confidence on the prediction are not correlated with the first and the second derivative of the network's output, our measure accurately captures the asymptotic expected generalization gap. For non-calibrated models, we connect a soft rank based flatness measure to the well-known Takeuchi Information Criterion and show that it still provides reliable estimates of generalization gaps for models that are not overly confident. Experimental results indicate that our approach offers a robust estimate of the generalization gap compared to baselines.

Neta Shoham, Tomer Avidor, Aviv Keren et al.

We tackle the problem of Federated Learning in the non i.i.d. case, in which local models drift apart, inhibiting learning. Building on an analogy with Lifelong Learning, we adapt a solution for catastrophic forgetting to Federated Learning. We add a penalty term to the loss function, compelling all local models to converge to a shared optimum. We show that this can be done efficiently for communication (adding no further privacy risks), scaling with the number of nodes in the distributed setting. Our experiments show that this method is superior to competing ones for image recognition on the MNIST dataset.

Liron Mor-Yosef, Haim Avron

Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large scale data. In this paper, we propose efficient algorithms for computing approximate PCR solutions that are, on one hand, high quality approximations to the true PCR solutions (when viewed as minimizer of a constrained optimization problem), and on the other hand entertain rigorous risk bounds (when viewed as statistical estimators). In particular, we propose an input sparsity time algorithms for approximate PCR. We also consider computing an approximate PCR in the streaming model, and kernel PCR. Empirical results demonstrate the excellent performance of our proposed methods.