5 accepted papers
We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $\delta$-similarity and $\mu$-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the…
In this paper, we study the non-local convergence properties of deep linear networks. Specifically, under the quadratic loss, we consider optimizing deep linear networks in which there is at least a layer with only one neuron. We describe the convergent point of trajectories with an arbitrary balanc…
In this paper, we study gradient methods for training deep linear neural networks with binary cross-entropy loss. In particular, we show global directional convergence guarantees from a polynomial rate to a linear rate for (deep) linear networks with spherically symmetric data distribution, which ca…
In this paper, we follow Rodomanov and Nesterov’s work to study quasi-Newton methods. We focus on the common SR1 and BFGS quasi-Newton methods to establish better explicit (local) superlinear convergence rates. First, based on the greedy quasi-Newton update which greedily selects the direction to ma…
Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of deep neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem through training a simple two-layer convolutional neural net…