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Thanks to the combination of state-of-the-art accelerators and highly optimized open software frameworks, there has been tremendous progress in the performance of deep neural networks. While these developments have been responsible for many breakthroughs, progress towards solving large-scale problems, such as video encoding and semantic segmentation in 3D, is hampered because access to on-premise memory is often limited. Instead of relying on (optimal) checkpointing or invertibility of the network layers -- to recover the activations during backpropagation -- we propose to approximate the gradient of convolutional layers in neural networks with a multi-channel randomized trace estimation technique. Compared to other methods, this approach is simple, amenable to analyses, and leads to a greatly reduced memory footprint. Even though the randomized trace estimation introduces stochasticity during training, we argue that this is of little consequence as long as the induced errors are of the same order as errors in the gradient due to the use of stochastic gradient descent. We discuss the performance of networks trained with stochastic backpropagation and how the error can be controlled while maximizing memory usage and minimizing computational overhead.
Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques from rand
We study the problem of estimating the trace of a matrix $A$ that can only be accessed through matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which computes a $(1 pm epsilon)$ approximation to $tr(A)$ for any positive
We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly outperforms
Over a complete Riemannian manifold of finite dimension, Greene and Wu introduced a convolution, known as Greene-Wu (GW) convolution. In this paper, we study properties of the GW convolution and apply it to non-Euclidean machine learning problems. In
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a Monte-Carlo sampli