While SGD, which samples from the data with replacement is widely studied in theory, a variant called Random Reshuffling (RR) is more common in practice. RR iterates through random permutations of the dataset and has been shown to converge faster than SGD. When the order is chosen deterministically, a variant called incremental gradient descent (IG), the existing convergence bounds show improvement over SGD but are worse than RR. However, these bounds do not differentiate between a good and a bad ordering and hold for the worst choice of order. Meanwhile, in some cases, choosing the right order when using IG can lead to convergence faster than RR. In this work, we quantify the effect of order on convergence speed, obtaining convergence bounds based on the chosen sequence of permutations while also recovering previous results for RR. In addition, we show benefits of using structured shuffling when various levels of abstractions (e.g. tasks, classes, augmentations, etc.) exists in the dataset in theory and in practice. Finally, relying on our measure, we develop a greedy algorithm for choosing good orders during training, achieving superior performance (by more than 14 percent in accuracy) over RR.
The design and implementation of efficient concurrent data structures has seen significant attention. However, most of this work has focused on concurrent data structures providing good worst-case guarantees. In real workloads, objects are often accessed at different rates, since access distributions may be non-uniform. Efficient distribution-adaptive data structures are known in the sequential case, e.g. the splay-trees; however, they often are hard to translate efficiently in the concurrent case.In this paper, we investigate distribution-adaptive concurrent data structures, and propose a new design called the splay-list. At a high level, the splay-list is similar to a standard skip-list, with the key distinction that the height of each element adapts dynamically to its access rate: popular elements "move up," whereas rarely-accessed elements decrease in height. We show that the splay-list provides order-optimal amortized complexity bounds for a subset of operations, while being amenable to efficient concurrent implementation. Experimental results show that the splay-list can leverage distribution-adaptivity to improve on the performance of classic concurrent designs, and can outperform the only previously-known distribution-adaptive design in certain settings. ACM Subject Classification Replace ccsdesc macro with valid one Keywords and phrases Dummy keywordDigital Object Identifier 10.4230/LIPIcs...
It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and-in asynchronous implementations-on the gradient staleness. Especially, it has been observed that the speedup saturates beyond a certain batch size and/or when the delays grow too large. We identify a data-dependent parameter that explains the speedup saturation in both these settings. Our comprehensive theoretical analysis, for strongly convex, convex and non-convex settings, unifies and generalized prior work directions that often focused on only one of these two aspects. In particular, our approach allows us to derive improved speedup results under frequently considered sparsity assumptions. Our insights give rise to theoretically based guidelines on how the learning rates can be adjusted in practice. We show that our results are tight and illustrate key findings in numerical experiments.
It has been widely observed in training of neural networks that when applying gradient descent (GD), a large step size is essential for obtaining superior models. However, the effect of large step sizes on the success of GD is not well understood theoretically. We argue that a complete understanding of the mechanics leading to GD's success may indeed require considering effects of using a large step size. To support this claim, we prove on a certain class of functions that GD with large step size follows a different trajectory than GD with a small step size, leading to convergence to the global minimum. We also demonstrate the difference in trajectories for small and large learning rates when GD is applied on a neural network, observing effects of an escape from a local minimum with a large step size, which shows this behavior is indeed relevant in practice. Finally, through a novel set of experiments, we show even though stochastic noise is beneficial, it is not enough to explain success of SGD and a large learning rate is essential for obtaining the best performance even in stochastic settings.
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