
How to decay your learning rate
Complex learning rate schedules have become an integral part of deep lea...
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Reconciling Modern Deep Learning with Traditional Optimization Analyses: The Intrinsic Learning Rate
Recent works (e.g., (Li and Arora, 2020)) suggest that the use of popula...
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A disciplined approach to neural network hyperparameters: Part 1  learning rate, batch size, momentum, and weight decay
Although deep learning has produced dazzling successes for applications ...
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Spherical Motion Dynamics of Deep Neural Networks with Batch Normalization and Weight Decay
We comprehensively reveal the learning dynamics of deep neural networks ...
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Understanding Decoupled and Early Weight Decay
Weight decay (WD) is a traditional regularization technique in deep lear...
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On the adequacy of untuned warmup for adaptive optimization
Adaptive optimization algorithms such as Adam (Kingma Ba, 2014) are ...
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On the Validity of Modeling SGD with Stochastic Differential Equations (SDEs)
It is generally recognized that finite learning rate (LR), in contrast t...
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An Exponential Learning Rate Schedule for Deep Learning
Intriguing empirical evidence exists that deep learning can work well with exoticschedules for varying the learning rate. This paper suggests that the phenomenonmay be due to Batch Normalization or BN(Ioffe Szegedy, 2015), which is ubiquitous and provides benefits in optimization and generalization across all standardarchitectures. The following new results are shown about BN with weight decay and momentum (in other words, the typical use case which was not considered inearlier theoretical analyses of standalone BN (Ioffe Szegedy, 2015; Santurkaret al., 2018; Arora et al., 2018). 1. Training can be done using SGD with momentum and an exponentially increasing learning rate schedule, i.e., learning rate increases by some (1 +α) factor in every epoch for some α >0. (Precise statement in the paper.) To the best of our knowledge this is the first time such a rate schedule has been successfully used, let alone for highly successful architectures. As expected, such training rapidly blows up network weights, but the net stays wellbehaved due to normalization. 2. Mathematical explanation of the success of the above rate schedule: a rigorous proof that it is equivalent to the standard setting of BN + SGD + StandardRate Tuning + Weight Decay + Momentum. This equivalence holds for other normalization layers as well, Group Normalization(Wu He, 2018), LayerNormalization(Ba et al., 2016), Instance Norm(Ulyanov et al., 2016), etc. 3. A workedout toy example illustrating the above linkage of hyperparameters. Using either weight decay or BN alone reaches global minimum, but convergence fails when both are used.
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