Variational autoencoders (VAEs) with an auto-regressive decoder have been applied for many natural language processing (NLP) tasks. The VAE objective consists of two terms, (i) reconstruction and (ii) KL regularization, balanced by a weighting hyper-parameter . One notorious training difficulty is that the KL term tends to vanish. In this paper we study scheduling schemes for , and show that KL vanishing is caused by the lack of good latent codes in training the decoder at the beginning of optimization. To remedy this, we propose a cyclical annealing schedule, which repeats the process of increasing multiple times. This new procedure allows the progressive learning of more meaningful latent codes, by leveraging the informative representations of previous cycles as warm re-starts. The effectiveness of cyclical annealing is validated on a broad range of NLP tasks, including language modeling, dialog response generation and unsupervised language pre-training.
Warm-restart techniques are common in optimization to deal with multimodal functions. The cyclical schedule has been used to train deep neural networks @cite_1 , warm restart stochastic gradient descent @cite_17 , improve convergence rates @cite_28 , obtain model ensembles @cite_8 and explore multimodal distributions in MCMC sampling @cite_11 . All these works applied cyclical schedules to the learning rate. In contrast, this paper represents the first to consider the cyclical schedule for @math in VAE. Though the techniques seem simple and similar, our motivation is different: we use the cyclical schedule to re-open Path A in Figure (b) and provide the opportunity to train the decoder with high-quality @math .
@cite_8 @cite_28 @cite_1 @cite_17 @cite_11
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Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple warm restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where we demonstrate new state-of-the-art results at 3.14 and 16.21 , respectively. We also demonstrate its advantages on a dataset of EEG recordings and on a downsampled version of the ImageNet dataset. Our source code is available at https: github.com loshchil SGDR Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on CIFAR-10 and CIFAR-100 datasets where we demonstrate new state-of-the-art results below 4 and 19 , respectively. Our source code is available at this https URL The posteriors over neural network weights are high dimensional and multimodal. Each mode typically characterizes a meaningfully different representation of the data. We develop Cyclical Stochastic Gradient MCMC (SG-MCMC) to automatically explore such distributions. In particular, we propose a cyclical stepsize schedule, where larger steps discover new modes, and smaller steps characterize each mode. We prove that our proposed learning rate schedule provides faster convergence to samples from a stationary distribution than SG-MCMC with standard decaying schedules. Moreover, we provide extensive experimental results to demonstrate the effectiveness of cyclical SG-MCMC in learning complex multimodal distributions, especially for fully Bayesian inference with modern deep neural networks. Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, corresponding theory for general SG-MCMCs has not been explored. In this paper we consider general SG-MCMCs with high-order integrators, and develop theory to analyze finite-time convergence properties and their asymptotic invariant measures. Our theoretical results show faster convergence rates and more accurate invariant measures for SG-MCMCs with higher-order integrators. For example, with the proposed efficient 2nd-order symmetric splitting integrator, the mean square error (MSE) of the posterior average for the SGHMC achieves an optimal convergence rate of L-4 5 at L iterations, compared to L-2 3 for the SGHMC and SGLD with 1st-order Euler integrators. Furthermore, convergence results of decreasing-step-size SG-MCMCs are also developed, with the same convergence rates as their fixed-step-size counterparts for a specific decreasing sequence. Experiments on both synthetic and real datasets verify our theory, and show advantages of the proposed method in two large-scale real applications.