Is the Rectified Adam (RAdam) optimizer actually better than the standard Adam optimizer? According to my 24 experiments, the answer is no, typically not (but there are cases where you do want to use it instead of Adam). In Liu et al.'s 2018 paper, On the Variance of the Adaptive Learning Rate and Beyond, the authors claim that Rectified Adam can obtain: The authors tested their hypothesis on three different datasets, including one NLP dataset and two computer vision datasets (ImageNet and CIFAR-10). In each case Rectified Adam outperformed standard Adam…but failed to outperform standard Stochastic Gradient Descent (SGD)! The Rectified Adam optimizer has some strong theoretical justifications -- but as a deep learning practitioner, you need more than just theory -- you need to see empirical results applied to a variety of datasets. And perhaps more importantly, you need to obtain a mastery level experience operating/driving the optimizer (or a small subset of optimizers) as well. If you haven't yet, go ahead and read part one to ensure you have a good understanding of how the Rectified Adam optimizer works. From there, read today's post to help you understand how to design, code, and run experiments used to compare deep learning optimizers. To learn how to compare Rectified Adam to standard Adam, just keep reading! In the first part of this tutorial, we'll briefly discuss the Rectified Adam optimizer, including how it works and why it's interesting to us as deep learning practitioners.

A deep neural network has relieved the burden of feature engineering by human experts, but comparable efforts are instead required to determine an effective architecture. On the other hands, as the size of a network has over-grown, a lot of resources are also invested to reduce its size. These problems can be addressed by sparsification of an over-complete model, which removes redundant parameters or connections by pruning them away after training or encouraging them to become zero during training. In general, however, these approaches are not fully differentiable and interrupt an end-to-end training process with the stochastic gradient descent in that they require either a parameter selection or a soft-thresholding step. In this paper, we propose a fully differentiable sparsification method for deep neural networks, which allows parameters to be exactly zero during training, and thus can learn the sparsified structure and the weights of networks simultaneously using the stochastic gradient descent. We apply the proposed method to various popular models in order to show its effectiveness.

Generative Adversarial Networks (GAN) training process, in most cases, apply uniform and Gaussian sampling methods in latent space, which probably spends most of the computation on examples that can be properly handled and easy to generate. Theoretically, importance sampling speeds up stochastic gradient algorithms for supervised learning by prioritizing training examples. In this paper, we explore the possibility for adapting importance sampling into adversarial learning. We use importance sampling to replace uniform and Gaussian sampling methods in latent space and combine normalizing flow with importance sampling to approximate latent space posterior distribution by density estimation. Empirically, results on MNIST and Fashion-MNIST demonstrate that our method significantly accelerates the convergence of generative process while retaining visual fidelity in generated samples.

It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing works, we investigate the gradient descent method for training two-layer neural networks for approximating some target continuous functions. By making use the generic chaining technique from probability theory, we show that gradient descent can yield an exponential convergence rate, while the width of the neural networks needed is independent of the size of the training data. The result also implies some strong approximation ability of the two-layer neural networks without curse of dimensionality.

Meta-learning is a paradigm in machine learning which aims to develop models and training algorithms which can quickly adapt to new tasks and data. Our focus in this paper is on meta-learning in reinforcement learning (RL), where data efficiency is of paramount importance because gathering new samples often requires costly simulations or interactions with the real world. A popular technique for RL meta-learning is Model Agnostic Meta Learning (MAML) (Finn et al., 2017, 2018), a model for training an agent (the meta-policy) which can quickly adapt to new and unknown tasks by performing one (or a few) gradient updates in the new environment. We provide a formal description of MAML in Section 2. MAML has proven to be successful for many applications. However, implementing and running MAML continues to be challenging. One major complication is that the standard version of MAML requires estimating second derivatives of the RL reward function, which is difficult when using backpropagation on stochastic policies; indeed, the original implementation of MAML (Finn et al., 2017) did so incorrectly, which spurred the development of unbiased higher-order estimators (DiCE, (Foerster et al., 2018)) and further analysis of the credit assignment mechanism in MAML (Rothfuss et al., 2019).

Stochastic gradient descent (SGD) is the method of choice for distributed machine learning, by virtue of its light complexity per iteration on compute nodes, leading to almost linear speedups in theory. Nevertheless, such speedups are rarely observed in practice, due to high communication overheads during synchronization steps. We alleviate this problem by introducing independent subnet training: a simple, jointly model-parallel and data-parallel, approach to distributed training for fully connected, feed-forward neural networks. During subnet training, neurons are stochastically partitioned without replacement, and each partition is sent only to a single worker. This reduces the overall synchronization overhead, as each worker only receives the weights associated with the subnetwork it has been assigned to. Subnet training also reduces synchronization frequency: since workers train disjoint portions of the network, the training can proceed for long periods of time before synchronization, similar to local SGD approaches. We empirically evaluate our approach on real-world speech recognition and product recommendation applications, where we observe that subnet training i) results into accelerated training times, as compared to state of the art distributed models, and ii) often results into boosting the testing accuracy, as it implicitly combines dropout and batch normalization regularizations during training.

We study the iteration complexity of stochastic gradient descent (SGD) for minimizing the gradient norm of smooth, possibly nonconvex functions. We provide several results, implying that the classical $\mathcal{O}(\epsilon^{-4})$ upper bound (for making the average gradient norm less than $\epsilon$) cannot be improved upon, unless a combination of additional assumptions is made. Notably, this holds even if we limit ourselves to convex quadratic functions. We also show that for nonconvex functions, the feasibility of minimizing gradients with SGD is surprisingly sensitive to the choice of optimality criteria.

This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification, statistical learning theory, and dimension independent generalization bounds. Implicit regularization in deep learning examples are presented, including data augmentation, adversarial training, and additive noise. These methods are re-framed as explicit gradient regularization.

The combination of the re-parameterization trick with the use of variational auto-encoders has caused a sensation in Bayesian deep learning, allowing the training of realistic generative models of images and has considerably increased our ability to use scalable latent variable models. The re-parameterization trick is necessary for models in which no analytical variational bound is available and allows noisy gradients to be computed for arbitrary models. However, for certain standard output layers of a neural network, analytical bounds are available and the variational auto-encoder may be used both without the re-parameterization trick or the need for any Monte Carlo approximation. In this work, we show that using Jaakola and Jordan bound, we can produce a binary classification layer that allows a Bayesian output layer to be trained, using the standard stochastic gradient descent algorithm. We further demonstrate that a latent variable model utilizing the Bouchard bound for multi-class classification allows for fast training of a fully probabilistic latent factor model, even when the number of classes is very large.

Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the dire ct use of gradient descent. This paper proposes a method of estimating gradient to perform gradient descent, that converges to a stationary point for general non-convex optimization problems. Beyond the first-order stati onary properties, the second-order stationary properties are important in machine learning applications to achieve b etter performance. Gradient descent and its variants (e.g., Stochastic Gradie nt Descent) are widely used in machine learning due to their favorable computational properties, for examp le, in optimizing weights of a deep neural network. Recently, second order stationary guarant ees have been studied by using a perturbed version of gradient de scent [2].