arXiv subjects

Nitish Shirish Keskar

Publications and source records attributed to Nitish Shirish Keskar.

28 records · Page 2Linked to original sources

arXiv2018

Using Mode Connectivity for Loss Landscape Analysis

Mode connectivity is a recently introduced frame- work that empirically establishes the connected- ness of minima by finding a high accuracy curve between two independently trained models. To investigate the limits of this setup, we examine the efficacy of this technique in extreme cases where the input models are trained or initialized differently. We find that the procedure is resilient to such changes. Given this finding, we propose using the framework for analyzing loss surfaces and training trajectories more generally, and in this direction, study SGD with cosine annealing and restarts (SGDR). We report that while SGDR moves over barriers in its trajectory, propositions claiming that it converges to and escapes from multiple local minima are not substantiated by our empirical results.

cs.LG↗

arXiv2018

Balancing Communication and Computation in Distributed Optimization

Methods for distributed optimization have received significant attention in recent years owing to their wide applicability in various domains. A distributed optimization method typically consists of two key components: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in the network requires some form of information exchange with its neighboring nodes (communication) and the computation step related to a (sub)-gradient (computation). The standard way of judging an algorithm via only the number of iterations overlooks the complexity associated with each iteration. Moreover, various applications deploying distributed methods may prefer a different composition of communication and computation. Motivated by this discrepancy, in this work we propose an adaptive cost framework which adjusts the cost measure depending on the features of various applications. We present a flexible algorithmic framework, where communication and computation steps are explicitly decomposed to enable algorithm customization for various applications. We apply this framework to the well-known distributed gradient descent (DGD) method, and show that the resulting customized algorithms, which we call DGD$^t$, NEAR-DGD$^t$ and NEAR-DGD$^+$, compare favorably to their base algorithms, both theoretically and empirically. The proposed NEAR-DGD$^+$ algorithm is an exact first-order method where the communication and computation steps are nested, and when the number of communication steps is adaptively increased, the method converges to the optimal solution. We test the performance and illustrate the flexibility of the methods, as well as practical variants, on quadratic functions and classification problems that arise in machine learning, in terms of iterations, gradient evaluations, communications and the proposed cost framework.

math.OC↗

arXiv2018

An Analysis of Neural Language Modeling at Multiple Scales

Many of the leading approaches in language modeling introduce novel, complex and specialized architectures. We take existing state-of-the-art word level language models based on LSTMs and QRNNs and extend them to both larger vocabularies as well as character-level granularity. When properly tuned, LSTMs and QRNNs achieve state-of-the-art results on character-level (Penn Treebank, enwik8) and word-level (WikiText-103) datasets, respectively. Results are obtained in only 12 hours (WikiText-103) to 2 days (enwik8) using a single modern GPU.

cs.CL↗

arXiv2017

Improving Generalization Performance by Switching from Adam to SGD

Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion of training but are outperformed by SGD at later stages of training. We investigate a hybrid strategy that begins training with an adaptive method and switches to SGD when appropriate. Concretely, we propose SWATS, a simple strategy which switches from Adam to SGD when a triggering condition is satisfied. The condition we propose relates to the projection of Adam steps on the gradient subspace. By design, the monitoring process for this condition adds very little overhead and does not increase the number of hyperparameters in the optimizer. We report experiments on several standard benchmarks such as: ResNet, SENet, DenseNet and PyramidNet for the CIFAR-10 and CIFAR-100 data sets, ResNet on the tiny-ImageNet data set and language modeling with recurrent networks on the PTB and WT2 data sets. The results show that our strategy is capable of closing the generalization gap between SGD and Adam on a majority of the tasks.

cs.LG↗

arXiv2017

Weighted Transformer Network for Machine Translation

State-of-the-art results on neural machine translation often use attentional sequence-to-sequence models with some form of convolution or recursion. Vaswani et al. (2017) propose a new architecture that avoids recurrence and convolution completely. Instead, it uses only self-attention and feed-forward layers. While the proposed architecture achieves state-of-the-art results on several machine translation tasks, it requires a large number of parameters and training iterations to converge. We propose Weighted Transformer, a Transformer with modified attention layers, that not only outperforms the baseline network in BLEU score but also converges 15-40% faster. Specifically, we replace the multi-head attention by multiple self-attention branches that the model learns to combine during the training process. Our model improves the state-of-the-art performance by 0.5 BLEU points on the WMT 2014 English-to-German translation task and by 0.4 on the English-to-French translation task.

cs.AI↗

arXiv2017

Regularizing and Optimizing LSTM Language Models

Recurrent neural networks (RNNs), such as long short-term memory networks (LSTMs), serve as a fundamental building block for many sequence learning tasks, including machine translation, language modeling, and question answering. In this paper, we consider the specific problem of word-level language modeling and investigate strategies for regularizing and optimizing LSTM-based models. We propose the weight-dropped LSTM which uses DropConnect on hidden-to-hidden weights as a form of recurrent regularization. Further, we introduce NT-ASGD, a variant of the averaged stochastic gradient method, wherein the averaging trigger is determined using a non-monotonic condition as opposed to being tuned by the user. Using these and other regularization strategies, we achieve state-of-the-art word level perplexities on two data sets: 57.3 on Penn Treebank and 65.8 on WikiText-2. In exploring the effectiveness of a neural cache in conjunction with our proposed model, we achieve an even lower state-of-the-art perplexity of 52.8 on Penn Treebank and 52.0 on WikiText-2.

cs.CL↗

arXiv2017

On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima

The stochastic gradient descent (SGD) method and its variants are algorithms of choice for many Deep Learning tasks. These methods operate in a small-batch regime wherein a fraction of the training data, say $32$-$512$ data points, is sampled to compute an approximation to the gradient. It has been observed in practice that when using a larger batch there is a degradation in the quality of the model, as measured by its ability to generalize. We investigate the cause for this generalization drop in the large-batch regime and present numerical evidence that supports the view that large-batch methods tend to converge to sharp minimizers of the training and testing functions - and as is well known, sharp minima lead to poorer generalization. In contrast, small-batch methods consistently converge to flat minimizers, and our experiments support a commonly held view that this is due to the inherent noise in the gradient estimation. We discuss several strategies to attempt to help large-batch methods eliminate this generalization gap.

cs.LG↗

arXiv2016

A Limited-Memory Quasi-Newton Algorithm for Bound-Constrained Nonsmooth Optimization

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with a variant of the weak Wolfe line search. The key ingredient of the method is an active-set selection strategy that defines the subspace in which search directions are computed. To overcome the inherent shortsightedness of the gradient for a nonsmooth function, we propose two strategies. The first relies on an approximation of the $ε$-minimum norm subgradient, and the second uses an iterative corrective loop that augments the active set based on the resulting search directions. We describe a Python implementation of the proposed algorithm and present numerical results on a set of standard test problems to illustrate the efficacy of our approach.

math.OC↗

arXiv2016

adaQN: An Adaptive Quasi-Newton Algorithm for Training RNNs

Recurrent Neural Networks (RNNs) are powerful models that achieve exceptional performance on several pattern recognition problems. However, the training of RNNs is a computationally difficult task owing to the well-known "vanishing/exploding" gradient problem. Algorithms proposed for training RNNs either exploit no (or limited) curvature information and have cheap per-iteration complexity, or attempt to gain significant curvature information at the cost of increased per-iteration cost. The former set includes diagonally-scaled first-order methods such as ADAGRAD and ADAM, while the latter consists of second-order algorithms like Hessian-Free Newton and K-FAC. In this paper, we present adaQN, a stochastic quasi-Newton algorithm for training RNNs. Our approach retains a low per-iteration cost while allowing for non-diagonal scaling through a stochastic L-BFGS updating scheme. The method uses a novel L-BFGS scaling initialization scheme and is judicious in storing and retaining L-BFGS curvature pairs. We present numerical experiments on two language modeling tasks and show that adaQN is competitive with popular RNN training algorithms.

cs.LG↗

arXiv2015

A Second-Order Method for Convex $\ell_1$-Regularized Optimization with Active Set Prediction

We describe an active-set method for the minimization of an objective function $ϕ$ that is the sum of a smooth convex function and an $\ell_1$-regularization term. A distinctive feature of the method is the way in which active-set identification and {second-order} subspace minimization steps are integrated to combine the predictive power of the two approaches. At every iteration, the algorithm selects a candidate set of free and fixed variables, performs an (inexact) subspace phase, and then assesses the quality of the new active set. If it is not judged to be acceptable, then the set of free variables is restricted and a new active-set prediction is made. We establish global convergence for our approach, and compare the new method against the state-of-the-art code LIBLINEAR.

math.OC↗