A Robust Adaptive Stochastic Gradient Method for Deep Learning

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose an adaptive learning rate algorithm, which utilizes stochastic curvature information of the loss function for automatically tuning the learning rates. The information about the element-wise curvature of the loss function is estimated from the local statistics of the stochastic first order gradients. We further propose a new variance reduction technique to speed up the convergence. In our experiments with deep neural networks, we obtained better performance compared to the popular stochastic gradient algorithms.

Memory Augmented Neural Networks with Wormhole Connections

Recent empirical results on long-term dependency tasks have shown that neural networks augmented with an external memory can learn the long-term dependency tasks more easily and achieve better generalization than vanilla recurrent neural networks (RNN). We suggest that memory augmented neural networks can reduce the effects of vanishing gradients by creating shortcut (or wormhole) connections. Based on this observation, we propose a novel memory augmented neural network model called TARDIS (Temporal Automatic Relation Discovery in Sequences). The controller of TARDIS can store a selective set of embeddings of its own previous hidden states into an external memory and revisit them as and when needed. For TARDIS, memory acts as a storage for wormhole connections to the past to propagate the gradients more effectively and it helps to learn the temporal dependencies. The memory structure of TARDIS has similarities to both Neural Turing Machines (NTM) and Dynamic Neural Turing Machines (D-NTM), but both read and write operations of TARDIS are simpler and more efficient. We use discrete addressing for read/write operations which helps to substantially to reduce the vanishing gradient problem with very long sequences. Read and write operations in TARDIS are tied with a heuristic once the memory becomes full, and this makes the learning problem simpler when compared to NTM or D-NTM type of architectures. We provide a detailed analysis on the gradient propagation in general for MANNs. We evaluate our models on different long-term dependency tasks and report competitive results in all of them.

Abstractive Text Summarization Using Sequence-to-Sequence RNNs and Beyond

In this work, we model abstractive text summarization using Attentional Encoder-Decoder Recurrent Neural Networks, and show that they achieve state-of-the-art performance on two different corpora. We propose several novel models that address critical problems in summarization that are not adequately modeled by the basic architecture, such as modeling key-words, capturing the hierarchy of sentence-to-word structure, and emitting words that are rare or unseen at training time. Our work shows that many of our proposed models contribute to further improvement in performance. We also propose a new dataset consisting of multi-sentence summaries, and establish performance benchmarks for further research.

Pointing the Unknown Words

The problem of rare and unknown words is an important issue that can potentially influence the performance of many NLP systems, including both the traditional count-based and the deep learning models. We propose a novel way to deal with the rare and unseen words for the neural network models using attention. Our model uses two softmax layers in order to predict the next word in conditional language models: one predicts the location of a word in the source sentence, and the other predicts a word in the shortlist vocabulary. At each time-step, the decision of which softmax layer to use choose adaptively made by an MLP which is conditioned on the context.~We motivate our work from a psychological evidence that humans naturally have a tendency to point towards objects in the context or the environment when the name of an object is not known.~We observe improvements on two tasks, neural machine translation on the Europarl English to French parallel corpora and text summarization on the Gigaword dataset using our proposed model.

Mollifying Networks

The optimization of deep neural networks can be more challenging than traditional convex optimization problems due to the highly non-convex nature of the loss function, e.g. it can involve pathological landscapes such as saddle-surfaces that can be difficult to escape for algorithms based on simple gradient descent. In this paper, we attack the problem of optimization of highly non-convex neural networks by starting with a smoothed -- or \textit{mollified} -- objective function that gradually has a more non-convex energy landscape during the training. Our proposition is inspired by the recent studies in continuation methods: similar to curriculum methods, we begin learning an easier (possibly convex) objective function and let it evolve during the training, until it eventually goes back to being the original, difficult to optimize, objective function. The complexity of the mollified networks is controlled by a single hyperparameter which is annealed during the training. We show improvements on various difficult optimization tasks and establish a relationship with recent works on continuation methods for neural networks and mollifiers.

Generating Factoid Questions With Recurrent Neural Networks: The 30M Factoid Question-Answer Corpus

Over the past decade, large-scale supervised learning corpora have enabled machine learning researchers to make substantial advances. However, to this date, there are no large-scale question-answer corpora available. In this paper we present the 30M Factoid Question-Answer Corpus, an enormous question answer pair corpus produced by applying a novel neural network architecture on the knowledge base Freebase to transduce facts into natural language questions. The produced question answer pairs are evaluated both by human evaluators and using automatic evaluation metrics, including well-established machine translation and sentence similarity metrics. Across all evaluation criteria the question-generation model outperforms the competing template-based baseline. Furthermore, when presented to human evaluators, the generated questions appear comparable in quality to real human-generated questions.

Theano: A Python framework for fast computation of mathematical expressions

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

Noisy Activation Functions

Common nonlinear activation functions used in neural networks can cause training difficulties due to the saturation behavior of the activation function, which may hide dependencies that are not visible to vanilla-SGD (using first order gradients only). Gating mechanisms that use softly saturating activation functions to emulate the discrete switching of digital logic circuits are good examples of this. We propose to exploit the injection of appropriate noise so that the gradients may flow easily, even if the noiseless application of the activation function would yield zero gradient. Large noise will dominate the noise-free gradient and allow stochastic gradient descent toexplore more. By adding noise only to the problematic parts of the activation function, we allow the optimization procedure to explore the boundary between the degenerate (saturating) and the well-behaved parts of the activation function. We also establish connections to simulated annealing, when the amount of noise is annealed down, making it easier to optimize hard objective functions. We find experimentally that replacing such saturating activation functions by noisy variants helps training in many contexts, yielding state-of-the-art or competitive results on different datasets and task, especially when training seems to be the most difficult, e.g., when curriculum learning is necessary to obtain good results.

Policy Distillation

Policies for complex visual tasks have been successfully learned with deep reinforcement learning, using an approach called deep Q-networks (DQN), but relatively large (task-specific) networks and extensive training are needed to achieve good performance. In this work, we present a novel method called policy distillation that can be used to extract the policy of a reinforcement learning agent and train a new network that performs at the expert level while being dramatically smaller and more efficient. Furthermore, the same method can be used to consolidate multiple task-specific policies into a single policy. We demonstrate these claims using the Atari domain and show that the multi-task distilled agent outperforms the single-task teachers as well as a jointly-trained DQN agent.

ADASECANT: Robust Adaptive Secant Method for Stochastic Gradient

Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose a new adaptive learning rate algorithm, which utilizes curvature information for automatically tuning the learning rates. The information about the element-wise curvature of the loss function is estimated from the local statistics of the stochastic first order gradients. We further propose a new variance reduction technique to speed up the convergence. In our preliminary experiments with deep neural networks, we obtained better performance compared to the popular stochastic gradient algorithms.