Knowledge Matters: Importance of Prior Information for Optimization

Jul 13, 2013

Çağlar Gülçehre, Yoshua Bengio

We explore the effect of introducing prior information into the intermediate level of neural networks for a learning task on which all the state-of-the-art machine learning algorithms tested failed to learn. We motivate our work from the hypothesis that humans learn such intermediate concepts from other individuals via a form of supervision or guidance using a curriculum. The experiments we have conducted provide positive evidence in favor of this hypothesis. In our experiments, a two-tiered MLP architecture is trained on a dataset with 64x64 binary inputs images, each image with three sprites. The final task is to decide whether all the sprites are the same or one of them is different. Sprites are pentomino tetris shapes and they are placed in an image with different locations using scaling and rotation transformations. The first part of the two-tiered MLP is pre-trained with intermediate-level targets being the presence of sprites at each location, while the second part takes the output of the first part as input and predicts the final task's target binary event. The two-tiered MLP architecture, with a few tens of thousand examples, was able to learn the task perfectly, whereas all other algorithms (include unsupervised pre-training, but also traditional algorithms like SVMs, decision trees and boosting) all perform no better than chance. We hypothesize that the optimization difficulty involved when the intermediate pre-training is not performed is due to the {\em composition} of two highly non-linear tasks. Our findings are also consistent with hypotheses on cultural learning inspired by the observations of optimization problems with deep learning, presumably because of effective local minima.
Jul 13, 2013

Çağlar Gülçehre, Yoshua Bengio

* 37 Pages, 5 figures, 5 tables JMLR Special Topics on Representation Learning Submission

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Memory Augmented Neural Networks with Wormhole Connections

Jan 30, 2017

Caglar Gulcehre, Sarath Chandar, Yoshua Bengio

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.
Jan 30, 2017

Caglar Gulcehre, Sarath Chandar, Yoshua Bengio

**Click to Read Paper and Get Code**

ADASECANT: Robust Adaptive Secant Method for Stochastic Gradient

Nov 01, 2015

Caglar Gulcehre, Marcin Moczulski, Yoshua Bengio

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.
Nov 01, 2015

Caglar Gulcehre, Marcin Moczulski, Yoshua Bengio

* 8 pages, 3 figures, ICLR workshop submission

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Plan, Attend, Generate: Planning for Sequence-to-Sequence Models

Nov 28, 2017

Francis Dutil, Caglar Gulcehre, Adam Trischler, Yoshua Bengio

We investigate the integration of a planning mechanism into sequence-to-sequence models using attention. We develop a model which can plan ahead in the future when it computes its alignments between input and output sequences, constructing a matrix of proposed future alignments and a commitment vector that governs whether to follow or recompute the plan. This mechanism is inspired by the recently proposed strategic attentive reader and writer (STRAW) model for Reinforcement Learning. Our proposed model is end-to-end trainable using primarily differentiable operations. We show that it outperforms a strong baseline on character-level translation tasks from WMT'15, the algorithmic task of finding Eulerian circuits of graphs, and question generation from the text. Our analysis demonstrates that the model computes qualitatively intuitive alignments, converges faster than the baselines, and achieves superior performance with fewer parameters.
Nov 28, 2017

Francis Dutil, Caglar Gulcehre, Adam Trischler, Yoshua Bengio

* NIPS 2017

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Plan, Attend, Generate: Character-level Neural Machine Translation with Planning in the Decoder

Jun 23, 2017

Caglar Gulcehre, Francis Dutil, Adam Trischler, Yoshua Bengio

We investigate the integration of a planning mechanism into an encoder-decoder architecture with an explicit alignment for character-level machine translation. We develop a model that plans ahead when it computes alignments between the source and target sequences, constructing a matrix of proposed future alignments and a commitment vector that governs whether to follow or recompute the plan. This mechanism is inspired by the strategic attentive reader and writer (STRAW) model. Our proposed model is end-to-end trainable with fully differentiable operations. We show that it outperforms a strong baseline on three character-level decoder neural machine translation on WMT'15 corpus. Our analysis demonstrates that our model can compute qualitatively intuitive alignments and achieves superior performance with fewer parameters.
Jun 23, 2017

Caglar Gulcehre, Francis Dutil, Adam Trischler, Yoshua Bengio

* Accepted to Rep4NLP 2017 Workshop at ACL 2017 Conference

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Dynamic Neural Turing Machine with Soft and Hard Addressing Schemes

Mar 17, 2017

Caglar Gulcehre, Sarath Chandar, Kyunghyun Cho, Yoshua Bengio

We extend neural Turing machine (NTM) model into a dynamic neural Turing machine (D-NTM) by introducing a trainable memory addressing scheme. This addressing scheme maintains for each memory cell two separate vectors, content and address vectors. This allows the D-NTM to learn a wide variety of location-based addressing strategies including both linear and nonlinear ones. We implement the D-NTM with both continuous, differentiable and discrete, non-differentiable read/write mechanisms. We investigate the mechanisms and effects of learning to read and write into a memory through experiments on Facebook bAbI tasks using both a feedforward and GRUcontroller. The D-NTM is evaluated on a set of Facebook bAbI tasks and shown to outperform NTM and LSTM baselines. We have done extensive analysis of our model and different variations of NTM on bAbI task. We also provide further experimental results on sequential pMNIST, Stanford Natural Language Inference, associative recall and copy tasks.
Mar 17, 2017

Caglar Gulcehre, Sarath Chandar, Kyunghyun Cho, Yoshua Bengio

* 13 pages, 3 figures

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A Robust Adaptive Stochastic Gradient Method for Deep Learning

Mar 02, 2017

Caglar Gulcehre, Jose Sotelo, Marcin Moczulski, Yoshua Bengio

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.
Mar 02, 2017

Caglar Gulcehre, Jose Sotelo, Marcin Moczulski, Yoshua Bengio

* IJCNN 2017 Accepted Paper, An extension of our paper, "ADASECANT: Robust Adaptive Secant Method for Stochastic Gradient"

**Click to Read Paper and Get Code**

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.

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Noisy Activation Functions

Apr 03, 2016

Caglar Gulcehre, Marcin Moczulski, Misha Denil, Yoshua Bengio

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.
Apr 03, 2016

Caglar Gulcehre, Marcin Moczulski, Misha Denil, Yoshua Bengio

**Click to Read Paper and Get Code**

Gated Feedback Recurrent Neural Networks

Jun 17, 2015

Junyoung Chung, Caglar Gulcehre, Kyunghyun Cho, Yoshua Bengio

In this work, we propose a novel recurrent neural network (RNN) architecture. The proposed RNN, gated-feedback RNN (GF-RNN), extends the existing approach of stacking multiple recurrent layers by allowing and controlling signals flowing from upper recurrent layers to lower layers using a global gating unit for each pair of layers. The recurrent signals exchanged between layers are gated adaptively based on the previous hidden states and the current input. We evaluated the proposed GF-RNN with different types of recurrent units, such as tanh, long short-term memory and gated recurrent units, on the tasks of character-level language modeling and Python program evaluation. Our empirical evaluation of different RNN units, revealed that in both tasks, the GF-RNN outperforms the conventional approaches to build deep stacked RNNs. We suggest that the improvement arises because the GF-RNN can adaptively assign different layers to different timescales and layer-to-layer interactions (including the top-down ones which are not usually present in a stacked RNN) by learning to gate these interactions.
Jun 17, 2015

Junyoung Chung, Caglar Gulcehre, Kyunghyun Cho, Yoshua Bengio

* 9 pages, removed appendix

**Click to Read Paper and Get Code**

Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling

Dec 11, 2014

Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, Yoshua Bengio

In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a long short-term memory (LSTM) unit and a recently proposed gated recurrent unit (GRU). We evaluate these recurrent units on the tasks of polyphonic music modeling and speech signal modeling. Our experiments revealed that these advanced recurrent units are indeed better than more traditional recurrent units such as tanh units. Also, we found GRU to be comparable to LSTM.
Dec 11, 2014

Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, Yoshua Bengio

* Presented in NIPS 2014 Deep Learning and Representation Learning Workshop

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Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks

Sep 02, 2014

Caglar Gulcehre, Kyunghyun Cho, Razvan Pascanu, Yoshua Bengio

In this paper we propose and investigate a novel nonlinear unit, called $L_p$ unit, for deep neural networks. The proposed $L_p$ unit receives signals from several projections of a subset of units in the layer below and computes a normalized $L_p$ norm. We notice two interesting interpretations of the $L_p$ unit. First, the proposed unit can be understood as a generalization of a number of conventional pooling operators such as average, root-mean-square and max pooling widely used in, for instance, convolutional neural networks (CNN), HMAX models and neocognitrons. Furthermore, the $L_p$ unit is, to a certain degree, similar to the recently proposed maxout unit (Goodfellow et al., 2013) which achieved the state-of-the-art object recognition results on a number of benchmark datasets. Secondly, we provide a geometrical interpretation of the activation function based on which we argue that the $L_p$ unit is more efficient at representing complex, nonlinear separating boundaries. Each $L_p$ unit defines a superelliptic boundary, with its exact shape defined by the order $p$. We claim that this makes it possible to model arbitrarily shaped, curved boundaries more efficiently by combining a few $L_p$ units of different orders. This insight justifies the need for learning different orders for each unit in the model. We empirically evaluate the proposed $L_p$ units on a number of datasets and show that multilayer perceptrons (MLP) consisting of the $L_p$ units achieve the state-of-the-art results on a number of benchmark datasets. Furthermore, we evaluate the proposed $L_p$ unit on the recently proposed deep recurrent neural networks (RNN).
Sep 02, 2014

Caglar Gulcehre, Kyunghyun Cho, Razvan Pascanu, Yoshua Bengio

* ECML/PKDD 2014

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How to Construct Deep Recurrent Neural Networks

Apr 24, 2014

Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Yoshua Bengio

In this paper, we explore different ways to extend a recurrent neural network (RNN) to a \textit{deep} RNN. We start by arguing that the concept of depth in an RNN is not as clear as it is in feedforward neural networks. By carefully analyzing and understanding the architecture of an RNN, however, we find three points of an RNN which may be made deeper; (1) input-to-hidden function, (2) hidden-to-hidden transition and (3) hidden-to-output function. Based on this observation, we propose two novel architectures of a deep RNN which are orthogonal to an earlier attempt of stacking multiple recurrent layers to build a deep RNN (Schmidhuber, 1992; El Hihi and Bengio, 1996). We provide an alternative interpretation of these deep RNNs using a novel framework based on neural operators. The proposed deep RNNs are empirically evaluated on the tasks of polyphonic music prediction and language modeling. The experimental result supports our claim that the proposed deep RNNs benefit from the depth and outperform the conventional, shallow RNNs.
Apr 24, 2014

Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Yoshua Bengio

* Accepted at ICLR 2014 (Conference Track). 10-page text + 3-page references

**Click to Read Paper and Get Code**

Recurrent Batch Normalization

Feb 28, 2017

Tim Cooijmans, Nicolas Ballas, César Laurent, Çağlar Gülçehre, Aaron Courville

We propose a reparameterization of LSTM that brings the benefits of batch normalization to recurrent neural networks. Whereas previous works only apply batch normalization to the input-to-hidden transformation of RNNs, we demonstrate that it is both possible and beneficial to batch-normalize the hidden-to-hidden transition, thereby reducing internal covariate shift between time steps. We evaluate our proposal on various sequential problems such as sequence classification, language modeling and question answering. Our empirical results show that our batch-normalized LSTM consistently leads to faster convergence and improved generalization.
Feb 28, 2017

Tim Cooijmans, Nicolas Ballas, César Laurent, Çağlar Gülçehre, Aaron Courville

**Click to Read Paper and Get Code**

Pointing the Unknown Words

Aug 21, 2016

Caglar Gulcehre, Sungjin Ahn, Ramesh Nallapati, Bowen Zhou, Yoshua Bengio

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.
Aug 21, 2016

Caglar Gulcehre, Sungjin Ahn, Ramesh Nallapati, Bowen Zhou, Yoshua Bengio

* ACL 2016 Oral Paper

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

Aug 26, 2016

Ramesh Nallapati, Bowen Zhou, Cicero Nogueira dos santos, Caglar Gulcehre, Bing Xiang

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.
Aug 26, 2016

Ramesh Nallapati, Bowen Zhou, Cicero Nogueira dos santos, Caglar Gulcehre, Bing Xiang

* The SIGNLL Conference on Computational Natural Language Learning (CoNLL), 2016

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Identifying and attacking the saddle point problem in high-dimensional non-convex optimization

Jun 10, 2014

Yann Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, Yoshua Bengio

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, neural network theory, and empirical evidence, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new approach to second-order optimization, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep or recurrent neural network training, and provide numerical evidence for its superior optimization performance.
Jun 10, 2014

Yann Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, Yoshua Bengio

* The theoretical review and analysis in this article draw heavily from arXiv:1405.4604 [cs.LG]

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Gated Orthogonal Recurrent Units: On Learning to Forget

Oct 25, 2017

Li Jing, Caglar Gulcehre, John Peurifoy, Yichen Shen, Max Tegmark, Marin Soljačić, Yoshua Bengio

We present a novel recurrent neural network (RNN) based model that combines the remembering ability of unitary RNNs with the ability of gated RNNs to effectively forget redundant/irrelevant information in its memory. We achieve this by extending unitary RNNs with a gating mechanism. Our model is able to outperform LSTMs, GRUs and Unitary RNNs on several long-term dependency benchmark tasks. We empirically both show the orthogonal/unitary RNNs lack the ability to forget and also the ability of GORU to simultaneously remember long term dependencies while forgetting irrelevant information. This plays an important role in recurrent neural networks. We provide competitive results along with an analysis of our model on many natural sequential tasks including the bAbI Question Answering, TIMIT speech spectrum prediction, Penn TreeBank, and synthetic tasks that involve long-term dependencies such as algorithmic, parenthesis, denoising and copying tasks.
Oct 25, 2017

Li Jing, Caglar Gulcehre, John Peurifoy, Yichen Shen, Max Tegmark, Marin Soljačić, Yoshua Bengio

**Click to Read Paper and Get Code**

Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation

Sep 03, 2014

Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, Yoshua Bengio

In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of the proposed model are jointly trained to maximize the conditional probability of a target sequence given a source sequence. The performance of a statistical machine translation system is empirically found to improve by using the conditional probabilities of phrase pairs computed by the RNN Encoder-Decoder as an additional feature in the existing log-linear model. Qualitatively, we show that the proposed model learns a semantically and syntactically meaningful representation of linguistic phrases.
Sep 03, 2014

Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, Yoshua Bengio

* EMNLP 2014

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Machine Comprehension by Text-to-Text Neural Question Generation

May 15, 2017

Xingdi Yuan, Tong Wang, Caglar Gulcehre, Alessandro Sordoni, Philip Bachman, Sandeep Subramanian, Saizheng Zhang, Adam Trischler

We propose a recurrent neural model that generates natural-language questions from documents, conditioned on answers. We show how to train the model using a combination of supervised and reinforcement learning. After teacher forcing for standard maximum likelihood training, we fine-tune the model using policy gradient techniques to maximize several rewards that measure question quality. Most notably, one of these rewards is the performance of a question-answering system. We motivate question generation as a means to improve the performance of question answering systems. Our model is trained and evaluated on the recent question-answering dataset SQuAD.
May 15, 2017

Xingdi Yuan, Tong Wang, Caglar Gulcehre, Alessandro Sordoni, Philip Bachman, Sandeep Subramanian, Saizheng Zhang, Adam Trischler

**Click to Read Paper and Get Code**