Scalability properties of deep neural networks raise key research questions, particularly as the problems considered become larger and more challenging. This paper expands on the idea of conditional computation introduced by Bengio, et. al., where the nodes of a deep network are augmented by a set of gating units that determine when a node should be calculated. By factorizing the weight matrix into a low-rank approximation, an estimation of the sign of the pre-nonlinearity activation can be efficiently obtained. For networks using rectified-linear hidden units, this implies that the computation of a hidden unit with an estimated negative pre-nonlinearity can be ommitted altogether, as its value will become zero when nonlinearity is applied. For sparse neural networks, this can result in considerable speed gains. Experimental results using the MNIST and SVHN data sets with a fully-connected deep neural network demonstrate the performance robustness of the proposed scheme with respect to the error introduced by the conditional computation process.

Low-Rank Approximations for Conditional Feedforward Computation in Deep Neural Networks

The aim of this paper is three-fold. First we show that Hessian-Free (Martens, 2010) and Krylov Subspace Descent (Vinyals and Povey, 2012) can be described as implementations of natural gradient descent due to their use of the extended Gauss-Newton approximation of the Hessian. Secondly we re-derive natural gradient from basic principles, contrasting the difference between two versions of the algorithm found in the neural network literature, as well as highlighting a few differences between natural gradient and typical second order methods. Lastly we show empirically that natural gradient can be robust to overfitting and particularly it can be robust to the order in which the training data is presented to the model.

Revisiting Natural Gradient for Deep Networks

Within the framework of AdaBoost.MH, we propose to train vector-valued decision trees to optimize the multi-class edge without reducing the multi-class problem to $K$ binary one-against-all classifications. The key element of the method is a vector-valued decision stump, factorized into an input-independent vector of length $K$ and label-independent scalar classifier. At inner tree nodes, the label-dependent vector is discarded and the binary classifier can be used for partitioning the input space into two regions. The algorithm retains the conceptual elegance, power, and computational efficiency of binary AdaBoost. In experiments it is on par with support vector machines and with the best existing multi-class boosting algorithm AOSOLogitBoost, and it is significantly better than other known implementations of AdaBoost.MH.

The return of AdaBoost.MH: multi-class Hamming trees

This paper introduces a new architecture for human pose estimation using a multi- layer convolutional network architecture and a modified learning technique that learns low-level features and higher-level weak spatial models. Unconstrained human pose estimation is one of the hardest problems in computer vision, and our new architecture and learning schema shows significant improvement over the current state-of-the-art results. The main contribution of this paper is showing, for the first time, that a specific variation of deep learning is able to outperform all existing traditional architectures on this task. The paper also discusses several lessons learned while researching alternatives, most notably, that it is possible to learn strong low-level feature detectors on features that might even just cover a few pixels in the image. Higher-level spatial models improve somewhat the overall result, but to a much lesser extent then expected. Many researchers previously argued that the kinematic structure and top-down information is crucial for this domain, but with our purely bottom up, and weak spatial model, we could improve other more complicated architectures that currently produce the best results. This mirrors what many other researchers, like those in the speech recognition, object recognition, and other domains have experienced.

Learning Human Pose Estimation Features with Convolutional Networks

This paper introduces EXMOVES, learned exemplar-based features for efficient recognition of actions in videos. The entries in our descriptor are produced by evaluating a set of movement classifiers over spatial-temporal volumes of the input sequence. Each movement classifier is a simple exemplar-SVM trained on low-level features, i.e., an SVM learned using a single annotated positive space-time volume and a large number of unannotated videos. Our representation offers two main advantages. First, since our mid-level features are learned from individual video exemplars, they require minimal amount of supervision. Second, we show that simple linear classification models trained on our global video descriptor yield action recognition accuracy approaching the state-of-the-art but at orders of magnitude lower cost, since at test-time no sliding window is necessary and linear models are efficient to train and test. This enables scalable action recognition, i.e., efficient classification of a large number of different actions even in large video databases. We show the generality of our approach by building our mid-level descriptors from two different low-level feature representations. The accuracy and efficiency of the approach are demonstrated on several large-scale action recognition benchmarks.

EXMOVES: Classifier-based Features for Scalable Action Recognition

We consider the problem of image representation for the tasks of unsupervised learning and semi-supervised learning. In those learning tasks, the raw image vectors may not provide enough representation for their intrinsic structures due to their highly dense feature space. To overcome this problem, the raw image vectors should be mapped to a proper representation space which can capture the latent structure of the original data and represent the data explicitly for further learning tasks such as clustering. Inspired by the recent research works on deep neural network and representation learning, in this paper, we introduce the multiple-layer auto-encoder into image representation, we also apply the locally invariant ideal to our image representation with auto-encoders and propose a novel method, called Graph regularized Auto-Encoder (GAE). GAE can provide a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. Extensive experiments on image clustering show encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-word cases.

Image Representation Learning Using Graph Regularized Auto-Encoders

We propose two novel zero-shot learning methods for semantic utterance classification (SUC) using deep learning. Both approaches rely on learning deep semantic embeddings from a large amount of Query Click Log data obtained from a search engine. Traditional semantic utterance classification systems require large amounts of labelled data, whereas our proposed methods make use of the structure of the task to allow classification without labeled data. We also develop a zero-shot semantic clustering algorithm for extracting discriminative features for supervised semantic utterance classification systems. We demonstrate the effectiveness of the zero-shot semantic learning algorithm on the SUC dataset collected by cite{DCN}. Furthermore, we show that extracting features using zero-shot semantic clustering for a linear SVM reaches state-of-the-art result on that dataset.

Zero-Shot Learning and Clustering for Semantic Utterance Classification

Dataset bias remains a significant barrier towards solving real world computer vision tasks. Though deep convolutional networks have proven to be a competitive approach for image classification, a question remains: have these models have solved the dataset bias problem? In general, training or fine-tuning a state-of-the-art deep model on a new domain requires a significant amount of data, which for many applications is simply not available. Transfer of models directly to new domains without adaptation has historically led to poor recognition performance. In this paper, we pose the following question: is a single image dataset, much larger than previously explored for adaptation, comprehensive enough to learn general deep models that may be effectively applied to new image domains? In other words, are deep CNNs trained on large amounts of labeled data as susceptible to dataset bias as previous methods have been shown to be? We show that a generic supervised deep CNN model trained on a large dataset reduces, but does not remove, dataset bias. Furthermore, we propose several methods for adaptation with deep models that are able to operate with little (one example per category) or no labeled domain specific data. Our experiments show that adaptation of deep models on benchmark visual domain adaptation datasets can provide a significant performance boost.

One-Shot Adaptation of Supervised Deep Convolutional Models

It is well known that direct training of deep multi-layer neural networks (DNNs) will generally lead to poor results. A major progress in recent years is the invention of various unsupervised pretraining methods to initialize network parameters and it was shown that such methods lead to good prediction performance. However, the reason for the success of the pretraining has not been fully understood, although it was argued that regularization and better optimization play certain roles. This paper provides another explanation for the effectiveness of the pretraining, where we empirically show the pretraining leads to a higher level of sparseness of hidden unit activation in the resulting neural networks, and the higher sparseness is positively correlated to faster training speed and better prediction accuracy. Moreover, we also show that rectified linear units (ReLU) can capture the sparseness benefits of the pretraining. Our implementation of DNNs with ReLU does not require the pretraining, but achieves comparable or better prediction performance than traditional DNNs with pretraining on standard benchmark datasets.

Why does the unsupervised pretraining encourage moderate-sparseness?

The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we empirically investigate several questions related to the efficacy of dropout, specifically as it concerns networks employing the popular rectified linear activation function. We investigate the quality of the test time weight-scaling inference procedure by evaluating the geometric average exactly in small models, as well as compare the performance of the geometric mean to the arithmetic mean more commonly employed by ensemble techniques. We explore the effect of tied weights on the ensemble interpretation by training ensembles of masked networks without tied weights. Finally, we investigate an alternative criterion based on a biased estimator of the maximum likelihood ensemble gradient.

An empirical analysis of dropout in piecewise linear networks

We pursue early stopping that helps Gaussian Restricted Boltzmann Machines (GRBMs) to gain good natural image representations in terms of overcompleteness and data fitting. GRBMs are widely considered as an unsuitable model for natural images because they gain non-overcomplete representations which include uniform filters that do not represent sharp edges. We have recently found that GRBMs once gain and subsequently lose sharp edge filters during their training, contrary to this common perspective. We attribute this phenomenon to a tradeoff between overcompleteness of GRBM representations and data fitting. To gain GRBM representations that are overcomplete and fit data well, we propose approximated infomax early stopping for GRBMs. The proposed method enables huge performance boosts of classifiers trained on GRBM representations.

Approximated Infomax Early Stopping: Revisiting Gaussian RBMs on Natural Images

Recent non-linear feature selection approaches employing greedy optimisation of Centred Kernel Target Alignment(KTA) exhibit strong results in terms of generalisation accuracy and sparsity. However, they are computationally prohibitive for large datasets. We propose randSel, a randomised feature selection algorithm, with attractive scaling properties. Our theoretical analysis of randSel provides strong probabilistic guarantees for correct identification of relevant features. RandSel's characteristics make it an ideal candidate for identifying informative learned representations. We've conducted experimentation to establish the performance of this approach, and present encouraging results, including a 3rd position result in the recent ICML black box learning challenge as well as competitive results for signal peptide prediction, an important problem in bioinformatics.

Learning Non-Linear Feature Maps, With An Application To Representation Learning

Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are robust and widely applicable across many different optimization landscapes. In this paper we develop a collection of unit tests for stochastic optimization. Each unit test rapidly evaluates an optimization algorithm on a small-scale, isolated, and well-understood difficulty, rather than in real-world scenarios where many such issues are entangled. Passing these unit tests is not sufficient, but absolutely necessary for any algorithms with claims to generality or robustness. We give initial quantitative and qualitative results on a dozen established algorithms. The testing framework is open-source, extensible, and easy to apply to new algorithms.

Unit Tests for Stochastic Optimization

This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional distributional semantics. Standard techniques from the neural networks literature are used to learn the tensors, which are tested on a selectional preference-style task with a simple 2-dimensional sentence space. Promising results are obtained against a competitive corpus-based baseline. We argue that extending this work beyond transitive verbs, and to higher-dimensional sentence spaces, is an interesting and challenging problem for the machine learning community to consider.

Learning Type-Driven Tensor-Based Meaning Representations

Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distribution. The result of training is therefore a machine that generates samples through this Markov chain. However, the previously introduced GSN consistency theorems suggest that in order to capture a wide class of distributions, the transition operator in general should be multimodal, something that has not been done before this paper. We introduce for the first time multimodal transition distributions for GSNs, in particular using models in the NADE family (Neural Autoregressive Density Estimator) as output distributions of the transition operator. A NADE model is related to an RBM (and can thus model multimodal distributions) but its likelihood (and likelihood gradient) can be computed easily. The parameters of the NADE are obtained as a learned function of the previous state of the learned Markov chain. Experiments clearly illustrate the advantage of such multimodal transition distributions over unimodal GSNs.

Multimodal Transitions for Generative Stochastic Networks

We propose a learning algorithm for auto-encoders based on a rate-distortion objective. Our goal is to minimize the mutual information between the inputs and the outputs of an auto-encoder subject to a fidelity constraint. Minimizing the mutual information acts as a regularization term whereas the fidelity constraint can be understood as a risk functional in the conventional statistical learning setting. The proposed algorithm uses a recently introduced measure of entropy based on infinitely divisible matrices that avoids the plug in estimation of densities. Experiments using over-complete bases show that the auto-encoder learns a regularized input-output map without explicit regularization terms or add-hoc constraints such as tied weights.

Rate-Distortion Auto-Encoders

Spontaneous cortical activity -- the ongoing cortical activities in absence of sensory input -- are considered to play a vital role in many aspects of both normal brain functions and mental dysfunctions. We present a centered Gaussian-binary deep Boltzmann machine (GDBM) for modeling the activity in visual cortex and relate the random sampling in DBMs to the spontaneous cortical activity. After training on natural image patches, the proposed model is able to learn the filters similar to the receptive fields of simple cells in V1. Furthermore, we show that the samples collected from random sampling in the centered GDBMs encompass similar activity patterns as found in the spontaneous cortical activity of the visual cortex. Specifically, filters having the same orientation preference tend to be active together during random sampling. Our work demonstrates the homeostasis learned by the centered GDBM and its potential for modeling visual cortical activity. Besides, the results support the hypothesis that the homeostatic mechanism exists in the cortex.

Modeling correlations in spontaneous activity of visual cortex with centered Gaussian-binary deep Boltzmann machines

Catastrophic forgetting is a problem faced by many machine learning models and algorithms. When trained on one task, then trained on a second task, many machine learning models 'forget'' how to perform the first task. This is widely believed to be a serious problem for neural networks. Here, we investigate the extent to which the catastrophic forgetting problem occurs for modern neural networks, comparing both established and recent gradient-based training algorithms and activation functions. We also examine the effect of the relationship between the first task and the second task on catastrophic forgetting.

An Empirical Investigation of Catastrophic Forgeting in Gradient-Based Neural Networks

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used to decide whether the approximation provided by the CD algorithm is good enough, though several authors (Schulz et al., 2010; Fischer & Igel, 2010) have raised doubts concerning the feasibility of this procedure. However, not many alternatives to the reconstruction error have been used in the literature. In this manuscript we investigate simple alternatives to the reconstruction error in order to detect as soon as possible the decrease in the log-likelihood during learning.

ICLR 2014 Submissions