In recent years, the convolutional neural network (CNN) has achieved great success in many computer vision tasks. Partially inspired by neuroscience, CNN shares many properties with the visual system of the brain. A prominent difference is that CNN is typically a feed-forward architecture while in the visual system recurrent connections are abundant. Inspired by this fact, we propose a recurrent CNN (RCNN) for object recognition by incorporating recurrent connections into each convolutional layer. Though the input is static, the activities of RCNN units evolve over time so that the activity of each unit is modulated by the activities of its neighboring units. This property enhances the ability of the model to integrate the context information, which is important for object recognition. Like other recurrent neural networks, unfolding the RCNN through time can result in an arbitrarily deep network with a fixed number of parameters. Furthermore, the unfolded network has multiple paths, which can facilitate the learning process. The model is tested on four benchmark object recognition datasets: CIFAR-10, CIFAR-100, MNIST and SVHN. With fewer trainable parameters, RCNN outperforms the state-of-the-art models on all of these datasets. Increasing the number of parameters leads to even better performance. These results demonstrate the advantage of the recurrent structure over purely feed-forward structure for object recognition.

Deep feedforward neural networks with piecewise linear activations are currently producing the state-of-the-art results in several public datasets. The combination of deep learning models and piecewise linear activation functions allows for the estimation of exponentially complex functions with the use of a large number of subnetworks specialized in the classification of similar input examples. During the training process, these subnetworks avoid overfitting with an implicit regularization scheme based on the fact that they must share their parameters with other subnetworks. Using this framework, we have made an empirical observation that can improve even more the performance of such models. We notice that these models assume a balanced initial distribution of data points with respect to the domain of the piecewise linear activation function. If that assumption is violated, then the piecewise linear activation units can degenerate into purely linear activation units, which can result in a significant reduction of their capacity to learn complex functions. Furthermore, as the number of model layers increases, this unbalanced initial distribution makes the model ill-conditioned. Therefore, we propose the introduction of batch normalisation units into deep feedforward neural networks with piecewise linear activations, which drives a more balanced use of these activation units, where each region of the activation function is trained with a relatively large proportion of training samples. Also, this batch normalisation promotes the pre-conditioning of very deep learning models. We show that by introducing maxout and batch normalisation units to the network in network model results in a model that produces classification results that are better than or comparable to the current state of the art in CIFAR-10, CIFAR-100, MNIST, and SVHN datasets.

Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer multiplicative factor alpha. The amazing by-product of discarding 75% of your data is that you build into the network a degree of invariance with respect to translations and elastic distortions. However, if you simply alternate convolutional layers with max-pooling layers, performance is limited due to the rapid reduction in spatial size, and the disjoint nature of the pooling regions. We have formulated a fractional version of max-pooling where alpha is allowed to take non-integer values. Our version of max-pooling is stochastic as there are lots of different ways of constructing suitable pooling regions. We find that our form of fractional max-pooling reduces overfitting on a variety of datasets: for instance, we improve on the state-of-the art for CIFAR-100 without even using dropout.

In this paper, we introduce a new deep convolutional neural network (ConvNet) module that promotes competition among a set of multi-scale convolutional filters. This new module is inspired by the inception module, where we replace the original collaborative pooling stage (consisting of a concatenation of the multi-scale filter outputs) by a competitive pooling represented by a maxout activation unit. This extension has the following two objectives: 1) the selection of the maximum response among the multi-scale filters prevents filter co-adaptation and allows the formation of multiple sub-networks within the same model, which has been shown to facilitate the training of complex learning problems; and 2) the maxout unit reduces the dimensionality of the outputs from the multi-scale filters. We show that the use of our proposed module in typical deep ConvNets produces classification results that are either better than or comparable to the state of the art on the following benchmark datasets: MNIST, CIFAR-10, CIFAR-100 and SVHN.

Good old on-line back-propagation for plain multi-layer perceptrons yields a very low 0.35% error rate on the famous MNIST handwritten digits benchmark. All we need to achieve this best result so far are many hidden layers, many neurons per layer, numerous deformed training images, and graphics cards to greatly speed up learning.

In this paper, we investigate the problem of learning feature representation from unlabeled data using a single-layer K-means network. A K-means network maps the input data into a feature representation by finding the nearest centroid for each input point, which has attracted researchers' great attention recently due to its simplicity, effectiveness, and scalability. However, one drawback of this feature mapping is that it tends to be unreliable when the training data contains noise. To address this issue, we propose a SVDD based feature learning algorithm that describes the density and distribution of each cluster from K-means with an SVDD ball for more robust feature representation. For this purpose, we present a new SVDD algorithm called C-SVDD that centers the SVDD ball towards the mode of local density of each cluster, and we show that the objective of C-SVDD can be solved very efficiently as a linear programming problem. Additionally, traditional unsupervised feature learning methods usually take an average or sum of local representations to obtain global representation which ignore spatial relationship among them. To use spatial information we propose a global representation with a variant of SIFT descriptor. The architecture is also extended with multiple receptive field scales and multiple pooling sizes. Extensive experiments on several popular object recognition benchmarks, such as STL-10, MINST, Holiday and Copydays shows that the proposed C-SVDDNet method yields comparable or better performance than that of the previous state of the art methods.

We present a neural network architecture and training method designed to enable very rapid training and low implementation complexity. Due to its training speed and very few tunable parameters, the method has strong potential for applications requiring frequent retraining or online training. The approach is characterized by (a) convolutional filters based on biologically inspired visual processing filters, (b) randomly-valued classifier-stage input weights, (c) use of least squares regression to train the classifier output weights in a single batch, and (d) linear classifier-stage output units. We demonstrate the efficacy of the method by applying it to image classification. Our results match existing state-of-the-art results on the MNIST (0.37% error) and NORB-small (2.2% error) image classification databases, but with very fast training times compared to standard deep network approaches. The network's performance on the Google Street View House Number (SVHN) (4% error) database is also competitive with state-of-the art methods.

Layer-sequential unit-variance (LSUV) initialization - a simple method for weight initialization for deep net learning - is proposed. The method consists of the two steps. First, pre-initialize weights of each convolution or inner-product layer with orthonormal matrices. Second, proceed from the first to the final layer, normalizing the variance of the output of each layer to be equal to one. Experiment with different activation functions (maxout, ReLU-family, tanh) show that the proposed initialization leads to learning of very deep nets that (i) produces networks with test accuracy better or equal to standard methods and (ii) is at least as fast as the complex schemes proposed specifically for very deep nets such as FitNets (Romero et al. (2015)) and Highway (Srivastava et al. (2015)). Performance is evaluated on GoogLeNet, CaffeNet, FitNets and Residual nets and the state-of-the-art, or very close to it, is achieved on the MNIST, CIFAR-10/100 and ImageNet datasets.

We describe a novel unsupervised method for learning sparse, overcomplete features. The model uses a linear encoder, and a linear decoder preceded by a sparsifying non-linearity that turns a code vector into a quasi-binary sparse code vector. Given an input, the optimal code minimizes the distance between the output of the decoder and the input patch while being as similar as possible to the encoder output. Learning proceeds in a two-phase EM-like fashion: (1) compute the minimum-energy code vector, (2) adjust the parameters of the encoder and decoder so as to decrease the energy. The model produces “stroke detectors” when trained on handwritten numerals, and Gabor-like filters when trained on natural image patches. Inference and learning are very fast, requiring no preprocessing, and no expensive sampling. Using the proposed unsupervised method to initialize the first layer of a convolutional network, we achieved an error rate slightly lower than the best reported result on the MNIST dataset. Finally, an extension of the method is described to learn topographical filter maps.

An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is encoded by a reproducing kernel. Unlike traditional approaches where neural networks are learned either to represent data or for solving a classification task, our network learns to approximate the kernel feature map on training data. Such an approach enjoys several benefits over classical ones. First, by teaching CNNs to be invariant, we obtain simple network architectures that achieve a similar accuracy to more complex ones, while being easy to train and robust to overfitting. Second, we bridge a gap between the neural network literature and kernels, which are natural tools to model invariance. We evaluate our methodology on visual recognition tasks where CNNs have proven to perform well, e.g., digit recognition with the MNIST dataset, and the more challenging CIFAR-10 and STL-10 datasets, where our accuracy is competitive with the state of the art.

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural networks (CNN) style architectures are being looked at: (1) transparency of the intermediate layers to the overall classification; (2) discriminativeness and robustness of learned features, especially in the early layers; (3) effectiveness in training due to the presence of the exploding and vanishing gradients. We introduce "companion objective" to the individual hidden layers, in addition to the overall objective at the output layer (a different strategy to layer-wise pre-training). We extend techniques from stochastic gradient methods to analyze our algorithm. The advantage of our method is evident and our experimental result on benchmark datasets shows significant performance gain over existing methods (e.g. all state-of-the-art results on MNIST, CIFAR-10, CIFAR-100, and SVHN).

Neural networks are a powerful technology for classification of visual inputs arising from documents. However, there is a confusing plethora of different neural network methods that are used in the literature and in industry. This paper describes a set of concrete best practices that document analysis researchers can use to get good results with neural networks. The most important practice is getting a training set as large as possible: we expand the training set by adding a new form of distorted data. The next most important practice is that convolutional neural networks are better suited for visual document tasks than fully connected networks. We propose that a simple “do-it-yourself” implementation of convolution with a flexible architecture is suitable for many visual document problems. This simple convolutional neural network does not require complex methods, such as momentum, weight decay, structure dependent learning rates, averaging layers, tangent prop, or even finely-tuning the architecture. The end result is a very simple yet general architecture which can yield state-of-the-art performance for document analysis. We illustrate our claims on the MNIST set of English digit images.

In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative modeling framework. The HOPE model itself can be learned unsupervised from unlabelled data based on the maximum likelihood estimation as well as discriminatively from labelled data. More interestingly, we have shown the proposed HOPE models are closely related to neural networks (NNs) in a sense that each hidden layer can be reformulated as a HOPE model. As a result, the HOPE framework can be used as a novel tool to probe why and how NNs work, more importantly, to learn NNs in either supervised or unsupervised ways. In this work, we have investigated the HOPE framework to learn NNs for several standard tasks, including image recognition on MNIST and speech recognition on TIMIT. Experimental results have shown that the HOPE framework yields significant performance gains over the current state-of-the-art methods in various types of NN learning problems, including unsupervised feature learning, supervised or semi-supervised learning.

A proper strategy to alleviate overfitting is critical to a deep neural network (DNN). In this paper, we introduce the cross-loss-function regularization for boosting the generalization capability of the DNN, which results in the multi-loss regularized DNN (ML-DNN) framework. For a particular learning task, e.g., image classification, only a single-loss function is used for all previous DNNs, and the intuition behind the multiloss framework is that the extra loss functions with different theoretical motivations (e.g., pairwise loss and LambdaRank loss) may drag the algorithm away from overfitting to one particular single-loss function (e.g., softmax loss). In the training stage, we pretrain the model with the single-core-loss function and then warm start the whole ML-DNN with the convolutional parameters transferred from the pretrained model. In the testing stage, the outputs by the ML-DNN from different loss functions are fused with average pooling to produce the ultimate prediction. The experiments conducted on several benchmark datasets (CIFAR-10, CIFAR-100, MNIST, and SVHN) demonstrate that the proposed ML-DNN framework, instantiated by the recently proposed network in network, considerably outperforms all other state-of-the-art methods.

We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and because it is a natural companion to dropout) designed to both facilitate optimization by dropout and improve the accuracy of dropout's fast approximate model averaging technique. We empirically verify that the model successfully accomplishes both of these tasks. We use maxout and dropout to demonstrate state of the art classification performance on four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN.

Theoretical and empirical evidence indicates that the depth of neural networks is crucial for their success. However, training becomes more difficult as depth increases, and training of very deep networks remains an open problem. Here we introduce a new architecture designed to overcome this. Our so-called highway networks allow unimpeded information flow across many layers on information highways. They are inspired by Long Short-Term Memory recurrent networks and use adaptive gating units to regulate the information flow. Even with hundreds of layers, highway networks can be trained directly through simple gradient descent. This enables the study of extremely deep and efficient architectures.

In this paper, we propose a deep neural network architecture for object recognition based on recurrent neural networks. The proposed network, called ReNet, replaces the ubiquitous convolution+pooling layer of the deep convolutional neural network with four recurrent neural networks that sweep horizontally and vertically in both directions across the image. We evaluate the proposed ReNet on three widely-used benchmark datasets; MNIST, CIFAR-10 and SVHN. The result suggests that ReNet is a viable alternative to the deep convolutional neural network, and that further investigation is needed.

Recognizing objects in natural images is an intricate problem involving multiple conflicting objectives. Deep convolutional neural networks, trained on large datasets, achieve convincing results and are currently the state-of-the-art approach for this task. However, the long time needed to train such deep networks is a major drawback. We tackled this problem by reusing a previously trained network. For this purpose, we first trained a deep convolutional network on the ILSVRC-12 dataset. We then maintained the learned convolution kernels and only retrained the classification part on different datasets. Using this approach, we achieved an accuracy of 67.68% on CIFAR-100, compared to the previous state-of-the-art result of 65.43%. Furthermore, our findings indicate that convolutional networks are able to learn generic feature extractors that can be used for different tasks.

We propose a novel deep network structure called "Network In Network" (NIN) to enhance model discriminability for local patches within the receptive field. The conventional convolutional layer uses linear filters followed by a nonlinear activation function to scan the input. Instead, we build micro neural networks with more complex structures to abstract the data within the receptive field. We instantiate the micro neural network with a multilayer perceptron, which is a potent function approximator. The feature maps are obtained by sliding the micro networks over the input in a similar manner as CNN; they are then fed into the next layer. Deep NIN can be implemented by stacking mutiple of the above described structure. With enhanced local modeling via the micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is easier to interpret and less prone to overfitting than traditional fully connected layers. We demonstrated the state-of-the-art classification performances with NIN on CIFAR-10 and CIFAR-100, and reasonable performances on SVHN and MNIST datasets.

Background: Keypoint detection is important for many computer vision applications. Existing methods suffer from insufficient selectivity regarding the shape properties of features and are vulnerable to contrast variations and to the presence of noise or texture. Methods: We propose a trainable filter which we call Combination Of Shifted FIlter REsponses (COSFIRE) and use for keypoint detection and pattern recognition. It is automatically configured to be selective for a local contour pattern specified by an example. The configuration comprises selecting given channels of a bank of Gabor filters and determining certain blur and shift parameters. A COSFIRE filter response is computed as the weighted geometric mean of the blurred and shifted responses of the selected Gabor filters. It shares similar properties with some shape-selective neurons in visual cortex, which provided inspiration for this work. Results: We demonstrate the effectiveness of the proposed filters in three applications: the detection of retinal vascular bifurcations (DRIVE dataset: 98.50 percent recall, 96.09 percent precision), the recognition of handwritten digits (MNIST dataset: 99.48 percent correct classification), and the detection and recognition of traffic signs in complex scenes (100 percent recall and precision). Conclusions: The proposed COSFIRE filters are conceptually simple and easy to implement. They are versatile keypoint detectors and are highly effective in practical computer vision applications.

In many recent object recognition systems, feature extraction stages are generally composed of a filter bank, a non-linear transformation, and some sort of feature pooling layer. Most systems use only one stage of feature extraction in which the filters are hard-wired, or two stages where the filters in one or both stages are learned in supervised or unsupervised mode. This paper addresses three questions: 1. How does the non-linearities that follow the filter banks influence the recognition accuracy? 2. does learning the filter banks in an unsupervised or supervised manner improve the performance over random filters or hardwired filters? 3. Is there any advantage to using an architecture with two stages of feature extraction, rather than one? We show that using non-linearities that include recti- fication and local contrast normalization is the single most important ingredient for good accuracy on object recognition benchmarks. We show that two stages of feature extraction yield better accuracy than one. Most surprisingly, we show that a two-stage system with random filters can yield almost 63% recognition rate on Caltech-101, provided that the proper non-linearities and pooling layers are used. Finally, we show that with supervised refinement, the system achieves state-of-the-art performance on NORB dataset (5.6%) and unsupervised pre-training followed by supervised refinement produces good accuracy on Caltech-101 (> 65%), and the lowest known error rate on the undistorted, unprocessed MNIST dataset (0.53%).

We present the application of different nonlinear image deformation models to the task of image recognition. The deformation models are especially suited for local changes as they often occur in the presence of image object variability. We show that, among the discussed models, there is one approach that combines simplicity of implementation, low-computational complexity, and highly competitive performance across various real-world image recognition tasks. We show experimentally that the model performs very well for four different handwritten digit recognition tasks and for the classification of medical images, thus showing high generalization capacity. In particular, an error rate of 0.54 percent on the MNIST benchmark is achieved, as well as the lowest reported error rate, specifically 12.6 percent, in the 2005 international ImageCLEF evaluation of medical image categorization.

This article focusses on the problems of feature extraction and the recognition of handwritten digits. A trainable feature extractor based on the LeNet5 convolutional neural network architecture is introduced to solve the first problem in a black box scheme without prior knowledge on the data. The classification task is performed by Support Vector Machines to enhance the generalization ability of LeNet5. In order to increase the recognition rate, new training samples are generated by affine transformations and elastic distortions. Experiments are performed on the well known MNIST database to validate the method and the results show that the system can outperfom both SVMs and LeNet5 while providing performances comparable to the best performance on this database. Moreover, an analysis of the errors is conducted to discuss possible means of enhancement and their limitations.

Practical experience has shown that in order to obtain the best possible performance, prior knowledge about invariances of a classification problem at hand ought to be incorporated into the training procedure. We describe and review all known methods for doing so in support vector machines, provide experimental results, and discuss their respective merits. One of the significant new results reported in this work is our recent achievement of the lowest reported test error on the well-known MNIST digit recognition benchmark task, with SVM training times that are also significantly faster than previous SVM methods.

We propose a method of feature extraction for digit recognition that is inspired by vision research: a sparse-coding strategy and a local maximum operation. We show that our method, despite its simplicity, yields state-of-the-art classification results on a highly competitive digit-recognition benchmark. We first employ the unsupervised Sparsenet algorithm to learn a basis for representing patches of handwritten digit images. We then use this basis to extract local coefficients. In a second step, we apply a local maximum operation in order to implement local shift invariance. Finally, we train a Support-Vector-Machine on the resulting feature vectors and obtain state-of-the-art classification performance in the digit recognition task defined by the MNIST benchmark. We compare the different classification performances obtained with sparse coding, Gabor wavelets, and principle component analysis. We conclude that the learning of a sparse representation of local image patches combined with a local maximum operation for feature extraction can significantly improve recognition performance.

We present an unsupervised method for learning a hierarchy of sparse feature detectors that are invariant to small shifts and distortions. The resulting feature extractor consists of multiple convolution filters, followed by a pointwise sigmoid non-linearity, and a feature-pooling layer that computes the max of each filter output within adjacent windows. A second level of larger and more invariant features is obtained by training the same algorithm on patches of features from the first level. Training a supervised classifier on these features yields 0.64% error on MNIST, and 54% average recognition rate on Caltech 101 with 30 training samples per category. While the resulting architecture is similar to convolutional networks, the layer-wise unsupervised training procedure alleviates the over-parameterization problems that plague purely supervised learning procedures, and yields good performance with very few labeled training samples.

In this work, we propose a very simple deep learning network for image classification which comprises only the very basic data processing components: cascaded principal component analysis (PCA), binary hashing, and block-wise histograms. In the proposed architecture, PCA is employed to learn multistage filter banks. It is followed by simple binary hashing and block histograms for indexing and pooling. This architecture is thus named as a PCA network (PCANet) and can be designed and learned extremely easily and efficiently. For comparison and better understanding, we also introduce and study two simple variations to the PCANet, namely the RandNet and LDANet. They share the same topology of PCANet but their cascaded filters are either selected randomly or learned from LDA. We have tested these basic networks extensively on many benchmark visual datasets for different tasks, such as LFW for face verification, MultiPIE, Extended Yale B, AR, FERET datasets for face recognition, as well as MNIST for hand-written digits recognition. Surprisingly, for all tasks, such a seemingly naive PCANet model is on par with the state of the art features, either prefixed, highly hand-crafted or carefully learned (by DNNs). Even more surprisingly, it sets new records for many classification tasks in Extended Yale B, AR, FERET datasets, and MNIST variations. Additional experiments on other public datasets also demonstrate the potential of the PCANet serving as a simple but highly competitive baseline for texture classification and object recognition.

We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.

In this paper we examine the effect of receptive field designs on classification accuracy in the commonly adopted pipeline of image classification. While existing algorithms usually use manually defined spatial regions for pooling, we show that learning more adaptive receptive fields increases performance even with a significantly smaller codebook size at the coding layer. To learn the optimal pooling parameters, we adopt the idea of over-completeness by starting with a large number of receptive field candidates, and train a classifier with structured sparsity to only use a sparse subset of all the features. An efficient algorithm based on incremental feature selection and retraining is proposed for fast learning. With this method, we achieve the best published performance on the CIFAR-10 dataset, using a much lower dimensional feature space than previous methods.

In this article, the task of classifying handwritten digits using a class of multilayer feedforward network called Convolutional Network is considered. A convolutional network has the advantage of extracting and using features information, improving the recognition of 2D shapes with a high degree of invariance to translation, scaling and other distortions. In this work, a novel type of convolutional network was implemented using Gabor filters as feature extractors at the first layer. A backpropagation algorithm specifically adapted to the problem was used in the training phase for the rest of layers. The training and test sets were taken from the MNIST database. A boosting method was applied to improve the results by using experts that learn different distributions of the training set and combining its results.

The predominant methodology in training deep learning advocates the use of stochastic gradient descent methods (SGDs). Despite its ease of implementation, SGDs are diffi- cult to tune and parallelize. These problems make it challenging to develop, debug and scale up deep learning algorithms with SGDs. In this paper, we show that more sophisticated off-the-shelf optimization methods such as Limited memory BFGS (L-BFGS) and Conjugate gradient (CG) with line search can significantly simplify and speed up the process of pretraining deep algorithms. In our experiments, the difference between LBFGS/CG and SGDs are more pronounced if we consider algorithmic extensions (e.g., sparsity regularization) and hardware extensions (e.g., GPUs or computer clusters). Our experiments with distributed optimization support the use of L-BFGS with locally connected networks and convolutional neural networks. Using L-BFGS, our convolutional network model achieves 0.69% on the standard MNIST dataset. This is a state-of-theart result on MNIST among algorithms that do not use distortions or pretraining.

The fully connected layers of a deep convolutional neural network typically contain over 90% of the network parameters, and consume the majority of the memory required to store the network parameters. Reducing the number of parameters while preserving essentially the same predictive performance is critically important for operating deep neural networks in memory constrained environments such as GPUs or embedded devices. In this paper we show how kernel methods, in particular a single Fastfood layer, can be used to replace all fully connected layers in a deep convolutional neural network. This novel Fastfood layer is also end-to-end trainable in conjunction with convolutional layers, allowing us to combine them into a new architecture, named deep fried convolutional networks, which substantially reduces the memory footprint of convolutional networks trained on MNIST and ImageNet with no drop in predictive performance.

Sparseness is a useful regularizer for learning in a wide range of applications, in particular in neural networks. This paper proposes a model targeted at classification tasks, where sparse activity and sparse connectivity are used to enhance classification capabilities. The tool for achieving this is a sparseness-enforcing projection operator which finds the closest vector with a pre-defined sparseness for any given vector. In the theoretical part of this paper, a comprehensive theory for such a projection is developed. In conclusion, it is shown that the projection is differentiable almost everywhere and can thus be implemented as a smooth neuronal transfer function. The entire model can hence be tuned end-to-end using gradient-based methods. Experiments on the MNIST database of handwritten digits show that classification performance can be boosted by sparse activity or sparse connectivity. With a combination of both, performance can be significantly better compared to classical non-sparse approaches.

This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between a genotype - the hypernetwork - and a phenotype - the main network. Though they are also reminiscent of HyperNEAT in evolution, our hypernetworks are trained end-to-end with backpropagation and thus are usually faster. The focus of this work is to make hypernetworks useful for deep convolutional networks and long recurrent networks, where hypernetworks can be viewed as relaxed form of weight-sharing across layers. Our main result is that hypernetworks can generate non-shared weights for LSTM and achieve near state-of-the-art results on a variety of sequence modelling tasks including character-level language modelling, handwriting generation and neural machine translation, challenging the weight-sharing paradigm for recurrent networks. Our results also show that hypernetworks applied to convolutional networks still achieve respectable results for image recognition tasks compared to state-of-the-art baseline models while requiring fewer learnable parameters.

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Early attempts at explaining this phenomenon focused on nonlinearity and overfitting. We argue instead that the primary cause of neural networks' vulnerability to adversarial perturbation is their linear nature. This explanation is supported by new quantitative results while giving the first explanation of the most intriguing fact about them: their generalization across architectures and training sets. Moreover, this view yields a simple and fast method of generating adversarial examples. Using this approach to provide examples for adversarial training, we reduce the test set error of a maxout network on the MNIST dataset.

There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks. Scaling such models to full-sized, high-dimensional images remains a difficult problem. To address this problem, we present the convolutional deep belief network, a hierarchical generative model which scales to realistic image sizes. This model is translation-invariant and supports efficient bottom-up and top-down probabilistic inference. Key to our approach is probabilistic max-pooling, a novel technique which shrinks the representations of higher layers in a probabilistically sound way. Our experiments show that the algorithm learns useful high-level visual features, such as object parts, from unlabeled images of objects and natural scenes. We demonstrate excellent performance on several visual recognition tasks and show that our model can perform hierarchical (bottom-up and top-down) inference over full-sized images.

In this paper, we propose a novel supervised hierarchical sparse coding model based on local image descriptors for classification tasks. The supervised dictionary training is performed via back-projection, by minimizing the training error of classifying the image level features, which are extracted by max pooling over the sparse codes within a spatial pyramid. Such a max pooling procedure across multiple spatial scales offer the model translation invariant properties, similar to the Convolutional Neural Network (CNN). Experiments show that our supervised dictionary improves the performance of the proposed model significantly over the unsupervised dictionary, leading to state-of-the-art performance on diverse image databases. Further more, our supervised model targets learning linear features, implying its great potential in handling large scale datasets in real applications.

KNN is one of the most popular classification methods, but it often fails to work well with inappropriate choice of distance metric or due to the presence of numerous class-irrelevant features. Linear feature transformation methods have been widely applied to extract class-relevant information to improve kNN classification, which is very limited in many applications. Kernels have been used to learn powerful non-linear feature transformations, but these methods fail to scale to large datasets. In this paper, we present a scalable non-linear feature mapping method based on a deep neural network pretrained with restricted boltzmann machines for improving kNN classification in a large-margin framework, which we call DNet-kNN. DNet-kNN can be used for both classification and for supervised dimensionality reduction. The experimental results on two benchmark handwritten digit datasets show that DNet-kNN has much better performance than large-margin kNN using a linear mapping and kNN based on a deep autoencoder pretrained with retricted boltzmann machines.

We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent expectations are estimated using a variational approximation that tends to focus on a single mode, and data independent expectations are approximated using persistent Markov chains. The use of two quite different techniques for estimating the two types of expectation that enter into the gradient of the log-likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer “pre-training” phase that allows variational inference to be initialized with a single bottomup pass. We present results on the MNIST and NORB datasets showing that deep Boltzmann machines learn good generative models and perform well on handwritten digit and visual object recognition tasks.

Deep Neural Networks (DNN) have achieved state-of-the-art results in a wide range of tasks, with the best results obtained with large training sets and large models. In the past, GPUs enabled these breakthroughs because of their greater computational speed. In the future, faster computation at both training and test time is likely to be crucial for further progress and for consumer applications on low-power devices. As a result, there is much interest in research and development of dedicated hardware for Deep Learning (DL). Binary weights, i.e., weights which are constrained to only two possible values (e.g. -1 or 1), would bring great benefits to specialized DL hardware by replacing many multiply-accumulate operations by simple accumulations, as multipliers are the most space and power-hungry components of the digital implementation of neural networks. We introduce BinaryConnect, a method which consists in training a DNN with binary weights during the forward and backward propagations, while retaining precision of the stored weights in which gradients are accumulated. Like other dropout schemes, we show that BinaryConnect acts as regularizer and we obtain near state-of-the-art results with BinaryConnect on the permutation-invariant MNIST, CIFAR-10 and SVHN.

This technical report proposes two innovations in the design of neural networks: (a) strong neurons – highly nonlinear/nonsmooth neurons with multiple outputs and (b) mostly unsupervised architecture – backpropagation-free design with all layers except for the last one being trained in a completely unsupervised setting. The new neural design (called StrongNet) was tested on a well-known MNIST benchmark. This demonstrated that StrongNet is able to capture structural information about images in the "mostly unsupervised" setting. Three-layer StrongNet has a test set error on MNIST as low as 1.1%. It outperforms 11 out of 14 two/three-layer networks cited on the MNIST homepage (as of Aug 2014). The most important result achieved by us is that StrongNet – architecture that includes only one supervised layer – successfully competes with "completely supervised" shallow networks, which have up to three supervised layers. This result demonstrates the feasibility of the new approach and suggests the performance of deeper StrongNets should be investigated.

In this project, we use a Deep Belief Network (Hinton et al., 2006) to learn words in a fixed-size vocabulary, given input in multiple modalities (image and audio data). The goal of this project is like that of Plunkett et al. (1992): to model vocabulary acquisition, and address the Symbol Grounding problem from a connectionist standpoint. Our model learns to classify both spoken and hand-written digits in three distinct learning tasks. First, we train our network only on the image data, second, we train only on the audio data, and finally, we train on a combined dataset of paired image and audio data. Unlike Plunkett et al. (1992), we use a generative model, which allows us to fix the class labels and generate input vectors that our model considers good representatives of that class. The model also achieves high accuracy on the classification tasks.

High-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer to reconstruct high-dimensional input vectors. Gradient descent can be used for fine-tuning the weights in such “autoencoder” networks, but this works well only if the initial weights are close to a good solution. We describe an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data.

The task of labeling data for training deep neural networks is daunting and tedious, requiring millions of labels to achieve the current state-of-the-art results. Such reliance on large amounts of labeled data can be relaxed by exploiting hierarchical features via unsupervised learning techniques. In this work, we propose to train a deep convolutional network based on an enhanced version of the k-means clustering algorithm, which reduces the number of correlated parameters in the form of similar filters, and thus increases test categorization accuracy. We call our algorithm convolutional k-means clustering. We further show that learning the connection between the layers of a deep convolutional neural network improves its ability to be trained on a smaller amount of labeled data. Our experiments show that the proposed algorithm outperforms other techniques that learn filters unsupervised. Specifically, we obtained a test accuracy of 74.1% on STL-10 and a test error of 0.5% on MNIST.

We show how nonlinear embedding algorithms popular for use with shallow semisupervised learning techniques such as kernel methods can be applied to deep multilayer architectures, either as a regularizer at the output layer, or on each layer of the architecture. This provides a simple alternative to existing approaches to deep learning whilst yielding competitive error rates compared to those methods, and existing shallow semi-supervised techniques.

We consider the problem of learning deep representation when target labels are available. In this paper, we show that there exists intrinsic relationship between target coding and feature representation learning in deep networks. Specifically, we found that distributed binary code with error correcting capability is more capable of encouraging discriminative features, in comparison to the 1-of-K coding that is typically used in supervised deep learning. This new finding reveals additional benefit of using error-correcting code for deep model learning, apart from its well-known error correcting property. Extensive experiments are conducted on popular visual benchmark datasets.