In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard ``deep learning'' datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.

Several mechanisms to focus attention of a neural network on selected parts of its input or memory have been used successfully in deep learning models in recent years. Attention has improved image classification, image captioning, speech recognition, generative models, and learning algorithmic tasks, but it had probably the largest impact on neural machine translation. Recently, similar improvements have been obtained using alternative mechanisms that do not focus on a single part of a memory but operate on all of it in parallel, in a uniform way. Such mechanism, which we call active memory, improved over attention in algorithmic tasks, image processing, and in generative modelling. So far, however, active memory has not improved over attention for most natural language processing tasks, in particular for machine translation. We analyze this shortcoming in this paper and propose an extended model of active memory that matches existing attention models on neural machine translation and generalizes better to longer sentences. We investigate this model and explain why previous active memory models did not succeed. Finally, we discuss when active memory brings most benefits and where attention can be a better choice.

We introduce a general simple structural design called "Multiplicative Integration" (MI) to improve recurrent neural networks (RNNs). MI changes the way of how the information flow gets integrated in the computational building block of an RNN, while introducing almost no extra parameters. The new structure can be easily embedded into many popular RNN models, including LSTMs and GRUs. We empirically analyze its learning behaviour and conduct evaluations on several tasks using different RNN models. Our experimental results demonstrate that Multiplicative Integration can provide a substantial performance boost over many of the existing RNN models.

Long Short-Term Memory (LSTM) is a popular approach to boosting the ability of Recurrent Neural Networks to store longer term temporal information. The capacity of an LSTM network can be increased by widening and adding layers. However, usually the former introduces additional parameters, while the latter increases the runtime. As an alternative we propose the Tensorized LSTM in which the hidden states are represented by tensors and updated via a cross-layer convolution. By increasing the tensor size, the network can be widened efficiently without additional parameters since the parameters are shared across different locations in the tensor; by delaying the output, the network can be deepened implicitly with little additional runtime since deep computations for each timestep are merged into temporal computations of the sequence. Experiments conducted on five challenging sequence learning tasks show the potential of the proposed model.

In this paper, we prove a conjecture published in 1989 and also partially address an open problem announced at the Conference on Learning Theory (COLT) 2015. For an expected loss function of a deep nonlinear neural network, we prove the following statements under the independence assumption adopted from recent work: 1) the function is non-convex and non-concave, 2) every local minimum is a global minimum, 3) every critical point that is not a global minimum is a saddle point, and 4) the property of saddle points differs for shallow networks (with three layers) and deeper networks (with more than three layers). Moreover, we prove that the same four statements hold for deep linear neural networks with any depth, any widths and no unrealistic assumptions. As a result, we present an instance, for which we can answer to the following question: how difficult to directly train a deep model in theory? It is more difficult than the classical machine learning models (because of the non-convexity), but not too difficult (because of the nonexistence of poor local minima and the property of the saddle points). We note that even though we have advanced the theoretical foundations of deep learning, there is still a gap between theory and practice.

By reparameterizing the weights in this way we improve the conditioning of the optimization problem and we speed up convergence of stochastic gradient descent. Our reparameterization is inspired by batch normalization but does not introduce any dependencies between the examples in a minibatch. This means that our method can also be applied successfully to recurrent models such as LSTMs and to noise-sensitive applications such as deep reinforcement learning or generative models, for which batch normalization is less well suited. Although our method is much simpler, it still provides much of the speed-up of full batch normalization. In addition, the computational overhead of our method is lower, permitting more optimization steps to be taken in the same amount of time. We demonstrate the usefulness of our method on applications in supervised image recognition, generative modelling, and deep reinforcement learning.

A novel variational autoencoder is developed to model images, as well as associated labels or captions. The Deep Generative Deconvolutional Network (DGDN) is used as a decoder of the latent image features, and a deep Convolutional Neural Network (CNN) is used as an image encoder; the CNN is used to approximate a distribution for the latent DGDN features/code. The latent code is also linked to generative models for labels (Bayesian support vector machine) or captions (recurrent neural network). When predicting a label/caption for a new image at test, averaging is performed across the distribution of latent codes; this is computationally efficient as a consequence of the learned CNN-based encoder. Since the framework is capable of modeling the image in the presence/absence of associated labels/captions, a new semi-supervised setting is manifested for CNN learning with images; the framework even allows unsupervised CNN learning, based on images alone.

A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of models that smoothly interpolates between two limiting cases can be constructed. One limit is referred to as the feature-matching mode of pattern recognition, and the other one as the prototype regime. On the deep learning side of the duality, this family corresponds to feedforward neural networks with one hidden layer and various activation functions, which transmit the activities of the visible neurons to the hidden layer. This family of activation functions includes logistics, rectified linear units, and rectified polynomials of higher degrees. The proposed duality makes it possible to apply energy-based intuition from associative memory to analyze computational properties of neural networks with unusual activation functions - the higher rectified polynomials which until now have not been used in deep learning. The utility of the dense memories is illustrated for two test cases: the logical gate XOR and the recognition of handwritten digits from the MNIST data set.

We propose ThalNet, a deep learning model inspired by neocortical communication via the thalamus. Our model consists of recurrent neural modules that send features through a routing center, endowing the modules with the flexibility to share features over multiple time steps. We show that our model learns to route information hierarchically, processing input data by a chain of modules. We observe common architectures, such as feed forward neural networks and skip connections, emerging as special cases of our architecture, while novel connectivity patterns are learned for the text8 compression task. Our model outperforms standard recurrent neural networks on several sequential benchmarks.

Person Re-Identification is the task of matching images of a person across multiple camera views. Almost all prior approaches address this challenge by attempting to learn the possible transformations that relate the different views of a person from a training corpora. Then, they utilize these transformation patterns for matching a query image to those in a gallery image bank at test time.