We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such data. We first show that the first two layers of a deep network can exactly embed points lying on a monotonic chain, a special type of piecewise linear manifold, mapping them to a low-dimensional Euclidean space. Remarkably, the network can do this using an almost optimal number of parameters. We also show that this network projects nearby points onto the manifold and then embeds them with little error. We then extend these results to more general manifolds.

We explore the question of whether the representations learned by classifiers can be used to enhance the quality of generative models. Our conjecture is that labels correspond to characteristics of natural data which are most salient to humans: identity in faces, objects in images, and utterances in speech. We propose to take advantage of this by using the representations from discriminative classifiers to augment the objective function corresponding to a generative model. In particular we enhance the objective function of the variational autoencoder, a popular generative model, with a discriminative regularization term. We show that enhancing the objective function in this way leads to samples that are clearer and have higher visual quality than the samples from the standard variational autoencoders.

We present a novel architecture, the "stacked what-where auto-encoders" (SWWAE), which integrates discriminative and generative pathways and provides a unified approach to supervised, semi-supervised and unsupervised learning without relying on sampling during training. An instantiation of SWWAE uses a convolutional net (Convnet) (LeCun et al. (1998)) to encode the input, and employs a deconvolutional net (Deconvnet) (Zeiler et al. (2010)) to produce the reconstruction. The objective function includes reconstruction terms that induce the hidden states in the Deconvnet to be similar to those of the Convnet. Each pooling layer produces two sets of variables: the "what" which are fed to the next layer, and its complementary variable "where" that are fed to the corresponding layer in the generative decoder.

In this paper we construct a learning architecture for high dimensional time series sampled by sensor arrangements. Using a redundant wavelet decomposition on a graph constructed over the sensor locations, our algorithm is able to construct discriminative features that exploit the mutual information between the sensors. The algorithm then applies scattering networks to the time series graphs to create the feature space. We demonstrate our method on a machine olfaction problem, where one needs to classify the gas type and the location where it originates from data sampled by an array of sensors. Our experimental results clearly demonstrate that our method outperforms classical machine learning techniques used in previous studies.

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves $91.31\%$ accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs.

The rapid growth of data size and accessibility in recent years has instigated a shift of philosophy in algorithm design for artificial intelligence. Instead of engineering algorithms by hand, the ability to learn composable systems automatically from massive amounts of data has led to ground-breaking performance in important domains such as computer vision, speech recognition, and natural language processing. The most popular class of techniques used in these domains is called deep learning, and is seeing significant attention from industry. However, these models require incredible amounts of data and compute power to train, and are limited by the need for better hardware acceleration to accommodate scaling beyond current data and model sizes. While the current solution has been to use clusters of graphics processing units (GPU) as general purpose processors (GPGPU), the use of field programmable gate arrays (FPGA) provide an interesting alternative. Current trends in design tools for FPGAs have made them more compatible with the high-level software practices typically practiced in the deep learning community, making FPGAs more accessible to those who build and deploy models. Since FPGA architectures are flexible, this could also allow researchers the ability to explore model-level optimizations beyond what is possible on fixed architectures such as GPUs. As well, FPGAs tend to provide high performance per watt of power consumption, which is of particular importance for application scientists interested in large scale server-based deployment or resource-limited embedded applications. This review takes a look at deep learning and FPGAs from a hardware acceleration perspective, identifying trends and innovations that make these technologies a natural fit, and motivates a discussion on how FPGAs may best serve the needs of the deep learning community moving forward.

We present a supervised neural network model for polyphonic piano music transcription. The architecture of the proposed model is analogous to speech recognition systems and comprises an acoustic model and a music language model. The acoustic model is a neural network used for estimating the probabilities of pitches in a frame of audio. The language model is a recurrent neural network that models the correlations between pitch combinations over time. The proposed model is general and can be used to transcribe polyphonic music without imposing any constraints on the polyphony. The acoustic and language model predictions are combined using a probabilistic graphical model. Inference over the output variables is performed using the beam search algorithm. We perform two sets of experiments. We investigate various neural network architectures for the acoustic models and also investigate the effect of combining acoustic and music language model predictions using the proposed architecture. We compare performance of the neural network based acoustic models with two popular unsupervised acoustic models. Results show that convolutional neural network acoustic models yields the best performance across all evaluation metrics. We also observe improved performance with the application of the music language models. Finally, we present an efficient variant of beam search that improves performance and reduces run-times by an order of magnitude, making the model suitable for real-time applications.

We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic.

Supervised, semi-supervised, and unsupervised learning estimate a function given input/output samples. Generalization of the learned function to unseen data can be improved by incorporating side information into learning. Side information are data that are neither from the input space nor from the output space of the function, but include useful information for learning it. In this paper we show that learning with side information subsumes a variety of related approaches, e.g. multi-task learning, multi-view learning and learning using privileged information. Our main contributions are (i) a new perspective that connects these previously isolated approaches, (ii) insights about how these methods incorporate different types of prior knowledge, and hence implement different patterns, (iii) facilitating the application of these methods in novel tasks, as well as (iv) a systematic experimental evaluation of these patterns in two supervised learning tasks.

Gesture recognition is one of the core components in the thriving research field of humancomputer interaction. The recognition of distinct hand and arm motions is becoming increasingly important, as it enables smart interactions with electronic devices. Furthermore, gesture identification in video can be seen as a first step towards sign language recognition, where even subtle differences in motion can play an important role. Some examples that complicate the identification of gestures are changes in background and lighting due to the varying environment, variations in the performance and speed of the gestures, different clothes worn by the performers and different positioning relative to the camera. Moreover, regular hand motion or out-of-vocabulary gestures should not to be confused with one of the target gestures. Convolutional neural networks (CNNs) (LeCun et al., 1998) are the de facto standard approach in computer vision. CNNs have the ability to learn complex hierarchies with increasing levels of abstraction while being end-to-end trainable. Their success has had a huge impact on vision based applications like image classification (Krizhevsky et al., 2012), object detection