Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

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Deep Residual Learning for Image Recognition

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

Adam: A Method for Stochastic Optimization

Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.

Long short-term memory

Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.

Deep learning

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. 
The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

Artificial neural networks capable of doing hard learning offer a new way to undertake automatic speech recognition. The Boltzmann machine algorithm and the error back-propagation algorithm have been used to perform speaker normalization. Spectral segments are represented by spectral lines. Speaker-independent recognition of place of articulation for vowels is performed on lines. Performance of the networks is shown to depend on the coding of the input data. Samples were extracted from continuous speech of 38 speakers. The error rate obtained (4.2% error on test set of 72 samples with the Boltzmann machine and 6.9% error with error back-propagation) is better than that of previous experiments, using the same data, with continuous Hidden Markov Models (7.3% error on test set and 3% error on training set). These experiments are part of an attempt to construct a data-driven speech recognition system with multiple neural networks specialized to different tasks. Results are also reported on the recognition performance of other trained networks, such as one trained on the E-set consonants.



Les reseaux neuraux artificiels en mesure d'effectuer des apprentissages difficiles offrent une nouvelle facon d'effectuer la reconnaissance automatique de la parole. L'algorithme de la machine de Boltzmann et l'algorithme de propagation arriere d'erreurs ont ete utilises pour effectuer la normalisation du locuteur. Les segments spectraux sont representes par des lignes spectrales. La reconnaissance independante de l'endroit de l'articulation des voyelles par le locuteur est effectuee sur des lignes. La performance des reseaux s'est revelee dependante de l'encodage des donnees d'entree. Des echantillons ont ete tires du discours continu de 38 locuteurs. Le taux d'erreur obtenu (4,2% d'erreur dans les 72 echantillons avec la machine de Boltzmann, 6,9% d'erreur avec l'algorithme de propagation arriere d'erreurs) est inferieur a celui des experiences precedentes, effectuees a l'aide des měmes donnees et avec les modeles continus de Markov (7,3% d'erreur avec la serie d'essai et 3% d'erreur avec la serie de formation). Ces experiences font partie d'un programme en vue d'elaborer un systeme de reconnaissance de la parole guidee par les donnees qui serait dote de reseaux neuraux multiples specialises dans diverses taches. Cet article presente egalement des donnees sur la performance d'autres reseaux formes.

Use of multilayer networks for the recognition of phonetic features and phonemes

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Reinforced Imitation Learning from Observations

Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally efficient Gibbs sampling procedures are crippled by poor mixing. In this work we propose a novel method of sampling from Boltzmann machines that demonstrates a computationally efficient way to promote mixing. Our approach leverages an under-appreciated property of deep generative models such as the Deep Belief Network (DBN), where Gibbs sampling from deeper levels of the latent variable hierarchy results in dramatically increased ergodicity. Our approach is thus to train an auxiliary latent hierarchical model, based on the DBN. When used in conjunction with parallel-tempering, the method is asymptotically guaranteed to simulate samples from the target RBM. Experimental results confirm the effectiveness of this sampling strategy in the context of RBM training.

Deep Tempering

Conditional text-to-image generation approaches commonly focus on generating a single image in a single step. One practical extension beyond one-step generation is an interactive system that generates an image iteratively, conditioned on ongoing linguistic input / feedback. This is significantly more challenging as such a system must understand and keep track of the ongoing context and history. In this work, we present a recurrent image generation model which takes into account both the generated output up to the current step as well as all past instructions for generation. We show that our model is able to generate the background, add new objects, apply simple transformations to existing objects, and correct previous mistakes. We believe our approach is an important step toward interactive generation.

Keep Drawing It: Iterative language-based image generation and editing

There are many frameworks for deep generative modeling, each often presented with their own specific training algorithms and inference methods. Here, we demonstrate the connections between existing deep generative models and the recently introduced GFlowNet framework, a probabilistic inference machine which treats sampling as a decision-making process. This analysis sheds light on their overlapping traits and provides a unifying viewpoint through the lens of learning with Markovian trajectories. Our framework provides a means for unifying training and inference algorithms, and provides a route to shine a unifying light over many generative models. Beyond this, we provide a practical and experimentally verified recipe for improving generative modeling with insights from the GFlowNet perspective.

Yoshua Bengio

Papers

Use of multilayer networks for the recognition of phonetic features and phonemes

Reinforced Imitation Learning from Observations

Deep Tempering

Keep Drawing It: Iterative language-based image generation and editing

Unifying Generative Models with GFlowNets and Beyond