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

In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth using an architecture with very small (3x3) convolution filters, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively. We also show that our representations generalise well to other datasets, where they achieve state-of-the-art results. We have made our two best-performing ConvNet models publicly available to facilitate further research on the use of deep visual representations in computer vision.

Very Deep Convolutional Networks for Large-Scale Image Recognition

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

We propose an architecture for learning complex controllable behaviors by having simple Policies Modulate Trajectory Generators (PMTG), a powerful combination that can provide both memory and prior knowledge to the controller. The result is a flexible architecture that is applicable to a class of problems with periodic motion for which one has an insight into the class of trajectories that might lead to a desired behavior. We illustrate the basics of our architecture using a synthetic control problem, then go on to learn speed-controlled locomotion for a quadrupedal robot by using Deep Reinforcement Learning and Evolutionary Strategies. We demonstrate that a simple linear policy, when paired with a parametric Trajectory Generator for quadrupedal gaits, can induce walking behaviors with controllable speed from 4-dimensional IMU observations alone, and can be learned in under 1000 rollouts. We also transfer these policies to a real robot and show locomotion with controllable forward velocity.

Policies Modulating Trajectory Generators

This paper presents a computationally efficient method for using multiple speech recognizers in a multi-pass framework to improve the rejection performance of an automatic speech recognition system. A set of criteria is proposed, which determine at run time when rescoring using a second pass is expected to improve the rejection performance. The second pass result is used along with a set of features derived from the first pass to compute a combined confidence score. The feature combination is optimized globally based on training data. The combined system significantly outperforms a simple two-pass system at little more computational cost than comparable one-pass and twopass systems.

Confidence scoring and rejection using multi-pass speech recognition.

We introduce a model that approximates full and block-diagonal covariances in a Gaussian mixture, while reducing significantly both the number of parameters to estimate and the computations required to evaluate the Gaussian likelihoods. The inverse covariance of each Gaussian is expressed as a mixture of a small set of prototype matrices. Estimation of both the mixture weights and the prototypes is performed using maximum likelihood estimation. Experiments on a variety of speech recognition tasks show that this model significantly outperforms a diagonal covariance model, while using the same number of Gaussian-dependent parameters.

Mixtures of inverse covariances

We describe a model which approximates full covariances in a Gaussian mixture while reducing significantly both the number of parameters to estimate and the computations required to evaluate the Gaussian likelihoods. In this model, the inverse covariance of each Gaussian in the mixture is expressed as a linear combination of a small set of prototype matrices that are shared across components. In addition, we demonstrate the benefits of a subspace-factored extension of this model when representing independent or near-independent product densities. We present a maximum likelihood estimation algorithm for these models, as well as a practical method for implementing it. We show through experiments performed on a variety of speech recognition tasks that this model significantly outperforms a diagonal covariance model, while using far fewer Gaussian-specific parameters. Experiments also demonstrate that a better speed/accuracy tradeoff can be achieved on a real-time speech recognition system.

A method and system for frame-level merging of HMM state predictions determined by different techniques is disclosed. An audio input signal may be transformed into a first and second sequence of feature vector, the sequences corresponding to each other and to a temporal sequence of frames of the audio input signal on a frame-by-frame basis. The first sequence may be processed by a neural network (NN) to determine NN-based state predictions, and the second sequence may be processed by a Gaussian mixture model (GMM) to determine GMM-based state predictions. The NN-based and GMM-based state predictions may be merged as weighted sums for each of a plurality of HMM state on a frame-by-frame basis to determine merged state predictions. The merged state predictions may then be applied to the HMMs to speech content of the audio input signal.

Vincent Vanhoucke

Papers

Policies Modulating Trajectory Generators

Confidence scoring and rejection using multi-pass speech recognition.

Mixtures of inverse covariances

Mixtures of inverse covariances

Frame-level combination of deep neural network and gaussian mixture models