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

We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overriding in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.

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ImageNet Classification with Deep Convolutional Neural Networks

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

Many of the existing methods for learning joint embedding of images and text use only supervised information from paired images and its textual attributes. Taking advantage of the recent success of unsupervised learning in deep neural networks, we propose an end-to-end learning framework that is able to extract more robust multi-modal representations across domains. The proposed method combines representation learning models (i.e., auto-encoders) together with cross-domain learning criteria (i.e., Maximum Mean Discrepancy loss) to learn joint embeddings for semantic and visual features. A novel technique of unsupervised-data adaptation inference is introduced to construct more comprehensive embeddings for both labeled and unlabeled data. We evaluate our method on Animals with Attributes and Caltech-UCSD Birds 200-2011 dataset with a wide range of applications, including zero and few-shot image recognition and retrieval, from inductive to transductive settings. Empirically, we show that our frame-work improves over the current state of the art on many of the considered tasks.

Learning Robust Visual-Semantic Embeddings

We revisit the choice of SGD for training deep neural networks by reconsidering the appropriate geometry in which to optimize the weights. We argue for a geometry invariant to rescaling of weights that does not affect the output of the network, and suggest Path-SGD, which is an approximate steepest descent method with respect to a path-wise regularizer related to max-norm regularization. Path-SGD is easy and efficient to implement and leads to empirical gains over SGD and AdaGrad.

Path-SGD: Path-Normalized Optimization in Deep Neural Networks

Restricted Boltzmann Machines for Neuroimaging: an Application in Identifying Intrinsic Networks

Despite the recent trend of increasingly large datasets for object detection, there still exist many classes with few training examples. To overcome this lack of training data for certain classes, we propose a novel way of augmenting the training data for each class by borrowing and transforming examples from other classes. Our model learns which training instances from other classes to borrow and how to transform the borrowed examples so that they become more similar to instances from the target class. Our experimental results demonstrate that our new object detector, with borrowed and transformed examples, improves upon the current state-of-the-art detector on the challenging SUN09 object detection dataset.

https://papers.nips.cc/paper/4461-transfer-learning-by-borrowing-examples-for-multiclass-object-detection.pdf

Transfer Learning by Borrowing Examples for Multiclass Object Detection

Multilayer perceptrons (MLPs) or neural networks are popular models used for nonlinear regression and classification tasks As regressors, MLPs model the conditional distribution of the predictor variables Y given the input variables X However, this predictive distribution is assumed to be unimodal (eg Gaussian) For tasks involving structured prediction, the conditional distribution should be multi-modal, resulting in one-to-many mappings By using stochastic hidden variables rather than deterministic ones, Sigmoid Belief Nets (SBNs) can induce a rich multimodal distribution in the output space However, previously proposed learning algorithms for SBNs are not efficient and unsuitable for modeling real-valued data In this paper, we propose a stochastic feedforward network with hidden layers composed of both deterministic and stochastic variables A new Generalized EM training procedure using importance sampling allows us to efficiently learn complicated conditional distributions Our model achieves superior performance on synthetic and facial expressions datasets compared to conditional Restricted Boltzmann Machines and Mixture Density Networks In addition, the latent features of our model improves classification and can learn to generate colorful textures of objects

/pdf/learning-stochastic-feedforward-neural-networks-39r6zu0o4j.pdf

Ruslan Salakhutdinov

Papers

Learning Robust Visual-Semantic Embeddings

Path-SGD: Path-Normalized Optimization in Deep Neural Networks

Restricted Boltzmann Machines for Neuroimaging: an Application in Identifying Intrinsic Networks

Transfer Learning by Borrowing Examples for Multiclass Object Detection

Learning Stochastic Feedforward Neural Networks