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.

/pdf/deep-residual-learning-for-image-recognition-b75jg61qrq.pdf

Deep Residual Learning for Image Recognition

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.

Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.

/pdf/batch-normalization-accelerating-deep-network-training-by-3dkqye6twt.pdf

Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

To decide the optimal size of learning machines is a central issue in the statistical learning theory, and that is why some theoretical criteria such as the BIC are developed. However, they cannot be applied to singular machines, and it is known that many practical learning machines e.g. mixture models, hidden Markov models, and Bayesian networks, are singular. Recently, we proposed the Singular Information Criterion (SingIC), which allows us to select the optimal size of singular machines. The SingIC is based on the analysis of the learning coefficient. So, the machines, to which the SingIC can be applied, are still limited. In this paper, we propose an extension of this criterion, which enables us to apply it to many singular machines, and evaluate the efficiency in Gaussian mixtures. The results offer an effective strategy to select the optimal size.

A Model Selection Method Based on Bound of Learning Coefficient

In the above-named work [ibid., vol. 23, no. 4, pp. 618–627, Jul. 2015], the affiliation for Klaus-Robert Mueller should have appeared as follows: K-R. Mueller is with the Machine Learning Laboratory, Berlin Institute of Technology, D-10587 Berlin, Germany, and also with the Bernstein Center for Computational Neuroscience (BCCN), D-10587 Berlin, Germany, and also with the Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul 136-713, Korea; (e-mail: klaus-robert.mueller@tu-berlin.de).

Correction to “Concurrent Adaptation of Human and Machine Improves Simultaneous and Proportional Myoelectric Control”

Recently, in order to overcome the disadvantages of unimodal brain-imaging modalities such as low signal-to-noise ratio and vulnerability to motion artifact and to improve system performance, a multimodal imaging system (so-called hybrid system) has been emerging as an attractive alternative. In the present study, to meet the increasing demand on a hybrid brain-imaging data, we introduce open access datasets of electroencephalography (EEG) and near-infrared spectroscopy (NIRS) simultaneously measured during various cognitive tasks. The datasets contain BCI data such as motor imagery (MI)-, and mental arithmetic (MA), and word generation (WG)-related brain signals, and cognitive task data such as n-back (NB)-, and discrimination/selection response (DSR)-related brain signals. We provide the reference results of these datasets, which were validated using analysis pipelines widely used in related research fields. In particular, it was confirmed from classification analysis that a hybrid EEG-NIRS system can yield better classification accuracy than each of unimodal brain-imaging systems.

Open access repository for hybrid EEG-NIRS data

Context-based adaptive binary arithmetic coding (CABAC) has proven to be an efficient technique in the area of video coding. This paper presents an approach for integrating CABAC into the framework of frame-based animated mesh compression (FAMC). It presents the specific modifications and adaptations that have been worked out to adapt CABAC to the specific requirements of FAMC in order to build a solution with a higher degree of coding efficiency. For a typical test set of animated meshes, average bit rate savings of 25% have been observed for the combination of CABAC and FAMC when compared to a previous version of FAMC using a conventional N-ary arithmetic coder. The presented approach has been recently adopted as part of the MPEG-4 AFX standard.

Klaus-Robert Müller

Papers

A Model Selection Method Based on Bound of Learning Coefficient

Correction to “Concurrent Adaptation of Human and Machine Improves Simultaneous and Proportional Myoelectric Control”

Open access repository for hybrid EEG-NIRS data

Context-adaptive binary arithmetic coding for frame-based animated mesh compression

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