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

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.

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

We present an application of the Layer-wise Relevance Propagation (LRP) algorithm to state of the art deep convolutional neural networks and Fisher Vector classifiers to compare the image perception and prediction strategies of both classifiers with the use of visualized heatmaps. Layer-wise Relevance Propagation (LRP) is a method to compute scores for individual components of an input image, denoting their contribution to the prediction of the classifier for one particular test point. We demonstrate the impact of different choices of decomposition cut-off points during the LRP-process, controlling the resolution and semantics of the heatmap on test images from the PASCAL VOC 2007 test data set.

Controlling Explanatory Heatmap Resolution and Semantics via Decomposition Depth

Principal component analysis (PCA) is often used to project high-dimensional signals to lower dimensional subspaces defined by basis vectors that maximize the variance of the projected signals. The projected values can be used as features for classification problems. Data containing variations of relatively short duration and small magnitude, such as those seen in EEG signals, may not be captured by PCA when applied to time series of long duration. Instead, PCA can be applied independently to short segments of data and the basis vectors themselves can be used as features for classification. Here this is called the short-time principal component analysis (STPCA). In addition, the time-embedding of EEG samples is investigated prior to STPCA, resulting in a representation that captures EEG variations in space and time. The resulting features of the analysis are then classified via a standard linear discriminant analysis (LDA). Results are shown for two datasets of EEG, one recorded from subjects performing five mental tasks, and one from the third BCI Competition recorded from subjects performing one mental task and two imagined movement tasks.

Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis

Linear discriminant analysis (LDA) is the most commonly used classification method for single trial data in a brain-computer interface (BCI) framework. The popularity of LDA arises from its robustness, simplicity and high accuracy. However, the standard LDA approach is not capable to exploit sublabel information (such as stimulus identity), which is accessible in data from event related potentials (ERPs): it assumes that the evoked potentials are independent of the stimulus identity and dependent only on the users' attentional state. We question this assumption and investigate several methods which extract subclass-specific features from ERP data. Moreover, we propose a novel classification approach which exploits subclass-specific features using mean shrinkage. Based on a reanalysis of two BCI data sets, we show that our novel approach outperforms the standard LDA approach, while being computationally highly efficient.

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Mean shrinkage improves the classification of ERP signals by exploiting additional label information

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A benchmark data set for in silico prediction of ames mutagenicity

Part I. Non-invasive Brain-Computer Interface.- Chapter 1. Future directions for brain-machine interfacing technology.- Chapter 2. Brain-Computer Interface for Smart Vehicle: Detection of Braking Intention during Simulated Driving.- Chapter 3. Benefits and limits of multimodal neuroimaging for Brain Computer Interfaces.- Chapter 4. Multifrequency Analysis of Brain-Computer Interfaces.- Part II. Cognitive- and Neural-rehabilitation Engineering.- Chapter 5. Current Trends in Memory Implantation and Rehabilitation.- Chapter 6. Moving Brain Controlled Devices Outside the Lab: Principles and Applications.- Part III. Big Data Neurocomputing.- Chapter 7. Across cultures: a Cognitive and Computational Analysis of Emotional and Conversational Facial Expressions in Germany and Korea.- Chapter 8. Bottom-Up Processing in Complex Scenes: a unifying perspective on segmentation, fixation saliency, candidate regions, base-detail decomposition, and image enhancement.- Chapter 9. Perception-based motion cueing: a Cybernetics approach to motion simulation.- Chapter 10. The other-race effect revisited: no effect for faces varying in race only.- Part IV. Early Diagnosis and Prediction of Neural Diseases.- Chapter 11. Functional neuromonitoring in acquired head injury.- Chapter 12. Diagnostic Optical Imaging Technology and its Principles.- Chapter 13. Detection of Brain Metastases using Magnetic Resonance Imaging.- Chapter 14. Deep Learning in Diagnosis of Brain Disorders.

Klaus-Robert Müller

Papers

Controlling Explanatory Heatmap Resolution and Semantics via Decomposition Depth

Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis

Mean shrinkage improves the classification of ERP signals by exploiting additional label information

A benchmark data set for in silico prediction of ames mutagenicity

Recent Progress in Brain and Cognitive Engineering