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

The present application is concerned with several aspects of improving the efficiency of distributed learning.

Concepts for distributed learning of neural networks and/or transmission of parameterization updates therefor

Analyzing biomedical data-e.g. from the brain-we encounter fundamental problems that lie largely in the fields of signal processing and machine learning. The current paper presents at first a method to deal with non-stationary signals, subsequently the signal processing technique of independent component analysis (ICA) is reviewed. We use EEG recordings of continuous auditory perception as illustration for the discussed algorithms.

Decomposition algorithms for analysing brain signals

Electroencephalogram (EEG) has been widely used for brain-computer interface (BCI) due to its high temporal resolution. Meanwhile, multimodal imaging techniques based on combined EEG and near infrared spectroscopy (NIRS) have been studied in BCI research and shown to lead to beneficiary results in terms of classification [1]. However, performance results of this study show that there is a difference of peak accuracy (about 5s) between NIRS and EEG caused by the high latency of the NIRS signal. Based on our experimental results and analysis, we show that even though there is high latency of NIRS signal in our proposed multimodal imaging technique, it can be reasonable system for real-time BCI.

Multimodal imaging technique for rapid response brain-computer interface feedback

Conventionally, neuroscientific data is analyzed based on the behavioral response of the participant. This approach assumes that behavioral errors of participants are in line with the neural processing. However, this may not be the case, in particular in experiments with time pressure or studies investigating the threshold of perception. In these cases, the error distribution deviates from uniformity due to the heteroscedastic nature of the underlying experimental set-up. This problem of systematic and structured (non-uniform) label noise is ignored when analysis are based on behavioral data, as is being done typically. Thus, we run the risk to arrive at wrong conclusions in our analysis. This paper proposes a remedy to handle this crucial problem: we present a novel approach for a) measuring label noise and b) removing structured label noise. We show its usefulness for an EEG data set recorded during a standard d2 test for visual attention.

When brain and behavior disagree: Tackling systematic label noise in EEG data with machine learning

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Klaus-Robert Müller

Papers

Concepts for distributed learning of neural networks and/or transmission of parameterization updates therefor

Decomposition algorithms for analysing brain signals

Multimodal imaging technique for rapid response brain-computer interface feedback

When brain and behavior disagree: Tackling systematic label noise in EEG data with machine learning

A Multi-Class Support Vector Machine Based on Scatter Criteria