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

Deep one-class classification variants for anomaly detection learn a mapping that concentrates nominal samples in feature space causing anomalies to be mapped away. Because this transformation is highly non-linear, finding interpretations poses a significant challenge. In this paper we present an explainable deep one-class classification method, Fully Convolutional Data Description (FCDD), where the mapped samples are themselves also an explanation heatmap. FCDD yields competitive detection performance and provides reasonable explanations on common anomaly detection benchmarks with CIFAR-10 and ImageNet. On MVTec-AD, a recent manufacturing dataset offering ground-truth anomaly maps, FCDD sets a new state of the art in the unsupervised setting. Our method can incorporate ground-truth anomaly maps during training and using even a few of these (~5) improves performance significantly. Finally, using FCDD's explanations we demonstrate the vulnerability of deep one-class classification models to spurious image features such as image watermarks.

Explainable Deep One-Class Classification

Lighting in modern-day devices is often discrete The sharp onsets and offsets of light are known to induce a steady-state visually evoked potential (SSVEP) in the electroencephalogram (EEG) at low frequencies However, it is not well-known how the brain processes visual flicker at the threshold of conscious perception and beyond To shed more light on this, we ran an EEG study in which we asked participants (N=6) to discriminate on a behavioral level between visual stimuli in which they perceived flicker and those that they perceived as constant wave light We found that high frequency flicker which is not perceived consciously anymore still elicits a neural response in the corresponding frequency band of EEG, con-tralateral to the stimulated hemifield The main contribution of this paper is to show the benefit of machine learning techniques for investigating this effect of subconscious processing: Common Spatial Pattern (CSP) filtering in combination with classification based on Linear Discriminant Analysis (LDA) could be used to reveal the effect for additional participants and stimuli, with high statistical significance We conclude that machine learning techniques are a valuable extension of conventional neurophysiological analysis that can substantially boost the sensitivity to subconscious effects, such as the processing of imperceptible flicker

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Revealing the neural response to imperceptible peripheral flicker with machine learning

We propose a new boosting algorithm which similarly to v- Support-Vector Classification allows for the possibility of a pre-specified fraction v of points to lie in the margin area or even on the wrong side of the decision boundary. It gives a nicely interpretable way of controlling the trade-off between minimizing training error and capacity. Furthermore, it can act as a filter for finding and selecting informative patterns from a database.

Robust Ensemble Learning for Data Mining

Neural Networks: Tricks of the Trade, this book is an outgrowth of a 1996 NIPS workshop

The application of deep learning (DL) models to the decoding of cognitive states from whole-brain functional Magnetic Resonance Imaging (fMRI) data is often hindered by the small sample size and high dimensionality of these datasets. Especially, in clinical settings, where patient data are scarce. In this work, we demonstrate that transfer learning represents a solution to this problem. Particularly, we show that a DL model, which has been previously trained on a large openly available fMRI dataset of the Human Connectome Project, outperforms a model variant with the same architecture, but which is trained from scratch, when both are applied to the data of a new, unrelated fMRI task. The pre-trained DL model variant is able to correctly decode 67.51% of the cognitive states from a test dataset with 100 individuals, when fine-tuned on a dataset of the size of only three subjects.

Klaus-Robert Müller

Papers

Explainable Deep One-Class Classification

Revealing the neural response to imperceptible peripheral flicker with machine learning

Robust Ensemble Learning for Data Mining

Neural Networks: Tricks of the Trade, this book is an outgrowth of a 1996 NIPS workshop

Deep Transfer Learning for Whole-Brain FMRI Analyses