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 networks are able to learn highly predictive models of video data. Due to video length, a common strategy is to train them on small video snippets. We apply the deep Taylor / LRP technique to understand the deep network's classification decisions, and identify a "border effect": a tendency of the classifier to look mainly at the bordering frames of the input. This effect relates to the step size used to build the video snippet, which we can then tune in order to improve the classifier's accuracy without retraining the model. To our knowledge, this is the the first work to apply the deep Taylor / LRP technique on any video analyzing neural network.

Understanding Patch-Based Learning by Explaining Predictions

We propose a new stopping condition for a Support Vector Machine (SVM) solver which precisely reflects the objective of the Leave-One-Out error computation. The stopping condition guarantees that the output on an intermediate SVM solution is identical to the output of the optimal SVM solution with one data point excluded from the training set. A simple augmentation of a general SVM training algorithm allows one to use a stopping criterion equivalent to the proposed sufficient condition. A comprehensive experimental evaluation of our method shows consistent speedup of the exact LOO computation by our method, up to the factor of 13 for the linear kernel. The new algorithm can be seen as an example of constructive guidance of an optimization algorithm towards achieving the best attainable expected risk at optimal computational cost.

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Stopping conditions for exact computation of leave-one-out error in support vector machines

A recently proposed novel statistical model estimates population effects and individual variability between subgroups simultaneously, by extending Lasso methods. We apply this l1-penalized linear regression mixed-effects model to a large scale real world problem: by exploiting a large set of brain computer interface data we are able to obtain a subject-independent classifier that compares favorably with prior zero-training algorithms. This unifying model inherently compensates shifts in the input space attributed to the individuality of a subject. In particular we are now able to differentiate within-subject and between-subject variability. A deeper understanding both of the underlying statistical and physiological structure of the data is gained.

l1-penalized linear mixed-effects models for BCI

We present a preliminary study on the Rate-Distortion (RD) gain that can be achieved applying RD optimization techniques in a multiview plus depth encoder. We consider the use of Multiview Video Coding (MVC) for both, color and depth sequences, and evaluate the improvement that can be obtained allowing a quantization parameter (QP) assignment on a macroblock basis compared to the use of a fixed QP for the whole sequence. The optimization criterion is the minimization of the distortion of the synthesized views generated at the receiver. Our motivation for this criterion is to capture the impact of depth coding according to its final purpose: the generation of virtual views. Since a unique objective quality metric for view synthesis artifacts evaluation has not been set yet, the performance of several algorithms for quality evaluation of the target synthesized view have been compared. Beyond obtaining a better RD performance, as could be expected, results also show that optimized synthesized views achieve absolute lower distortion values than the best result of the approach that uses a fixed QP for the whole sequence.

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Block based Rate-Distortion analysis for quality improvement of synthesized views

Objective: In medical applications, neuroscience and brain-computer interface research, bimodal acquisition of brain activity using Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS) is at the moment achieved by combining separate commercial devices. We have investigated quantitatively whether dedicated hybrid systems exhibit more advantageous properties. Methods: We studied intermodality electrical crosstalk and timing jitter in two separate and one hybrid EEG-NIRS acquisition device. Results: Analysis revealed significantly higher impact of electrical NIRS current crosstalk into the EEG inputs and timing jitters between EEG-NIRS markers in separate devices compared to the hybrid system. Conclusion: The results support hybrid acquisition systems to be advantageous in setups that require high performance in timing and signal quality.

Klaus-Robert Müller

Papers

Understanding Patch-Based Learning by Explaining Predictions

Stopping conditions for exact computation of leave-one-out error in support vector machines

l1-penalized linear mixed-effects models for BCI

Block based Rate-Distortion analysis for quality improvement of synthesized views

Why build an integrated EEG-NIRS? About the advantages of hybrid bio-acquisition hardware