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Deeply-supervised Knowledge Synergy
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Abstract
Convolutional Neural Networks (CNNs) have become deeper and more complicated compared with the pioneering AlexNet. However, current prevailing training scheme follows the previous way of adding supervision to the last layer of the network only and propagating error information up layer-by-layer. In this paper, we propose Deeply-supervised Knowledge Synergy (DKS), a new method aiming to train CNNs with improved generalization ability for image classification tasks without introducing extra computational cost during inference. Inspired by the deeply-supervised learning scheme, we first append auxiliary supervision branches on top of certain intermediate network layers. While properly using auxiliary supervision can improve model accuracy to some degree, we go one step further to explore the possibility of utilizing the probabilistic knowledge dynamically learnt by the classifiers connected to the backbone network as a new regularization to improve the training. A novel synergy loss, which considers pairwise knowledge matching among all supervision branches, is presented. Intriguingly, it enables dense pairwise knowledge matching operations in both top-down and bottom-up directions at each training iteration, resembling a dynamic synergy process for the same task. We evaluate DKS on image classification datasets using state-of-the-art CNN architectures, and show that the models trained with it are consistently better than the corresponding counterparts. For instance, on the ImageNet classification benchmark, our ResNet-152 model outperforms the baseline model with a 1.47% margin in Top-1 accuracy. Code is available at https://github.com/sundw2014/DKS.
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Diverse input data modalities can provide complementary cues for several tasks, usually leading to more robust algorithms and better performance. However, while a (training) dataset could be accurately designed to include a variety of sensory inputs, it is often the case that not all modalities are available in real life (testing) scenarios, where a model has to be deployed. This raises the challenge of how to learn robust representations leveraging multimodal data in the training stage, while considering limitations at test time, such as noisy or missing modalities. This paper presents a new approach for multimodal video action recognition, developed within the unified frameworks of distillation and privileged information, named generalized distillation. Particularly, we consider the case of learning representations from depth and RGB videos, while relying on RGB data only at test time. We propose a new approach to train an hallucination network that learns to distill depth features through multiplicative connections of spatiotemporal representations, leveraging soft labels and hard labels, as well as distance between feature maps. We report state-of-the-art results on video action classification on the largest multimodal dataset available for this task, the NTU RGB+D, as well as on the UWA3DII and Northwestern-UCLA.
Recent work has shown that convolutional networks can be substantially deeper, more accurate and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper we embrace this observation and introduce the Dense Convolutional Network (DenseNet), where each layer is directly connected to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections, one between each layer and its subsequent layer (treating the input as layer 0), our network has L(L+1)/2 direct connections. For each layer, the feature maps of all preceding layers are treated as separate inputs whereas its own feature maps are passed on as inputs to all subsequent layers. Our proposed connectivity pattern has several compelling advantages: it alleviates the vanishing gradient problem and strengthens feature propagation; despite the increase in connections, it encourages feature reuse and leads to a substantial reduction of parameters; its models tend to generalize surprisingly well. We evaluate our proposed architecture on five highly competitive object recognition benchmark tasks. The DenseNet obtains significant improvements over the state-of-the-art on all five of them (e.g., yielding 3.74% test error on CIFAR-10, 19.25% on CIFAR-100 and 1.59% on SVHN).
In this work, we present a simple, highly efficient and modularized Dual Path Network (DPN) for image classification which presents a new topology of connection paths internally. By revealing the equivalence of the state-of-the-art Residual Network (ResNet) and Densely Convolutional Network (DenseNet) within the HORNN framework, we find that ResNet enables feature re-usage while DenseNet enables new features exploration which are both important for learning good representations. To enjoy the benefits from both path topologies, our proposed Dual Path Network shares common features while maintaining the flexibility to explore new features through dual path architectures. Extensive experiments on three benchmark datasets, ImagNet-1k, Places365 and PASCAL VOC, clearly demonstrate superior performance of the proposed DPN over state-of-the-arts. In particular, on the ImagNet-1k dataset, a shallow DPN surpasses the best ResNeXt-101(64x4d) with 26% smaller model size, 25% less computational cost and 8% lower memory consumption, and a deeper DPN (DPN-131) further pushes the state-of-the-art single model performance with more than 3 times faster training speed. Experiments on the Places365 large-scale scene dataset, PASCAL VOC detection dataset, and PASCAL VOC segmentation dataset also demonstrate its consistently better performance than DenseNet, ResNet and the latest ResNeXt model over various applications.
Model distillation is an effective and widely used technique to transfer knowledge from a teacher to a student network. The typical application is to transfer from a powerful large network or ensemble to a small network, that is better suited to low-memory or fast execution requirements. In this paper, we present a deep mutual learning (DML) strategy where, rather than one way transfer between a static pre-defined teacher and a student, an ensemble of students learn collaboratively and teach each other throughout the training process. Our experiments show that a variety of network architectures benefit from mutual learning and achieve compelling results on CIFAR-100 recognition and Market-1501 person re-identification benchmarks. Surprisingly, it is revealed that no prior powerful teacher network is necessary -- mutual learning of a collection of simple student networks works, and moreover outperforms distillation from a more powerful yet static teacher.
While depth tends to improve network performances, it also makes
gradient-based training more difficult since deeper networks tend to be more
non-linear. The recently proposed knowledge distillation approach is aimed at
obtaining small and fast-to-execute models, and it has shown that a student
network could imitate the soft output of a larger teacher network or ensemble
of networks. In this paper, we extend this idea to allow the training of a
student that is deeper and thinner than the teacher, using not only the outputs
but also the intermediate representations learned by the teacher as hints to
improve the training process and final performance of the student. Because the
student intermediate hidden layer will generally be smaller than the teacher's
intermediate hidden layer, additional parameters are introduced to map the
student hidden layer to the prediction of the teacher hidden layer. This allows
one to train deeper students that can generalize better or run faster, a
trade-off that is controlled by the chosen student capacity. For example, on
CIFAR-10, a deep student network with almost 10.4 times less parameters
outperforms a larger, state-of-the-art teacher network.
The ImageNet Large Scale Visual Recognition Challenge is a benchmark in
object category classification and detection on hundreds of object categories
and millions of images. The challenge has been run annually from 2010 to
present, attracting participation from more than fifty institutions.
This paper describes the creation of this benchmark dataset and the advances
in object recognition that have been possible as a result. We discuss the
challenges of collecting large-scale ground truth annotation, highlight key
breakthroughs in categorical object recognition, provide detailed a analysis of
the current state of the field of large-scale image classification and object
detection, and compare the state-of-the-art computer vision accuracy with human
accuracy. We conclude with lessons learned in the five years of the challenge,
and propose future directions and improvements.
We investigate multiple techniques to improve upon the current state of the
art deep convolutional neural network based image classification pipeline. The
techiques include adding more image transformations to training data, adding
more transformations to generate additional predictions at test time and using
complementary models applied to higher resolution images. This paper summarizes
our entry in the Imagenet Large Scale Visual Recognition Challenge 2013. Our
system achieved a top 5 classification error rate of 13.55% using no external
data which is over a 20% relative improvement on the previous year's winner.
We consider the problem of designing models to leverage a recently introduced
approximate model averaging technique called dropout. We define a simple new
model called maxout (so named because its output is the max of a set of inputs,
and because it is a natural companion to dropout) designed to both facilitate
optimization by dropout and improve the accuracy of dropout's fast approximate
model averaging technique. We empirically verify that the model successfully
accomplishes both of these tasks. We use maxout and dropout to demonstrate
state of the art classification performance on four benchmark datasets: MNIST,
CIFAR-10, CIFAR-100, and SVHN.
We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perfo rm more informative gradient-based learning. The adaptation, in essence, allows us to find needl es in haystacks in the form of very predictive yet rarely observed features. Our paradigm stems from recent advances in online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies the task of setting a learning rate and results in regret guar antees that are provably as good as the best proximal function that can be chosen in hindsight. We corroborate our theoretical results with experiments on a text classification task, showing substant ial improvements for classification with sparse datasets.
Estimating the travel time of a path is of great importance to smart urban mobility. Existing approaches are either based on estimating the time cost of each road segment which are not able to capture many cross-segment complex factors, or designed heuristically in a non-learning-based way which fail to leverage the natural abundant temporal labels of the data, i.e., the time stamp of each trajectory point. In this paper, we leverage on new development of deep neural networks and propose a novel auxiliary supervision model, namely DeepTravel, that can automatically and effectively extract different features, as well as make full use of the temporal labels of the trajectory data. We have conducted comprehensive experiments on real datasets to demonstrate the out-performance of DeepTravel over existing approaches.
Modern semantic segmentation frameworks usually combine low-level and high-level features from pre-trained backbone convolutional models to boost performance. In this paper, we first point out that a simple fusion of low-level and high-level features could be less effective because of the gap in semantic levels and spatial resolution. We find that introducing semantic information into low-level features and high-resolution details into high-level features is more effective for the later fusion. Based on this observation, we propose a new framework, named ExFuse, to bridge the gap between low-level and high-level features thus significantly improve the segmentation quality by 4.0\% in total. Furthermore, we evaluate our approach on the challenging PASCAL VOC 2012 segmentation benchmark and achieve 87.9\% mean IoU, which outperforms the previous state-of-the-art results.
In this paper, we study the problem of semi-supervised image recognition, which is to learn classifiers using both labeled and unlabeled images. We present Deep Co-Training, a deep learning based method inspired by the Co-Training framework. The original Co-Training learns two classifiers on two views which are data from different sources that describe the same instances. To extend this concept to deep learning, Deep Co-Training trains multiple deep neural networks to be the different views and exploits adversarial examples to encourage view difference, in order to prevent the networks from collapsing into each other. As a result, the co-trained networks provide different and complementary information about the data, which is necessary for the Co-Training framework to achieve good results. We test our method on SVHN, CIFAR-10/100 and ImageNet datasets, and our method outperforms the previous state-of-the-art methods by a large margin.
We propose Efficient Neural Architecture Search (ENAS), a fast and inexpensive approach for automatic model design. In ENAS, a controller learns to discover neural network architectures by searching for an optimal subgraph within a large computational graph. The controller is trained with policy gradient to select a subgraph that maximizes the expected reward on the validation set. Meanwhile the model corresponding to the selected subgraph is trained to minimize a canonical cross entropy loss. Thanks to parameter sharing between child models, ENAS is fast: it delivers strong empirical performances using much fewer GPU-hours than all existing automatic model design approaches, and notably, 1000x less expensive than standard Neural Architecture Search. On the Penn Treebank dataset, ENAS discovers a novel architecture that achieves a test perplexity of 55.8, establishing a new state-of-the-art among all methods without post-training processing. On the CIFAR-10 dataset, ENAS designs novel architectures that achieve a test error of 2.89%, which is on par with NASNet (Zoph et al., 2018), whose test error is 2.65%.
We propose a method for learning CNN structures that is more efficient than previous approaches: instead of using reinforcement learning (RL) or genetic algorithms (GA), we use a sequential model-based optimization (SMBO) strategy, in which we search for architectures in order of increasing complexity, while simultaneously learning a surrogate function to guide the search, similar to A* search. On the CIFAR-10 dataset, our method finds a CNN structure with the same classification accuracy (3.41% error rate) as the RL method of Zoph et al. (2017), but 2 times faster (in terms of number of models evaluated). It also outperforms the GA method of Liu et al. (2017), which finds a model with worse performance (3.63% error rate), and takes 5 times longer. Finally we show that the model we learned on CIFAR also works well at the task of ImageNet classification. In particular, we match the state-of-the-art performance of 82.9% top-1 and 96.1% top-5 accuracy.
Deep learning networks have achieved state-of-the-art accuracies on computer vision workloads like image classification and object detection. The performant systems, however, typically involve big models with numerous parameters. Once trained, a challenging aspect for such top performing models is deployment on resource constrained inference systems - the models (often deep networks or wide networks or both) are compute and memory intensive. Low-precision numerics and model compression using knowledge distillation are popular techniques to lower both the compute requirements and memory footprint of these deployed models. In this paper, we study the combination of these two techniques and show that the performance of low-precision networks can be significantly improved by using knowledge distillation techniques. Our approach, Apprentice, achieves state-of-the-art accuracies using ternary precision and 4-bit precision for variants of ResNet architecture on ImageNet dataset. We present three schemes using which one can apply knowledge distillation techniques to various stages of the train-and-deploy pipeline.
Large deep neural networks are powerful, but exhibit undesirable behaviors such as memorization and sensitivity to adversarial examples. In this work, we propose mixup, a simple learning principle to alleviate these issues. In essence, mixup trains a neural network on convex combinations of pairs of examples and their labels. By doing so, mixup regularizes the neural network to favor simple linear behavior in-between training examples. Our experiments on the ImageNet-2012, CIFAR-10, CIFAR-100, Google commands and UCI datasets show that mixup improves the generalization of state-of-the-art neural network architectures. We also find that mixup reduces the memorization of corrupt labels, increases the robustness to adversarial examples, and stabilizes the training of generative adversarial networks.
Can a large convolutional neural network trained for whole-image classification on ImageNet be coaxed into detecting objects in PASCAL? We show that the answer is yes, and that the resulting system is simple, scalable, and boosts mean average precision, relative to the venerable deformable part model, by more than 40% (achieving a final mAP of 48% on VOC 2007). Our framework combines powerful computer vision techniques for generating bottom-up region proposals with recent advances in learning high-capacity convolutional neural networks. We call the resulting system R-CNN: Regions with CNN features. The same framework is also competitive with state-of-the-art semantic segmentation methods, demonstrating its flexibility. Beyond these results, we execute a battery of experiments that provide insight into what the network learns to represent, revealing a rich hierarchy of discriminative and often semantically meaningful features.
In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively.
Rectified activation units (rectifiers) are essential for state-of-the-art neural networks. In this work, we study rectifier neural networks for image classification from two aspects. First, we propose a Parametric Rectified Linear Unit (PReLU) that generalizes the traditional rectified unit. PReLU improves model fitting with nearly zero extra computational cost and little overfitting risk. Second, we derive a robust initialization method that particularly considers the rectifier nonlinearities. This method enables us to train extremely deep rectified models directly from scratch and to investigate deeper or wider network architectures. Based on our PReLU networks (PReLU-nets), we achieve 4.94% top-5 test error on the ImageNet 2012 classification dataset. This is a 26% relative improvement over the ILSVRC 2014 winner (GoogLeNet, 6.66%). To our knowledge, our result is the first to surpass human-level performance (5.1%, Russakovsky et al.) on this visual recognition challenge.
We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 dif- ferent classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implemen- tation of the convolution operation. To reduce overfitting in the fully-connected layers we employed a recently-developed regularization method called dropout that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry
Attention plays a critical role in human visual experience. Furthermore, it has recently been demonstrated that attention can also play an important role in the context of applying artificial neural networks to a variety of tasks from fields such as computer vision and NLP. In this work we show that, by properly defining attention for convolutional neural networks, we can actually use this type of information in order to significantly improve the performance of a student CNN network by forcing it to mimic the attention maps of a powerful teacher network. To that end, we propose several novel methods of transferring attention, showing consistent improvement across a variety of datasets and convolutional neural network architectures.
Scene parsing is challenging for unrestricted open vocabulary and diverse scenes. In this paper, we exploit the capability of global context information by different-region-based context aggregation through our pyramid pooling module together with the proposed pyramid scene parsing network (PSPNet). Our global prior representation is effective to produce good quality results on the scene parsing task, while PSPNet provides a superior framework for pixel-level prediction tasks. The proposed approach achieves state-of-the-art performance on various datasets. It came first in ImageNet scene parsing challenge 2016, PASCAL VOC 2012 benchmark and Cityscapes benchmark. A single PSPNet yields new record of mIoU score as 85.4% on PASCAL VOC 2012 and 80.2% on Cityscapes.
We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, codenamed ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart.
Neural networks are powerful and flexible models that work well for many difficult learning tasks in image, speech and natural language understanding. Despite their success, neural networks are still hard to design. In this paper, we use a recurrent network to generate the model descriptions of neural networks and train this RNN with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation set. On the CIFAR-10 dataset, our method, starting from scratch, can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy. Our CIFAR-10 model achieves a test error rate of 3.84, which is only 0.1 percent worse and 1.2x faster than the current state-of-the-art model. On the Penn Treebank dataset, our model can compose a novel recurrent cell that outperforms the widely-used LSTM cell, and other state-of-the-art baselines. Our cell achieves a test set perplexity of 62.4 on the Penn Treebank, which is 3.6 perplexity better than the previous state-of-the-art.
This work introduces a novel convolutional network architecture for the task of human pose estimation. Features are processed across all scales and consolidated to best capture the various spatial relationships associated with the body. We show how repeated bottom-up, top-down processing used in conjunction with intermediate supervision is critical to improving the performance of the network. We refer to the architecture as a “stacked hourglass” network based on the successive steps of pooling and upsampling that are done to produce a final set of predictions. State-of-the-art results are achieved on the FLIC and MPII benchmarks outcompeting all recent methods.
When building a unified vision system or gradually adding new capabilities to a system, the usual assumption is that training data for all tasks is always available. However, as the number of tasks grows, storing and retraining on such data becomes infeasible. A new problem arises where we add new capabilities to a Convolutional Neural Network (CNN), but the training data for its existing capabilities are unavailable. We propose our Learning without Forgetting method, which uses only new task data to train the network while preserving the original capabilities. Our method performs favorably compared to commonly used feature extraction and fine-tuning adaption techniques and performs similarly to multitask learning that uses original task data we assume unavailable. A more surprising observation is that Learning without Forgetting may be able to replace fine-tuning as standard practice for improved new task performance.
Convolutional networks are powerful visual models that yield hierarchies of features. We show that convolutional networks by themselves, trained end-to-end, pixels-to-pixels, improve on the previous best result in semantic segmentation. Our key insight is to build "fully convolutional" networks that take input of arbitrary size and produce correspondingly-sized output with efficient inference and learning. We define and detail the space of fully convolutional networks, explain their application to spatially dense prediction tasks, and draw connections to prior models. We adapt contemporary classification networks (AlexNet, the VGG net, and GoogLeNet) into fully convolutional networks and transfer their learned representations by fine-tuning to the segmentation task. We then define a skip architecture that combines semantic information from a deep, coarse layer with appearance information from a shallow, fine layer to produce accurate and detailed segmentations. Our fully convolutional network achieves improved segmentation of PASCAL VOC (30% relative improvement to 67.2% mean IU on 2012), NYUDv2, SIFT Flow, and PASCAL-Context, while inference takes one tenth of a second for a typical image.
Deep residual networks were shown to be able to scale up to thousands of layers and still have improving performance. However, each fraction of a percent of improved accuracy costs nearly doubling the number of layers, and so training very deep residual networks has a problem of diminishing feature reuse, which makes these networks very slow to train. To tackle these problems, in this paper we conduct a detailed experimental study on the architecture of ResNet blocks, based on which we propose a novel architecture where we decrease depth and increase width of residual networks. We call the resulting network structures wide residual networks (WRNs) and show that these are far superior over their commonly used thin and very deep counterparts. For example, we demonstrate that even a simple 16-layer-deep wide residual network outperforms in accuracy and efficiency all previous deep residual networks, including thousand-layer-deep networks, achieving new state-of-the-art results on CIFAR-10, CIFAR-100 and SVHN.
Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. © 2014 Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever and Ruslan Salakhutdinov.
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 tools have recently gained much attention in applied machine
learning. However such tools for regression and classification do not allow us
to capture model uncertainty. Bayesian models offer us the ability to reason
about model uncertainty, but usually come with a prohibitive computational
cost.
We show that dropout in multilayer perceptron models (MLPs) can be
interpreted as a Bayesian approximation. Results are obtained for modelling
uncertainty for dropout MLP models - extracting information that has been
thrown away so far, from existing models. This mitigates the problem of
representing uncertainty in deep learning without sacrificing computational
performance or test accuracy.
We perform an exploratory study of the dropout uncertainty properties.
Various network architectures and non-linearities are assessed on tasks of
extrapolation, interpolation, and classification. We show that model
uncertainty is important for classification tasks using MNIST as an example,
and use the model's uncertainty in a Bayesian pipeline, with deep reinforcement
learning as a concrete example.
We develop a new edge detection algorithm that tackles two important issues
in this long-standing vision problem: (1) holistic image training and
prediction; and (2) multi-scale and multi-level feature learning. Our proposed
method, holistically-nested edge detection (HED), performs image-to-image
prediction by means of a deep learning model that leverages fully convolutional
neural networks and deeply-supervised nets. HED automatically learns rich
hierarchical representations (guided by deep supervision on side responses)
that are important in order to approach the human ability resolve the
challenging ambiguity in edge and object boundary detection. We significantly
advance the state-of-the-art on the BSD500 dataset (ODS F-score of .782) and
the NYU Depth dataset (ODS F-score of .746), and do so with an improved speed
(0.4 second per image) that is orders of magnitude faster than some recent
CNN-based edge detection algorithms.
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. It also acts as a regularizer, in
some cases eliminating 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 4.9% top-5
validation error (and 4.8% test error), exceeding the accuracy of human raters.
We introduce Adam, an algorithm for first-order gradient-based optimization
of stochastic objective functions. The method is straightforward to implement
and is based an adaptive estimates of lower-order moments of the gradients. The
method is computationally efficient, has little memory requirements and is well
suited for problems that are large in terms of data and/or parameters. The
method is also ap- propriate for non-stationary objectives and problems with
very noisy and/or sparse gradients. The method exhibits invariance to diagonal
rescaling of the gradients by adapting to the geometry of the objective
function. The hyper-parameters have intuitive interpretations and typically
require little tuning. Some connections to related algorithms, on which Adam
was inspired, are discussed. We also analyze the theoretical convergence
properties of the algorithm and provide a regret bound on the convergence rate
that is comparable to the best known results under the online convex
optimization framework. We demonstrate that Adam works well in practice when
experimentally compared to other stochastic optimization methods.
In modern face recognition, the conventional pipeline consists of four stages: detect => align => represent => classify. We revisit both the alignment step and the representation step by employing explicit 3D face modeling in order to apply a piecewise affine transformation, and derive a face representation from a nine-layer deep neural network. This deep network involves more than 120 million parameters using several locally connected layers without weight sharing, rather than the standard convolutional layers. Thus we trained it on the largest facial dataset to-date, an identity labeled dataset of four million facial images belonging to more than 4,000 identities, where each identity has an average of over a thousand samples. The learned representations coupling the accurate model-based alignment with the large facial database generalize remarkably well to faces in unconstrained environments, even with a simple classifier. Our method reaches an accuracy of 97.25% on the Labeled Faces in the Wild (LFW) dataset, reducing the error of the current state of the art by more than 25%, closely approaching human-level performance.
Restricted Boltzmann machines were developed using binary stochastic hidden units. These can be generalized by replacing each binary unit by an infinite number of copies that all have the same weights but have progressively more negative biases. The learning and inference rules for these “Stepped Sigmoid Units ” are unchanged. They can be approximated efficiently by noisy, rectified linear units. Compared with binary units, these units learn features that are better for object recognition on the NORB dataset and face verification on the Labeled Faces in the Wild dataset. Unlike binary units, rectified linear units preserve information about relative intensities as information travels through multiple layers of feature detectors. 1.
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