Welcome to ShortScience.org! |

- ShortScience.org is a platform for post-publication discussion aiming to improve accessibility and reproducibility of research ideas.
- The website has 1519 public summaries, mostly in machine learning, written by the community and organized by paper, conference, and year.
- Reading summaries of papers is useful to obtain the perspective and insight of another reader, why they liked or disliked it, and their attempt to demystify complicated sections.
- Also, writing summaries is a good exercise to understand the content of a paper because you are forced to challenge your assumptions when explaining it.
- Finally, you can keep up to date with the flood of research by reading the latest summaries on our Twitter and Facebook pages.

Mask R-CNN

He, Kaiming and Gkioxari, Georgia and Dollár, Piotr and Girshick, Ross B.

arXiv e-Print archive - 2017 via Local Bibsonomy

Keywords: dblp

He, Kaiming and Gkioxari, Georgia and Dollár, Piotr and Girshick, Ross B.

arXiv e-Print archive - 2017 via Local Bibsonomy

Keywords: dblp

[link]
Mask RCNN takes off from where Faster RCNN left, with some augmentations aimed at bettering instance segmentation (which was out of scope for FRCNN). Instance segmentation was achieved remarkably well in *DeepMask* , *SharpMask* and later *Feature Pyramid Networks* (FPN). Faster RCNN was not designed for pixel-to-pixel alignment between network inputs and outputs. This is most evident in how RoIPool , the de facto core operation for attending to instances, performs coarse spatial quantization for feature extraction. Mask RCNN fixes that by introducing RoIAlign in place of RoIPool. #### Methodology Mask RCNN retains most of the architecture of Faster RCNN. It adds the a third branch for segmentation. The third branch takes the output from RoIAlign layer and predicts binary class masks for each class. ##### Major Changes and intutions **Mask prediction** Mask prediction segmentation predicts a binary mask for each RoI using fully convolution - and the stark difference being usage of *sigmoid* activation for predicting final mask instead of *softmax*, implies masks don't compete with each other. This *decouples* segmentation from classification. The class prediction branch is used for class prediction and for calculating loss, the mask of predicted loss is used calculating Lmask. Also, they show that a single class agnostic mask prediction works almost as effective as separate mask for each class, thereby supporting their method of decoupling classification from segmentation **RoIAlign** RoIPool first quantizes a floating-number RoI to the discrete granularity of the feature map, this quantized RoI is then subdivided into spatial bins which are themselves quantized, and finally feature values covered by each bin are aggregated (usually by max pooling). Instead of quantization of the RoI boundaries or bin bilinear interpolation is used to compute the exact values of the input features at four regularly sampled locations in each RoI bin, and aggregate the result (using max or average). **Backbone architecture** Faster RCNN uses a VGG like structure for extracting features from image, weights of which were shared among RPN and region detection layers. Herein, authors experiment with 2 backbone architectures - ResNet based VGG like in FRCNN and ResNet based [FPN](http://www.shortscience.org/paper?bibtexKey=journals/corr/LinDGHHB16) based. FPN uses convolution feature maps from previous layers and recombining them to produce pyramid of feature maps to be used for prediction instead of single-scale feature layer (final output of conv layer before connecting to fc layers was used in Faster RCNN) **Training Objective** The training objective looks like this ![](https://i.imgur.com/snUq73Q.png) Lmask is the addition from Faster RCNN. The method to calculate was mentioned above #### Observation Mask RCNN performs significantly better than COCO instance segmentation winners *without any bells and whiskers*. Detailed results are available in the paper |

Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks

Ren, Shaoqing and He, Kaiming and Girshick, Ross B. and Sun, Jian

Neural Information Processing Systems Conference - 2015 via Local Bibsonomy

Keywords: dblp

Ren, Shaoqing and He, Kaiming and Girshick, Ross B. and Sun, Jian

Neural Information Processing Systems Conference - 2015 via Local Bibsonomy

Keywords: dblp

[link]
**Object detection** is the task of drawing one bounding box around each instance of the type of object one wants to detect. Typically, image classification is done before object detection. With neural networks, the usual procedure for object detection is to train a classification network, replace the last layer with a regression layer which essentially predicts pixel-wise if the object is there or not. An bounding box inference algorithm is added at last to make a consistent prediction (see [Deep Neural Networks for Object Detection](http://papers.nips.cc/paper/5207-deep-neural-networks-for-object-detection.pdf)). The paper introduces RPNs (Region Proposal Networks). They are end-to-end trained to generate region proposals.They simoultaneously regress region bounds and bjectness scores at each location on a regular grid. RPNs are one type of fully convolutional networks. They take an image of any size as input and output a set of rectangular object proposals, each with an objectness score. ## See also * [R-CNN](http://www.shortscience.org/paper?bibtexKey=conf/iccv/Girshick15#joecohen) * [Fast R-CNN](http://www.shortscience.org/paper?bibtexKey=conf/iccv/Girshick15#joecohen) * [Faster R-CNN](http://www.shortscience.org/paper?bibtexKey=conf/nips/RenHGS15#martinthoma) * [Mask R-CNN](http://www.shortscience.org/paper?bibtexKey=journals/corr/HeGDG17) |

Fast R-CNN

Girshick, Ross B.

International Conference on Computer Vision - 2015 via Local Bibsonomy

Keywords: dblp

Girshick, Ross B.

International Conference on Computer Vision - 2015 via Local Bibsonomy

Keywords: dblp

[link]
This method is based on improving the speed of R-CNN \cite{conf/cvpr/GirshickDDM14} 1. Where R-CNN would have two different objective functions, Fast R-CNN combines localization and classification losses into a "multi-task loss" in order to speed up training. 2. It also uses a pooling method based on \cite{journals/pami/HeZR015} called the RoI pooling layer that scales the input so the images don't have to be scaled before being set an an input image to the CNN. "RoI max pooling works by dividing the $h \times w$ RoI window into an $H \times W$ grid of sub-windows of approximate size $h/H \times w/W$ and then max-pooling the values in each sub-window into the corresponding output grid cell." 3. Backprop is performed for the RoI pooling layer by taking the argmax of the incoming gradients that overlap the incoming values. This method is further improved by the paper "Faster R-CNN" \cite{conf/nips/RenHGS15} |

FaceNet: A Unified Embedding for Face Recognition and Clustering

Florian Schroff and Dmitry Kalenichenko and James Philbin

arXiv e-Print archive - 2015 via Local arXiv

Keywords: cs.CV

**First published:** 2015/03/12 (5 years ago)

**Abstract:** Despite significant recent advances in the field of face recognition,
implementing face verification and recognition efficiently at scale presents
serious challenges to current approaches. In this paper we present a system,
called FaceNet, that directly learns a mapping from face images to a compact
Euclidean space where distances directly correspond to a measure of face
similarity. Once this space has been produced, tasks such as face recognition,
verification and clustering can be easily implemented using standard techniques
with FaceNet embeddings as feature vectors.
Our method uses a deep convolutional network trained to directly optimize the
embedding itself, rather than an intermediate bottleneck layer as in previous
deep learning approaches. To train, we use triplets of roughly aligned matching
/ non-matching face patches generated using a novel online triplet mining
method. The benefit of our approach is much greater representational
efficiency: we achieve state-of-the-art face recognition performance using only
128-bytes per face.
On the widely used Labeled Faces in the Wild (LFW) dataset, our system
achieves a new record accuracy of 99.63%. On YouTube Faces DB it achieves
95.12%. Our system cuts the error rate in comparison to the best published
result by 30% on both datasets.
We also introduce the concept of harmonic embeddings, and a harmonic triplet
loss, which describe different versions of face embeddings (produced by
different networks) that are compatible to each other and allow for direct
comparison between each other.
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Florian Schroff and Dmitry Kalenichenko and James Philbin

arXiv e-Print archive - 2015 via Local arXiv

Keywords: cs.CV

[link]
FaceNet directly maps face images to $\mathbb{R}^{128}$ where distances directly correspond to a measure of face similarity. They use a triplet loss function. The triplet is (face of person A, other face of person A, face of person which is not A). Later, this is called (anchor, positive, negative). The loss function is learned and inspired by LMNN. The idea is to minimize the distance between the two images of the same person and maximize the distance to the other persons image. ## LMNN Large Margin Nearest Neighbor (LMNN) is learning a pseudo-metric $$d(x, y) = (x -y) M (x -y)^T$$ where $M$ is a positive-definite matrix. The only difference between a pseudo-metric and a metric is that $d(x, y) = 0 \Leftrightarrow x = y$ does not hold. ## Curriculum Learning: Triplet selection Show simple examples first, then increase the difficulty. This is done by selecting the triplets. They use the triplets which are *hard*. For the positive example, this means the distance between the anchor and the positive example is high. For the negative example this means the distance between the anchor and the negative example is low. They want to have $$||f(x_i^a) - f(x_i^p)||_2^2 + \alpha < ||f(x_i^a) - f(x_i^n)||_2^2$$ where $\alpha$ is a margin and $x_i^a$ is the anchor, $x_i^p$ is the positive face example and $x_i^n$ is the negative example. They increase $\alpha$ over time. It is crucial that $f$ maps the images not in the complete $\mathbb{R}^{128}$, but on the unit sphere. Otherwise one could double $\alpha$ by simply making $f' = 2 \cdot f$. ## Tasks * **Face verification**: Is this the same person? * **Face recognition**: Who is this person? ## Datasets * 99.63% accuracy on Labeled FAces in the Wild (LFW) * 95.12% accuracy on YouTube Faces DB ## Network Two models are evaluated: The [Zeiler & Fergus model](http://www.shortscience.org/paper?bibtexKey=journals/corr/ZeilerF13) and an architecture based on the [Inception model](http://www.shortscience.org/paper?bibtexKey=journals/corr/SzegedyLJSRAEVR14). ## See also * [DeepFace](http://www.shortscience.org/paper?bibtexKey=conf/cvpr/TaigmanYRW14#martinthoma) |

Group Normalization

Yuxin Wu and Kaiming He

arXiv e-Print archive - 2018 via Local arXiv

Keywords: cs.CV, cs.LG

**First published:** 2018/03/22 (2 years ago)

**Abstract:** Batch Normalization (BN) is a milestone technique in the development of deep
learning, enabling various networks to train. However, normalizing along the
batch dimension introduces problems --- BN's error increases rapidly when the
batch size becomes smaller, caused by inaccurate batch statistics estimation.
This limits BN's usage for training larger models and transferring features to
computer vision tasks including detection, segmentation, and video, which
require small batches constrained by memory consumption. In this paper, we
present Group Normalization (GN) as a simple alternative to BN. GN divides the
channels into groups and computes within each group the mean and variance for
normalization. GN's computation is independent of batch sizes, and its accuracy
is stable in a wide range of batch sizes. On ResNet-50 trained in ImageNet, GN
has 10.6% lower error than its BN counterpart when using a batch size of 2;
when using typical batch sizes, GN is comparably good with BN and outperforms
other normalization variants. Moreover, GN can be naturally transferred from
pre-training to fine-tuning. GN can outperform its BN-based counterparts for
object detection and segmentation in COCO, and for video classification in
Kinetics, showing that GN can effectively replace the powerful BN in a variety
of tasks. GN can be easily implemented by a few lines of code in modern
libraries.
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Yuxin Wu and Kaiming He

arXiv e-Print archive - 2018 via Local arXiv

Keywords: cs.CV, cs.LG

[link]
If you were to survey researchers, and ask them to name the 5 most broadly influential ideas in Machine Learning from the last 5 years, I’d bet good money that Batch Normalization would be somewhere on everyone’s lists. Before Batch Norm, training meaningfully deep neural networks was an unstable process, and one that often took a long time to converge to success. When we added Batch Norm to models, it allowed us to increase our learning rates substantially (leading to quicker training) without the risk of activations either collapsing or blowing up in values. It had this effect because it addressed one of the key difficulties of deep networks: internal covariate shift. To understand this, imagine the smaller problem, of a one-layer model that’s trying to classify based on a set of input features. Now, imagine that, over the course of training, the input distribution of features moved around, so that, perhaps, a value that was at the 70th percentile of the data distribution initially is now at the 30th. We have an obvious intuition that this would make the model quite hard to train, because it would learn some mapping between feature values and class at the beginning of training, but that would become invalid by the end. This is, fundamentally, the problem faced by higher layers of deep networks, since, if the distribution of activations in a lower layer changed even by a small amount, that can cause a “butterfly effect” style outcome, where the activation distributions of higher layers change more dramatically. Batch Normalization - which takes each feature “channel” a network learns, and normalizes [normalize = subtract mean, divide by variance] it by the mean and variance of that feature over spatial locations and over all the observations in a given batch - helps solve this problem because it ensures that, throughout the course of training, the distribution of inputs that a given layer sees stays roughly constant, no matter what the lower layers get up to. On the whole, Batch Norm has been wildly successful at stabilizing training, and is now canonized - along with the likes of ReLU and Dropout - as one of the default sensible training procedures for any given network. However, it does have its difficulties and downsides. One salient one of these comes about when you train using very small batch sizes - in the range of 2-16 examples per batch. Under these circumstance, the mean and variance calculated off of that batch are noisy and high variance (for the general reason that statistics calculated off of small sample sizes are noisy and high variance), which takes away from the stability that Batch Norm is trying to provide. One proposed alternative to Batch Norm, that didn’t run into this problem of small sample sizes, is Layer Normalization. This operates under the assumption that the activations of all feature “channels” within a given layer hopefully have roughly similar distributions, and, so, you an normalize all of them by taking the aggregate mean over all channels, *for a given observation*, and use that as the mean and variance you normalize by. Because there are typically many channels in a given layer, this means that you have many “samples” that go into the mean and variance. However, this assumption - that the distributions for each feature channel are roughly the same - can be an incorrect one. A useful model I have for thinking about the distinction between these two approaches is the idea that both are calculating approximations of an underlying abstract notion: the in-the-limit mean and variance of a single feature channel, at a given point in time. Batch Normalization is an approximation of that insofar as it only has a small sample of points to work with, and so its estimate will tend to be high variance. Layer Normalization is an approximation insofar as it makes the assumption that feature distributions are aligned across channels: if this turns out not to be the case, individual channels will have normalizations that are biased, due to being pulled towards the mean and variance calculated over an aggregate of channels that are different than them. Group Norm tries to find a balance point between these two approaches, one that uses multiple channels, and normalizes within a given instance (to avoid the problems of small batch size), but, instead of calculating the mean and variance over all channels, calculates them over a group of channels that represents a subset. The inspiration for this idea comes from the fact that, in old school computer vision, it was typical to have parts of your feature vector that - for example - represented a histogram of some value (say: localized contrast) over the image. Since these multiple values all corresponded to a larger shared “group” feature. If a group of features all represent a similar idea, then their distributions will be more likely to be aligned, and therefore you have less of the bias issue. One confusing element of this paper for me was that the motivation part of the paper strongly implied that the reason group norm is sensible is that you are able to combine statistically dependent channels into a group together. However, as far as I an tell, there’s no actually clustering or similarity analysis of channels that is done to place certain channels into certain groups; it’s just done so semi-randomly based on the index location within the feature channel vector. So, under this implementation, it seems like the benefits of group norm are less because of any explicit seeking out of dependant channels, and more that just having fewer channels in each group means that each individual channel makes up more of the weight in its group, which does something to reduce the bias effect anyway. The upshot of the Group Norm paper, results-wise, is that Group Norm performs better than both Batch Norm and Layer Norm at very low batch sizes. This is useful if you’re training on very dense data (e.g. high res video), where it might be difficult to store more than a few observations in memory at a time. However, once you get to batch sizes of ~24, Batch Norm starts to do better, presumably since that’s a large enough sample size to reduce variance, and you get to the point where the variance of BN is preferable to the bias of GN. |

Feature Pyramid Networks for Object Detection

Lin, Tsung-Yi and Dollár, Piotr and Girshick, Ross B. and He, Kaiming and Hariharan, Bharath and Belongie, Serge J.

arXiv e-Print archive - 2016 via Local Bibsonomy

Keywords: dblp

Lin, Tsung-Yi and Dollár, Piotr and Girshick, Ross B. and He, Kaiming and Hariharan, Bharath and Belongie, Serge J.

arXiv e-Print archive - 2016 via Local Bibsonomy

Keywords: dblp

[link]
Feature Pyramid Networks (FPNs) build on top of the state-of-the-art implementation for object detection net - Faster RCNN. Faster RCNN faces a major problem in training for scale-invariance as the computations can be memory-intensive and extremely slow. So FRCNN only applies multi-scale approach while testing. On the other hand, feature pyramids were mainstream when hand-generated features were used -primarily to counter scale-invariance. Feature pyramids are collections of features computed at multi-scale versions of the same image. Improving on a similar idea presented in *DeepMask*, FPN brings back feature pyramids using different feature maps of conv layers with differing spatial resolutions with predictiosn happening on all levels of pyramid. Using feature maps directly as it is, would be tough as initial layers tend to contain lower level representations and poor semantics but good localisation whereas deeper layers tend to constitute higher level representations with rich semantics but suffer poor localisation due to multiple subsampling. ##### Methodology FPN can be used with any normal conv architecture, that's used for classification. In such an architecture all layers have progressively decreasing spatial resolutions (say C1, C2,..C5). FPN would now take C5 and convolve with 1x1 kernel to reduce filters to give P5. Next, P5 is upsampled and merged it to C4 (C4 is convolved with 1x1 kernel to decrease filter size in order to match that of upsampled P5) by adding element wise to produce P4. Similarly P4 is upsampled and merged with C3(in a similar way) to give P3 and so on. The final set of feature maps, in this case {P2 .. P5} are used as feature pyramids. This is how pyramids would look like ![](https://i.imgur.com/oHFmpww.png) *Usage of combination of {P2,..P5} as compared to only P2* : P2 produces highest resolution, most semantic features and could as well be the default choice but because of shared weights across rest of feature layers and the learned scale invariance makes the pyramidal variant more robust to generating false ROIs For next steps, it could be RPN or RCNN, the regression and classifier would share weights across for all *anchors* (of varying aspect ratios) at each level of the feature pyramids. This step is similar to [Single Shot Detector (SSD) Networks ](http://www.shortscience.org/paper?bibtexKey=conf/eccv/LiuAESRFB16) ##### Observation The FPN was used in FRCNN in both parts of RPN and RCNN separately and then combined FPN in both parts and produced state-of-the-art result in MS COCO challenges bettering results of COCO '15 & '16 winner models ( Faster RCNN +++ & GMRI) for mAP. FPN also can be used for instance segmentation by using fully convolutional layers on top of the image pyramids. FPN outperforms results from *DeepMask*, *SharpMask*, *InstanceFCN* |

Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks

Zhu, Jun-Yan and Park, Taesung and Isola, Phillip and Efros, Alexei A.

arXiv e-Print archive - 2017 via Local Bibsonomy

Keywords: dblp

Zhu, Jun-Yan and Park, Taesung and Isola, Phillip and Efros, Alexei A.

arXiv e-Print archive - 2017 via Local Bibsonomy

Keywords: dblp

[link]
_Objective:_ Image-to-image translation to perform visual attribute transfer using unpaired images. _Dataset:_ [Cityscapes](https://www.cityscapes-dataset.com/), [CMP Facade](http://cmp.felk.cvut.cz/%7Etylecr1/facade/), [UT Zappos50k](http://vision.cs.utexas.edu/projects/finegrained/utzap50k/) and [ImageNet](http://www.image-net.org/). _Code:_ [CycleGAN](https://github.com/junyanz/CycleGAN) ## Inner-workings: Basically two GANs for each domain with their respective Generator and Discriminator plus two additional losses (called consistency losses) to make sure that translating to the other domain then back yields an image that is still realistic. [![screen shot 2017-06-02 at 10 24 45 am](https://cloud.githubusercontent.com/assets/17261080/26717449/bcd8a9cc-477d-11e7-9137-fd277a0ec04f.png)](https://cloud.githubusercontent.com/assets/17261080/26717449/bcd8a9cc-477d-11e7-9137-fd277a0ec04f.png) For the consistency los they use a pixel-wise L1 norm: [![screen shot 2017-06-02 at 10 31 22 am](https://cloud.githubusercontent.com/assets/17261080/26717733/bc088cdc-477e-11e7-96af-2defa06a1660.png)](https://cloud.githubusercontent.com/assets/17261080/26717733/bc088cdc-477e-11e7-96af-2defa06a1660.png) ## Architecture: Based on [Perceptual losses for real-time style transfer and super-resolution](https://arxiv.org/pdf/1603.08155.pdf), code available [here](https://github.com/jcjohnson/fast-neural-style). Training seems to employ several tricks and then even use a batch of 1. ## Results: Very impressive and the really key point is that you don't need paired images which makes this trainable on any domain with the same representation behind. [![screen shot 2017-06-02 at 10 26 29 am](https://cloud.githubusercontent.com/assets/17261080/26717502/f6d1fb7e-477d-11e7-8174-7bdd621cf1b6.png)](https://cloud.githubusercontent.com/assets/17261080/26717502/f6d1fb7e-477d-11e7-8174-7bdd621cf1b6.png) |

Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks

Alec Radford and Luke Metz and Soumith Chintala

arXiv e-Print archive - 2015 via Local arXiv

Keywords: cs.LG, cs.CV

**First published:** 2015/11/19 (4 years ago)

**Abstract:** In recent years, supervised learning with convolutional networks (CNNs) has
seen huge adoption in computer vision applications. Comparatively, unsupervised
learning with CNNs has received less attention. In this work we hope to help
bridge the gap between the success of CNNs for supervised learning and
unsupervised learning. We introduce a class of CNNs called deep convolutional
generative adversarial networks (DCGANs), that have certain architectural
constraints, and demonstrate that they are a strong candidate for unsupervised
learning. Training on various image datasets, we show convincing evidence that
our deep convolutional adversarial pair learns a hierarchy of representations
from object parts to scenes in both the generator and discriminator.
Additionally, we use the learned features for novel tasks - demonstrating their
applicability as general image representations.
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Alec Radford and Luke Metz and Soumith Chintala

arXiv e-Print archive - 2015 via Local arXiv

Keywords: cs.LG, cs.CV

[link]
# Deep Convolutional Generative Adversarial Nets ## Introduction * The paper presents Deep Convolutional Generative Adversarial Nets (DCGAN) - a topologically constrained variant of conditional GAN. * [Link to the paper](https://arxiv.org/abs/1511.06434) ## Benefits * Stable to train * Very useful to learn unsupervised image representations. ## Model * GANs difficult to scale using CNNs. * Paper proposes following changes to GANs: * Replace any pooling layers with strided convolutions (for discriminator) and fractional strided convolutions (for generators). * Remove fully connected hidden layers. * Use batch normalisation in both generator (all layers except output layer) and discriminator (all layers except input layer). * Use LeakyReLU in all layers of the discriminator. * Use ReLU activation in all layers of the generator (except output layer which uses Tanh). ## Datasets * Large-Scale Scene Understanding. * Imagenet-1K. * Faces dataset. ## Hyperparameters * Minibatch SGD with minibatch size of 128. * Weights initialized with 0 centered Normal distribution with standard deviation = 0.02 * Adam Optimizer * Slope of leak = 0.2 for LeakyReLU. * Learning rate = 0.0002, β1 = 0.5 ## Observations * Large-Scale Scene Understanding data * Demonstrates that model scales with more data and higher resolution generation. * Even though it is unlikely that model would have memorized images (due to low learning rate of minibatch SGD). * Classifying CIFAR-10 dataset * Features * Train in Imagenet-1K and test on CIFAR-10. * Max pool discriminator's convolutional features (from all layers) to get 4x4 spatial grids. * Flatten and concatenate to get a 28672-dimensional vector. * Linear L2-SVM classifier trained over the feature vector. * 82.8% accuracy, outperforms K-means (80.6%) * Street View House Number Classifier * Similar pipeline as CIFAR-10 * 22.48% test error. * The paper contains many examples of images generated by final and intermediate layers of the network. * Images in the latent space do not show sharp transitions indicating that network did not memorize images. * DCGAN can learn an interesting hierarchy of features. * Networks seems to have some success in disentangling image representation from object representation. * Vector arithmetic can be performed on the Z vectors corresponding to the face samples to get results like `smiling woman - normal woman + normal man = smiling man` visually. |

Ensemble Robustness of Deep Learning Algorithms

Jiashi Feng and Tom Zahavy and Bingyi Kang and Huan Xu and Shie Mannor

arXiv e-Print archive - 2016 via Local arXiv

Keywords: cs.LG, cs.CV, stat.ML

**First published:** 2016/02/07 (4 years ago)

**Abstract:** The question why deep learning algorithms perform so well in practice has
attracted increasing research interest. However, most of well-established
approaches, such as hypothesis capacity, robustness or sparseness, have not
provided complete explanations, due to the high complexity of the deep learning
algorithms and their inherent randomness. In this work, we introduce a new
approach~\textendash~ensemble robustness~\textendash~towards characterizing the
generalization performance of generic deep learning algorithms. Ensemble
robustness concerns robustness of the \emph{population} of the hypotheses that
may be output by a learning algorithm. Through the lens of ensemble robustness,
we reveal that a stochastic learning algorithm can generalize well as long as
its sensitiveness to adversarial perturbation is bounded in average, or
equivalently, the performance variance of the algorithm is small. Quantifying
ensemble robustness of various deep learning algorithms may be difficult
analytically. However, extensive simulations for seven common deep learning
algorithms for different network architectures provide supporting evidence for
our claims. Furthermore, our work explains the good performance of several
published deep learning algorithms.
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Jiashi Feng and Tom Zahavy and Bingyi Kang and Huan Xu and Shie Mannor

arXiv e-Print archive - 2016 via Local arXiv

Keywords: cs.LG, cs.CV, stat.ML

[link]
Zahavy et al. introduce the concept of ensemble robustness and show that it can be used as indicator for generalization performance. In particular, the main idea is to lift he concept of robustness against adversarial examples to ensemble of networks – as trained, e.g. through Dropout or Bayes-by-Backprop. Letting $Z$ denote the sample set, a learning algorithm is $(K, \epsilon)$ robust if $Z$ can be divided into $K$ disjoint sets $C_1,\ldots,C_K$ such that for every training set $s_1,\ldots,s_n \in Z$ it holds: $\forall i, \forall z \in Z, \forall k = 1,\ldots, K$: if $s,z \in C_k$, then $l(f,s_i) – l(f,z)| \leq \epsilon(s_1,\ldots,s_n)$ where $f$ is the model produced by the learning algorithm, $l$ measures the loss and $\epsilon:Z^n \mapsto \mathbb{R}$. For ensembles (explicit or implicit) this definition is extended by considering the maximum generalization loss under the expectation of a randomized learning algorithm: $\forall i, \forall k = 1,\ldots,K$: if $s \in C_k$, then $\mathbb{E}_f \max_{z \in C_k} |l(f,s_i) – l(f,z)| \leq \epsilon(s_1,\ldots,s_n)$ Here, the randomized learning algorithm computes a distribution over models given a training set. Also view this summary at [davidstutz.de](https://davidstutz.de/category/reading/). |

Towards Stable and Efficient Training of Verifiably Robust Neural Networks

Zhang, Huan and Chen, Hongge and Xiao, Chaowei and Li, Bo and Boning, Duane S. and Hsieh, Cho-Jui

arXiv e-Print archive - 2019 via Local Bibsonomy

Keywords: dblp

Zhang, Huan and Chen, Hongge and Xiao, Chaowei and Li, Bo and Boning, Duane S. and Hsieh, Cho-Jui

arXiv e-Print archive - 2019 via Local Bibsonomy

Keywords: dblp

[link]
Zhang et al. combine interval bound propagation and CROWN, both approaches to obtain bounds on a network’s output, to efficiently train robust networks. Both interval bound propagation (IBP) and CROWN allow to bound a network’s output for a specific set of allowed perturbations around clean input examples. These bounds can be used for adversarial training. The motivation to combine BROWN and IBP stems from the fact that training using IBP bounds usually results in instabilities, while training with CROWN bounds usually leads to over-regularization. Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/). |

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