Munoz-Gonzalez et al. propose a multi-class data poisening attack against deep neural networks based on back-gradient optimization. They consider the common poisening formulation stated as follows:

$ \max_{D_c} \min_w \mathcal{L}(D_c \cup D_{tr}, w)$

where $D_c$ denotes a set of poisened training samples and $D_{tr}$ the corresponding clea dataset. Here, the loss $\mathcal{L}$ used for training is minimized as the inner optimization problem. As result, as long as learning itself does not have closed-form solutions, e.g., for deep neural networks, the problem is computationally infeasible. To resolve this problem, the authors propose using back-gradient optimization. Then, the gradient with respect to the outer optimization problem can be computed while only computing a limited number of iterations to solve the inner problem, see the paper for detail. In experiments, on spam/malware detection and digit classification, the approach is shown to increase test error of the trained model with only few training examples poisened.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

# Object detection system overview.

https://i.imgur.com/vd2YUy3.png
 
1.	takes an input image,
2.	extracts around 2000 bottom-up region proposals, 
3.	computes features for each proposal using a large convolutional neural network (CNN), and then
4.	classifies each region using class-specific linear SVMs.
* R-CNN achieves a mean average precision (mAP) of 53.7% on PASCAL VOC 2010.
* On the 200-class ILSVRC2013 detection dataset, R-CNN’s mAP is 31.4%, a large improvement over OverFeat , which had the previous best result at 24.3%.

## There is a 2 challenges faced in object detection 
1.	localization problem
2.	labeling the data

1 localization problem :
*  One approach frames localization as a regression problem.  they report a mAP of 30.5% on VOC 2007 compared to the 58.5% achieved by our method.
* An alternative is to build a sliding-window detector.  considered adopting a sliding-window approach increases the number of convolutional layers to 5, have very large receptive fields (195 x 195 pixels) and strides (32x32 pixels) in the input image, which makes precise localization within the sliding-window paradigm.

2 labeling the data:
* The conventional solution to this problem is to use unsupervised pre-training, followed by supervise fine-tuning 
* supervised pre-training on a large auxiliary dataset (ILSVRC), followed by domain specific fine-tuning on a small dataset (PASCAL),
* fine-tuning for detection improves mAP performance by 8 percentage points. 
* Stochastic gradient descent via back propagation was used to  effective for training convolutional neural networks (CNNs)
 
##  Object detection with R-CNN
This  system consists of three modules
* The first generates category-independent region proposals. These proposals define the set of candidate detections available to our detector.
*  The second module is a large convolutional neural network that extracts a fixed-length feature vector from each region.
* The third module is a set of class specific linear SVMs.

Module design

1 Region proposals 
* which detect mitotic cells by applying a CNN to regularly-spaced square crops.
* use selective search method in fast mode (Capture All Scales, Diversification, Fast to Compute).
* the time spent computing region proposals and features (13s/image on a GPU or 53s/image on a CPU)

2 Feature extraction.
* extract a 4096-dimensional feature vector from each region proposal using the Caffe  implementation of the CNN 
* Features are computed by forward propagating a mean-subtracted 227x227 RGB image through five convolutional layers and two fully connected layers.
* warp all pixels in a tight bounding box around it to the required size
* The feature matrix is typically 2000x4096 

3 Test time detection
* At test time, run selective search on the test image to extract around 2000 region proposals (we use selective search’s “fast mode” in all experiments).
*  warp each proposal and forward propagate it through the CNN in order to compute features. Then, for each class, we score each extracted feature vector using the SVM trained for that class.
* Given all scored regions in an image, we apply a greedy non-maximum suppression (for each class independently) that rejects a region if it has an intersection-over union (IoU) overlap with a higher scoring selected region larger than a learned threshold.
## Training

1 Supervised pre-training:
 * pre-trained the CNN on a large auxiliary dataset (ILSVRC2012 classification)  using image-level annotations only (bounding box labels are not available for this data)

2  Domain-specific fine-tuning.
* use the stochastic gradient descent (SGD) training of the CNN parameters using only warped region proposals with  learning rate of 0.001.

3  Object category classifiers.
*   use intersection-over union (IoU) overlap threshold method  to label a region with The overlap threshold of 0.3.
* Once features are extracted and training labels are applied, we optimize one linear SVM per class.
* adopt the standard hard negative mining method to fit large training data in memory.

### Results on PASCAL VOC 201012

1  VOC 2010
* compared against four strong baselines including SegDPM, DPM, UVA, Regionlets. 
* Achieve a large improvement in mAP, from 35.1% to 53.7% mAP,  while also being much faster
 https://i.imgur.com/0dGX9b7.png
2 ILSVRC2013 detection.
* ran R-CNN on the 200-class ILSVRC2013 detection dataset
* R-CNN achieves a mAP of 31.4%
https://i.imgur.com/GFbULx3.png
#### Performance layer-by-layer, without fine-tuning
1 pool5 layer 
* which is the max pooled output of the network’s fifth and final convolutional layer.
*The pool5 feature map is 6 x6 x 256 = 9216 dimensional
* each pool5 unit has a receptive field of 195x195 pixels in the original 227x227 pixel input

2 Layer fc6
* fully connected to pool5
*  it multiplies a 4096x9216 weight matrix by the pool5 feature map (reshaped as a 9216-dimensional vector) and then adds a vector of biases

3 Layer fc7
* It is implemented by multiplying the features computed by fc6 by a 4096 x 4096 weight matrix, and similarly adding a vector of biases and applying half-wave rectification
#### Performance layer-by-layer, with fine-tuning
* CNN’s parameters  fine-tuned on PASCAL.
* fine-tuning increases mAP by 8.0 % points to 54.2%

### Network architectures
* 16-layer deep network, consisting of 13 layers of 3 _ 3 convolution kernels, with five max pooling layers interspersed, and topped with three fully-connected layers. We refer to this network as “O-Net” for OxfordNet and the baseline as “T-Net” for TorontoNet.
* RCNN with O-Net substantially outperforms R-CNN with TNet, increasing mAP from 58.5% to 66.0%
* drawback in terms of compute time, with in terms of compute time, with than T-Net.

1 The ILSVRC2013 detection dataset
* dataset is split into three sets: train (395,918), val (20,121), and test (40,152) 

#### CNN features for segmentation.
* full R-CNN: The first strategy (full) ignores the re region’s shape and computes CNN features directly on the warped window. Two regions might have very similar bounding boxes while having very little overlap. 
* fg R-CNN: the second strategy (fg) computes CNN features only on a region’s foreground mask. We replace the background with the mean input so that background regions are zero after mean subtraction.
* full+fg R-CNN: The third strategy (full+fg) simply concatenates the full and fg features
 https://i.imgur.com/n1bhmKo.png

# Very Short

The authors propose **learning** an optimizer **to** optimally **learn** a function (the *optimizee*) which is being trained **by gradient descent**.  This optimizer, a recurrent neural network, is trained to make optimal parameter updates to the optimizee **by gradient descent**.

# Short

Let's suppose we have a stochastic function $f: \mathbb R^{\text{dim}(\theta)} \rightarrow \mathbb R^+$, (the *optimizee*) which we wish to minimize with respect to $\theta$.  Note that this is the typical situation we encounter when training a neural network with Stochastic Gradient Descent - where the stochasticity comes from sampling random minibatches of the data (the data is omitted as an argument here).  

The "vanilla" gradient descent update is: $\theta_{t+1} = \theta_t - \alpha_t \nabla_{\theta_t} f(\theta_t)$, where $\alpha_t$ is some learning rate.  Other optimizers (Adam, RMSProp, etc) replace the multiplication of the gradient by $-\alpha_t$ with some sort of weighted sum of the history of gradients.

This paper proposes to apply an optimization step $\theta_{t+1} = \theta_t + g_t$, where the update $g_t \in \mathbb R^{\text{dim}(\theta)}$ is defined by a recurrent network $m_\phi$: 

$$(g_t, h_{t+1}) := m_\phi (\nabla_{\theta_t} f(\theta_t), h_t)$$

Where in their implementation, $h_t \in \mathbb R^{\text{dim}(\theta)}$ is the hidden state of the recurrent network.  To make the number of parameters in the optimizer manageable, they implement their recurrent network $m$ as a *coordinatewise* LSTM (i.e. A set of $\text{dim}(\theta)$ small LSTMs that share parameters $\phi$).   They train the optimizer networks's parameters $\phi$ by "unrolling" T subsequent steps of optimization, and minimizing:

$$\mathcal L(\phi) := \mathbb E_f[f(\theta^*(f, \phi))]  \approx \frac1T \sum_{t=1}^T f(\theta_t)$$

Where $\theta^*(f, \phi)$ are the final optimizee parameters.  In order to avoid computing second derivatives while calculating $\frac{\partial \mathcal L(\phi)}{\partial \phi}$, they make the approximation $\frac{\partial}{\partial \phi}  \nabla_{\theta_t}f(\theta_t) \approx 0$ (corresponding to the dotted lines in the figure, along which gradients are not backpropagated).  

https://i.imgur.com/HMaCeip.png
**The computational graph of the optimization of the optimizer, unrolled across 3 time-steps.  Note that $\nabla_t := \nabla_{\theta_t}f(\theta_t)$.  The dotted line indicates that we do not backpropagate across this path.**

The authors demonstrate that their method usually outperforms traditional optimizers (ADAM, RMSProp, SGD, NAG), on a synthetic dataset, MNIST, CIFAR-10, and Neural Style Transfer.  They argue that their algorithm constitutes a form of transfer learning, since a pre-trained optimizer can be applied to accelerate training of a newly initialized network.  

Ilyas et al. present a follow-up work to their paper on the trade-off between accuracy and robustness. Specifically, given a feature $f(x)$ computed from input $x$, the feature is considered predictive if

$\mathbb{E}_{(x,y) \sim \mathcal{D}}[y f(x)] \geq \rho$;

similarly, a predictive feature is robust if

$\mathbb{E}_{(x,y) \sim \mathcal{D}}\left[\inf_{\delta \in \Delta(x)} yf(x + \delta)\right] \geq \gamma$.

This means, a feature is considered robust if the worst-case correlation with the label exceeds some threshold $\gamma$; here the worst-case is considered within a pre-defined set of allowed perturbations $\Delta(x)$ relative to the input $x$. Obviously, there also exist predictive features, which are however not robust according to the above definition. In the paper, Ilyas et al. present two simple algorithms for obtaining adapted datasets which contain only robust or only non-robust features. The main idea of these algorithms is that an adversarially trained model only utilizes robust features, while a standard model utilizes both robust and non-robust features. Based on these datasets, they show that non-robust, predictive features are sufficient to obtain high accuracy; similarly training a normal model on a robust dataset also leads to reasonable accuracy but also increases robustness. Experiments were done on Cifar10. These observations are supported by a theoretical toy dataset consisting of two overlapping Gaussians; I refer to the paper for details.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

This paper describes a learning algorithm for deep neural networks that can be understood as an extension of stacked denoising autoencoders. In short, instead of reconstructing one layer at a time and greedily stacking, a unique unsupervised objective involving the reconstruction of all layers is optimized jointly by all parameters (with the relative importance of each layer cost controlled by hyper-parameters). 

In more details:

* The encoding (forward propagation) adds noise (Gaussian) at all layers, while decoding is noise-free.
* The target at each layer is the result of noise-less forward propagation.
* Direct connections (also known as skip-connections) between a layer and its decoded reconstruction are used. The resulting encoder/decoder architecture thus ressembles a ladder (hence the name Ladder Networks).
* Miniature neural networks with a single hidden unit and skip-connections are used to decode the left and top layers into a reconstruction. Each network is applied element-wise (without parameter sharing across reconstructed units).
* The unsupervised objective is combined with a supervised objective, corresponding to the regular negative class log-likelihood objective (using an output softmax layer). Two losses are used for each input/target pair: one based on the noise-free forward propagation (which also provides the target of the denoising objective) and one with the noise added (which also corresponds to the encoding stage of the unsupervised autoencoder objective).
Batch normalization is used to train the network.
Since the model combines unsupervised and supervised learning, it can be used for semi-supervised learning, where unlabeled examples can be used to update the network using the unsupervised objective only. State of the art results in the semi-supervised setting are presented, for both the MNIST and CIFAR-10 datasets.

#### My two cents

What I find most exciting about this paper is its performance. On MNIST, with only 100 labeled examples, it achieves 1.13% error! That is essentially the performance of stacked denoising autoencoders, trained on the entire training set (though that was before ReLUs and batch normalization, which this paper uses)! This confirms a current line of thought in Deep Learning (DL) that, while recent progress in DL applied on large labeled datasets does not rely on any unsupervised learning (unlike at the "beginning" of DL in the mid 2000s), unsupervised learning might instead be crucial for success in low-labeled data regime, in the semi-supervised setting.

Unfortunately, there is one little issue in the experiments, disclosed by the authors: while they used few labeled examples for training, model selection did use all 10k labels in the validation set. This is of course unrealistic. But model selection in the low data regime is arguably, in itself, an open problem. So I like to think that this doesn't invalidate the progress made in this paper, and only suggests that some research needs to be done on doing effective hyper-parameter search with a small validation set.

Generally, I really hope this paper will stimulate more research on DL methods to the specific case of small labeled dataset / large unlabeled dataset. While this isn't a problem that is as "flashy" as tasks such as the ImageNet Challenge which comes with lots of labeled data, I think this is a crucial research direction for AI in general. Indeed, it seems naive to me to expect that we will be able to collect large labeled dataset for each and every task, on our way to real AI.