They introduce the concept of counting in images by predicting a density map. Their training only requires dot annotations on the center of objects. Each dot is expanded to a gaussian to form a density. A model is trained to predict this density and then the total count is recovered by integrating over the resulting density map.

They create a function to produce the density based on quantized dense SIFT features \cite{lowe03distinctive} from every pixel in the image. A simple version of the definition of $F$ is shown below. Each pixel becomes an $x_p$ vector which is used to train and model to implement the function $F$.

$$\forall p \in I, \hspace{10pt } F(p|w) = wx_p $$

The obtained quantized dense SIFT features using the [VLFEAT](http://www.vlfeat.org/overview/dsift.html) library. The significant part of the code is shown below:

```
im = imread(['data/' num2str(j, '%03d') 'cell.png']);
im = im(:,:,3); %using the blue channel to compute data

disp('Computing dense SIFT...');
[f d] = vl_dsift(single(im)); %computing the dense sift descriptors centered at each pixel
%estimating the crop parameters where SIFTs were not computed:
minf = floor(min(f,[],2));
maxf = floor(max(f,[],2));
minx = minf(1);
miny = minf(2);
maxx = maxf(1);
maxy = maxf(2);   

%simple quantized dense SIFT, each image is encoded as MxNx1 numbers of
%dictionary entries numbers with weight 1 (see the NIPS paper):
disp('Quantizing SIFTs...');
features{j} = vl_ikmeanspush(uint8(d),Dict);
features{j} = reshape(features{j}, maxy-miny+1, maxx-minx+1);
weights{j} = ones(size(features{j}));   
```

The benchmark their algorithm using "Bacterial cells in fluorescence-light microscopy images". The heatmap to the right shows the predicted density.

https://i.imgur.com/Vz463nu.png

The evaluation is performed by training on $N$ images (with $N$ in a validation set) and the testing on 100 randomly picked images in a hold out set. They show that using more images results in less variance and higher accuracy.

https://i.imgur.com/hihfC8V.png

Paper website: http://www.robots.ox.ac.uk/~vgg/research/counting/index_org.html

The paper presents a framework to learn to classify images that can come either from known or unknown classes. This is done by first mapping both images and classes into a joint embedding space. Furthermore, the probability of an image being of an unknown class is estimated using a mixture of Gaussians. Experiments on CIFAR-10 show how performance vary depending on the threshold use to determine if an image is of a known class or not.

The model first tries to detect whether an image contains an object from a so-far unseen category. If not, the model relies on a regular, state-of-the art supervised classifier to assign the image to known classes. Otherwise, it attempts to identify what this object is, based on a comparison between the image and each unseen class, in a learned joint image/class representation space. The method relies on pre-trained word representations, extracted from unlabelled text, to represent the classes. Experiments evaluate the compromise between classification accuracy on the seen classes and the unseen classes, as a threshold for identifying an unseen class is varied. 

The goal is to compress a neural network based on figuring out the most significant neurons. They sample from Determinantal Point Process (DPP) in order to find set of neurons that have the most dissimilar activations and then project remaining neurons to them in order to reduce number of neurons overall.

DPPs compute the probability of volume of dissimilarity over volume of all neurons:

$$P(\text{subset } Y) = \frac{det(L_Y)}{det(L+I)}$$ 

More dissimilarity means higher probability. A simple sample of the neurons outputs are taken given the training set.

This paper analyses fully connected networks with dropout and ReLU activation functions.

This paper takes up the question of whether rhetorical relations can be automatically derived and classified. It focuses, in particular, on discourse markers. These may be ambigious (e.g 'since', 'yet' have multiple uses and are sometimes, but not always, discourse markers); and these discourse markers may also be missing altogether.

The authors comment that: "what is needed is a model which can classify rhetorical relations in the absence of an explicit discourse marker." (p4). Previous work (e.g. Marcu & Echihabi 2002) has suggested creating training data for a classifier by labelling examples which contain an unambiguous lexically marked rhetorical relation, then removing the markers. The main purpose of this paper is to empirically test this.

It also provides an interesting theoretical observation: Two conditions are needed for training on marked examples to work well:

"First, there has to be a certain amount of redundancy between the discourse marker and the general linguistic context, i.e. removing the discourse marker should still leave enough residual information for the classifier to learn how to distinguish different relations."

Second, similarity between marked and unmarked examples is needed so that a classifier can make generalizations.

The paper suggests that texts with lexically marked and lexically unmarked rhetorical relations may be inherently different, in so far as removing discourse markers may change the meaning of a sentence, and classifiers built based on removing markers from classified sentences work little better than chance.