This summary builds substantially on my summary of NERFs, so if you haven't yet read that, I recommend doing so first! 

The idea of a NERF is learn a neural network that represents a 3D scene, and from which you can, once the model is trained, sample an image of that scene from any desired angle. This involves structuring your neural network as a function that predicts the RGB color and density/opacity for a given point in 3D space (x, y, z), from a given viewing angle (theta, phi). With such a function, you can generate predictions of what images taken from certain angles would look like by sampling along a viewing ray, and integrating the combined hue and opacity into an aggregated view. This prediction can then be compared to a true image taken from that direction, and gradients passed backwards into the prediction model. 

An important assumption of this model is that the scene being photographed is static; specifically, that every point in space is always inhabited by the same part of the 3D object, regardless of what angle it's viewed from. This is a reasonable assumption for photos of inanimate objects, or of humans in highly controlled lab settings, but it is often not true for humans when you, say, ask them to take a selfie video of themselves. Even if they're trying to keep roughly still, there will be slight shifts in the location and position of their head between frames, and the authors of this paper show that this can lead to strange artifacts if you naively try to train a NERF from the images (including a particularly odd one where it hallucinates tiny copies of the image in the air surrounding the face). 

https://i.imgur.com/IUVh6uM.png

The fix proposed by this paper is to apply a learnable deformation field to each image, where the notion is to deform each view into being in one canonical position (fixed per network, since, again, one network corresponds to a single scene). This means that, along with learning the parameters of the NERF itself, you're also learning what deformation to apply to each training image to get it into this canonical position. This is done by parametrizing the deformation in a particular way, and then having that deformation be conditioned by a latent vector that's trained similar to how you'd train an embedding (one learned vector per image example). The parametrization of the deformation is honestly a little bit over my head, given my lack of grounding in 3D modeling, but my general sense is that it applies some constraints and regularization to ensure that the learned deformations are realistic, insofar as humans are mostly rigid (one patch of skin on my forehead generally doesn't move except in concordance with the rest of my forehead), but with some possibility for elasticity (skin can stretch if I, say, smile). The authors also include an annealing scheme whereby, early in training, the model focuses on learning course (large-scale) deformations, and later in training, it's allowed to also learn weights for more precise deformations. This is to hopefully match macro-scale shifts before adding the noise of precise changes. 

This addition of a learned deformation is most of the contribution of this method: with it applied, they show that they're able to learn realistic NERFs from selfies, which they term "NERFIES". They mention a few pieces of concurrent work that try to solve the same problem of non-static human subjects in different ways, but I haven't had a chance to read those, so I can't really comment on how NERFIES stacks up to alternate approaches, but it appears to be as least one empirically convincing solution to the problem it's aiming at.

This paper suggests a novel explanation for why dropout training is helpful: because it corresponds to an adaptive data augmentation method. Indeed, the authors point out that, when sampling a mask of the hidden units in a network (effectively setting the corresponding units to 0), the same effect would have been obtained by feeding as input an example tailored to yield activations of 0 for these units and otherwise the same activation for all other units. Since this "ghost" example will have to be different from the original example, and since each different mask would correspond to a different "ghost" example, then effectively mask sampling is similar to data augmentation.

While in practice finding a ghost example that replicates exactly the same dropout hidden activations might not be possible, the authors show that finding an "approximate" ghost example that minimizes a distance between the target dropout activation and the deterministic activation of the ghost example works well. Indeed, they show that training a deep neural net on additional data generated by this procedure yields results that are at least as good as regular dropout on MNIST and CIFAR-10 (actually, the deterministic neural net still uses regular dropout at the input layer, however they do show that the additional ghost examples are necessary to match the neural net trained with dropout at all layers).

Then the authors use that interpretation to justify a variation of dropout where the dropout rate isn't fixed, but itself is randomly sampled in some range for each example. Indeed, if we think of dropout at a fixed rate as a specific class of ghost data being added, varying the dropout rate corresponds to enriching even more the ghost data pool. The experiments show that this can help, though not by much.

Finally, the authors propose an explanation of a property of dropout: that it tends to generate hidden representations that are sparser. Again, the authors rely on their interpretation of dropout as data augmentation. The explanation goes as follows. Training on the ghost data distribution might imply that the classification problem has become significantly harder. Specifically, it is quite possible that the addition of new ghost examples generates new isolated class clusters in input space that the model most now learn to  discriminate. And they hypothesize that the generation of such additional clusters would encourage sparsity. To test this hypothesis, the authors synthetically simulate this scenario, by sampling data on a circle, which is clustered in small arcs each assigned to one of 10 possible classes in cycling order. Decreasing the arc length thus increases the number of arcs, i.e. class clusters. They show that training deep networks on datasets with increasing number of class clusters does yield representations that are increasingly sparser. This thus suggests that dropout might indeed be equivalent to modifying the input distribution by adding such isolated class-specific clusters in input space. 

One assumption behind this analysis is that the sparsity patterns (i.e. the set of non-zero dimensions) play an important role in classification and incorporate most of the discriminative class information. This assumption is also confirmed in experiments, where converting the ReLU activation function by a binary activation (that is 1 if the pre-activation is positive and 0 otherwise) after training still yields a network with good performance (though slightly worse).


#### My two cents

This is a really original and thought provoking paper. One interpretation I make of these results is that the inductive bias corresponding to using a deep neural network with ReLU activations is more valuable than one might have thought, and that the usefulness of deep neural networks goes beyond just being black boxes that can learn data-dependent representations. Otherwise, it's not clear to me why the ghost data implicitly generated by the architecture would be useful at all. This also suggests an experiment where such ghost samples would be fed to  another type of classifier, such as an SVM, to test whether the data augmentation is useful in itself and reflects meaningful structure in the data, as opposed to being somehow useful only for neural nets.

I note that the results are mostly specific to architectures based on ReLU activations (not that this is a problem, but one should keep this in mind).

I'd really like to see what the ghost samples look like. Do they correspond to interpretable images? The authors also mention that exploring how the samples change with training would be interesting to investigate, and I agree.

Finally, I think there might be a typo in Figure 1. While the labels of a) and b) states that the arc length is smaller for a) than b), the plot clearly show otherwise.

Pathogen perception by the plant innate immune system is of central importance to plant survival and productivity. The Arabidopsis protein RIN4 is a negative regulator of plant immunity. In order to identify additional proteins involved in RIN4-mediated immune signal transduction, we purified components of the RIN4 protein complex. We identified six novel proteins that had not previously been implicated in RIN4 signaling, including the plasma membrane (PM) H+-ATPases AHA1 and/or AHA2. RIN4 interacts with AHA1 and AHA2 both in vitro and in vivo. RIN4 overexpression and knockout lines exhibit differential PM H+-ATPase activity. PM H+-ATPase activation induces stomatal opening, enabling bacteria to gain entry into the plant leaf; inactivation induces stomatal closure thus restricting bacterial invasion. The rin4 knockout line exhibited reduced PM H+-ATPase activity and, importantly, its stomata could not be re-opened by virulent Pseudomonas syringae. We also demonstrate that RIN4 is expressed in guard cells, highlighting the importance of this cell type in innate immunity. These results indicate that the Arabidopsis protein RIN4 functions with the PM H+-ATPase to regulate stomatal apertures, inhibiting the entry of bacterial pathogens into the plant leaf during infection. Author Summary Top Plants are continuously exposed to microorganisms. In order to resist infection, plants rely on their innate immune system to inhibit both pathogen entry and multiplication. We investigated the function of the Arabidopsis protein RIN4, which acts as a negative regulator of plant innate immunity. We biochemically identified six novel RIN4-associated proteins and characterized the association between RIN4 and the plasma membrane H+-ATPase pump. Our results indicate that RIN4 functions in concert with this pump to regulate leaf stomata during the innate immune response, when stomata close to block the entry of bacterial pathogens into the leaf interior.

$\bf Summary:$
The paper is about squeezing the number of parameters in a convolutional neural network. The number of parameters in a convolutional layer is given by (number of input channels)$\times$(number of filters)$\times$(size of filter$\times$size of filter).

The paper proposes 2 strategies: (i) replace 3x3 filters with 1x1 filters and (ii) decrease the number of input channels. They assume the budget of the filter is given, i,e., they do not tinker with the number of filters. Decrease in number of parameters will lead to less accuracy. To compensate, the authors propose to downsample late in the network. 

The results are quite impressive. Compared to AlexNet, they achieve a 50x reduction is model size while preserving the accuracy. Their model can be further compressed with existing methods like Deep Compression which are orthogonal to this paper's approach and this can give in total of around 510x reduction while still preserving accuracy of AlexNet.

$\bf Question$: The impact on running times (specially on feed forward phase which may be more typical on embedded devices) is not clear to me. Is it certain to be reduced as well or at least be *no worse* than the baseline models? 

This paper is ultimately relatively straightforward, for all that it's embedded in the somewhat new-to-me literature around graph-based Neural Architecture Search - the problem of iterating through options to find a graph representing an optimized architecture. The authors want to understand whether in this problem, as in many others in deep learning, we can benefit from building our supervised models off of representations learned during an unsupervised pretraining step. In this case, the unsupervised pretraining is conceptually simple - a variational autoencoder - even though the components of the VAE are more complex by dint of being made up of graph networks. This autoencoder, termed arch2vec, is trained on a simple reconstruction loss, and uses the Graph Isomorphism Network (or, GIN) architecture in its encoder, rather than a more typical Graph Convolutional Network. I don't feel like I fully follow the intuitive difference between these two structures, but have the general sense that GIN architectures are simpler; calculating a weighted sum of current central node features with the features of neighboring nodes, rather than learning a function of the full concatenated (current_node, sum_of_neighbors) vector. 

First, the authors investigate the quality of their embedding space, compared to the representation implicitly learned by doing end-to-end supervised (i.e. with accuracies as labels) NAS. They show that (1) distances in their continuous embedding space correlate more strongly with the edit distance between graphs, compared to the embedding learned by the supervised model, and that (2) their embedding fills more of the space (as would be expected from the KL regularization term) and leads to high-performing networks being naturally concentrated within the space. 

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

Looking into their representation as an initialization point, they demonstrate that their initializations do lead to lower long-term regret over the course of the architecture search process, particularly differentiating themselves from random initializations at the end of training. 

https://i.imgur.com/4DG7lZd.png
The authors argue that this is because the representations learned by the supervised methods are "biased towards weight-free operations, which are often preferred in the early stage of the search process, resulting in lower final accuracies." I admit I don't fully understand why this would be true, though they do cite a few papers they say demonstrate it. My initial thought was that weight-free architectures would overperform early in the training of each individual network, but my understanding was that the dataset used here is a labeled static dataset of architectures and accuracies, so the within-training-run dynamics wouldn't obviously play a role. Nevertheless, there does seem to be empirical benefit that comes from using these pretrained representations, even if I don't follow the intuition behind it fully.