Deeper networks should never have a higher **training** error than smaller ones. In the worst case, the layers should "simply" learn identities. It seems as this is not so easy with conventional networks, as they get much worse with more layers. So the idea is to add identity functions which skip some layers. The network only has to learn the **residuals**. 

Advantages:

* Learning the identity becomes learning 0 which is simpler
* Loss in information flow in the forward pass is not a problem anymore
    * No vanishing / exploding gradient
* Identities don't have parameters to be learned

## Evaluation

The learning rate starts at 0.1 and is divided by 10 when the error plateaus. Weight decay of 0.0001 ($10^{-4}$), momentum of 0.9. They use mini-batches of size 128.

* ImageNet ILSVRC 2015: 3.57% (ensemble)
* CIFAR-10: 6.43%
* MS COCO: 59.0% mAp@0.5 (ensemble)
* PASCAL VOC 2007: 85.6% mAp@0.5
* PASCAL VOC 2012: 83.8% mAp@0.5

## See also

* [DenseNets](http://www.shortscience.org/paper?bibtexKey=journals/corr/1608.06993)

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}

This was an amusingly-timed paper for me to read, because just yesterday I was listening to a different paper summary where the presenter offhandedly mentioned the idea of compressing the sequence length in Transformers through subsequent layers (the way a ConvNet does pooling to a smaller spatial dimension in the course of learning), and it made me wonder why I hadn't heard much about that as an approach. And, lo, I came on this paper in my list the next day, which does exactly that. 

As a refresher, Transformers work by starting out with one embedding per token in the first layer, and, on each subsequent layer, they create new representations for each token by calculating an attention mechanism over all tokens in the prior layer. This means you have one representation per token for the full sequence length, and for the full depth of the network. In addition, you typically have a CLS token that isn't connected to any particular word, but is the designated place where sequence-level representations aggregate and are used for downstream tasks. 

This paper notices that many applications of trained transformers care primarily about that aggregated representation, rather than precise per-word representations. For cases where that's true, you're spending a lot of computation power on continually calculating the SeqLength^2 attention maps in later layers, when they might not be bringing you that much value in your downstream transfer tasks. 

A central reason why you do generally need per-token representations in training Transformers, though, even if your downstream tasks need them less, is that the canonical Masked Language Model and newer ELECTRA loss functions require token-level predictions for the specific tokens being masked. To accommodate this need, the authors of this paper structure their "Funnel" Transformer as more of an hourglass. It turns it into basically a VAE-esque Encoder/Decoder structure, where attention downsampling layers reduce the length of the internal representation down, and then a "decoder" amplifies it back to the full sequence size, so you have one representation per token for training purposes (more on the exact way this works in a bit). The nifty thing here is that, for downstream tasks, you can chop off the decoder, and be left with a network with comparatively less computation cost per layer of depth. 

https://i.imgur.com/WC0VQXi.png

The exact mechanisms of downsampling and upsampling in this paper are quite clever. 

To perform downsampling at a given attention layer, you take a sequence of representations h, and downsampling it to h' of half the size by mean-pooling adjacent tokens. However, in the attention calculation, you only use h' for the queries, and use the full sequence h for the keys and values. Essentially, this means that you have an attention layer where the downsampled representations attend to and pull information from the full scope of the (non-downsampled) representations of the layer below. This means you have a much more flexible downsampling operation, since the attention mechanism can choose to pull information into the downsampled representation, rather than it being calculated automatically by a pooling operation 

The paper inflates the bottleneck-ed representations back up to the full sequence length by first tiling the downsampled representation (for example, if you had downsampled from 20 to 5, you would tile the first representation 4 times, then the second representation 4 times, and so on until you hit 20). That tiled representation, which can roughly be though to represent a large region of the sequence, is then added, ResNet-style, to the full-length sequence of representations that came out of the first attention layer, essentially combining shallow token-level representations with deep region-level representations. This aggregated representation is then used for token-level loss prediction 

The authors benchmark again common baseline models, using deeper models with fewer tokens per layer, and find that they can reach similar or higher levels of performance with fewer FLOPs on text aggregation tasks. They fall short of full-sequence models for tasks that require strong per-token representations, which fits with my expectation.

Large-scale transformers on unsupervised text data have been wildly successful in recent years; arguably, the most successful single idea in the last ~3 years of machine learning. Given that, it's understandable that different domains within ML want to take their shot at seeing whether the same formula will work for them as well. This paper applies the principles of (1) transformers and (2) large-scale unlabeled data to the problem of learning informative embeddings of molecular graphs. 

Labeling is a problem in much of machine learning - it's costly, and narrowly defined in terms of a certain task - but that problem is even more exacerbated when it comes to labeling properties of molecules, since they typically require wetlab chemistry to empirically measure. Given that, and also given the fact that we often want to predict new properties - like effectiveness against a new targetable drug receptor - that we don't yet have data for, finding a way to learn and transfer from unsupervised data has the potential to be quite valuable in the molecular learning sphere. 

There are two main conceptual parts to this paper and its method - named GROVER, in true-to-ML-form tortured acronym style. The first is the actual architecture of their model itself, which combines both a message-passing Graph Neural Network to aggregate local information, and a Transformer to aggregate global information. The paper was a bit vague here, but the way I understand it is: 

https://i.imgur.com/JY4vRdd.png
- There are parallel GNN + Transformer stacks for both edges and nodes, each of which outputs both a node and edge embedding, for four embeddings total. I'll describe the one for nodes, and the parallel for edges operates the same way, except that hidden states live on edges rather than nodes, and attention is conducted over edges rather than nodes
- In the NodeTransformer version, a message passing NN (of I'm not sure how many layers) performs neighborhood aggregation (aggregating the hidden states of neighboring nodes and edges, then weight-transforming them, then aggregating again) until each node has a representation that has "absorbed" in information from a few hops out of its surrounding neighborhood. My understanding is that there is a separate MPNN for queries, keys, and values, and so each nodes end up with three different vectors for these three things.
- Multi-headed attention is then performed over these node representations, in the normal way, where all keys and queries are dot-product-ed together, and put into a softmax to calculate a weighted average over the values
- We now have node-level representations that combine both local and global information. These node representations are then aggregated into both node and edge representations, and each is put into a MLP layer and Layer Norm before finally outputting a node-based node and edge representation. This is then joined by an edge-based node and edge representation from the parallel stack. These are aggregated on a full-graph level to predict graph-level properties

https://i.imgur.com/NNl6v4Y.png

The other component of the GROVER model is the way this architecture is actually trained - without explicit supervised labels. The authors use two tasks - one local, and one global. The local task constructs labels based on local contextual properties of a given atom - for example, the atom here has one double-bonded Nitrogen and one single-bonded Oxygen in its local environment - and tries to predict those labels given the representations of that atom (or node). The global task uses RDKit (an analytically constructed molecular analysis kit) to identify 85 different modifs or functional groups in the molecule, and encodes those into an 85-long one-hot vector that is being predicted on a graph level. 

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

With these two components, GROVER is pretrained on 10 million unlabeled molecules, and then evaluated in transfer settings where its representations are fine-tuned on small amounts of labeled data. The results are pretty impressive - it achieves new SOTA performance by relatively large amounts on all tasks, even relative to exist semi-supervised pretraining methods that similarly have access to more data. The authors perform ablations to show that it's important to do the graph-aggregation step before a transformer (the alternative being just doing a transformer on raw node and edge features), and also show that their architecture without pretraining (just used directly in downstream tasks) also performs worse. One thing I wish they'd directly ablated was the value-add of the local (also referred to as "contextual") and global semi-supervised tasks. Naively, I'd guess that most of the performance gain came from the global task, but it's hard to know without them having done the test directly.

This paper explores the use of convolutional (PixelCNN) and recurrent units (PixelRNN) for modeling the distribution of images, in the framework of autoregression distribution estimation. In this framework, the input distribution $p(x)$ is factorized into a product of conditionals $\Pi p(x_i | x_i-1)$. Previous work has shown that very good models can be obtained by using a neural network parametrization of the conditionals (e.g. see our work on NADE \cite{journals/jmlr/LarochelleM11}). Moreover, unlike other approaches based on latent stochastic units that are directed or undirected, the autoregressive approach is able to compute log-probabilities tractably. 

So in this paper, by considering the specific case of x being an image, they exploit the topology of pixels and investigate appropriate architectures for this.

Among the paper's contributions are:

1. They propose Diagonal BiLSTM units for the PixelRNN, which are efficient (thanks to the use of convolutions) while making it possible to, in effect, condition a pixel's distribution on all the pixels above it (see Figure 2 for an illustration).

2. They demonstrate that the use of residual connections (a form of skip connections, from hidden layer i-1 to layer $i+1$) are very effective at learning very deep distribution estimators (they go as deep as 12 layers).

3. They show that it is possible to successfully model the distribution over the pixel intensities (effectively an integer between 0 and 255) using a softmax of 256 units.

4. They propose a multi-scale extension of their model, that they apply to larger 64x64 images.

The experiments show that the PixelRNN model based on Diagonal BiLSTM units achieves state-of-the-art performance on the binarized MNIST benchmark, in terms of log-likelihood. They also report excellent log-likelihood on the CIFAR-10 dataset, comparing to previous work based on real-valued density models. Finally, they show that their model is able to generate high quality image samples.