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)

# Summary

This paper presents state-of-the-art methods for both caption generation of images and visual question answering (VQA). The authors build on previous methods by adding what they call a "bottom-up" approach to previous "top-down" attention mechanisms. They show that using their approach they obtain SOTA on both Image captioning (MSCOCO) and the Visual Question and Answering (2017 VQA challenge). They propose a specific network configurations for each. Their biggest contribution is using Faster-R-CNN to retrieve the "important" parts of an image to focus on in both models.

## Top Down

Up until this paper, the traditional approach was to use a "top-down" approach, in which the last feature map layer of a CNN is used to obtain a latent representation of the given input image. These features, along with the context of the caption being generated, were used to generate attention weights that were used to predict the next sequence in the context of caption generation. The network would learn to focus its attention on regions of the feature map that matters most. This is the approach used in previous SOTA methods like [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention](https://arxiv.org/abs/1502.03044).

## Bottom-up

The authors argue that the feature map of a CNN is too generic and can be thought of operating on a uniform, grid-like feature map. In other words, there is no particular reason to think that the feature map of generated by a CNN would give optimal regions to attend to. Also, carefully choosing the dimensions of the feature map can be very arbitrary.

In order to fix this, the authors propose combining object detection methods in a *bottom-up* approach. To do so, the authors propose using Faster-R-CNN to identify regions of interest in an image. Given an input image, Faster-R-CNN will identify bounding boxes of the image that likely correspond to objects of a given category and simultaneously compute a feature vector of that bounding box. Figure 1 shows the difference between the Bottom-up and Top-Down approach.

![image](https://user-images.githubusercontent.com/18450628/61817263-2683cd00-ae1c-11e9-971a-d3b531dbbd98.png)

## Combining the two

In this paper, the authors suggest using the bottom-up approach to compute the salient regions of the image the network should focus on using Faster-R-CNN. FRCNN is carefully pretrained on both imagenet and the Visual Genome dataset. It is then frozen and only used to generate bounding boxes of regions with high confidence of being of interest. The top-down approach is then used on the features obtained from the bottom-up approach. In order to "enhance" the FRCNN performance, they initialize their FRCNN with a ResNet-101 pre-trained on imagenet. They train their FRCNN on the Visual Genome dataset, adding attributes to the loss function that are available from the Visual Genome dataset, attributes such as color (black, white, gold etc.),  state (open, close, dark, bright, etc.). A sample of FRCNN outputs are shown in figure 2. It is important to stress that only the feature representations and not the actual outputs (i.e. not the labels) are used in their model.

![image](https://user-images.githubusercontent.com/18450628/61817487-aca01380-ae1c-11e9-90fa-134033b95bb0.png)

## Caption Generation

Figure 3 provides a high-level overview of the model being used for caption generation for images. The image is first passed through FRCNN which produces a set of image features *V*. In their specific implementation, *V* consists of *k* vectors of size 1x2048. Their model consists of two LSTM blocks, one for attention and the other for language generation.

![image](https://user-images.githubusercontent.com/18450628/61818488-effb8180-ae1e-11e9-8ae4-14355115429a.png)

The first block of their model is a Top-Down Attention LSTM layer. It takes as input the mean-pooled features *V* , i.e. 1/k*sum(v_i), concatenated with the previous timestep's hidden representation of the language LSTM as well as the word embedding of the previously generated word. The word embedding is learned and not pretrained. 

The output of the first LSTM is used to compute the attention for each vector using an MLP and softmax:

![image](https://user-images.githubusercontent.com/18450628/61819982-21298100-ae22-11e9-80a9-99640896413d.png)

The attention weighted image feature is then used as an input to the language LSTM model, concatenated with the output from the top-down Attention LSTM and a softmax is used to predict the next word in the sequence. The loss function seeks to minimize the cross-entropy of the generated sentence. 

## VQA Model

The VQA task differs to the image generation in that a text-based question accompanies an input image and the network must produce an answer. The VQA model proposed is different to that of the caption generation model previously described, however they both use the same bottom-up approach to generate the feature vectors of the image based on the FRCNN architecture. A high-level overview of the architecture for the VQA model is presented in Figure 4.

![image](https://user-images.githubusercontent.com/18450628/61821988-8da67f00-ae26-11e9-8456-3c9e5ec60787.png)

Each word from the question is converted to a learned word embedding which is used as input to a GRU. The number of words for each question is limited to 14 for computational efficiency. The output from the GRU is concatenated with each of the *k* image features, and attention weights are computed for each *k*th feature using an MLP and softmax, similar to what is done in the attention for caption generation. The weighted sum of the feature vectors is then passed through an linear layer such that its shape is compatible with the gru output, and the Hadamard product (element-wise product) is computed over the GRU output and attention-weighted image feature representation. Finally, a tanh non-linear activation is used. This results in a "gated tanh", which have been shown empirically to outperform both ReLU and tanh. Finally, a softmax probability distribution is generated at the output which selects a candidate answer among all possible candidate answers.

## Results and experiments

### Resnet Baseline

To demonstrate that their contribution of bottom-up mechanism actually improves on results, the authors use a ResNet trained on imagenet as a baseline for generating the image feature vectors (they resize the final CNN layers using bilinear interpolation when needed). They consistently obtain better results when using the bottom-up approach over the ResNet approach in both caption generation and VQA.

## MSCOCO

The authors demonstrate that they outperform all results on all metrics on the MSCOCO test server.

![image](https://user-images.githubusercontent.com/18450628/61824157-4f5f8e80-ae2b-11e9-8d90-657db453e26e.png)

They also show how using the bottom-up approach over ResNet consistently scores them higher on detecting instances of objects, attributes, relations, etc:

![image](https://user-images.githubusercontent.com/18450628/61824238-7fa72d00-ae2b-11e9-81b3-b5a7f80153f3.png)

The authors, like their predecessors, insist on demonstrating their network's frisbee ability:

![image](https://user-images.githubusercontent.com/18450628/61824344-bed57e00-ae2b-11e9-87cd-597568587e1d.png)

## VQA Results

They also demonstrate that the addition of bottom-up attention improves results over a ResNet baseline. 

![image](https://user-images.githubusercontent.com/18450628/61824500-28ee2300-ae2c-11e9-9016-2120a91917e4.png)

They also show that their model outperformed all other submissions on the VQA submission. They mention using an ensemble of 30 models for their submission. 

![image](https://user-images.githubusercontent.com/18450628/61824634-83877f00-ae2c-11e9-8d84-9589e0ea2be2.png)


A sample image of what is attended in an image given a proper answer is shown in figure 6.

![image](https://user-images.githubusercontent.com/18450628/61824608-736f9f80-ae2c-11e9-9d4e-8cb6bd0a1a92.png)


# Comments

The authors introduce a new way to select portions of the image on which to focus attention. The idea is very original and came at a time when object detection was making significant progress (i.e. FRCNN).

A few comments:

* This method might not generalize well to other types of data. It requires pre-training on larger datasets (visual genome, imagenet, etc.) which consist of categories that overlap with both the MSCOCO and VQA datasets (i.e. cars, people, etc.). It would be interesting to see an end-to-end model that does not rely on pre-training on other similar datasets.

* No insight is given to the computational complexity nor to the inference time or training time. I imagine that FRCNN is resource intensive, and having to do a forward pass of FRCNN for every pass of the network must be a computational bottleneck. Not to mention that they ensembled 30 of them!

This paper estimate 3D hand shape from **single** RGB images based on deep learning. The overall pipeline is the following:
https://i.imgur.com/H72P5ns.png
1. **Hand Segmentation** network is derived from this [paper](https://arxiv.org/pdf/1602.00134.pdf) but, in essence, any segmentation network would do the job. Hand image is cropped from the original image by utilizing segmentation mask and resized to a fixed size (256x256) with bilinear interpolation.
2. **Detecting hand keypoints**. 2D Keypoint detection is formulated as predicting score map for each hand joints (fixed size = 21). Encoder-decoder architecture is used. 
3. **3D hand pose estimation**. 
https://i.imgur.com/uBheX3o.png
    - In this paper, the hand pose is represented as $w_i = (x_i, y_i, z_i)$, where $i$ is index for a particular hand joint. This representation is further normalized $w_i^{norm} = \frac{1}{s} \cdot w_i$, where $s = ||w_{k+1} - w_{k} ||$, and relative position to a reference joint $r$ (palm) is obtained as $w_i^{rel} = w_i^{norm} - w_r^{norm}$.
    - The network predicts coordinates within a canonical frame and additionally estimate the transformation into the canonical frame (as opposite to predicting absolute 3D coordinates). Therefore, the network predicts $w^{c^*} = R(w^{rel}) \cdot w^{rel}$ and $R(w^{rel}) = R_y \cdot R_{xz}$.
Information whether left/right hand is the input is concatenated to flattened feature representation. The training loss is composed of a separate term for canonical coordinates and canonical transformation matrix L2 losses.

Contribution: 
- Apparently, the first method to perform 3D hand shape estimation from a single RGB image rather than using both RGB and depth sensors;
- Possible extension to sign language recognition problem by attaching classifier on predicted 3D poses.

While this approach quite accurately predicts hand 3D poses among frames, they often fluctuate among frames. Probably several techniques (i.e. optical flow, RNN, post-processing smoothing) can be used for ensuring temporal consistency and make predictions more stable across frames.

The main contribution of this paper is introducing a new transformation that the authors call Batch Normalization (BN). The need for BN comes from the fact that during the training of deep neural networks (DNNs) the distribution of each layer’s input change. This phenomenon is called internal covariate shift (ICS).

#### What is BN?
Normalize each (scalar) feature independently with respect to the mean and variance of the mini batch. Scale and shift the normalized values with two new parameters (per activation) that will be learned. The BN consists of making normalization part of the model architecture.

#### What do we gain?
According to the author, the use of BN provides a great speed up in the training of DNNs. In particular, the gains are greater when it is combined with higher learning rates. In addition, BN works as a regularizer for the model which allows to use less dropout or less L2 normalization. Furthermore, since the distribution of the inputs is normalized, it also allows to use sigmoids as activation functions without the saturation problem.

#### What follows?
This seems to be specially promising for training recurrent neural networks (RNNs). The vanishing and exploding gradient problems \cite{journals/tnn/BengioSF94} have their origin in the iteration of transformation that scale up or down the activations in certain directions (eigenvectors). It seems that this regularization would be specially useful in this context since this would allow the gradient to flow more easily. When we unroll the RNNs, we usually have ultra deep networks.

#### Like
* Simple idea that seems to improve training.
* Makes training faster.
* Simple to implement. Probably.
* You can be less careful with initialization.

#### Dislike
* Does not work with stochastic gradient descent (minibatch size = 1).
* This could reduce the parallelism of the algorithm since now all the examples in a mini batch are tied.
* Results on ensemble of networks for ImageNet makes it harder to evaluate the relevance of BN by itself. (Although they do mention the performance of a single model).

[Parsey McParseface](http://github.com/tensorflow/models/tree/master/syntaxnet) is  a parser of English sentences capable of finding parts of speech and dependency parsing. By Michael Collins and google NY.

This paper is more than just about google's data collection and computing powers. The parser uses a feed forward NN, which is much faster than the RNN usually used for parsing. Also the paper is using a global method to solve the label bias problem. This method can be used for many tasks and indeed in the paper it is used also to shorten sentences by throwing unnecessary words.

The label bias problem arises when predicting each label in a sequence using a softmax over all possible label values in each step. This is a local approach but what we are really interested in is a global approach in which the sequence of all labels that appeared in a training example are normalized by all possible sequences. This is intractable so instead a beam search is performed to generate alternative sequences to the training sequence. The search is stopped when the training sequence drops from the beam or ends. The different beams with the training sequence are then used to compute the global loss. 

Similar method is used in [seq2seq by Sasha Rush](http://arxiv.org/pdf/1606.02960.pdf) and  [talk](https://github.com/udibr/notes/blob/master/Talk%20by%20Sasha%20Rush%20-%20Interpreting%2C%20Training%2C%20and%20Distilling%20Seq2Seq%E2%80%A6.pdf)

This paper proposes a variant of Neural Turing Machine (NTM) for meta-learning or "learning to learn", in the specific context of few-shot learning (i.e. learning from few examples). Specifically, the proposed model is trained to ingest as input a training set of examples and improve its output predictions as examples are processed, in a purely feed-forward way. This is a form of meta-learning because the model is trained so that its forward pass effectively executes a form of "learning" from the examples it is fed as input.

During training, the model is fed multiples sequences (referred to as episodes) of labeled examples $({\bf x}_1, {\rm null}), ({\bf x}_2, y_1), \dots, ({\bf x}_T, y_{T-1})$, where $T$ is the size of the episode. For instance, if the model is trained to learn how to do 5-class classification from 10 examples per class, $T$ would be $5 \times 10 = 50$. Mainly, the paper presents experiments on the Omniglot dataset, which has 1623 classes. In these experiments, classes are separated into 1200 "training classes" and 423 "test classes", and each episode is generated by randomly selecting 5 classes (each assigned some arbitrary vector representation, e.g. a  one-hot vector that is consistent within the episode, but not across episodes) and constructing a randomly ordered sequence of 50 examples from within the chosen 5 classes. Moreover, the correct label $y_t$ of a given input ${\bf x}_t$ is always provided only at the next time step, but the model is trained to be good at its prediction of the label of ${\bf x}_t$ at the current time step. This is akin to the scenario of online learning on a stream of examples, where the label of an example is revealed only once the model has made a prediction.

The proposed NTM is different from the original NTM of Alex Graves, mostly in how it writes into its memory. The authors propose to focus writing to either the least recently used memory location or the most recently used memory location. Moreover, the least recently used memory location is reset to zero before every write (an operation that seems to be ignored when backpropagating gradients).

Intuitively, the proposed NTM should learn a strategy by which, given a new input, it looks into its memory for information from other examples earlier in the episode (perhaps similarly to what a nearest neighbor classifier would do) to predict the class of the new input.

The paper presents experiments in learning to do multiclass classification on the Omniglot dataset and regression based on functions synthetically generated by a GP. The highlights are that:

1. The proposed model performs much better than an LSTM and better than an NTM with the original write mechanism of Alex Graves (for classification).
2. The proposed model even performs better than a 1st nearest neighbor classifier.
3. The proposed model is even shown to outperform human performance, for the 5-class scenario.
4. The proposed model has decent performance on the regression task, compared to GP predictions using the groundtruth kernel.

**My two cents**

This is probably one of my favorite ICML 2016 papers. I really think meta-learning is a problem that deserves more attention, and this paper presents both an interesting proposal for how to do it and an interesting empirical investigation of it. 

Much like previous work [\[1\]][1] [\[2\]][2], learning is based on automatically generating a meta-learning training set. This is clever I think, since a very large number of such "meta-learning" examples (the episodes) can be constructed, thus transforming what is normally a "small data problem" (few shot learning) into a "big data problem", for which deep learning is more effective.

I'm particularly impressed by how the proposed model outperforms a 1-nearest neighbor classifier. That said, the proposed NTM actually performs 4 reads at each time step, which suggests that a fairer comparison might be with a 4-nearest neighbor classifier. I do wonder how this baseline would compare.

I'm also impressed with the observation that the proposed model surpassed humans.

The paper also proposes to use 5-letter words to describe classes, instead of one-hot vectors. The motivation is that this should make it easier for the model to scale to much more than 5 classes. However, I don't entirely follow the logic as to why one-hot vectors are problematic. In fact, I would think that arbitrarily assigning 5-letter words to classes would instead imply some similarity between classes that share letters that is arbitrary and doesn't reflect true class similarity. 

Also, while I find it encouraging that the performance for regression of the proposed model is decent, I'm curious about how it would compare with a GP approach that incrementally learns the kernel's hyper-parameter (instead of using the groundtruth values, which makes this baseline unrealistically strong).

Finally, I'm still not 100% sure how exactly the NTM is able to implement the type of feed-forward inference I'd expect to be required. I would expect it to learn a memory representation of examples that combines information from the input vector ${\bf x}_t$ *and* its label $y_t$. However, since the label of an input is presented at the following time step in an episode, it is not intuitive to me then how the read/write mechanisms are able to deal with this misalignment. My only guess is that since the controller is an LSTM, then it can somehow remember ${\bf x}_t$ until it gets $y_t$ and appropriately include the combined information into the memory. This could be supported by the fact that using a non-recurrent feed-forward controller is much worse than using an LSTM controller. But I'm not 100% sure of this either.

All the above being said, this is still a really great paper, which I hope will help stimulate more research on meta-learning. Hopefully code for this paper can eventually be released, which would help in popularizing the topic.

[1]: http://snowedin.net/tmp/Hochreiter2001.pdf
[2]: http://www.thespermwhale.com/jaseweston/ram/papers/paper_16.pdf

**Problem Setting:**

Sequence to Sequence learning (seq2seq) is one of the most successful techniques in machine learning nowadays. The basic idea is to encode a sequence into a vector (or a sequence of vectors if using attention based encoder) and then use a recurrent decoder to decode the target sequence conditioned on the encoder output. While researchers have explored various architectural changes to this basic encoder-decoder model, the standard way of training such seq2seq models is to maximize the likelihood of each successive target word conditioned on the input sequence and the *gold* history of target words. This is also known as *teacher-forcing* in RNN literature. Such an approach has three major issues:

1. **Exposure Bias:** Since we teacher-force the model with *gold* history during training, the model is never exposed to its errors during training. At test time, we will not have access to *gold* history and we feed the history generated by the model. If it is erroneous, the model does not have any clue about how to rectify it.

2. **Loss-Evaluation Mismatch:** While we evaluate the model using sequence level metrics (such as BLEU for Machine Translation), we are training the model with word level cross entropy loss.

3. **Label bias:** Since the word probabilities are normalized at each time step (by using softmax over the final layer of the decoder), this can result in label bias if we vary the number of possible candidates in each step. More about this later. 

**Solution:**

This paper proposes an alternative training procedure for seq2seq models which attempt to solve all the 3 major issues listed above. The idea is to pose seq2seq learning as beam-search optimization problem. Authors begin by removing the final softmax activation function from the decoder. Now instead of probability distributions, we will get score for next possible word. Then the training procedure is changed as follows: At every time step $t$, they maintain a set $S_t$ of $K$ candidate sequences of length $t$. Now the loss function is defined with the following characteristics:

1. If the *gold* sub-sequence of length $t$ is in set $S_t$ and the score for *gold* sub-sequence exceeds the score of the $K$-th ranked candidate by a margin, the model incurs no loss. Now the candidates for next time-step are chosen in a way similar to regular beam-search with beam-size $K$.

2. If the *gold* sub-sequence of length $t$ is in set $S_t$ and it is the $K$-th ranked candidate, then the loss will push the *gold* sequence up by increasing its score. The candidates for next time-step are chosen in a way similar as first case.

3. If the *gold* sub-sequence of length $t$ is NOT in set $S_t$, then the score of the *gold* sequence is increased to be higher than $K$-th ranked candidate by a margin. In this case, candidates for next step or chosen by only considering *gold* word at time $t$ and getting its top-$K$ successors.

4. Further, since we want the full *gold* sequence to be at top of the beam at the end of the search, when $t=T$, the loss is modified to require the score of *gold* sequence to exceed the score of the *highest* ranked incorrect prediction by a margin. 

This non-probabilistic training method has several advantages:

* The model is trained in a similar way it would be tested, since we use beam-search during training as well as testing. Hence this helps to eliminate exposure bias.

* The score based loss can be easily scaled by a mistake-specific cost function. For example, in MT, one could use a cost function which is inversely proportional to BLEU score. So there is no loss-evaluation mismatch.

* Each time step can have different set of successor words based on any hard constraints in the problem. Note that the model is non-probabilistic and hence this varying successor function will not introduce any label bias. Refer [this set of slides][1] for an excellent illustration of label bias.

Cost of forward-prop grows linearly with respect to beam size $K$. However, GPU implementation should help to reduce this cost. Authors propose a clever way of doing BPTT which makes the back-prop almost same cost as ordinary seq2seq training.

**Additional Tricks**

1. Authors pre-train the seq2seq model with regular word level cross-entropy loss and this is crucial since random initialization did not work.

2. Authors use "curriculum beam" strategy in training where they start with beam size of 2 and increase the beam size by 1 for every 2 epochs until it reaches the required beam size. You have to train your model with training beam size of at least test beam size + 1. (i.e $K_{tr} >= K_{te} + 1$).

3. When you use drop-out, you need to be careful to use the same dropout value during back-prop. Authors do this by sharing a single dropout across all sequences in a time step.

**Experiments**

Authors compare the proposed model against basic seq2seq in word ordering, dependency parsing and MT tasks. The proposed model achieves significant improvement over the strong baseline.

**Related Work:**

The whole idea of the paper is based on [learning as search optimization (LaSO) framework][2] of Daume III and Marcu (2005). Other notable related work are training seq2seq models using mix of cross-entropy and REINFORCE called [MIXER][3] and [an actor-critic based seq2seq training][4]. Authors compare with MIXER and they do significantly better than MIXER. 

**My two cents:**

This is one of the important research directions in my opinion. While other recent methods attempt to use reinforcement learning to avoid the issues in word-level cross-entropy training, this paper proposes a really simple score based solution which works very well. While most of the language generation research is stuck with probabilistic framework (I am saying this w.r.t Deep NLP research), this paper highlights the benefits on non-probabilistic generation models. I see this as one potential way of avoiding the nasty scalability issues that come with softmax based generative models.

[1]: http://www.cs.stanford.edu/~nmramesh/crf
[2]: https://www.isi.edu/~marcu/papers/daume05laso.pdf
[3]: http://arxiv.org/pdf/1511.06732v7.pdf
[4]: https://arxiv.org/pdf/1607.07086v2.pdf

TLDR; The authors adopt Generative Adversarial Networks (GANs) to RNNs and train a discriminator to distinguish between sequences generated using teacher forcing (feeding ground truth inputs to the RNN) and scheduled sampling (feeding generated outputs as the next inputs). The inputs to the discriminator are both the predictions and the hidden states of the generative RNN. The generator is trained to fool the discriminator, forcing the dynamics of teacher forcing and scheduled sampling to become more similar. This procedure acts as regularizer, and results in better sample quality and generalization, particularly for long sequences. The authors evaluate their framework on Language Model (PTB), Pixel Generation (Sequential MNIST), Handwriting Generation, and Musisc Synthesis.

### Key Points

- Problem: During inference, errors in an RNN easily compound because the conditioning context may diverge from what is seen during training when the ground-truth labels are fed as inputs (teacher forcing).
- Goal of professor forcing: Make the generative (free-run) behavior and the teacher-forced behavior match as closely as possible.
- Discriminator Details
  - Input is a behavior sequence `B(x, y, theta)` from the generative RNN that contains the hidden states and outputs.
  - The training objective is to correctly classify whether or not a behavior sequence is generated using teacher forcing vs. scheduled sampling.
- Generator
  - Standard RNN with MLE training objective and an additional term to fool the discrimator: Change the free-running behavior as to match the teacher-forced behavior while keeping the latter constant.
  - Second optional another term: Change the teacher-forced behavior to match the free-running behavior.
  - Like GAN, backprop from discriminator into generator.
- Architectures
  - Generator is a standard GRU Recurrent Neural Network with softmax
  - Behavior function `B(x, y, theta)` outputs pre-tanh activation of GRU states and tje softmax output
  - Discriminator: Bidirectional GRU with 3-layer MLP on top
  - Training trick: To prevent "bad gradients" the authors backprop from the discriminator into the generator only if the classification accuracy is between 75% and 99%.
  - Trained used Adam optimizer
- Experiments
  - PTB Chracter-Level Modeling: Reduction in test NLL, profesor forcing seem to act as a regularizier. 1.48 BPC
  - Sequential MNIST: Second-best NLL (79.58) after PixelCNN
  - Handwriting generation: Professor forcing is better at generating longer sequences than seen during training as per human eval.
  - Music Synthesis: Human eval significantly better for Professor forcing
  - Negative Results on word-level modeling: Professor forcing doesn't have any effect. Perhaps because long-term dependencies are more pronounced in character-level modeling.
  - The authors show using t-SNE that the hidden state distributions actually become more similar when using professor forcing

### Thoughts

- Props to the authors for a very clear and well-written paper. This is rarer than it should be :)
- It's an intersting idea to also match the states of the RNN instead of just the outputs. Intuitively, matching the outputs should implicitly match the state distribution. I wonder if the authors tried this and it didn't work as expected.
- Note from [Ethan Caballero](https://github.com/ethancaballero) about why they chose to match hidden states: It's significantly harder to use GANs on sampled (argmax) output tokens because they are discrete as (as opposed to continuous like the hidden states and their respective softmaxes). They would have had to estimate discrete outputs with policy gradients like in [seqGAN](https://github.com/dennybritz/deeplearning-papernotes/blob/master/notes/seq-gan.md) which is [harder to get to converge](https://www.quora.com/Do-you-have-any-ideas-on-how-to-get-GANs-to-work-with-text), which is why they probably just stuck with the hidden states which already contain info about the discrete sampled outputs (the index of the highest probability in the the distribution) anyway. Professor Forcing method is unique in that one has access to the continuous probability distribution of each token at each timestep of the two sequence generation modes trying to be pushed closer together. Conversely, when applying GANs to pushing real samples and generated samples closer together as is traditionally done in models like seqGAN, one only has access to the next dicrete token (not continuous probability distributions of next token) at each timestep, which prevents straight-forward differentiation (used in professor forcing) from being applied and forces one to use policy gradient estimation. However, there's a chance one might be able to use straight-forward differentiation to train seqGANs in the traditional sampling case if one swaps out each discrete sampled token with its continuous distributional word embedding (from pretrained word2vec, GloVe, etc.), but no one has tried it yet TTBOMK.
- I would've liked to see a comparison of  the two regularization terms in the generator. The experiments don't make it clear if both or only of them them is used.
- I'm guessing that this architecture is quite challenging to train. Woul've liked to see a bit more detail about when/how they trade off the training of discriminator and generator.
- Translation is another obvious task to apply this too. I'm interested whether or not this works for seq2seq.

This is a paper where I keep being torn between the response of “this is so simple it’s brilliant; why haven’t people done it before,” and “this is so simple it’s almost tautological, and the results I’m seeing aren’t actually that surprising”. The basic observation this paper makes is one made frequently before, most recently to my memory by Geoff Hinton in his Capsule Net paper: sometimes the translation invariance of convolutional networks can be a bad thing, and lead to worse performance. In a lot of ways, translation invariance is one of the benefits of using a convolutional architecture in the first place: instead of having to learn separate feature detectors for “a frog in this corner” and “a frog in that corner,” we can instead use the same feature detector, and just move it over different areas of the image. However, this paper argues, this makes convolutional networks perform worse than might naively be expected at tasks that require them to remember or act in accordance with coordinates of elements within an image. 

For example, they find that normal convolutional networks take nearly an hour and 200K worth of parameters to learn to “predict” the one-hot encoding of a pixel, when given the (x,y) coordinates of that pixel as input, and only get up to about 80% accuracy. Similarly, trying to take an input image with only one pixel active, and predict the (x,y) coordinates as output, is something the network is able to do successfully, but only when the test points are sampled from the same spatial region as the training points: if the test points are from a held-out quadrant, the model can’t extrapolate to the (x, y) coordinates there, and totally falls apart. 

https://i.imgur.com/x6phN4p.png

The solution proposed by the authors is a really simple one: at one or more layers within the network, in addition to the feature channels sent up from the prior layer, add two addition channels: one with a with deterministic values going from -1 (left) to 1 (right), and the other going top to bottom. This essentially adds two fixed “features” to each pixel, which jointly carry information about where it is in space. Just by adding this small change, we give the network the ability to use spatial information or not, as it sees fit. If these features don’t prove useful, their weights will stay around their initialization values of expectation-zero, and the behavior should be much like a normal convolutional net. However, if it proves useful, convolution filters at the next layer can take position information into account. It’s easy to see how this would be useful for this paper’s toy problems: you can just create a feature detector for “if this pixel is active, pass forward information about it’s spatial position,” and predict the (x, y) coordinates out easily. You can also imagine this capability helping with more typical image classification problems, by having feature filters that carry with them not only content information, but information about where a pattern was found spatially.  

The authors do indeed find comparable performance or small benefits to ImageNet, MNIST, and Atari RL, when applying their layers in lieu of normal convolutional layer. On GANs in particular, they find less mode collapse, though I don’t yet 100% follow the intuition of why this would be the case. 
https://i.imgur.com/wu7wQZr.png

### Summary
Knowing when a model is qualified to make a prediction is critical to safe deployment of ML technology. Model-independent / Unsupervised Out-of-Distribution (OoD) detection is appealing mostly because it doesn't require task-specific labels to train. It is tempting to suggest a simple one-tailed test in which lower likelihoods are OoD (assigned by a Likelihood Model), but the intuition that In-Distribution (ID) inputs should have highest likelihoods _does not hold in higher dimension_. The authors propose to use the Watanabe-Akaike Information Criterion (WAIC) to circumvent this problem and empirically show the robustness of the approach.

### Counterintuitive Properties of Likelihood Models:
https://i.imgur.com/4vo0Ff5.png
So a GLOW model with Gaussian prior maps SVHN closer to the origin than Cifar (but never actually generates SVHN because Gaussian samples are on the shell). This is bad news for OoD detection.

### Proposed Methodology:
Use the WAIC criterion for OoD detection which gives an asymptotically correct estimate of the gap between the training set and test set expectations:
https://i.imgur.com/vasSxuk.png
Basically,  the correction term subtracts the variance in likelihoods across independent samples from the posterior. This acts to robustify the estimate, ensuring that points that are sensitive to the particular choice of posterior are penalized. They use an ensemble of generative models as a proxy for posterior samples i.e. the ensembles acts as approximate posterior samples.
Now, OoD can be detected with a Likelihood Model:
https://i.imgur.com/M3CDKOA.png
### Discussion
Interestingly, GLOW maps Cifar and other datasets INSIDE the gaussian shell (which is an annulus of radius $\sqrt{dim} = \sqrt{3072} \approx 55.4$
https://i.imgur.com/ERdgOaz.png
This is in itself quite disturbing, as it suggests that better flow-based generative models (for sampling) can be obtained by encouraging the training distribution to overlap better with the typical set in latent
space.