This paper introduces a deep universal word embedding based on using a bidirectional LM (in this case, biLSTM). First words are embedded with a CNN-based, character-level, context-free, token embedding into $x_k^{LM}$ and then each sentence is parsed using a biLSTM, maximizing the log-likelihood of a word given it's forward and backward context (much like a normal language model). 

The innovation is in taking the output of each layer of the LSTM ($h_{k,j}^{LM}$ being the output at layer $j$) 
$$
\begin{align}
R_k &= \{x_k^{LM}, \overrightarrow{h}_{k,j}^{LM}, \overleftarrow{h}_{k,j}^{LM} | j = 1 \ldots L \} \\
&= \{h_{k,j}^{LM} | j = 0 \ldots L \}
\end{align}
$$
and allowing the user to learn a their own task-specific weighted sum of these hidden states as the embedding:
$$
ELMo_k^{task} = \gamma^{task} \sum_{j=0}^L s_j^{task} h_{k,j}^{LM}
$$

The authors show that this weighted sum is better than taking only the top LSTM output (as in their previous work or in CoVe) because it allows capturing syntactic information in the lower layer of the LSTM and semantic information in the higher level. Table below shows that the second layer is more useful for the semantic task of word sense disambiguation, and the first layer is more useful for the syntactic task of POS tagging.

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

On other benchmarks, they show it is also better than taking the average of the layers (which could be done by setting $\gamma = 1$)
https://i.imgur.com/f78gmKu.png

To add the embeddings to your supervised model,  ELMo is concatenated with your context-free embeddings, $\[ x_k; ELMo_k^{task} \]$. It can also be concatenated with the output of your RNN model $\[ h_k; ELMo_k^{task} \]$ which can show improvements on the same benchmarks

https://i.imgur.com/eBqLe8G.png

Finally, they show that adding ELMo to a competitive but simple baseline gets SOTA (at the time) on very many NLP benchmarks

https://i.imgur.com/PFUlgh3.png

It's all open-source and there's a tutorial [here](https://github.com/allenai/allennlp/blob/master/tutorials/how_to/elmo.md)

Cohen et al. study robustness bounds of randomized smoothing, a region-based classification scheme where the prediction is averaged over Gaussian samples around the test input. Specifically, given a test input, the predicted class is the class whose decision region has the largest overlap with a normal distribution of pre-defined variance. The intuition of this approach is that, for small perturbations, the decision regions of classes can’t vary too much. In practice, randomized smoothing is applied using samples. In the paper, Cohen et al. show that this approach conveys robustness against radii R depending on the confidence difference between the actual class and the “runner-up” class. In practice, the radii also depend on the number of samples used.

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

This is an interestingly pragmatic paper that makes a super simple observation. Often, we may want a usable network with fewer parameters, to make our network more easily usable on small devices. It's been observed (by these same authors, in fact), that pruned networks can achieve comparable weights to their fully trained counterparts if you rewind and retrain from early in the training process, to compensate for the loss of the (not ultimately important) pruned weights. This observation has been dubbed the "Lottery Ticket Hypothesis", after the idea that there's some small effective subnetwork you can find if you sample enough networks. 

Given these two facts - the usefulness of pruning, and the success of weight rewinding - the authors explore the effectiveness of various ways to train after pruning. Current standard practice is to prune low-magnitude weights, and then continue training remaining weights from values they had at pruning time, keeping the final learning rate of the network constant. The authors find that: 
1. Weight rewinding, where you rewind weights to *near* their starting value, and then retrain using the learning rates of early in training, outperforms fine tuning from the place weights were when you pruned 

but, also 
2. Learning rate rewinding, where you keep weights as they are, but rewind learning rates to what they were early in training, are actually the most effective for a given amount of training time/search cost 

To me, this feels a little bit like burying the lede: the takeaway seems to be that when you prune, it's beneficial to make your network more "elastic" (in the metaphor-to-neuroscience sense) so it can more effectively learn to compensate for the removed neurons. So, what was really valuable in weight rewinding was the ability to "heat up" learning on a smaller set of weights, so they could adapt more quickly. And the fact that learning rate rewinding works better than weight rewinding suggests that there is value in the learned weights after all, that value is just outstripped by the benefit of rolling back to old learning rates. 

All in all, not a super radical conclusion, but a useful and practical one to have so clearly laid out in a paper.

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.

The typical model based reinforcement learning (RL) loop consists of collecting data, training a model of the environment, using the model to do model predictive control (MPC). If however the model is wrong, for example for state-action pairs that have been barely visited, the dynamics model might be very wrong and the MPC fails as the imagined model and the reality align to longer. Boney et a. propose to tackle this with a denoising autoencoder for trajectory regularization according to the familiarity of a trajectory. 

MPC uses at each time t the learned model $s_{t+1} = f_{\theta}(s_t, a_t)$  to select a plan of actions, that is maximizing the sum of expected future reward:
$
G(a_t, \dots, a_{t+h}) = \mathbb{E}[\sum_{k=t}^{t+H}r(o_t, a_t)] ,$

 where $r(o_t, a_t)$ is the observation and action dependent reward. The plan obtained by trajectory optimization is subsequently unrolled for H steps. 

Boney et al. propose to regularize trajectories by the familiarity of the visited states leading to the regularized objective:
$G_{reg} = G + \alpha \log p(o_k, a_k, \dots, o_{t+H}, a_{t+H})
$
Instead of regularizing over the whole trajectory they propose to regularize over marginal probabilities of windows of length w:
$G_{reg} = G + \alpha \sum_{k = t}^{t+H-w} \log p(x_k), \text{ where } x_k = (o_k, a_k, \dots, o_{t+w}, a_{t+w}).$
Instead of explicitly learning a generative model of the familiarity $p(x_k)$ a denoising auto-encoder is used that approximates instead the derivative of the log probability density $\frac{\delta}{\delta x} \log p(x)$. This allows the following back-propagation rule:
$ \frac{\delta G_{reg}}{\delta_i} = \frac{\delta G}{\delta a_i} + \alpha \sum_{k = i}^{i+w} \frac{\delta x_k}{\delta a_i} \frac{\delta}{\delta x} \log p(x).$

The experiments show that the proposed method has competitive sample-efficiency. For example on Halfcheetah the asymptotic performance of PETS is not matched.

This is due to the biggest limitation of this approach, the hindering of exploration. Penalizing the unfamiliarity of states is in contrast to approaches like optimism in the face of uncertainty, which is a core principle of exploration. Aiming to avoid states of high unfamiliarity, the proposed method is the precise opposite of curiosity driven exploration. The appendix proposes preliminary experiments to account for exploration. I would expect, that the pure penalization of unfamiliarity works best in a batch RL setting, which would be an interesting extension of this work.