This article makes the argument for *interactive* language learning, motivated by some nice recent small-domain success. I can certainly agree with the motivation: if language is used in conversation, shouldn't we be building models which know how to behave in conversation?

The authors develop a standard multi-agent communication paradigm, where two agents learn communicate in a single-round reference game. (No references to e.g. Kirby or any [ILM][1] work, which is in the same space.) Agent `A1` examines a referent `R` and "transmits" a one-hot utterance representation to `A2`, who must successfully identify `R` given the utterance. The one-round conversations are a success when `A2` picks the correct referent `R`. The two agents are jointly trained to maximize this success metric via REINFORCE (policy gradient).

**This is mathematically equivalent to [the NVIL model (Mnih and Gregor, 2014)][2]**, an autoencoder with "hard" latent codes which is likewise trained by policy gradient methods.

They perform a nice thorough evaluation on both successful and "cheating" models. This will serve as a useful reference point / starting point for people interested in interactive language acquisition.

The way clear is forward, I think: let's develop agents in more complex environments, interacting in multi-round conversations, with more complex / longer utterances.

[1]: http://cocosci.berkeley.edu/tom/papers/IteratedLearningEvolutionLanguage.pdf
[2]: https://arxiv.org/abs/1402.0030

Authors test different variant of CNN architectures, non-linearities, poolings, etc. on ImageNet.

Summary:
-  use ELU non-linearity without batchnorm or ReLU with it.
-  apply a learned colorspace transformation of RGB (2 layers of 1x1 convolution ).
-  use the linear learning rate decay policy.
-  use a sum of the average and max pooling layers.
-  use mini-batch size around 128 or 256. If this is too big for your GPU,
decrease the learning rate proportionally to the batch size.
- use fully-connected layers as convolutional and average the predictions for
the final decision.
- when investing in increasing training set size, check if a plateau has not
been reach.
- cleanliness of the data is more important then the size.
- if you cannot increase the input image size, reduce the stride in the consequent
layers, it has roughly the same effect.
- if your network has a complex and highly optimized architecture, like e.g.
GoogLeNet, be careful with modifications.

This paper derives an algorithm for passing gradients through a sample from a mixture of Gaussians. While the reparameterization trick allows to get the gradients with respect to the Gaussian means and covariances, the same trick cannot be invoked for the mixing proportions parameters (essentially because they are the parameters of a multinomial discrete distribution over the Gaussian components, and the reparameterization trick doesn't extend to discrete distributions).

One can think of the derivation as proceeding in 3 steps:

1. Deriving an estimator for gradients a sample from a 1-dimensional density $f(x)$ that is such that $f(x)$ is differentiable and its cumulative distribution function (CDF) $F(x)$ is tractable:

  $\frac{\partial \hat{x}}{\partial \theta} = - \frac{1}{f(\hat{x})}\int_{t=-\infty}^{\hat{x}} \frac{\partial f(t)}{\partial \theta} dt$

  where $\hat{x}$ is a sample from density $f(x)$ and $\theta$ is any parameter of $f(x)$ (the above is a simplified version of Equation 6). This is probably the most important result of the paper, and is based on a really clever use of the general form of the Leibniz integral rule.

2. Noticing that one can sample from a $D$-dimensional Gaussian mixture by decomposing it with the product rule $f({\bf x}) = \prod_{d=1}^D f(x_d|{\bf x}_{<d})$ and using ancestral sampling, where each $f(x_d|{\bf x}_{<d})$ are themselves 1-dimensional mixtures (i.e. with differentiable densities and tractable CDFs)

3. Using the 1-dimensional gradient estimator (of Equation 6) and the chain rule to backpropagate through the ancestral sampling procedure. This requires computing the integral in the expression for $\frac{\partial \hat{x}}{\partial \theta}$ above, where $f(x)$ is one of the 1D conditional Gaussian mixtures and $\theta$ is a mixing proportion parameter $\pi_j$. As it turns out, this integral has an analytical form (see Equation 22).

**My two cents**

This is a really surprising and neat result. The author mentions it could be applicable to variational autoencoders (to support posteriors that are mixtures of Gaussians), and I'm really looking forward to read about whether that can be successfully done in practice. 

The paper provides the derivation only for mixtures of Gaussians with diagonal covariance matrices. It is mentioned that extending to non-diagonal covariances is doable. That said, ancestral sampling with non-diagonal covariances would become more computationally expensive, since the conditionals under each Gaussian involves a matrix inverse.

Beyond the case of Gaussian mixtures, Equation 6 is super interesting in itself as its application could go beyond that case. This is probably why the paper also derived a sampling-based estimator for Equation 6, in Equation 9. However, that estimator might be inefficient, since it involves sampling from Equation 10 with rejection, and it might take a lot of time to get an accepted sample if $\hat{x}$ is very small. Also, a good estimate of Equation 6 might require *multiple* samples from Equation 10. 

Finally, while I couldn't find any obvious problem with the mathematical derivation, I'd be curious to see whether using the same approach to derive a gradient on one of the Gaussian mean or standard deviation parameters gave a gradient that is consistent with what the reparameterization trick provides.

Carlini and Wagner propose three novel methods/attacks for adversarial examples and show that defensive distillation is not effective. In particular, they devise attacks for all three commonly used norms $L_1$, $L_2$ and $L_\infty$ – which are used to measure the deviation of the adversarial perturbation from the original testing sample. In the course of the paper, starting with the targeted objective
$\min_\delta d(x, x + \delta)$ s.t. $f(x + \delta) = t$ and $x+\delta \in [0,1]^n$,
they consider up to 7 different surrogate objectives to express the constraint $f(x + \delta) = t$. Here, $f$ is the neural network to attack and $\delta$ denotes the perturbation. This leads to the formulation

$\min_\delta \|\delta\|_p + cL(x + \delta)$ s.t. $x + \delta \in [0,1]^n$

where $L$ is the surrogate loss. After extensive evaluation, the loss $L$ is taken to be

$L(x') = \max(\max\{Z(x')_i : i\neq t\} - Z(x')_t, -\kappa)$

where $x' = x + \delta$ and $Z(x')_i$ refers to the logit for class $i$; $\kappa$ is a constant ($=0$ in their experiments) that can be used to control the confidence of the adversarial example. In practice, the box constraint $[0,1]^n$ is encoded through a change of variable by expressing $\delta$ in terms of the hyperbolic tangent, see the paper for details. Carlini and Wagner then discuss the detailed attacks for all three norms, i.e. $L_1$, $L_2$ and $L_\infty$ where the first and latter are discussed in more detail as they impose non-differentiability.

This paper introduces a new regularization technique that aims at reducing over-fitting without reducing the capacity of a model. It draws on the claim that models start to over-fit data when co-label similarities start to disappear, e.g. when the model output does not show that dogs of similar breeds like German shepherd and Belgian shepherd are similar anymore.

The idea is that models in an early training phase *do* show these similarities. In order to keep this information in the model, target labels $Y^t_c$ for training step $t$ are changed by adding the exponential mean of output labels of previous training steps $\hat{Y}^t$:

$$
\hat{Y}^t = \beta \hat{Y}^{t-1} + (1-\beta)F(X, W),\\
Y_c^t = \gamma\hat{Y}^t  + (1-\gamma)Y,
$$

where $F(X,W)$ is the current network's output, and $Y$ are the ground truth labels. This way, the network should remember which classes are similar to each other. The paper shows that training using the proposed regularization scheme preserves co-label similarities (compared to an over-fitted model) similarly to dropout. This confirms the intuition the proposed method is based on.

The method introduces several new hyper-parameters:
 - $\beta$, defining the exponential decay parameter for averaging old predictions
 - $\gamma$, defining the weight of soft targets to ground truth targets
 - $n_b$, the number of 'burn-in' epochs, in which the network is trained with hard targets only
 - $n_t$, the number of epochs between soft-target updates

Results on MNIST, CIFAR-10 and SVHN are encouraging, as networks with soft-target regularization achieve lower losses on almost all configurations. However, as of today, the paper does not show how this translates to classification accuracy. Also, it seems that the results are from one training run only, so it is difficult to assess if this improvement is systematic.