Published as a conference paper at ICLR 2018 LEARNING DEEP MEAN FIELD GAMES FOR MODEL- ING LARGE POPULATION BEHAVIOR
We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded on game theory for understanding the aggregate effect of individual actions and predicting the temporal evolution of population distributions. We achieve a synthesis of MFG and Markov decision processes (MDP) by showing that a special MFG is reducible to an MDP. This enables us to broaden the scope of mean field game theory and infer MFG models of large real-world systems via deep inverse reinforcement learning. Our method learns both the reward function and forward dynamics of an MFG from real data, and we report the first empirical test of a mean field game model of a real-world social media population.

This paper attacks an important problems with an interesting and promising methodology.  The authors deal with inference in models of collective behavior, specifically at how to infer the parameters of a mean field game representation of collective behavior. The technique the authors innovate is to specify a mean field game as a model, and then use inverse reinforcement learning to learn the reward functions of agents in the mean field game.
This work has many virtues, and could be an impactful piece. There is still minimal work at the intersection of machine learning and collective behavior, and this paper could help to stimulate the growth of that intersection.  The application to collective behavior could be an interesting novel application to many in machine learning, and conversely the inference techniques that are innovated should be novel to many researchers in collective behavior.
At the same time, the scientific content of the work has critical conceptual flaws.  Most fundamentally, the authors appear to implicitly center their work around highly controversial claims about the ontological status of group optimization, without the careful justification necessary to make this kind of argument.  In addition to that, the authors appear to implicitly assume that utility function inference can be used for causal inference.
That is, there are two distinct mistakes the authors make in their scientific claims:
1) The authors write as if mean field games represent population optimization (Mean field games are not about what a _group_ optimizes; they are about what _individuals_ optimize, and this individual optimization leads to certain patterns in collective behaviors)
2) The authors write as if utility/reward function inference alone can provide causal understanding of collective or individual behavior
1 -
I should say that I am highly sympathetic to the claim that many types of collective behavior can be viewed as optimizing some kind of objective function.  However, this claim is far from mainstream, and is in fact highly contested.  For instance, many prominent pieces of work in the study of collective behavior have highlighted its irrational aspects, from the madness of crowds to herding in financial markets.
Since it is so fringe to attribute causal agency to groups, let alone optimal agency, in the remainder of my review I will give the authors the benefit of the doubt and assume when they say things like "population behavior may be optimal", they mean "the behavior of individuals within a population may be optimal".  If the authors do mean to say this, they should be more careful about their language use in this regard (individuals are the actors, not populations).  If the authors do indeed mean to attribute causal agency to groups (as suggested in their MDP representation), they will run into all the criticisms I would have about an individual-level analysis and more.  Suffice it to say, mean field games themselves don't make claims about aggregate-level optimization.  A Nash equilibrium achieves a balance between individual-level reward functions. These reward functions are only interpretable at the individual level.  There is no objective function the group itself in aggregate is optimizing in mean field games.  For instance, even though the mean field game model of the Mexican wave produces wave solutions, the model is premised on people having individual utility functions that lead to emergent wave behavior.  The model does not have the representational capacity to explain that people actually intend to create the emergent behavior of a wave (even though in this case they do).  Furthermore, the fact that mean field games aggregate to a single-agent MDP does not imply that that the group can rightfully be thought of as an agent optimizing the reward function, because there is an exact correspondence between the rewards of the individual agents in the MFG and of the aggregate agent in the MDP by construction.
2 -
The authors also claim that their inference methods can help explain why people choose to talk about certain topics. As far as the extent to which utility / reward function inference can provide causal explanations of individual (or collective) behavior, the argument that is invariably brought against a claim of optimization is that almost any behavior can be explained as optimal post-hoc with enough degrees of freedom in the utiliy function of the behavioral model. Since optimization frameworks are so flexible, they have little explanatory power and are hard to falsify.  In fact, there is literally no way that the modeling framework of the authors even affords the possibility that individual/collective behavior is not optimal.  Optimality is taken as an assumption that allows the authors to infer what reward function is being optimized.
The authors state that the reward function they infer helps to interpret collective behavior because it reveals what people are optimizing.  However, the reward function actually discovered is not interpretable at all. It is simply a summary of the statistical properties of changes in popularity of the topics of conversation in the Twitter data the authors' study. To quote the authors' insights: "The learned reward function reveals that a real social media population favors states characterized by a highly non-uniform distribution with negative mass gradient in decreasing order of topic popularity, as well as transitions that increase this distribution imbalance."  The authors might as well have simply visualized the topic popularities and changes in popularities to arrive at such an insight. To take the authors claims literally, we would say that people have an intrinsic preference for everyone to arbitrarily be talking about the same thing, regardless of the content or relevance of that topic.  To draw an analogy, this is like observing that on some days everybody on the street is carrying open umbrellas and on other days not, and inferring that the people on the street have a preference for everyone having their umbrellas open together (and the model would then predict that if one person opens an umbrella on a sunny day, everybody else will too).
To the authors credit, they do make a brief attempt to present empirical evidence for their optimization view, stating succinctly: "The high prediction accuracy of the learned policy provides evidence that real population behavior can be understood and modeled as the result of an emergent population-level optimization with respect to a reward function." Needless to say, this one-sentence argument for a highly controversial scientific claims falls flat on closer inspection. Setting aside the issues of correlation versus causation, predictive accuracy does not in and of itself provide scientific plausibility. When an n-gram model produces text that is in the style of a particular writer, we do not conclude that the writer must have been composing based on the n-gram's generative mechanism.  Predictive accuracy only provides evidence when combined in the first place with scientific plausibility through other avenues of evidence.
The authors could attempt to address these issues by making what is called an "as-if" argument, but it's not even clear such an argument could work here in general.
With all this in mind, it would be more instructive to show that the inference method the authors introduce could infer the correct utility functions used in standard mean field games, such as modeling traffic congestion and the Mexican wave.
--
All that said, the general approach taken in the authors' work is highly promising, and there are many fruitful directions I would be exicted to see this work taken --- e.g., combining endogenous and exogenous rewards or looking at more complex applications.  As a technical contribution, the paper is wonderful, and I would enthusiastically support acceptance.  The authors simply either need to be much more careful with the scientific claims about collective behavior they make, or limit the scope of the contribution of the paper to be modeling / inference  in the area of collective behavior.  Mean field games are an important class of models in collective behavior, and being able to infer their parameters is a nice step forward purely due to the importance of that class of games.  Identifying where the authors' inference method could be applied to draw valid scientific conclusions about collective behavior could then be an avenue for future work.  Examples of plausible scientific applications might include parameter inference in settings where mean field games are already typically applied in order to improve the fit of those models or to learn about trade-offs people make in their utility functions in those settings.
--
Other minor comments:
- (Introduction) It is not clear at all how the Arab Spring, Black Lives Matter, and fake news are similar --- i.e., whether a single model could provide insight into these highly heterogeneous events --- nor is it clear what end the authors hope to achieve by modeling them --- the ethics of modeling protests in a field crowded with powerful institutional actors is worth carefully considering.
- If I understand correctly, the fact that the authors assume a factored reward function seems limiting. Isn't the major benefit of game theory it's ability to accommodate utility functions that depend on the actions of others?
- The authors state that one of their essential insights is that "solving the optimization problem of a single-agent MDP is equivalent to solving the inference problem of an MFG." This statement feels a bit too cute at the expense of clarity. The authors perform inference via inverse-RL, so it's more clear to say the authors are attempting to use statistical inference to figure out what is being optimized.
- The relationship between MFGs and a single-agent MDP is nice and a fine observation, but not as surprising as the authors frame it as. Any multiagent MDP can be naively represented as a single-agent MDP where the agent has control over the entire population, and we already know that stochastic games are closely related to MDPs.  It's therefore hard to imagine that there woudn't be some sort of correspondence.


Recent work on encoder-decoder models for sequence-to-sequence mapping has shown that integrating both temporal and spatial attentional mechanisms into neural networks increases the performance of the system substantially. We report on a new modular network architecture that applies an attentional mechanism not on temporal and spatial regions of the input, but on sensor selection for multi-sensor setups. This network called the sensor transformation attention network (STAN) is evaluated in scenarios which include the presence of natural noise or synthetic dynamic noise. We demonstrate how the attentional signal responds dynamically to changing noise levels and sensor-specific noise, leading to reduced word error rates (WERs) on both audio and visual tasks using TIDIGITS and GRID; and also on CHiME-3, a multi-microphone real-world noisy dataset. The improvement grows as more channels are corrupted as demonstrated on the CHiME-3 dataset. Moreover, the proposed STAN architecture naturally introduces a number of advantages including ease of removing sensors from existing architectures, attentional interpretability, and increased robustness to a variety of noise environments.

Summary:
The authors consider the use of attention for sensor, or channel, selection. The idea is tested on several speech recognition datasets, including TIDIGITS and CHiME3, where the attention is over audio channels, and GRID, where the attention is over video channels. Results on TIDIGITS and GRID show a clear benefit of attention (called STAN here) over concatenation of features. The results on CHiME3 show gain over the CHiME3 baseline in channel-corrupted data.
Review:
The paper reads well, but as a standard application of attention lacks novelty. The authors mention that related work is generalized but fail to differentiate their work relative to even the cited references (Kim & Lane, 2016; Hori et al., 2017). Furthermore, while their approach is sold as a general sensor fusion technique, most of their experimentation is on microphone arrays with attention directly over magnitude-based input features, which cannot utilize the most important feature for signal separation using microphone arrays---signal phase. Their results on CHiME3 are terrible: the baseline CHiME3 system is very weak, and their system is only slightly better! The winning system has a WER of only 5.8%(vs. 33.4% for the baseline system), while more than half of the submissions to the challenge were able to cut the WER of the baseline system in half or better! http://spandh.dcs.shef.ac.uk/chime_challenge/chime2015/results.html. Their results wrt channel corruption on CHiME3, on the other hand, are reasonable, because the model matches the problem being addressed…
Overall Assessment:
In summary, the paper lacks novelty wrt technique, and as an “application-of-attention” paper fails to be even close to competitive with the state-of-the-art approaches on the problems being addressed. As such, I recommend that the paper be rejected.
Additional comments:
-	The experiments in general lack sufficient detail: Were the attention masks trained supervised or unsupervised? Were the baselines with concatenated features optimized independently? Why is there no multi-channel baseline for the GRID results?
-	Issue with noise bursts plot (Input 1+2 attention does not sum to 1)
-	A concatenation based model can handle a variable #inputs: it just needs to be trained/normalized properly during test (i.e. like dropout)…


Published as a conference paper at ICLR 2018 LEARNING AN EMBEDDING SPACE FOR TRANSFERABLE ROBOT SKILLS
We present a method for reinforcement learning of closely related skills that are parameterized via a skill embedding space. We learn such skills by taking advantage of latent variables and exploiting a connection between reinforcement learning and variational inference. The main contribution of our work is an entropyregularized policy gradient formulation for hierarchical policies, and an associated, data-efficient and robust off-policy gradient algorithm based on stochastic value gradients. We demonstrate the effectiveness of our method on several simulated robotic manipulation tasks. We find that our method allows for discovery of multiple solutions and is capable of learning the minimum number of distinct skills that are necessary to solve a given set of tasks. In addition, our results indicate that the hereby proposed technique can interpolate and/or sequence previously learned skills in order to accomplish more complex tasks, even in the presence of sparse rewards.

The paper presents a new approach for hierarchical reinforcement learning which aims at learning a versatile set of skills. The paper uses a variational bound for entropy regularized RL to learn a versatile latent space which represents the skill to execute. The variational bound is used to diversify the learned skills as well as to make the skills identifyable from their state trajectories. The algorithm is tested on a simple point mass task and on simulated robot manipulation tasks.
This is a very intersting paper which is also very well written. I like the presented approach of learning the skill embeddings using the variational lower bound. It represents one of the most principled approches for hierarchical RL.
Pros:
- Interesting new approach for hiearchical reinforcement learning that focuses on skill versatility
- The variational lower bound is one of the most principled formulations for hierarchical RL that I have seen so far
- The results are convincing
Cons:
- More comparisons against other DRL algorithms such as TRPO and PPO would be useful
Summary: This is an interesting deep reinforcement learning paper that introduces a new principled framework for learning versatile skills. This is a good paper.
More comments:
- There are several papers that focus on learning versatile skills in the context of movement primitive libraries, see [1],[2],[3]. These papers should be discussed.
[1] Daniel, C.; Neumann, G.; Kroemer, O.; Peters, J. (2016). Hierarchical Relative Entropy Policy Search, Journal of Machine Learning Research (JMLR),
[2] End, F.; Akrour, R.; Peters, J.; Neumann, G. (2017). Layered Direct Policy Search for Learning Hierarchical Skills, Proceedings of the International Conference on Robotics and Automation (ICRA).
[3] Gabriel, A.; Akrour, R.; Peters, J.; Neumann, G. (2017). Empowered Skills, Proceedings of the International Conference on Robotics and Automation (ICRA).


We propose an efficient online hyperparameter optimization method which uses a joint dynamical system to evaluate the gradient with respect to the hyperparameters. While similar methods are usually limited to hyperparameters with a smooth impact on the model, we show how to apply it to the probability of dropout in neural networks. Finally, we show its effectiveness on two distinct tasks.

Summary of paper:
This work proposes an extension to an existing method (Franceschi 2017) to optimize regularization hyperparameters. Their method claims increased stability in contrast to the existing one.
Summary of review:
This is an incremental change of an existing method. This is acceptable as long as the incremental change significantly improves results or the paper presents some convincing theoretical arguments. I did not find either to be the case. The theoretical arguments are interesting but lacking in rigor. The proposed method introduces hyper-hyperparameters which may be hard to tune. The experiments are small scale and it is unclear how much the method improves random grid search. For these reasons, I cannot recommend this paper for acceptance.
Comments:
1. Paper should cite Domke 2012 in related work section.
2. Should state and verify conditions for application of implicit function theorem on page 2.
3. Fix notation on page 3. Dot is used on the right hand side to indicate an argument but not left hand side for equation after "with respect to \lambda".
4. I would like to see more explanation for the figure in Appendix A. What specific optimization is being depicted? This figure could be moved into the paper's main body with some additional clarification.
5. I did not understand the paragraph beginning with "This poor estimation". Is this just a restatement of the previous paragraph, which concluded convergence will be slow if \eta is too small?
6. I do understand the notation used in equation (8) on page 4. Are <, > meant to denote less than/greater than or something else?
7. Discussion of weight decay on page 5 seems tangential to main point of the paper. Could be reduced to a sentence or two.
8. I would like to see some experimental verification that the proposed method significantly reduces the dropout gradient variance (page 6), if the authors claim that tuning dropout probabilities is an area they succeed where others don't.
9. Experiments are unconvincing. First, only one hyperparameter is being optimized and random search/grid search are sufficient for this. Second, it is unclear how close the proposed method is to finding the optimal regularization parameter \lambda. All one can conclude is that it performs slightly better than grid search with a small number of runs. I would have preferred to see an extensive grid search done to find the best possible \lambda, then seen how well the proposed method does compared to this.
10. I would have liked to see a plot of how the value of lambda changes throughout optimization. If one can initialize lambda arbitrarily and have this method find the optimal lambda, that is more impressive than a method that works simply because of a fortunate initialization.
Typos:
1. Optimization -> optimize (bottom of page 2)
2. Should be a period after sentence starting "Several algorithms" on page 2.
3. In algorithm box on page 5, enable_projection is never used. Seems like warmup_time should also be an input to the algorithm.


Humans can understand and produce new utterances effortlessly, thanks to their systematic compositional skills. Once a person learns the meaning of a new verb "dax," he or she can immediately understand the meaning of "dax twice" or "sing and dax." In this paper, we introduce the SCAN domain, consisting of a set of simple compositional navigation commands paired with the corresponding action sequences. We then test the zero-shot generalization capabilities of a variety of recurrent neural networks (RNNs) trained on SCAN with sequence-to-sequence methods. We find that RNNs can generalize well when the differences between training and test commands are small, so that they can apply "mix-and-match" strategies to solve the task. However, when generalization requires systematic compositional skills (as in the "dax" example above), RNNs fail spectacularly. We conclude with a proof-of-concept experiment in neural machine translation, supporting the conjecture that lack of systematicity is an important factor explaining why neural networks need very large training sets.

This paper focuses on the zero-shot learning compositional capabilities of modern sequence-to-sequence RNNs.  Through a series of experiments and a newly defined dataset, it exposes the short-comings of current seq2seq RNN architectures.  The proposed dataset, called the SCAN dataset, is a selected subset of the CommonAI navigation tasks data set.  This subset is chosen such that each command sequence corresponds to exactly one target action sequence, making it possible to apply standard seq2seq methods.  Existing methods are then compared based on how accurately they can produce the target action sequence based on the command input sequence.
The introduction covers relevant literature and nicely describes the motivation for later experiments. Description of the model architecture is largely done in the appendix, this puts the focus of the paper on the experimental section. This choice seems to be appropriate, since standard methods are used. Figure 2 is sufficient to illustrate the model to readers familiar with the literature.
The experimental part establishes a baseline using standard seq2seq models on the new dataset, by exploring large variations of model architectures and a large part of the hyper-parameter space.   This papers experimentation sections sets a positive example by exploring a comparatively large space of standard model architectures on the problem it proposes. This search enables the authors to come to convincing conclusions regarding the shortcomings of current models. The paper explores in particular:
1.) Model generalization to unknown data similar to the training set.
2.) Model generalization to data-sequences longer than the training set.
3.) Generalization to composite commands, where  a part of the command is never observed in sequence in the training set.
4.) A recreation of a similar problem in the machine translation context.
These experiments show that modern sequence to sequence models do not solve the systematicity problem, while making clear by application to machine translation, why such a solution would be desirable. The SCAN data-set has the potential to become an interesting test-case for future research in this direction.
The experimental results shown in this paper are clearly compelling in exposing the weaknesses of current seq2seq RNN models.  However, where the paper falls a bit short is in the discussion / outlook in terms of suggestions of how one can go about tackling these shortcomings.


Published as a conference paper at ICLR 2018 LEARNING SPARSE NEURAL NETWORKS THROUGH L 0 REGULARIZATION
We propose a practical method for L 0 norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of L 0 regularization. However, since the L 0 norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected L 0 regularized objective is differentiable with respect to the distribution parameters. We further propose the hard concrete distribution for the gates, which is obtained by "stretching" a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer.

Learning sparse neural networks through L0 regularisation
Summary:
The authors introduce a gradient-based approach to minimise an objective function with an L0 sparse penalty. The problem is relaxed onto a continuous optimisation by changing an expectation over discrete variables (representing whether a variable is present or not) to an expectation over continuous variables, inspired by earlier work from Maddison et al (ICLR 2017) where a similar transformation was used to learn over discrete variable prediction tasks with neural networks. Here the application is to learn sparse feedforward networks in standard classification tasks, although the framework described is quite general and could be used to impose L0 sparsity to any objective function in principal. The method provides equivalent accuracy and sparsity to published state-of-the-art results on these datasets but it is argue that learning sparsity during the training process will lead to significant speed-ups - this is demonstrated by comparing to a theoretical benchmark (standard training with dropout) rather than through empirical testing against other implementations.
Pros:
The paper is well written and the derivation of the method is easy to follow with a good explanation of the underlying theory.
Optimisation under L0 regularisation is a difficult and generally important topic and certainly has advantages over other sparse inference objective functions that impose shrinkage on non-sparse parameters.
The work is put in context and related to some previous relaxation approaches to sparsity.
The method allows for sparsity to be learned during training rather than after training (as in standard dropout approaches) and this allows the algorithm to obtain significant per-iteration speed-ups, which improves through training.
Cons:
The method is applied to standard neural network architectures and performance in terms of accuracy and final achieved sparsity is comparable to the state-of-the-art methods. Therefore the main advance is in terms of learning speed to obtain this similar performance. However, the learning speed-up is presented against a theoretical FLOPs estimate per iteration for a similar network with dropout. It would be useful to know whether the number of iterations to achieve a particular performance is equivalent for all the different architectures considered, e.g. does the proposed sparse learning method converge at the same rate as the others? I felt a more thorough experimental section would have greatly improved the work, focussing on this learning speed aspect.
It was unclear how much tuning of the lambda hyper-parameter, which tunes the sparsity, would be required in a practical application since tuning this parameter would increase computation time. It might be useful to provide a full Bayesian treatment so that the optimal sparsity can be chosen through hyper-parameter learning.
Minor point: it wasn’t completely clear to me why the fact (3) is a variational approximation to a spike-and-slab is important (Appendix). I don’t see why the spike-and-slab is any more fundamental than the L0 norm prior in (2), it is just more convenient in Bayesian inference because it is an iid prior and potentially allows an informative prior over each parameter. In the context here this didn’t seem a particularly relevant addition to the paper.


Published as a conference paper at ICLR 2018 TRAINING AND INFERENCE WITH INTEGERS IN DEEP NEURAL NETWORKS
Researches on deep neural networks with discrete parameters and their deployment in embedded systems have been active and promising topics. Although previous works have successfully reduced precision in inference, transferring both training and inference processes to low-bitwidth integers has not been demonstrated simultaneously. In this work, we develop a new method termed as "WAGE" to discretize both training and inference, where weights (W), activations (A), gradients (G) and errors (E) among layers are shifted and linearly constrained to low-bitwidth integers. To perform pure discrete dataflow for fixed-point devices, we further replace batch normalization by a constant scaling layer and simplify other components that are arduous for integer implementation. Improved accuracies can be obtained on multiple datasets, which indicates that WAGE somehow acts as a type of regularization. Empirically, we demonstrate the potential to deploy training in hardware systems such as integer-based deep learning accelerators and neuromorphic chips with comparable accuracy and higher energy efficiency, which is crucial to future AI applications in variable scenarios with transfer and continual learning demands.

The authors describe a method called WAGE, which quantize all operands and operators in a neural network, specifically, the weights (W), activations (A), gradients (G), and errors (E) . The idea is using quantizers with clipping (denoted in the paper with Q(x,k)) and some additional operators like shift (denoted with shift(x)) and stochastic rounding. The main motivation of the authors in this work is to reduce the number of bits for representation in a network for all the WAGE operations and operands which influences the power consumption and silicon area in hardware implementations.
After introducing the idea and related work, the authors in Section 3 give details about how to perform the quantization. They introduce the additional operators needed for training in such network. Since quantization may loss some information, the authors need to quantize the signals in the network around the dynamic range in order not to "kill" the signal. The authors describe how to do that. Afterward, as in other techniques for quantization, they describe how to initialize the network values. Also, they argue that batch normalization in this network is replaced with the shift-quantize operations, and what is matter in this case is (1) the relative values (“orientations”) and not the absolute values and (2) small values in errors are negligible.
Afterward, the authors conduct experiments on MNIST, SVHN, CIFAR10, and ILSVRC12 datasets, where they show promising results compared to the errors provided by previous works. The WAGE parameters (i.e., the quantized no. of bits used) are 2-8-8-8, respectively. For understand more the WAGE, the authors compare on CIFAR10 the test error rate with vanilla CNN and show is small loss in using their network. The authors investigate mainly the bitwidth of errors and gradients.
In overall, this paper is an accept since it shows good performance on standard problems and invent some nice tricks to implement NN in hardware, for *both* training and inference. For inference only, other works has more to offer but this is a promising technique for learning. The things that are still missing in this work are some power reduction estimates as well as area reduction estimations. This will give the hardware community a clear vision of how such methods may be implemented both in data centers as well as on end portable devices.


Long Short-Term Memory (LSTM) units have the ability to memorise and use long-term dependencies between inputs to generate predictions on time series data. We introduce the concept of modifying the cell state (memory) of LSTMs using rotation matrices parametrised by a new set of trainable weights. This addition shows significant increases of performance on some of the tasks from the bAbI dataset.

The paper proposes to add a rotation operation in long short-term memory (LSTM) cells. It performs experiments on bAbI tasks and showed that the results are better than the simple baselines with original LSTM cells. There are a few problems with the paper.
Firstly, the title and abstract discuss "modifying memories", but the content is only about a rotation operation. Perhaps the title should be "Rotation Operation in Long Short-Term Memory"?
Secondly, the motivation of adding the rotation operation is not properly justified. What does it do that a usual LSTM cell could not learn? Does it reduce the excess representational power compared to the LSTM cell that could result in better models? Or does it increase its representational capacity so that some pattern is modeled in the new cell structure that was not possible before? This is not clear at all after reading the paper. Besides, the idea of using a rotation operation in recurrent networks has been explored before [3].
Finally, the task (bAbI) and baseline models (LSTM from a Keras tutorial) are too weak. There have been recent works that nearly solved the bAbI tasks to perfection (e.g., [1][2][4][5], and many others). The paper presented a solution that is weak compared to these recent results.
In a summary, the main idea of adding rotation to LSTM cells is not properly justified in the paper, and the results presented are quite weak for publication in ICLR 2018.
[1] Sainbayar Sukhbaatar, Jason Weston, Rob Fergus. End-to-end memory networks, NIPS 2015
[2] Caiming Xiong, Stephen Merity, Richard Socher. Dynamic Memory Networks for Visual and Textual Question Answering, ICML 2016
[3] Mikael Henaff, Arthur Szlam, Yann LeCun, Recurrent Orthogonal Networks and Long-Memory Tasks, ICML 2016
[4] Caglar Gulcehre, Sarath Chandar, Kyunghyun Cho, Yoshua Bengio, Dynamic Neural Turing Machine with Soft and Hard Addressing Schemes, ICLR 2017
[5] Mikael Henaff, Jason Weston, Arthur Szlam, Antoine Bordes, Yann LeCun, Tracking the World State with Recurrent Entity Networks, ICLR 2017


Published as a conference paper at ICLR 2018 DISTRIBUTED DISTRIBUTIONAL DETERMINISTIC POLICY GRADIENTS
This work adopts the very successful distributional perspective on reinforcement learning and adapts it to the continuous control setting. We combine this within a distributed framework for off-policy learning in order to develop what we call the Distributed Distributional Deep Deterministic Policy Gradient algorithm, D4PG. We also combine this technique with a number of additional, simple improvements such as the use of N -step returns and prioritized experience replay. Experimentally we examine the contribution of each of these individual components, and show how they interact, as well as their combined contributions. Our results show that across a wide variety of simple control tasks, difficult manipulation tasks, and a set of hard obstacle-based locomotion tasks the D4PG algorithm achieves state of the art performance.

A DeepRL algorithm is presented that represents distributions over Q values, as applied to DDPG,
and in conjunction with distributed evaluation across multiple actors, prioritized experience replay, and
N-step look-aheads. The algorithm is called Distributed Distributional Deep Deterministic Policy Gradient algorithm, D4PG.
SOTA results are generated for a number of challenging continuous domain learning problems,
as compared to benchmarks that include DDPG and PPO, in terms of wall-clock time, and also (most often) in terms
of sample efficiency.
pros/cons
+ the paper provides a thorough investigation of the distributional approach, as applied to difficult continuous
  action problems, and in conjunction with a set of other improvements (with ablation tests)
- the story is a bit mixed in terms of the benefits, as compared to the non-distributional approach, D3PG
- it is not clear which of the baselines are covered in detail in the cited paper:
  "Anonymous. Distributed prioritized experience replay. In submission, 2017.",
   i.e., should readers assume that D3PG already exists and is attributable to this other submission?
Overall, I believe that the community will find this to be interesting work.
Is a video of the results available?
It seems that the distributional model often does not make much of a difference,
as compared to D3PG non-prioritized.  However, sometimes it does make a big difference, i.e., 3D parkour; acrobot.
Do the examples where it yields the largest payoff share a particular characteristic?
The benefit of the distributional models is quite different between the 1-step and 5-step versions. Any ideas why?
Occasionally, D4PG with N=1 fails very badly, e.g., fish, manipulator (bring ball), swimmer.
Why would that be? Shouldn't it do at least as well as D3PG in general?
How many atoms are used for the categorical representation?
As many as [Bellemare et al.], i.e., 51 ?
How much "resolution" is necessary here in order to gain most of the benefits of the distributional representation?
As far as I understand, V_min and V_max are not the global values, but are specific to the current distribution.
Hence the need for the projection. Is that correct?
Would increasing the exploration noise result in a larger benefit for the distributional approach?
Figure 2: DDPG performs suprisingly poorly in most examples. Any comments on this,
or is DDPG best avoided in normal circumstances for continuous problems? :-)
Is the humanoid stand so easy because of large (or unlimited) torque limits?
The wall-clock times are for a cluster with K=32 cores for Figure 1?
"we utilize a network architecture as specified in Figure 1 which processes the terrain info in order to reduce its dimensionality"
Figure 1 provides no information about the reduced dimensionality of the terrain representation, unless I am somehow failing to see this.
"the full critic architecture is completed by attaching a critic head as defined in Section A"
I could find no further documenation in the paper with regard to the "head" or a separate critic for the "head".
It is not clear to me why multiple critics are needed.
Do you have an intuition as to why prioritized replay might be reducing performance in many cases?


UNSUPERVISED LEARNING OF GOAL SPACES FOR INTRINSICALLY MOTIVATED GOAL EXPLORATION
Intrinsically motivated goal exploration algorithms enable machines to discover repertoires of policies that produce a diversity of effects in complex environments. These exploration algorithms have been shown to allow real world robots to acquire skills such as tool use in high-dimensional continuous state and action spaces. However, they have so far assumed that self-generated goals are sampled in a specifically engineered feature space, limiting their autonomy. In this work, we propose to use deep representation learning algorithms to learn an adequate goal space. This is a developmental 2-stage approach: first, in a perceptual learning stage, deep learning algorithms use passive raw sensor observations of world changes to learn a corresponding latent space; then goal exploration happens in a second stage by sampling goals in this latent space. We present experiments where a simulated robot arm interacts with an object, and we show that exploration algorithms using such learned representations can match the performance obtained using engineered representations.

[Edit: After revisions, the authors have made a good-faith effort to improve the clarity and presentation of their paper: figures have been revised, key descriptions have been added, and (perhaps most critically) a couple of small sections outlining the contributions and significance of this work have been written. In light of these changes, I've updated my score.]
Summary:
The authors aim to overcome one of the central limitations of intrinsically motivated goal exploration algorithms by learning a representation without relying on a "designer" to manually specify the space of possible goals. This work is significant as it would allow one to learn a policy in complex environments even in the absence of a such a designer or even a clear notion of what would constitute a "good" distribution of goal states.
However, even after multiple reads, much of the remainder of the paper remains unclear. Many important details, including the metrics by which the authors evaluate performance of their work, can only be found in the appendix; this makes the paper very difficult to follow.
There are too many metrics and too few conclusions for this paper. The authors introduce a handful of metrics for evaluating the performance of their approach; I am unfamiliar with a couple of these metrics and there is not much exposition justifying their significance and inclusion in the paper. Furthermore, there are myriad plots showing the performance of the different algorithms, but very little explanation of the importance of the results. For instance, in the middle of page 9, it is noted that some of the techniques "yield almost as low performance as" the randomized baseline, yet no attempt is made to explain why this might be the case or what implications it has for the authors' approach. This problem pervades the paper: many metrics are introduced for how we might want to evaluate these techniques, yet there is no provided reason to prefer one over another (or even why we might want to prefer them over the classical techniques).
Other comments:
- There remain open questions about the quality of the MSE numbers; there are a number of instances in which the authors cite that the "Meta-Policy MSE is not a simple to interpret" (The remainder of this sentence is incomplete in the paper), yet little is done to further justify why it was used here, or why many of the deep representation techniques do not perform very well.
- The authors do not list how many observations they are given before the deep representations are learned. Why is this? Additionally, is it possible that not enough data was provided?
- The authors assert that 10 dimensions was chosen arbitrarily for the size of the latent space, but this seems like a hugely important choice of parameter. What would happen if a dimension of 2 were chosen? Would the performance of the deep representation models improve? Would their performance rival that of RGE-FI?
- The authors should motivate the algorithm on page 6 in words before simply inserting it into the body of the text. It would improve the clarity of the paper.
- The authors need to be clearer about their notation in a number of places. For instance, they use \gamma to represent the distribution of goals, yet it does not appear on page 7, in the experimental setup.
- It is never explicitly mentioned exactly how the deep representation learning methods will be used. It is pretty clear to those who are familiar with the techniques that the latent space is what will be used, but a few equations would be instructive (and would make the paper more self-contained).
In short, the paper has some interesting ideas, yet lacks a clear takeaway message. Instead, it contains a large number of metrics and computes them for a host of different possible variations of the proposed techniques, and does not include significant explanation for the results. Even given my lack of expertise in this subject, the paper has some clear flaws that need addressing.
Pros:
- A clear, well-written abstract and introduction
- While I am not experienced enough in the field to really comment on the originality, it does seem that the approach the authors have taken is original, and applies deep learning techniques to avoid having to custom-design a "feature space" for their particular family of problems.
Cons:
- The figure captions are all very "matter-of-fact" and, while they explain what each figure shows, provide no explanation of the results. The figure captions should be as self-contained as possible (I should be able to understand the figures and the implications of the results from the captions alone).
- There is not much significance in the current form of the paper, owing to the lack of clear message. While the overarching problem is potentially interesting, the authors seem to make very little effort to draw conclusions from their results. I.e. it is difficult for me to easily visualize all of the "moving parts" of this work: a figure showing the relationship bet
- Too many individual ideas are presented in the paper, hurting clarity. As a result, the paper feels scattered. The authors do not have a clear message that neatly ties the results together.


VOICELOOP: VOICE FITTING AND SYNTHESIS VIA A PHONOLOGICAL LOOP
We present a new neural text to speech (TTS) method that is able to transform text to speech in voices that are sampled in the wild. Unlike other systems, our solution is able to deal with unconstrained voice samples and without requiring aligned phonemes or linguistic features. The network architecture is simpler than those in the existing literature and is based on a novel shifting buffer working memory. The same buffer is used for estimating the attention, computing the output audio, and for updating the buffer itself. The input sentence is encoded using a context-free lookup table that contains one entry per character or phoneme. The speakers are similarly represented by a short vector that can also be fitted to new identities, even with only a few samples. Variability in the generated speech is achieved by priming the buffer prior to generating the audio. Experimental results on several datasets demonstrate convincing capabilities, making TTS accessible to a wider range of applications. In order to promote reproducibility, we release our source code and models 1 .

This paper present the application of the memory buffer concept to speech synthesis, and additionally learns a "speaker vector" that makes the system adaptive and work reasonably well on "in-the-wild" speech data. This is a relevant problem, and a novel solution, but synthesis is a wicked problem to evaluate, so I am not sure if ICLR is the best venue for this paper. I see two competing goals:
- If the focus is on showing that the presented approach outperforms other approaches under given conditions, a different task would be better (for example recognition, or some sort of trajectory reconstruction)
- If the focus is on showing that the system outperforms other synthesis systems, then a speech oriented venue might be best (and it is unfortunate that optimized hyper-parameters for the other systems are not available for a fair comparsion)
- If fair comparisons with the other appraoches cannot be made, my sense is that the multi-speaker (post-training fitting) option is really the most interesting and novel contribution here, which could be discussed in mroe detail
Still, the approach is creative and interesting and deserves to be presented. I have a few questions/ suggestions:
Introduction
- The link to Baddeley's "phonological loop" concept seems weak at best. There is nothing phonological about the features that this model stores and retrieves, and no evidence that the model behaves in a way consistent with "phonologcial" (or articulatory) assumptions or models - maybe best to avoid distracting the reader with this concept and strengthen the speaker adaptation aspect?
- The memory model is not an RNN, but it is a recurrently called structure (as the name "phonological loop" also implies) - so I would also not highlight this point much
- Why would the four properties of the proposed method (mid of p. 2, end of introduction: memory buffer, shared memory, shallow fully connected networks, and simple reader mechanism) lead to better robustness and improve performance on noisy and limited training data? Maybe the proposed approach works better for any speech synthesis task? Why specifically for "in-the-wild" data? The results in Table 2 show that the proposed system outperforms other systems on Blizzard 2013, but not Blizzard 2011 - does this support the previous argument?
- Why not also evaluate MCD scores? This should be a quick and automatic way to diagnose what the system is doing? Or is this not meaningful with the noisy training data?
Previous work
- Please introduce abbreviations the first time they are used ("CBHG" for example)
- There is other work on using "in-the-wild" speech as well: Pallavi Baljekar and Alan W Black. Utterance Selection Techniques for TTS Systems using Found Speech, SSW 2016, Sunnyvale, USA Sept 2016
The architecture
- Please explain the "GMM" (Gaussian Mixture Model?) attention mechanism in a bit more detail, how does back-propagation work in this case?
- Why was this approach chosen? Does it promise to be robust or good for low data situations specifically?
- The fonts in Figure 2 are very small, please make them bigger, and the Figure may not print well in b/w. Why does the mean of the absolute weights go up for high buffer positions? Is there some "leaking" from even longer contexts?
- I don't understand "However, human speech is not deterministic and one cannot expect [...] truth". You are saying that the model cannot be excepted to reproduce the input exactly? Or does this apply only to the temporal distribution of the sequence (but not the spectral characteristics)? The previous sentence implies that it does. And how does teacher-forcing help in this case?
- what type of speed is "x5"? Five times slower or faster than real-time?
Experiments
- Table 2: maybe mention how these results were computed, i.e. which systems use optimized hyper parameters, and which don't? How do these results support the interpretation of hte results in the introruction re in-the-wild data and found data?
- I am not sure how to read Figure 4. Maybe it would be easier to plot the different phone sequences against each other and show how the timings are off, i.e. plot the time of the center of panel one vs the time of the center of panel 2 for the corresponding phone, and show how this is different from a straight line. Or maybe plot phones as rectangles that get deformed from square shape as durations get learned?
- Figure 5: maybe provide spectrograms and add pitch contours to better show the effect of the dfifferent intonations?
- Figure 4 uses a lot of space, could be reduced, if needed
Discussion
- I think the first claim is a bit to broad - nowhere is it shown that the method is inherently more robust to clapping and laughs, and variable prosody. The authors will know the relevant data-sets better than I do, maybe they can simply extend the discussion to show that this is what happens.
- Efficiency: I think Wavenet has also gotten much faster and runs in less than real-time now - can you expand that discussion a bit, or maybe give estimates in times of FLOPS required, rather than anecdotal evidence for systems that may or may not be comparable?
Conclusion
- Now the advantage of the proposed model is with the number of parameters, rather than the computation required. Can you clarify? Are your models smaller than competing models?


SCALABLE PRIVATE LEARNING WITH PATE
The rapid adoption of machine learning has increased concerns about the privacy implications of machine learning models trained on sensitive data, such as medical records or other personal information. To address those concerns, one promising approach is Private Aggregation of Teacher Ensembles, or PATE, which transfers to a "student" model the knowledge of an ensemble of "teacher" models, with intuitive privacy provided by training teachers on disjoint data and strong privacy guaranteed by noisy aggregation of teachers' answers. However, PATE has so far been evaluated only on simple classification tasks like MNIST, leaving unclear its utility when applied to larger-scale learning tasks and real-world datasets. In this work, we show how PATE can scale to learning tasks with large numbers of output classes and uncurated, imbalanced training data with errors. For this, we introduce new noisy aggregation mechanisms for teacher ensembles that are more selective and add less noise, and prove their tighter differential-privacy guarantees. Our new mechanisms build on two insights: the chance of teacher consensus is increased by using more concentrated noise and, lacking consensus, no answer need be given to a student. The consensus answers used are more likely to be correct, offer better intuitive privacy, and incur lower-differential privacy cost. Our evaluation shows our mechanisms improve on the original PATE on all measures, and scale to larger tasks with both high utility and very strong privacy (ε < 1.0).

This paper considers the problem of private learning and uses the PATE framework to achieve differential privacy. The dataset is partitioned and multiple learning algorithms produce so-called teacher classifiers. The labels produced by the teachers are aggregated in a differentially private manner and the aggregated labels are then used to train a student classifier, which forms the final output. The novelty of this work is a refined aggregation process, which is improved in three ways:
a) Gaussian instead of Laplace noise is used to achieve differential privacy.
b) Queries to the aggregator are "filtered" so that the limited privacy budget is only expended on queries where the teachers are confident and the student is uncertain or wrong.
c) A data-dependent privacy analysis is used to attain sharper bounds on the privacy loss with each query.
I think this is a nice modular framework form private learning, with significant refinements relative to previous work that make the algorithm more practical. On this basis, I think the paper should be accepted. However, I think some clarification is needed with regard to item c above:
Theorem 2 gives a data-dependent privacy guarantee. That is, if there is one label backed by a clear majority of teachers, then the privacy loss (as measured by Renyi divergence) is low. This data-dependent privacy guarantee is likely to be much tighter than the data-independent guarantee.
However, since the privacy guarantee now depends on the data, it is itself sensitive information. How is this issue resolved? If the final privacy guarantee is data-dependent, then this is very different to the way differential privacy is usually applied. This would resemble the "privacy odometer" setting of Rogers-Roth-Ullman-Vadhan [ https://arxiv.org/abs/1605.08294 ].
Another way to resolve this would be to have an output-dependent privacy guarantee. That is, the privacy guarantee would depend only on public information, rather than the private data. The widely-used "sparse vector" technique [ http://www.cis.upenn.edu/~aaroth/Papers/privacybook.pdf#page=59 ] does this.
In any case, this is an important issue that needs to be clarified, as it is not clear to me how this is resolved.
The algorithm in this work is similar to the so-called median mechanism [ https://www.cis.upenn.edu/~aaroth/Papers/onlineprivacy.pdf ] and private multiplicative weights [ http://mrtz.org/papers/HR10mult.pdf ]. These works also involve a "student" being trained using sensitive data with queries being answered in a differentially private manner. And, in particular, these works also filter out uninformative queries using the sparse vector technique. It would be helpful to add a comparison.


While Bayesian optimization (BO) has achieved great success in optimizing expensive-to-evaluate black-box functions, especially tuning hyperparameters of neural networks, methods such as random search (Li et al., 2016) and multifidelity BO (e.g. Klein et al. (2017)) that exploit cheap approximations, e.g. training on a smaller training data or with fewer iterations, can outperform standard BO approaches that use only full-fidelity observations. In this paper, we propose a novel Bayesian optimization algorithm, the continuous-fidelity knowledge gradient (cfKG) method, that can be used when fidelity is controlled by one or more continuous settings such as training data size and the number of training iterations. cfKG characterizes the value of the information gained by sampling a point at a given fidelity, choosing to sample at the point and fidelity with the largest value per unit cost. Furthermore, cfKG can be generalized, following Wu et al.  (2017), to settings where derivatives are available in the optimization process, e.g. large-scale kernel learning, and where more than one point can be evaluated simultaneously. Numerical experiments show that cfKG outperforms state-of-art algorithms when optimizing synthetic functions, tuning convolutional neural networks (CNNs) on CIFAR-10 and SVHN, and in large-scale kernel learning.

Many black-box optimization problems are "multi-fidelity", in which it
is possible to acquire data with different levels of cost and
associated uncertainty.  The training of machine learning models is a
common example, in which more data and/or more training may lead to
more precise measurements of the quality of a hyperparameter
configuration.  This has previously been referred to as a special case
of "multi-task" Bayesian optimization, in which the tasks can be
constructed to reflect different fidelities.  The present paper
examines this construction with three twists: using the knowledge
gradient acquisition function, using batched function evaluations, and
incorporating derivative observations.  Broadly speaking, the idea is
to allow fidelity to be represented as a point in a hypercube and then
include this hypercube as a covariate in the Gaussian process.  The
knowledge gradient acquisition function then becomes "knowledge
gradient per unit cost" the KG equivalent to the "expected improvement
per unit cost" discussed in Snoek et al (2012), although that paper
did not consider treating fidelity separately.
I don't understand the claim that this is "the first multi-fidelity
algorithm that can leverage gradients".  Can't any Gaussian process
model use gradient observations trivially, as discussed in the
Rasmussen and Williams book?  Why can't any EI or entropy search
method also use gradient observations?  This doesn't usually come up
in hyperparameter optimization, but it seems like a grandiose claim.
Similarly, although I don't know of a paper that explicitly does "A +
B" for multi-fidelity BO and parallel BO, it is an incremental
contribution to combine them, not least because no other parallel BO
methods get evaluated as baselines.
Figure 1 does not make sense to me.  How can the batched algorithm
outperform the sequential algorithm on total cost?  The sequential
cfKG algorithm should always be able to make better decisions with its
remaining budget than 8-cfKG.  Is the answer that "cost" here means
"wall-clock time when parallelism is available"?  If that's the case,
then it is necessary to include plots of parallelized EI, entropy
search, and KG.  The same is true for Figure 2; other parallel BO
algorithms need to appear.


CASCADE ADVERSARIAL MACHINE LEARNING REG- ULARIZED WITH A UNIFIED EMBEDDING
Injecting adversarial examples during training, known as adversarial training, can improve robustness against one-step attacks, but not for unknown iterative attacks. To address this challenge, we first show iteratively generated adversarial images easily transfer between networks trained with the same strategy. Inspired by this observation, we propose cascade adversarial training, which transfers the knowledge of the end results of adversarial training. We train a network from scratch by injecting iteratively generated adversarial images crafted from already defended networks in addition to one-step adversarial images from the network being trained. We also propose to utilize embedding space for both classification and low-level (pixel-level) similarity learning to ignore unknown pixel level perturbation. During training, we inject adversarial images without replacing their corresponding clean images and penalize the distance between the two embeddings (clean and adversarial). Experimental results show that cascade adversarial training together with our proposed low-level similarity learning efficiently enhances the robustness against iterative attacks, but at the expense of decreased robustness against one-step attacks. We show that combining those two techniques can also improve robustness under the worst case black box attack scenario.

The paper presents a novel adversarial training setup, based on distance based loss of the feature embedding.
+ novel loss
+ good experimental evaluation
+ better performance
- way too long
- structure could be improved
- pivot loss seems hacky
The distance based loss is novel, and significantly different from prior work. It seems to perform well in practice as shown in the experimental section.
The experimental section is extensive, and offers new insights into both the presented algorithm and baselines. Judging the content of the paper alone, it should be accepted.
However, the exposition needs significant improvements to warrant acceptance. First, the paper is way too long and unfocused. The recommended length is 8 pages + 1 page for citations. This paper is 12+1 pages long, plus a 5 page supplement. I'd highly recommend the authors to cut a third of their text, it would help focus the paper on the actual message: pushing their new algorithm. Try to remove any sentence or word that doesn't serve a purpose (help sell the algorithm).
The structure of the paper could also be improved. For example the cascade adversarial training is buried deep inside the experimental section. Considering that it is part of the title, I would have expected a proper exposition of the idea in the technical section (before any results are presented). While condensing the paper, consider presenting all technical material before evaluation.
Finally, the pivot "loss" seems a bit hacky. First, the pivot objective and bidirectional loss are exactly the same thing. While the bidirectional loss is a proper loss and optimized as such (by optimizing both E^adv and E), the pivot objective is no loss function, as it does not correspond to any function any optimization algorithm could minimize. I'd recommend the just remove the pivot objective, or at least not call it a loss.
In summary, the results and presented method are good, and eventually deserve publication. However the exposition needs to significantly improve for the paper to be ready for ICLR.


We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. We propose to use more efficient numerical integration technique to obtain better estimates of the integrals compared to the state-of-the-art methods. Our approach allows the use of information about the integrand to enhance approximation and facilitates fast computations. We derive the convergence behavior and conduct an extensive empirical study that supports our hypothesis.

The authors offer a novel version of the random feature map approach to approximately solving large-scale kernel problems: each feature map evaluates the "fourier feature" corresponding to the kernel at a set of randomly sampled quadrature points. This gives an unbiased kernel estimator; they prove a bound its variance and provide experiment evidence that for Gaussian and arc-cos kernels, their suggested qaudrature rule outperforms previous random feature maps in terms of kernel approximation error and in terms of downstream classification and regression tasks. The idea is straightforward, the analysis seems correct, and the experiments suggest the method has superior accuracy compared to prior RFMs for shift-invariant kernels. The work is original, but I would say incremental, and the relevant literature is cited.
The method seems to give significantly lower kernel approximation errors, but the significance of the performance difference in downstream ML tasks is unclear --- the confidence intervals of the different methods overlap sufficiently to make it questionable whether the relative complexity of this method is worth the effort. Since good performance on downstream tasks is the crucial feature that we want RFMs to have, it is not clear that this method represents a true improvement over the state-of-the-art. The exposition of the quadrature method is difficult to follow, and the connection between the quadrature rules and the random feature map is never explicitly stated: e.g. equation 6 says how the kernel function is approximated as an integral, but does not give the feature map that an ML practitioner should use to get that approximate integral.
It would have been a good idea to include figures showing the time-accuracy tradeoff of the various methods, which is more important in large-scale ML applications than the kernel approximation error. It is not clear that the method is *not* more expensive in practice than previous methods (Table 1 gives superior asymptotic runtimes, but I would like to see actual run times, as evaluating the feature maps sound relatively complicated compared to other RFMs). On a related note, I would also like to have seen this method applied to kernels where the probability density in the Bochner integral was not the Gaussian density (e.g., the Laplacian kernel): the authors suggested that their method works there as well when one uses a Gaussian approximation of the density (which is not clear to me),  --- and it may be the case that sampling from their quadrature distribution is faster than sampling from the original non-Gaussian density.


We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally propagating information between the subgraphs. To efficiently partition graphs, we experiment with spectral partitioning and also propose a modified multi-seed flood fill for fast processing of large scale graphs. We extensively test our model on a variety of semi-supervised node classification tasks. Experimental results indicate that GPNNs are either superior or comparable to state-of-the-art methods on a wide variety of datasets for graph-based semi-supervised classification. We also show that GPNNs can achieve similar performance as standard GNNs with fewer propagation steps.

The authors investigate different message passing schedules for GNN learning.  Their proposed approach is to partition the graph into disjoint subregions, pass many messages on the sub regions and pass fewer messages between regions (an approach that is already considered in related literature, e.g., the BP literature), with the goal of minimizing the number of messages that need to be passed to convey information between all pairs of nodes in the network.  Experimentally, the proposed approach seems to perform comparably to existing methods (or slightly worse on average in some settings).  The paper is well-written and easy to read.  My primary concern is with novelty.  Many similar ideas have been floating around in a variety of different message-passing communities.  With no theoretical reason to prefer the proposed approach, it seems like it may be of limited interest to the community if speed is its only benefit (see detailed comments below).
Specific comments:
1)  "When information from any one node has reached all other nodes in the graph for the first time, this problem is considered as solved."
Perhaps it is my misunderstanding of the way in which GNNs work, but isn't the objective actually to reach a set of fixed point equations.  If so, then simply propagating information from one side of the graph may not be sufficient.
2)  The experimental results in Section 4.4 are almost impossible to interpret.  Perhaps it is better to plot number of edges updated versus accuracy?  This at least would put them on equal footing.   In addition, the experiments that use randomness should be repeated and plotted on average (just in case you happened to pick a bad schedule).
3)  More generally, why not consider random schedules (i.e., just pick a random edge, update, repeat) or random partitions?  I'm not certain that a fixed set will perform best independent of the types of updates being considered, and random schedules, like the fully synchronous case for an important baseline (especially if update speed is all you care about).
Typos:
-pg. 6, "Thm. 2" -> "Table 2"


Several state of the art convolutional networks rely on inter-connecting different layers to ease the flow of information and gradient between their input and output layers. These techniques have enabled practitioners to successfully train deep convolutional networks with hundreds of layers. Particularly, a novel way of interconnecting layers was introduced as the Dense Convolutional Network (DenseNet) and has achieved state of the art performance on relevant image recognition tasks. Despite their notable empirical success, their theoretical understanding is still limited. In this work, we address this problem by analyzing the effect of layer interconnection on the overall expressive power of a convolutional network. In particular, the connections used in DenseNet are compared with other types of inter-layer connectivity. We carry out a tensor analysis on the expressive power inter-connections on convolutional arithmetic circuits (ConvACs) and relate our results to standard convolutional networks. The analysis leads to performance bounds and practical guidelines for design of ConvACs. The generalization of these results are discussed for other kinds of convolutional networks via generalized tensor decompositions.

SUMMARY
Traditional convolutional neural networks consist of a sequence of information processing layers. However, one can relax this sequential design constraint so that higher layers receive inputs from one, some, or all preceding layers. This modification allows information to travel more freely throughout the network and has been shown to improve performance, e.g., in image recognition tasks. However, it is not clear whether this change in architecture truly increases representational capacity or it merely facilitates network training.
In this paper, the authors present a theoretical analysis of the gain in representational capacity induced by additional inter-layer connections. The authors restrict their analysis to convolutional arithmetic circuits (ConvACs), a class of networks whose representational capacity has been studied previously. An important property of ConvACs is that the network mapping can be recast as a homogeneous polynomial over the input, with coefficients stored in a "grid tensor" $\mathcal{A}^y$. The grid tensor itself is a function of the hidden weight vectors $\mathbf{a}^{z,i}$. The authors first extend ConvACs to accommodate "dense" inter-layer connections and describe how adding dense connections affects the grid tensor. This analysis gives a potentially useful perspective for understanding the mappings that densely connected ConvACs compute.
The authors' main results (Theorems 5.1-5.3) analyze the "dense gain" of a densely connected ConvAC. This quantity roughly captures how much wider a standard ConvAC would need to be in order to represent the network mapping of a generic densely connected ConvAC. This is in a way a measure of the added representational power obtained from dense connections. The authors give upper bounds on this quantity, but also produce a case in which the upper bound is achieved. Importantly, the upper bounds are inversely proportional to a parameter $\lambda \leq 1$ controlling the rate at which hidden layer widths decay with increasing depth. The implication is that indeed densely connected ConvACs can have greater representational capacity, however the gain is limited to the case where hidden layers shrink exponentially with increasing depth.
These results are partly unsurprising, since densely connected ConvACs contain more trainable parameters than standard ConvACs. In Proposition 3, the authors give some criteria for evaluating when it is nonetheless worthwhile to add dense connections to a ConvAC.
COMMENTS
(1.) The authors address an interesting and important problem: explaining the empirical success of densely connected CNNs such as ResNets & DenseNets, relative to standard CNNs. The tensor algebra machinery built around ConvACs is impressive and seems to generate sound insights. However, I feel the current presentation fails to provide adequate intuition and interpretation of the results. Moreover, there is no overarching narrative linking the formal results together. This makes it difficult for the reader to grasp the main ideas and significance of the work without diving into all the details. For example:
- In Proposition 1, the authors comment that including a dense connection increases the rank of the grid tensor for a shallow densely connected convAC. However, the significance of grid tensor rank is not discussed.
- In Proposition 2, the authors do not explain why it is important that the added term $g(\mathbf{X})$ contains only polynomial terms of strictly smaller degree. It is not clear how Propositions 1 & 2 relate to the main Theorems 5.1-5.3. Is the characterization of the grid tensor in Proposition 1 used to obtain the bounds in the later Theorems?
- In Section 5, the authors introduce a parameter $\lambda \leq 1$ controlling how the widths of the hidden layers decay with increasing depth. This parameter seems central to the following bounds on dense gain, yet the authors do not motivate it, and there is no discussion of decaying hidden layer widths in previous sections.
- The practical significance of Proposition 3 is not sufficiently well explained. First, it is not clear how to use this result if all we have is an upper bound for $G_w$, as given by Theorems 5.1-5.2. It seems we would need a lower bound to be able to conclude that the ratio $\Delta P_{stand}/ \Delta P_{dense}$ is large. Second, it would be helpful if the authors commented on the implication for the special case $k=1$ and $r \leq (1/1+\lambda) \sqrt{M}$, where the dense gain is known.
(2.) Moreover, because the authors choose not to sketch the main proof ideas, it is difficult to identify the key novel insights, and how the special structure of densely connected ConvACs factors into the analysis. After studying the proofs in some detail, I have some specific concerns outlined below, which diminish the significance of the results and raise some doubts about soundness.
- In Theorem 5.1, the authors upper bound the dense gain by showing that arbitrary $(L, r, \lambda, k)$ dense ConvACs can be represented as standard $(L, r^\prime, \lambda, 0)$ ConvACs of sufficient width $r^\prime \geq G_w r$. The mechanism of the proof is to relate the grid tensor ranks of dense and standard ConvACs. However, a worst case bound on the grid tensor rank of a dense ConvAC is used, which does not seem to rely on the formulation of dense ConvACs. Thus, this result does not tell us anything in particular about dense ConvACs, but rather is a general result relating the expressive capacity of arbitrary depth-$L$ ConvACs and $(L, r^\prime, \lambda, 0)$ ConvACs with decaying widths.
- Central to Theorem 5.2 is the observation that a densely connected ConvAC can be viewed as a standard ConvAC, only with "virtually enlarged" hidden layers (of width $\tilde{r}_\ell = (1 + 1/\lambda)r_\ell$ for $k=1$, using the notation of the paper), and blocks of weights fixed to represent the identity mapping. This is a relatively simple idea, and one that seems to hold for general architectures. Thus, I believe Theorem 5.2 can be shown more simply and in greater generality, and without use of the tensor algebra machinery.
- There is some intuitive inconsistency in Theorem 5.3 which I would like some help resolving. We have seen that dense ConvACs can be viewed as standard ConvACs with larger hidden layers and some weights fixed. Effectively, the proof of Theorem 5.3 argues for a regime on $r, \lambda, M$ where this induced ConvAC uses its full representational capacity. This is surprising to me however, as I would have guessed that having some weights fixed makes this impossible. It would be very helpful if the authors could weigh in on this confusion. Perhaps there is an issue with the application of Lemmas 2 & 3 in the proof of Theorem 5.3. In Lemmas 2 & 3, we assume the tensors $\mathcal{A}$ and $\mathcal{B}$ are random. These Lemmas are applied in the proof of Theorem 5.3 to tensors $\phi^{\alpha, j, \gamma}$ appearing in the construction of the dense ConvAC grid tensor. However, the $\phi^{\alpha, j, \gamma}$ tensors do not seem completely random, as there are blocks of fixed weights. Can the authors please clarify how the randomness assumption is satisfied?
(3.) Lastly, I am concerned that the authors do not at least sketch how to generalize these results to architectures of more practical interest. As the authors point out, there is previous work generalizing theoretical results for ConvACs to convolutional rectifier networks. The authors should discuss whether a similar strategy might apply in this case.


We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with up to 144 layers, and show that bipolar activation functions help learning in this setting. On the Penn Treebank and Text8 language modeling tasks we obtain competitive results, improving on the best reported results for non-gated networks. In experiments with convolutional neural networks without batch normalization, we find that bipolar activations produce a faster drop in training error, and results in a lower test error on the CIFAR-10 classification task.

This paper proposes a self-normalizing bipolar extension for the ReLU activation family. For every neuron out of two, authors propose to preserve the negative inputs. Such activation function allows to shift the mean of i.i.d. variables to zeros in the case of ReLU or to a given saturation value in the case of ELU.
Combined with variance preserving initialization scheme, authors empirically observe that the bipolar ReLU allows to better preserve the mean and variance of the activations through training compared to regular ReLU for a deep stacked RNN.
Authors evaluate their bipolar activation on PTB and Text8 using a deep stacked RNN.  They show that bipolar activations allow to train deeper RNN (up to some limit) and leads to better generalization performances compared to the ReLU /ELU activation functions. They also show that they can train deep residual network architecture on CIFAR without the use of BN.
Question:
- Which layer mean and variance are reported in Figure 2? What is the difference between the left and right plots?
- In Table 1, we observe that ReLU-RNN (and BELU-RNN for very deep stacked RNN) leads to worst validation performances. It would be nice to report the training loss to see if this is an optimization or a generalization problem.
- How does bipolar activation compare to model train with BN on CIFAR10?
- Did you try bipolar activation function for gated recurrent neural networks for LSTM or GRU?
- As stated in the text, BELU-RNN outperforms BN-LSTM for PTB. However, BN-LSTM outperforms BELU-RNN on Text8. Do you know why the trend is not consistent across datasets?
-Clarity/Quality
The paper is well written and pleasant to read
- Originality:
Self-normalizing function have been explored also in scaled ELU, however the application of self-normalizing function to RNN seems novel.
- Significance:
Activation function is still a very active research topic and self-normalizing function could potentially be impactful for RNN given that the normalization approaches (batch norm, layer norm) add a significant computational cost. In this paper, bipolar activations are used to train very deep stacked RNN. However, the stacked RNN with bipolar activation are not competitive regarding to other recurrent architectures. It is not clear what are the advantage of deep stacked RNN in that context.


We propose the set autoencoder, a model for unsupervised representation learning for sets of elements. It is closely related to sequence-to-sequence models, which learn fixed-sized latent representations for sequences, and have been applied to a number of challenging supervised sequence tasks such as machine translation, as well as unsupervised representation learning for sequences. In contrast to sequences, sets are permutation invariant. The proposed set autoencoder considers this fact, both with respect to the input as well as the output of the model. On the input side, we adapt a recently-introduced recurrent neural architecture using a content-based attention mechanism. On the output side, we use a stable marriage algorithm to align predictions to labels in the learning phase. We train the model on synthetic data sets of point clouds and show that the learned representations change smoothly with translations in the inputs, preserve distances in the inputs, and that the set size is represented directly. We apply the model to supervised tasks on the point clouds using the fixed-size latent representation. For a number of difficult classification problems, the results are better than those of a model that does not consider the permutation invariance. Especially for small training sets, the set-aware model benefits from unsupervised pretraining.

Summary
This paper proposes an autoencoder for sets. An input set is encoded into a
fixed-length representation using an attention mechanism (previously proposed by
[1]). The decoder generates the output sequentially and the generated sequence
is matched to the best-matching ordering of the target output set.
Experiments are done on synthetic datasets to demonstrate properties of the
learned representation.
Pros
- Experiments show that the autoencoder helps improve classification accuracy
  for small training set sizes on the shape classification task.
- The analysis of how the decoder generates data is insightful.
Cons
- The experiments are on toy datasets only. Given the availability of point
  cloud data sets, for example, KITTI which has a widely used benchmark for
point cloud based object detection, it would make the paper stronger if this
model was benchmarked against published baselines.
- The autoencoder does not seem to help much on the regression tasks where even
  for the smaller training set size setting, directly using the encoder to solve
the task often works best. Even finetuning is unable to recover from the
pretrained weights. Therefore, it seems that the decoder (which is the novel
aspect of this work) is perhaps not working well, or is not well suited to the
regression tasks being considered.
- The classification task, for which the learned representations work well
  empirically, seems to be geared towards representing object shape. It doesn't
really require remembering each point. On the other hand, the regression tasks
that could require remembering the points don't seem to be benefit much from the
autoencoder pretraining. This suggests that while the model is able to represent
overall shape, it has a hard time remembering individual elements of the set.
This seems like a drawback, since a general "set auto-encoder" should be able
to perform a wide variety of tasks on the input set which could require remembering
the set's elements.
Quality
This paper describes the proposed model quite well and provides encouraging
preliminary results.
Clarity
The paper is easy to understand.
Originality
The novelty in the model is using a matching algorithm to find the best ordering
of the target output set to match with the sequentially generated decoder
output. However, the paper makes a choice of one ranking based matching scheme
and does not compare to other alternatives.
Significance
This paper proposes a way of learning representations of sets which will be of
broad interest across the machine learning community. These models are likely to
become more relevant with increasing prevelance of point cloud data.
References
[1] Oriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order matters: Sequence to
sequence for sets. arXiv preprint arXiv:1511.06391.


In this paper, we propose a novel approach to interpret a well-trained classification model through systematically investigating effects of its hidden units on prediction making. We search for the core hidden units responsible for predicting inputs as the class of interest under the generative Bayesian inference framework. We model such a process of unit selection as an Indian Buffet Process, and derive a simplified objective function via the MAP asymptotic technique. The induced binary optimization problem is efficiently solved with a continuous relaxation method by attaching a Switch Gate layer to the hidden layers of interest. The resulted interpreter model is thus end-to-end optimized via standard gradient back-propagation. Experiments are conducted with two popular deep convolutional classifiers, respectively well-trained on the MNIST dataset and the CI-FAR10 dataset. The results demonstrate that the proposed interpreter successfully finds the core hidden units most responsible for prediction making. The modified model, only with the selected units activated, can hold correct predictions at a high rate. Besides, this interpreter model is also able to extract the most informative pixels in the images by connecting a Switch Gate layer to the input layer.

Pros
- The paper proposes a novel formulation of the problem of finding hidden units
  that are crucial in making a neural network come up with a certain output.
- The method seems to be work well in terms of isolating a few hidden units that
  need to be kept while preserving classification accuracy.
Cons
- Sections 3.1 and 3.2 are hard to understand. There seem to be inconsistencies
  in the notation. For example,
(1) It would help to clarify whether y^b_n is the prediction score or its
transformation into [0, 1]. The usage is inconsistent.
(2) It is not clear how "y^b_n can be expressed as \sum_{k=1}^K z_{nk}f_k(x_n)"
in general. This is only true for the penultimate layer, and when y^b_n denotes
the input to the output non-linearity. However, this analysis seems to be
applied for any hidden layer and y^b_n is the output of the non-linearity unit
("The new prediction scores are transformed into a scalar ranging from 0 to 1,
denoted as y^b_n.")
(3) Section 3.1 denotes the DNN classifier as F(.), but section 3.2 denotes the
same classifier as f(.).
(4) Why is r_n called the "center" ? I could not understand in what sense is
this the center, and of what ? It seems that the max value has been subtracted
from all the logits into a softmax (which is a fairly standard operation).
- The analysis seems to be about finding neurons that contribute evidence for
  a particular class. This does not address the issue of understanding why the
network makes a certain prediction for a particular input. Therefore this
approach will be of limited use.
- The paper should include more analysis of how this method helps interpret the
  actions of the neural net, once the core units have been identified.
Currently, the focus seems to be on demonstrating that the classifier
performance is maintained as a significant fraction of hidden units are masked.
However, there is not enough analysis on showing whether and how the identified
hidden units help "interpret" the model.
Quality
The idea explored in the paper is interesting and the experiments are described
in enough detail. However, the writing still needs to be polished.
Clarity
The problem formulation and objective function (Section 3.1) was hard to follow.
Originality
This approach to finding important hidden units is novel.
Significance
The paper addresses an important problem of trying to have more interpretable
neural networks. However, it only identifies hidden units that are important for
a class, not what are important for any particular input.  Moreover, the main
thesis of the paper is to describe a method that helps interpret neural network
classifiers. However, the experiments only focus on identifying important hidden
units and fall short of actually providing an interpretation using these hidden
units.


Neural network-based classifiers parallel or exceed human-level accuracy on many common tasks and are used in practical systems. Yet, neural networks are susceptible to adversarial examples, carefully perturbed inputs that cause networks to misbehave in arbitrarily chosen ways. When generated with standard methods, these examples do not consistently fool a classifier in the physical world due to a combination of viewpoint shifts, camera noise, and other natural transformations. Adversarial examples generated using standard techniques require complete control over direct input to the classifier, which is impossible in many real-world systems. We introduce the first method for constructing real-world 3D objects that consistently fool a neural network across a wide distribution of angles and viewpoints. We present a general-purpose algorithm for generating adversarial examples that are robust across any chosen distribution of transformations. We demonstrate its application in two dimensions, producing adversarial images that are robust to noise, distortion, and affine transformation. Finally, we apply the algorithm to produce arbitrary physical 3D-printed adversarial objects, demonstrating that our approach works end-to-end in the real world. Our results show that adversarial examples are a practical concern for real-world systems.

The authors present a method to enable robust generation of adversarial visual
inputs for image classification.
They develop on the theme that 'real-world' transformations typically provide a
countermeasure against adversarial attacks in the visual domain, to show that
contextualising the adversarial exemplar generation by those very
transformations can still enable effective adversarial example generation.
They adapt an existing method for deriving adversarial examples to act under a
projection space (effectively a latent-variable model) which is defined through
a transformations distribution.
They demonstrate the effectiveness of their approach in the 2D and 3D
(simulated and real) domains.
The paper is clear to follow and the objective employed appears to be sound. I
like the idea of using 3D generation, and particularly, 3D printing, as a means
of generating adversarial examples -- there is definite novelty in that
particular exploration for adversarial examples.
I did however have some concerns:
1. What precisely is the distribution of transformations used for each
   experiment? Is it a PCFG? Are the different components quantised such that
   they are discrete rvs, or are there still continuous rvs? (For example, is
   lighting discretised to particular locations or taken to be (say) a 3D
   Gaussian?) And on a related note, how were the number of sampled
   transformations chosen?
   Knowing the distribution (and the extent of it's support) can help situate
   the effectiveness of the number of samples taken to derive the adversarial
   input.
2. While choosing the distance metric in transformed space, LAB is used, but
   for the experimental results, l_2 is measured in RGB space -- showing the
   RGB distance is perhaps not all that useful given it's not actually being
   used in the objective. I would perhaps suggest showing LAB, maybe in
   addition to RGB if required.
3. Quantitative analysis: I would suggest reporting confidence intervals;
   perhaps just the 1st standard deviation over the accuracies for the true and
   'adversarial' labels -- the min and max don't help too much in understanding
   what effect the monte-carlo approximation of the objective has on things.
   Moreover, the min and max are only reported for the 2D and rendered 3D
   experiments -- it's missing for the 3D printing experiment.
4. Experiment power: While the experimental setup seems well thought out and
   structured, the sample size (i.e, the number of entities considered) seems a
   bit too small to draw any real conclusions from. There are 5 exemplar
   objects for the 3D rendering experiment and only 2 for the 3D printing one.
   While I understand that 3D printing is perhaps not all that scalable to be
   able to rattle off many models, the 3D rendering experiment surely can be
   extended to include more models? Were the turtle and baseball models chosen
   randomly, or chosen for some particular reason? Similar questions for the 5
   models in the 3D rendering experiment.
5. 3D printing experiment transformations: While the 2D and 3D rendering
   experiments explicitly state that the sampled transformations were random,
   the 3D printing one says "over a variety of viewpoints". Were these
   viewpoints chosen randomly?
Most of these concerns are potentially quirks in the exposition rather than any
issues with the experiments conducted themselves. For now, I think the
submission is good for a weak accept –- if the authors address my concerns, and/or
correct my potential misunderstanding of the issues, I'd be happy to upgrade my
review to an accept.


Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to converge to less redundant states. We introduce a novel bottom-up approach to expand representations in fixed-depth architectures. These architectures start from just a single feature per layer and greedily increase width of individual layers to attain effective representational capacities needed for a specific task. While network growth can rely on a family of metrics, we propose a computationally efficient version based on feature time evolution and demonstrate its potency in determining feature importance and a networks' effective capacity. We demonstrate how automatically expanded architectures converge to similar topologies that benefit from lesser amount of parameters or improved accuracy and exhibit systematic correspondence in representational complexity with the specified task. In contrast to conventional design patterns with a typical monotonic increase in the amount of features with increased depth, we observe that CNNs perform better when there is more learnable parameters in intermediate, with falloffs to earlier and later layers.

This paper introduces a simple correlation-based metric to measure whether filters in neural networks are being used effectively, as a proxy for effective capacity. The authors then introduce a greedy algorithm that expands the different layers in a neural network until the metric indicates that additional features will end up not being used effectively.
The application of this algorithm is shown to lead to architectures that differ substantially from hand-designed models with the same number of layers: most of the parameters end up in intermediate layers, with fewer parameters in earlier and later layers. This indicates that common heuristics to divide capacity over the layers of a network are suboptimal, as they tend to put most parameters in later layers. It's also nice that simpler tasks yield smaller models (e.g. MNIST vs. CIFAR in figure 3).
The experimental section is comprehensive and the results are convincing. I especially appreciate the detailed analysis of the results (figure 3 is great). Although most experiments were conducted on the classic benchmark datasets of MNIST, CIFAR-10 and CIFAR-100, the paper also includes some promising preliminary results on ImageNet, which nicely demonstrates that the technique scales to more practical problems as well. That said, it would be nice to demonstrate that the algorithm also works for other tasks than image classification.
I also like the alternative perspective compared to pruning approaches, which most research seems to have been focused on in the past. The observation that the cross-correlation of a weight vector with its initial values is a good measure for effective filter use seems obvious in retrospect, but hindsight is 20/20 and the fact is that apparently this hasn't been tried before. It is definitely surprising that a simple method like this ends up working this well.
The fact that all parameters are reinitialised whenever any layer width changes seems odd at first, but I think it is sufficiently justified. It would be nice to see some comparison experiments as well though, as the intuitive thing to do would be to just keep the existing weights as they are.
Other remarks:
Formula (2) seems needlessly complicated because of all the additional indices. Maybe removing some of those would make things easier to parse. It would also help to mention that it is basically just a normalised cross-correlation. This is mentioned two paragraphs down, but should probably be mentioned right before the formula is given instead.
page 6, section 3.1: "it requires convergent training of a huge architecture with lots of regularization before complexity can be introduced", I guess this should be "reduced" instead of "introduced".