Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 8: Accept
review_content: This paper investigates the problem of fault telorance
on NN: basically how the predictions are affected by
failure of certain neurons at prediction time. The analysis
is theoretical under the classical assumption of lipschitz
bounded non-linearities and looking at the limit case
of an infinite number of neurons. The paper is well
written and comes with public code that allows to replicate
the experiments illustrating the theoretical derivations.

The paper is well motivated and addresses a timely matter.

Typos

- "the error of the output of" -> "the error of the output"

review_title: Official Blind Review #2

final_score: rating: 3: Weak Reject
review_content: This contribution studies the impact of deletions of random neurons on prediction accuracy of trained architecture, with the application to failure analysis and the specific context of neuromorphic hardware. The manuscript shows that worst-case analysis of failure modes is NP hard and contributes a theoretical analysis of the average case impact of random perturbations with Bernouilli noise on prediction accuracy, as well as a training algorithm based on aggregation. The difficulty of tight bounds comes from the fact that with many layers a neural network can have a very large Lipschitz constant. The average case analysis is based on wide neural networks and an assumption of a form of smoothness in the values of hidden units as the width increases. The improve fitting procedure is done by adding a set of regularizing terms, including regularizing the spectral norm of the layers.

The robustness properties can be interesting to a wider community than that of neuromorphic hardware. In this sense, the manuscript provides interesting content, although I do fear that it is not framed properly. Indeed, the introduction and conclusion mention robustness as a central concern, which it is indeed, but the neuron failures are quite minor in this respect. More relevant questions would be: is the approach introduced here useful to limit the impact of adversarial examples? Does it provide good regularizations that improve generalization? I would believe that the regularization provided are interesting by looking at their expression; in particular the regularization of the operator norm of layers makes a lot of sense. That said, there is some empirical evidence that batch norm achieves similar effects, but with a significantly reduced cost.

Another limitation of the work is that it pushes towards very wide networks and ensemble predictions. These significantly increase the prediction cost and are often frowned upon by applications.

It seems to me that the manuscript has readability issues: the procedure introduced is quite unclear and could not be reimplemented from reading the manuscript (including the supplementary materials). Also, the results in the main part of the manuscript are presented to tersely: I do not understand where in table 2 dropout is varied.

The contributed algorithm has many clauses to tune dynamically the behavior of the regularizations and the architecture. These are very hard to control in theory. They would need strong empirical validation on many different datasets.

It is also very costly, as it involves repeatedly training from scratch a neural network.

The manuscript discusses in several places a median aggregation, which gives robustness properties to the predictor. I must admit that I have not been available to see it in the algorithm. This worries me, because it reveals that I do not understand the approach. The beginning of section 6.1, in the appendix, suggests details that are not understandable from the algorithm description.

Finally, a discussion of the links to dropout would be interesting: both in practice, as dropout can be seen as simulating neuron failure during training, as well as from the point of view of theory, as there has been many attempts to analyze theoretically dropout (starting with Wager NIPS 2013, but more advanced work is found in Gal ICML 2015, Helmbold JMLR 2015, Mianjy ICML 2018).
review_title: Official Blind Review #3

final_score: rating: 1: Reject
review_content: 

Review: This paper considers the problem of dropping neurons from a neural network.  In the case where this is done randomly, this corresponds to the widely studied dropout algorithm.  If the goal is to become robust to randomly dropped neurons during evaluation, then it seems sufficient to just train with dropout (there is also a gaussian approximation to dropout using the central limit theorem called "fast dropout").  

I think there are two directions I find interesting that are touched on by this paper.  One is the idea of dropping neurons as an adversarial attack, which I think has been studied empirically but not theoretically (to my knowledge).  However then it would be important to specify the budget of the attack - how many neurons can they remove and how precisely can they pick which neuron to remove?  Another would be studying the conditions for dropout to be useful as a regularizer (and not underfit), which are again somewhat understood experimentally but could deserve a more theoretical treatment.  

However I don't think this paper solved a sufficiently clear problem and the motivation is somewhat confusing to me, especially when it seems like an analysis of dropout, and that isn't even mentioned until the 7th page.  

Notes: 
  -Paper considers loss of function from loss of a few neurons.  

  -Idea is to study more rigorously the fault tolerance of neural networks to losing a subset of the neurons.  

  -In terms of impact of the work, one thing to consider is that even if a normally or arbitrarily trained network doesn't have perfect fault tolerance to dropping neurons, a neural network *trained* with dropping networks could learn hidden states which become more fault tolerant.  


Minor Comments: 
  -I'm a bit unhappy with the argument about the brain losing neurons unless it has better referencing from neuroscience.  I imagine it's true in general but I wouldn't be surprised if some neurons were really essential.  For example squid have a few giant neurons that control propulsion.  It's just the first sentence so maybe I'm nitpicking.  

  -  It also seems weird that the opening of the paper doesn't give more attention to dropout, since it's a well known regularizer and seems rather closely related conceptually.  

  - In the intro it says neuromorphic hardware would pass information at the speed of light.  Is this really true?  My understanding is neuromorphic hardware would still generally use electrical or chemical signals but not pass things at the speed of light.  

  - The citation format is not valid for ICLR. 

review_title: Official Blind Review #1

Meta-review:  This paper focuses on the problem of robustness in the network with random loss of neurons.  However, reviewers had issues with insufficient clarity of the presentation, and lack of discussion about closely related dropout approach.

 
 
Decision: Reject