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2
Based on the results by Lee et al, which shows that first order methods converge to local minimum solution (instead of saddle points), it can be concluded that the global minima of this problem can be found by any manifold descent techniques, including standard gradient descent methods.[problem-NEU], [CMP-POS, EMP-POS]
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In general I found this paper clearly written and technically sound.[paper-POS], [CLA-POS, EMP-POS]
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I also appreciate the effort of developing theoretical results for deep learning, even though the current results are restrictive to very simple NN architectures.[theoretical results-POS], [EMP-POS]
theoretical results
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Contribution: As discussed in the literature review section, apart from previous results that studied the theoretical convergence properties for problems that involves a single hidden unit NN, this paper extends the convergence results to problems that involves NN with two hidden units.[literature review section-NEU, previous results-NEU, paper-NEU], [CMP-NEU]
literature review section
previous results
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The analysis becomes considerably more complicated,[analysis-NEG], [EMP-NEG]
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and the contribution seems to be novel and significant.[contribution-POS], [NOV-POS, IMP-POS]
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I am not sure why did the authors mentioned the work on over-parameterization though.[null], [EMP-NEG]
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It doesn't seem to be relevant to the results of this paper (because the NN architecture proposed in this paper is rather small).[results-NEU], [EMP-NEG]
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Comments on the Assumptions: - Please explain the motivation behind the standard Gaussian assumption of the input vector x.[motivations-NEU], [EMP-NEU]
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- Please also provide more motivations regarding the assumption of the orthogonality of weights: w_1^top w_2 0 (or the acute angle assumption in Section 6).[motivations-NEU, assumption-NEU, Section-NEU], [EMP-NEU]
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Without extra justifications, it seems that the theoretical result only holds for an artificial problem setting.[theoretical result-NEG], [EMP-NEG]
theoretical result
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While the ReLU activation is very common in NN architecture, without more motivations I am not sure what are the impacts of these results.[motivations-NEU, impacts-NEU], [EMP-NEG, IMP-NEU]
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General Comment: The technical section is quite lengthy, and unfortunately I am not available to go over every single detail of the proofs.[technical section-NEG], [SUB-NEG]
technical section
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From the analysis in the main paper, I believe the theoretical contribution is correct and sound.[analysis-NEU, theoretical contribution-POS], [EMP-POS]
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While I appreciate the technical contributions,[technical contributions-POS], [EMP-POS]
technical contributions
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in order to improve the readability of this paper, it would be great to see more motivations of the problem studied in this paper (even with simple examples).[motivations-NEU], [SUB-NEG]
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Furthermore, it is important to discuss the technical assumptions on the 1) standard Gaussianity of the input vector,[assumptions-NEU], [SUB-NEU, EMP-NEU]
assumptions
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and 2) the orthogonality of the weights (and the acute angle assumption in Section 6) on top of the discussions in Section 8.1, as they are critical to the derivations of the main theorems. [Section-NEU], [SUB-NEU, EMP-NEU]
Section
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The propose data augmentation and BC learning is relevant, much robust than frequency jitter or simple data augmentation.[null], [EMP-POS]
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In equation 2, please check the measure of the mixture.[equation-NEU], [EMP-NEU]
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Why not simply use a dB criteria ?[null], [EMP-NEG]
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The comments about applying a CNN to local features or novel approach to increase sound recognition could be completed with some ICLR 2017 work towards injected priors using Chirplet Transform.[comments-NEU, novel approach-NEU], [NOV-NEU, CMP-NEU]
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novel approach
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The authors might discuss more how to extend their model to image recognition, or at least of other modalities as suggested.[discuss-NEU, model-NEU], [EMP-NEU]
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Section 3.2.2 shall be placed later on, and clarified.[Section-NEU], [CLA-NEU, PNF-NEU]
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Discussion on mixing more than two sounds leads could be completed by associative properties, we think... ? [Discussion-NEU], [EMP-NEU]
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I am overall a fan of the general idea of this paper; scaling up to huge inputs is definitely a necessary research direction for QA.[idea-POS], [EMP-POS]
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However, I have some concerns about the specific implementation and model discussed here.[model-NEU], [EMP-NEU]
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How much of the proposed approach is specific to getting good results on bAbI (e.g., conditioning the knowledge encoder on only the previous sentence, time stamps in the knowledge tuple, super small RNNs, four simple functions in the n-gram machine, structure tweaking) versus having a general-purpose QA model for natural language?[proposed approach-NEU], [EMP-NEU]
proposed approach
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Addressing some of these issues would likely prevent scaling to millions of (real) sentences, as the scalability is reliant on programs being efficiently executed (by simple string matching) against a knowledge storage.[issues-NEU], [SUB-NEG, EMP-NEG]
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The paper is missing a clear analysis of NGM's limitations...[analysis-NEG], [EMP-NEG]
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the examples of knowledge storage from bAbI in the supplementary material are also underwhelming as the model essentially just has to learn to ignore stopwords since the sentences are so simple.[null], [EMP-NEG]
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In its current form, I am borderline but leaning towards rejecting this paper.[paper-NEG], [REC-NEG]
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Other questions: - is -gram really the most appropriate term to use for the symbolic representation?[null], [PNF-NEU]
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N-grams are by definition contiguous sequences... The authors may want to consider alternatives.[null], [EMP-NEU]
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The evaluations are only conducted on 5 of the 20 bAbI tasks, so it is hard to draw any conclusions from the results as to the validity of this approach.[evaluations-NEG], [SUB-NEG]
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Can the authors comment on how difficult it will be to add functions to the list in Table 2 to handle the other 15 tasks? Or is NGM strictly for extractive QA?[Table-NEU], [EMP-NEU]
Table
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- beam search is performed on each sentence in the input story to obtain knowledge tuples... while the answering time may not change (as shown in Figure 4) as the input story grows, the time to encode the story into knowledge tuples certainly grows, which likely necessitates the tiny RNN sizes used in the paper.[null], [EMP-NEU]
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How long does the encoding time take with 10 million sentences?[null], [EMP-NEU]
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- Need more detail on the programmer architecture, is it identical to the one used in Liang et al., 2017? [detail-NEU], [SUB-NEU, EMP-NEU]
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None of these ideas are new before but I haven't seen them combined in this way before.[ideas-NEU], [NOV-NEG]
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This is a very practical idea, well-explained with a thorough set of experiments across three different tasks.[idea-POS, paper-POS], [EMP-POS]
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The paper is not surprising[paper-NEG], [NOV-NEG]
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but this seems like an effective technique for people who want to build effective systems with whatever data they've got. [technique-POS], [EMP-POS]]
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The exposition of the model architecture could use some additional detail to clarify some steps and possibly fix some minor errors (see below).[model architecture-NEG, detail-NEG], [SUB-NEG]
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I would prefer less material but better explained.[material-NEU], [EMP-NEU]
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The paper could be more focused around a single scientific question: does the PATH function as formulated help?[paper-NEU], [EMP-NEU]
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The authors do provide a novel formulation and demonstrate the gains on a variety of concrete problems taken form the literature.[experiments-POS, problems-POS], [NOV-POS]
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I also like that they try to design experiments to understand the role of specific parts of the proposed architecture.[experiments-POS, proposed architecture-POS], [EMP-POS]
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The graphs are WAY TOO SMALL to read.[graphs-NEG], [PNF-NEG]
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Figure #s are missing off several figures.[Figure-NEG], [PNF-NEG]
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MODEL & ARCHITECTURE The PATH function given a current state s and a goal state s', returns a distribution over the best first action to take to get to the goal P(A).[null], [EMP-POS]
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( If the goal state s' was just the next state, then this would just be a dynamics model and this would be model-based learning?[null], [EMP-NEU]
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So I assume there are multiple steps between s and s'?).[null], [EMP-NEU]
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68
At the beginning of section 2.1, I think the authors suggest the PATH function could be pre-trained independently by sampling a random state in the state space to be the initial state and a second random state to be the goal state and then using an RL algorithm to find a path.[section-NEU], [EMP-NEU]
section
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Presumably, once one had found a path ( (s, a0), (s1, a1), (s2, a2), ..., (sn-1,an-1), s' ) one could then train the PATH policy on the triple (s, s', a0) ?[null], [EMP-NEU]
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This seems like a pretty intense process: solving some representative subset of all possible RL problems for a particular environment ... Maybe one choses s and s' so they are not too far away from each other (the experimental section later confirms this distance is > 7.[section-NEU], [EMP-NEU]
section
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Maybe bring this detail forward)?[detail-NEU], [EMP-NEU]
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The expression Trans'( (s,s), a)' (Trans(s,a), s') was confusing.[expression-NEG], [CLA-NEG]
expression
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I think the idea here is that the expression Trans'( (s,s) , a )' represents the n-step transition function and 'a' represents the first action?[expression-NEU], [EMP-NEU]
expression
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The second step is to train the goal function for a specific task.[task-NEU], [EMP-NEU]
task
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So I gather our policy takes the form of a composed function and the chain rule gives close to their expression in 2.2[expression-NEU], [EMP-NEU]
expression
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What is confusing is that they define A( s, a, th^p, th^g, th^v ) sum_i gamma^i r_{t+1} + gamma^k V( s_{t+k} ; th^v ) - V( s_t ; th^v )[null], [CLA-NEG]
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The left side contains th^p and th^g, but the right side does not.[null], [EMP-NEG]
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Should these parameters be take out of the n-step advantage function A?[null], [EMP-NEU]
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81
The second alternative for training the goal function tau seems confusing.[null], [EMP-NEG]
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82
I get that tau is going to be constrained by whatever representation PATH function was trained on and that this representation might affect the overall performance - performance.[performance-NEU], [EMP-NEU]
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83
I didn't get the contrast with method one.[method-NEG], [EMP-NEG]
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How do we treat the output of Tau as an action?[output-NEU], [EMP-NEU]
output
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Are you thinking of the gradient coming back through PATH as a reward signal?[null], [EMP-NEU]
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86
More detail here would be helpful.[detail-NEG], [SUB-NEG]
detail
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SUB
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87
EXPERIMENTS: Lavaworld: authors show that pretraining the PATH function on longer 7-11 step policies leads to better performance when given a specific Lava world problem to solve.[performance-POS, problem-POS], [EMP-POS]
performance
problem
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EMP
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POS
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88
So the PATH function helps and longer paths are better.[null], [EMP-POS]
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POS
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90
What is the upper bound on the size of PATH lengths you can train?[null], [EMP-NEU]
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EMP
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NEU
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92
From a scientific point of view, this seems orthogonal to the point of the paper, though is relevant if you were trying to build a system.[paper-POS], [EMP-POS]
paper
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EMP
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94
This isn't too surprising.[null], [EMP-NEG]
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EMP
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NEG
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95
Both picking up the passenger (reachability) and dropping them off somewhere are essentially the same task: moving to a point.[null], [EMP-NEU]
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EMP
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NEU
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96
It is interesting that the Task function is able to encode the higher level structure of the TAXI problem's two phases.[Task function-POS], [EMP-POS]
Task function
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EMP
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POS
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POS
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97
Another task you could try is to learn to perform the same task in two different environments.[task-POS], [EMP-POS]
task
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EMP
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POS
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98
Perhaps the TAXI problem, but you have two different taxis that require different actions in order to execute the same path in state space.[null], [EMP-NEU]
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EMP
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99
This would require a phi(s) function that is trained in a way that doesn't depend on the action a.[null], [EMP-NEU]
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EMP
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NEU
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101
Is this where you artificially return an agent to a state that would normally be hard to reach?[null], [EMP-NEU]
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NEU
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102
The authors show that UA results in gains on several of the games.[null], [EMP-POS]
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POS
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103
The authors also demonstrate that using multiple agents with different policies can be used to collect training examples for the PATH function that improve its utility over training examples collected by a single agent policy.[training examples-NEU], [EMP-NEU]
training examples
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104
RELATED WORK: Good contrast to hierarchical learning: we don't have switching regimes here between high-level options[regimes-POS], [CMP-POS]
regimes
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CMP
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POS
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POS
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105
I don't understand why the authors say the PATH function can be viewed as an inverse?[null], [CLA-NEG]
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CLA
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106
Oh - now I get it. Because it takes an extended n-step transition and generates an action.[null], [CLA-POS]
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CLA
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108
-I think title is misleading, as the more concise results in this paper is about linear networks I recommend adding linear in the title i.e. changing the title to ... deep LINEAR networks[title-NEG, results-NEU], [EMP-NEU, PNF-NEG]
title
results
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EMP
PNF
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NEU
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NEG
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109
- Theorems 2.1, 2.2 and the observation (2) are nice![Theorems-POS, observation-POS], [EMP-POS]
Theorems
observation
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EMP
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POS
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POS
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110
- Theorem 2.2 there is no discussion about the nature of the saddle point is it strict?[Theorem-NEU, discussion-NEG], [SUB-NEG]
Theorem
discussion
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SUB
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NEG
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111
Does this theorem imply that the global optima can be reached from a random initialization?[theorem-NEU], [EMP-NEU]
theorem
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EMP
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112
Regardless of if this theorem can deal with these issues, a discussion of the computational implications of this theorem is necessary.[theorem-NEU, issues-NEU, discussion-NEU], [SUB-NEU]
theorem
issues
discussion
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113
- I'm a bit puzzled by Theorems 4.1 and 4.2 and why they are useful.[Theorems-NEU], [EMP-NEU]
Theorems
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EMP
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114
Since these results do not seem to have any computational implications about training the neural nets what insights do we gain about the problem by knowing this result? [results-NEG, insights-NEU, problem-NEU], [EMP-NEG]
results
insights
problem
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EMP
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NEU
NEU
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115
Further discussion would be helpful. [discussion-NEU], [SUB-NEU]
discussion
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SUB
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120
The performance improvement is expected and validated by experiments.[performance-POS, experiments-POS], [EMP-POS]
performance
experiments
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EMP
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POS
POS
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POS
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121
But I am not sure if the novelty is strong enough for an ICLR paper. [novelty-NEU], [APR-NEU, NOV-NEU]
novelty
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APR
NOV
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125
The suggested techniques are nice and show promising results.[techniques-POS, results-POS], [EMP-POS]
techniques
results
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EMP
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POS
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126
But I feel a lot can still be done to justify them, even just one of them.[null], [EMP-NEU]
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127
For instance, the authors manipulate the objective of G using a new parameter alpha_new and divide heuristically the range of its values.[null], [EMP-NEU]
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128
But, in the experimental section results are shown only for a single value, alpha_new 0.9 The authors also suggest early stopping but again (as far as I understand) only a single value for the number of iterations was tested.[results-NEU], [EMP-NEU]
results
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EMP
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