__ Summary and Contributions__: This paper proposed a SSL method with non-uniform weight for unlabeled samples. To learn the per-sample weight on unlabeled data, a bi-level optimization algorithm is introduced to iteratively update the model parameter and per-sample weight until convergence. Experiments are carried out on synthetic and two real datasets.

__ Strengths__: The motivation for per-sample weighted semi-supervised learning is valid and there is very little prior works on this topic.
The per-sample weight is estimated with a bi-level optimization algorithm which is straightforward.

__ Weaknesses__: The model parameter which minimizes the full loss (supervised + unsupervised losses) often does not necessarily minimize the supervised loss part. If this holds, the bi-level optimization second step is not reasonable. The minimizer of \Lambda does not necessarily generalize to either train labeled or test data. The author may want to discuss on this point.
How does this algorithm avoid trivial solution? A possible trivial one is setting all \lambda=0 and the second step of bi-level optimization is minimized without any regularization. The author may discuss this point. This may also depends on the initialization. The author should elaborate how \lambda is initialized to avoid trivial solution.
Given the marginal improvements, sometimes no improvement at all, over the baseline (CTA), the experiment lacks additional insight. In particular, how the final per-sample weight is distributed? This is further demonstrate the effectiveness of the proposed method.

__ Correctness__: There are some issues with the assumption of minimizing the unsupervised loss corresponding to better generalization. Moreover, there is a trivial solution issue.

__ Clarity__: This paper is well written and easy to follow.

__ Relation to Prior Work__: Related works are properly discussed.

__ Reproducibility__: Yes

__ Additional Feedback__: The author should discuss the assumption and trivial solution issues. The experiment section should be improved as well, in particular, what are the per-sample weights and give insight into how it improves upon uniform weight.
After reading the response from authors, I feel the overall weights for unlabeled samples are all close to 1, as shown in the figure in rebuttal. This does not discriminately tell which unlabeled samples are important and which are not because giving 10% higher or lower weight does not change the model too much. But in general, the problem proposed in this paper is valid and it could inspire more following works and I will raise my score to a marginal accept.

__ Summary and Contributions__: This paper studies on automatically tuning different weights for different unlabeled samples during training in semi-supervised learning (SSL). The learning of the weights relies on influence function, which can approximate each sample's contribution to the learned model's performance. Because computing influence function is costly on large data, this paper proposed methods of handling its computational bottlenecks. The paper demonstrates the benefits of their SSL per-example weight optimization algorithm via influence function by comparing to different benchmarks, and justifies the components of their algorithm with ablation studies. Two main contributions of this paper are: 1) it proposes a per-example weight optimization algorithm for SSL and empirically demonstrates it can improve SSL performance; 2) it proposes a fast and effective approximation of influence function to make it scalable to realistic SSL settings

__ Strengths__: 1) This paper considers an ignorable case in SSL where not all unlabeled data should be treated equally during training. Though automatic weight tuning for different samples is already studies in supervised learning setting, it is new in SSL context to my best knowledge. Therefore, the motivation is clear and valid. The proposed algorithm is simple and practical and demonstrates benefits compared to different baselines, so the paper worked towards its motivation.
2) To learn the weights for different unlabeled data, this paper connects influence function to the weight tuning in SSL. Influence function is a tool of measuring models' dependency on samples in train set. It is previously mainly studied in the area of model interpretability and robust learning, but not widely applied to tuning sample weights in learning models, probably due to its costly computation. This paper addressed influence function's bottlenecks in their algorithm context by 1) making computing per-sample gradient more efficient via utilizing gradient information from layer activation; 2) approximating the hessian matrix from partial training parameters and samples at each iteration. The experiments of comparing to other approximation strategies show the benefits of their approximation methods, providing new approaches and insights for practical use of influence functions in future applications.
3) This paper demonstrates sound empirical evaluation to justify the proposed algorithm. From synthetic experiments, it presents visually the benefits from weighting differently on unlabeled data; from experiments on real data, it compares their algorithm to competitive benchmarks; from ablation studies, it justifies different components of their methods

__ Weaknesses__: I have mainly two concerns.
1) The paper's per-sample weight tuning method relies on influence function. However, the explanation of the influence function holds only when the upweight (i.e. parameter weights in this paper's context) is very close to 0. Otherwise, the theoretical approximation of each sample's contribution from Taylor's first-order expansion is not valid any more. If that's the case (e.g. weights are far away from 0 during training iteration), the influence function might not reflect each sample's influence correctly and the weights produced might be unreliable.
2) I think in the experiment, some interesting baselines are missing. For example, supervise learning methods with per-sample weight tuning, and SSL with other existing per-sample weight tuning methods from supervised learning studies if possible. Further, in the ablation studies section, as the proposed algorithm can be extended to all training samples rather than limited to only unlabeled sample, it could shed more insights if comparing to applying influence function to all training sample, and comparing to weight tuning only on labeled data while the weights fixed on unlabeled samples. These comparisons can help us understand better the roles played by per-sample weight tuning.

__ Correctness__: The general idea and empirical evaluation is correct and valid. But there are some concerns about some details of the correctness, which are mentioned in the weakness section.

__ Clarity__: This paper is well written. The story is clearly told and developed and the statement is easy to follow. One thing I feel not clear is that in the section of Ablation Studies and Analysis, I am not sure if the experiments are multiple runs or a single run. If it is multiple runes, what's the reported statistics (e.g. average, median, etc). If it is single run, why not make it multiple runs as in the section 4.2?

__ Relation to Prior Work__: To my best knowledge, this paper mentioned important related previous works and discussed how their methods differ and improve from existing ones.

__ Reproducibility__: Yes

__ Additional Feedback__: I hope the authors could defend their ideas or answer my questions about the concerns mentioned in the weakness section. I will consider improve my overall score if satisfied with their response.
Some tiny suggestions: In the Figure 1 and Figure 2, the weight color range seems too large so I cannot distinguish well between different samples at least at my machine. Perhaps the authors can consider decrease the color range for the weight resolution so more different colors can be viewed. Also, for all figures and tables, the fonts can be a little bit larger.
------------------------After Authors' Response--------------------------------------------------------------------
The authors' response answers all my main concerns. I am satisfied with all of them except for the proof of equation (6). I thought \lambda worked as \epsilon in the original proof of Koh and Liang's ICML paper, where it must be near 0, but in the appendix F of this paper, the authors use \epsilon as the increment to \lambda. However, in the last line of the authors' proof, I don't think it is correct to say that \frac{\partial \theta}{\partial \lambda} = \frac{\partial \Delta}{\partial \epsilon}. In my opinion, it holds when \epsilon has nothing to do with \lambda, but as \lambda is updated iteratively from the current value, \lambda will be related to \epsilon. Perhaps the effects are tiny and it is still a good approximation, but it is unclear. Besides, I agree with R3 about convergence analysis. Though authors response that similar analysis is done in previous work, I think it is best to include it explicitly for their specific algorithm.

__ Summary and Contributions__: This paper studies the problem of semi-supervised learning (SSL) and claims that all unlabeled (U) data should not be treated equally in SSL. Then they propose a learning-to-reweight method to adjust the per-example weights using influence function and provide some fast approximations. Experiments on several benchmarks show their method works comparatively or a bit better than state-of-the-art methods.

__ Strengths__: -The idea of the paper is simple and clear. They argue that not all U data are equal and using the same weight for all of them is suboptimal, so they propose to learn per-example weights instead.
-The effort made on fast and empirically effective approximations of calculating influence function is another contribution.

__ Weaknesses__: -My first concern is their motivation. From line 32~34, the authors argue that not all U data are equal, because if the label-estimate of U data is incorrect then training on them will hurt the performance. This is not that convincing. As reviewed in Sec. 2, many other SSL methods do not rely on label-estimate, and I don’t see how this argument hold for those methods, why is this a clear drawback?
-Noticing that in Tabel 1, the proposed per-example weight method performs much better than label-estimate based SSL method (Pseudo-Label), but has less or no improvement on consistency based SSL method (UDA, FixMatch), which somehow justifies my concern. Could the authors explain more on this?

__ Correctness__: In Figure 4, the per-example weight method has only limited improvement on single weight method. But in Table 1, the best single weight method can achieve almost the same performance as the per-example weight method. What was the single weight method here?

__ Clarity__: The problem of SSL widely exists in the real world and has been a hot research area in recent years. This paper studies it in the different point of view, not all U data are equal, the idea is interesting but there are some unclear parts in the paper that can be further clarified and improved.

__ Relation to Prior Work__: The bi-level optimization problem in Eq 2 seems a bit similar to Eq 1~2 in Reweight [Ren et al., ICML’18], which learns weights of noisy training examples (U data here) by minimize a validation risk. This paper proposes a different approximation method and is shown to work well empirically. But is this algorithm guaranteed to converge under some assumptions? A convergence analysis would be very helpful.

__ Reproducibility__: Yes

__ Additional Feedback__: After rebuttal:
I have read the rebuttal and all the reviews. The authors have addressed most of my questions in the rebuttal, so I choose to raise my score.