Learning From Biased Soft Labels

Summary

The authors analyse the learnability properties of (biased) soft labels, e.g., originating from a teacher model in a student-teacher setup, with respect to classifier consistency and ERM learnability. To this end, two indicator measures of the quality of the proxy labels are suggested, which are used in a theoretical analysis to derive bounds about the aforementioned quality dimensions. Moreover, a heuristic loss for training skillful but bad teachers is developed.

Strengths

- Investigates a highly relevant matter - Technically sound and valid theoretical results - Covers multiple special cases of weakly-supervised learning as a practically relevant problem setup

Weaknesses

Major: - I find the distinction between incomplete supervision and partial label learning confusing. Typically, incomplete supervision and partial label learning are more or less the same thing. What the authors here refer to in the case of incomplete supervision is semi-supervised learning, which is a special case of partial label learning, namely that you can either observe a precise (i.e., unambiguous) label, or no label at all resp. the complete target space. In order to preserve consistency with related literature on this (e.g., as in your reference [58]), I would recommend sticking to this ontology. - The empirical analysis of SBTs does not contain any baseline. Overall, it is hard to judge the appropriateness of the developed indicators and the SBT loss proposals, perhaps the experimental setup can be overhauled. - It is hard to assess the looseness resp. tightness of the bound in Theorem 2. I would love to see the authors elaborating on this matter, e.g., by putting individual term components in a context, comparing it to “classical” bounds in multi-class learning, potentially with respect to label noise. Minor: - The page limit for submissions was 9 pages, but there is content on page 10. - I think there is a missing $\max$ (or a different aggregator) in Eq. (1), right? - Also, “ambiguity degree” is a term that is already being used in the PLL literature, as also indicated by referring to [5]. This is not precisely an equivalent ambiguity degree formulation, so it should be distinguished.

Questions

- How did you determine the hyperparameters being used in the experiments? Did you repeat the experiments multiple times with different seeds? How about the standard deviations?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

4 excellent

Presentation

3 good

Contribution

3 good

Limitations

Yes.

Summary

This paper studies the effectiveness of biased soft labels in knowledge distillation and weakly-supervised learning. The paper introduces two indicators to measure the effectiveness of soft labels, and proposes moderate conditions to ensure that biased soft label learning is classifier-consistent and ERM learnable. The paper also presents a heuristic method to train skillful but bad teachers, and shows that they can teach students to achieve high accuracy on CIFAR-10/100. The paper applies the theoretical framework to three weakly-supervised learning paradigms, and validates the indicators with experiments.

Strengths

1. The paper is well-written and a pleasure to read. 2. The paper provides thorough theoretical analysis for three different weak supervision settings.

Weaknesses

1. The paper only conducts experiments on CIFAR-10/100 datasets, and does not provide experiments on larger and mainstream datasets, such as ImageNet. The paper also does not compare the proposed method with other state-of-the-art weakly-supervised methods, especially those based on knowledge distillation. 2. The paper is suggested to provide more visualizations of the the prediction results (class probabilities) of large-biased soft labels (generated by SBTs) and good student. 3. The paper does not provide experiments on different backbones, and cannot demonstrate the effectiveness of the proposed indicators and method on different architectures. The paper also does not discuss how the choice of the backbone affects the performance and robustness of the method. 4. The paper exceeds the page limit. The paper is suggested to be shortened to meet the page limit requirement.

Questions

1. In the introduction, the paper claims that “Empirical Risk Minimization (ERM) learners’ performance can generalize to the entire data distribution.” However, previous studies have pointed out the drawbacks of ERM, such as (1) neural networks trained with ERM change their predictions drastically when evaluated on examples just outside the training distribution[1], also known as adversarial examples; (2) ERM allows large neural networks to memorize (instead of generalize from) the training data even in the presence of strong regularization, or in classification problems where the labels are assigned at random [1]. In general, using ERM for optimization may affect the generalization ability of the model. Does this contradict the conclusion of this paper? Does the conclusion of this paper have any prior studies or experiments to support it? [1]Zhang, Hongyi, et al. "mixup: Beyond empirical risk minimization." *arXiv preprint arXiv:1710.09412* (2017). 2. The paper mentioned “skillful but bad teachers”. How to define the skillfulness of the bad teachers? 3. As you mentioned in Section 5.3, is your main contribution the two methods of evaluating soft labels (unreliability degree and ambiguity degree), rather than the heuristic method of “bad teacher can teach good student”? 4. The conclusion that “the accuracy of the students decrease when unreliability degree and ambiguity degree increase” does not seem to be obvious in Figure 2(b). Also, in Figure 3 (a) and (b), the ambiguity degree γ does not change much as the student accuracy increases. The same situation also occurs in Figure 5 in the appendix, which seems to not support the effectiveness of the ambiguity degree γ indicator in these weakly-supervised settings.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

Some of the paper’s experimental results show that the two indicators proposed by the paper cannot well characterize the effectiveness of soft labels in all weakly-supervised settings. For example, under some of the weakly-supervision settings, the paper shows that the indicators are not consistent with the performance of the student model. The paper does not provide sufficient explanation or analysis for this phenomenon, and does not discuss how to improve or modify the indicators to better capture the effectiveness of soft labels.

Summary

The authors propose a clever theoretical framework for studying learnability under supervision with imperfect soft labels.

Strengths

- Learning from imperfect soft labels is an important and interesting area that is prevalent not only in knowledge distillation but also in cognitive science, human-AI interaction, and pretty much any modeling that aim to take into account noise and uncertainty. - The authors conduct a promising theoretical analysis of this setting by recasting it as a noisy top-k oracle problem (where teachers provide a set of k labels which with some probability contains the true label).

Weaknesses

- Clarity could be improved by providing more intuitions and explanations for terminology throughout. For example, "biased soft label" is never formally defined, and the implied definition (based on the notions of ambiguity and unreliability) does not fully agree with what I would normally think of when thinking of statistical notions of bias. Some additional editorial revision (fixing typos, etc.) would also be helpful, but I am not taking that into account in my score. - I think the assumptions are not quite as moderate as the authors imply and would like some more clarification about these. For example, one of the assumptions seem to be that labels occur in the top-k with equal probability, but this is clearly not the case in practice (e.g. you may believe a picture of a dog could be a wolf, but certainly not an airplane) which the authors mention when designing their experiments as they find that the top-k labels are correlated. The experiments are then designed to satisfy this assumption which means there is very little evidence that the proposed theory describes a realistic setting. Another assumption (Assumption 2 in 4.1) seems to pre-assume that the metrics considered by the authors are inversely correlated with accuracy which feels circular since I believe this is one of the things the authors want to claim. - As mentioned in the section above, the empirical results are currently unconvincing. In addition to the assumption mentioned above, it seems like in both experiments, the true label has the highest probability in >15% of the cases. For CIFAR10 this is reasonable since random chance is 10%, but for CIFAR100, this is quite high. Is there a disconnect between the theory setting and the experimental setting, in that the theory is focused on learning from the top-k set where all top-k labels are treated equally while in the experimental setting, learning still takes into account the actual probabilities? Perhaps a more compelling experiment would be to isolate various top-k cases and show that the curves are robust to changes in k? - There are a number of existing papers that study the informativeness of soft labels. It would be great to see some discussion of how this study fits into that literature.

Questions

See weaknesses section.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

2 fair

Presentation

2 fair

Contribution

3 good

Limitations

- The authors have listed both limitations and assumptions, though I think the assumptions may be more of a limitation than suggested.

Summary

This paper aims to study the effectiveness of biased soft labels for knowledge distillation. They propose two indicators to measure the effectiveness of the biased soft labels: unreliability degree and ambiguity degree. They provide a theoretical guarantee that the biased soft labels are effective in training a good student in three weakly-supervised learning paradigms: incomplete supervision, partial label learning, and learning with additive noise. Their experiments reveal that largely biased soft labels can also teach good students and the proposed indicators are effective in measuring the effectiveness of soft labels.

Strengths

* The motivation of the paper is original and novel. It is intriguing to see that learning from largely biased soft labels can achieve comparable performance, and the proposed indicators can be a valuable contribution to measuring their effectiveness in learning a good student for downstream tasks. * The paper provides an in-depth theoretical guarantee of the biased soft labels in three weakly supervised learning settings. * The experiment results validate that the proposed indicators (unreliability and ambiguity degree) are indeed effective in measuring the effectiveness of the soft labels (i.e. high accuracy of students) across the three weakly supervised learning paradigms. * Overall, the paper sufficiently informs the readers of technical and implementation details.

Weaknesses

* The paper shows limited experiment results on CIFAR-10 and CIFAR-100 (Figure 2). The authors should perform experiment on a wider range of benchmark datasets to validate the generality of the method. Are the proposed indicators effective in more complex datasets as the authors suggested? * The introduction could be better organized. The paper should clearly present the definition of a large-biased soft label and better motivate the readers on why utilizing them is valuable. * The paper exceeds the nine page limit.

Questions

* Does the proposed indicators work well across other benchmark datasets?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The authors did not address the limitations of their work.

Summary

This paper explores the concept of learning from weak, or "soft," labels that may be biased or diverge from the ground truth labels in a dataset. In contrast to existing theories that focus on the importance of close alignment between soft and ground truth labels, the authors probe the efficacy of learning from significantly biased soft labels. They introduce two indicators to gauge the effectiveness of these soft labels and propose conditions under which learning from such labels can be successful, including large-biased labels. The authors further devise a heuristic method for training what they call Skillful but Bad Teachers (SBTs), referring to models with relatively low accuracy that can nevertheless effectively train high-performing student models. They show that these teachers can achieve up to 90% accuracy on the CIFAR-10 dataset, demonstrating the validity of their approach. Additionally, the authors adapt their theoretical framework to examine the utility of soft labels in three specific weakly-supervised learning paradigms: incomplete supervision, partial label learning, and learning with additive noise. Experimental results are presented to support the proposed indicators and the viability of biased soft labels in these scenarios. Key contributions include: Discovery that learning from largely biased soft labels can achieve comparable performance, and an exploration of the mechanisms behind this phenomenon. The proposal of two indicators to evaluate the effectiveness of soft labels and conditions to ensure their usefulness. A heuristic method to train SBTs, using new concepts of unreliability degree and ambiguity degree. A theoretical framework that illuminates the role of soft labels in three weakly-supervised learning paradigms, accompanied by theoretical guarantees for their learnability and supporting experimental results.

Strengths

Theoretical Analysis: The paper provides a comprehensive theoretical framework for analyzing the effectiveness of soft labels, which are often employed in the realm of machine learning for teaching student models. Definitions and Indicators: The paper introduces and defines new concepts like unreliability degree and ambiguity degree, and relates them to the effectiveness of soft labels. This could provide valuable insight for the development of future machine learning models. Extension to Weakly-Supervised Learning (WSL): The research effectively applies the theoretical findings to weakly-supervised learning paradigms, thus demonstrating the applicability and extensibility of their findings.

Weaknesses

Selective Conditions: While the paper provides conditions for classifier-consistency and ERM learnability, it doesn't clearly outline how to meet these conditions in a real-world context. Furthermore, the condition of balancing unreliability degree and ambiguity degree might be challenging to achieve in practice.

Questions

It's mentioned that the soft labels generated by SBTs are large-biased, which could potentially impact the model's ability to generalize to new, unseen data. While the authors note that students still have good accuracy despite the bias, how does the authors propose the current approach tackles this situation?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

3 good

Contribution

4 excellent

Limitations

The process of inhibiting correct predictions, reducing unreliability and ambiguity degrees, and randomly selecting k-1 labels for each training instance could increase the computational complexity and time required to train the models. The evaluation is mainly based on the accuracy of the student models, which might not be the most comprehensive measure. There could be other performance metrics that are important in the context of this problem.