Paper: Exploring the Impact of Information Entropy Change in Learning Systems (ICLR-2024)

Reviewer comment (Experiments):
Limited analysis between data augmentation and the proposed noise injection. It seems more like a feature augmentation method for different layers. The article claims that the positive noise is benefit of the classification network, but it is hard to measure the noise level for the positive/negative influence. It is encouraged to compare the difference between the data augmentation with noise and the proposed method.

Author response:
Thanks for your questions. The information entropy of the learning system framework proposed in our works provides theoretical explanations for data augmentation. 

Data augmentation can be divided into two aspects:

Image Level Data Augmentation, such as flips, translations, rotations, CutOut, MixUp, CutMix, and etc.  
As the reviewer eupP already pointed out, the pioneering work on Positive-Incentive Noise (IEEE Transactions on Neural Networks and Learning Systems, 2022) has provided a theoretical framework for image-level data augmentation. 

Latent Data Augmentation, such as adding noise to embeddings, feature mixup, and etc.
Our work provided a theoretical framework for latent data augmentation. 

Therefore, our work provides theoretical guidance for exploring possible effective data augmentation methods in the future.
Our work provides quantitative tools for analyzing the influence of adding noise to learning systems. Combined with the previous work on Positive-Incentive Noise in IEEE TNNLS 2022, readers can analyze the effects of adding noise at both the image and latent levels.

Reviewer comment (Theory):
Noise definition confusion. Unlike Gaussian noise and salt-and-pepper noise with the specific probability distribution, the linear transform is not a kind of noise, but a simple operation.

Author response:
Thank you for bringing this up. For a specific image X1, Gaussian noise, salt-and-pepper noise are considered noise; this is no doubt for reviewer FieS. However, in our definition, we consider another image X2 as noise when it is added to X1. We will emphasize this point if there is confusion for the reviewer.

Reviewer comment (Experiments):
Limited analysis of the tasks. The authors leverage the proposed method in image classification tasks, including domain adaptation. It is encouraged to conduct the noise injection in image object detection/segmentation tasks, or some NLP tasks, to verify the effectiveness of the proposed method.

Author response:
Great question. Your suggestions are the directions we will work on, but our expertise lies in image classification, domain adaptation, and semi-supervised learning. We may need collaborators to expand our research. For NLP tasks, there was an arXiv submission last month that utilized uniform noise as positive noise, where they significantly improved instruction fine-tuning in large language models. For object detection/segmentation, we are interested in applying positive noise in these areas, but we need time to delve into it.

Reviewer comment (Experiments):
The technique is only evaluated on classification using ImageNet and domain adaptation. It would be good to see results on other tasks like object detection perhaps, and specially domains like Natural Language Processing, which differ from vision based tasks.

Author response:
Great suggestions. We have found other works submitted on ArXiv in the last month that utilize positive noise to enhance instruction finetuning in large language models. At the very least, the application of positive noise to NLP has been verified.
Since our expertise lies primarily in image classification, domain adaptation, and semi-supervised learning, we are actively seeking potential collaborators to apply our methodology in other areas across CV and NLP.  If the reviewer is an expert in related areas, we would be more than happy to discuss potential opportunities.

Reviewer comment (Evaluation):
Given that the improvement is so large on ResNet-18, do the authors have an explanation for why ViT-T does not improve similarly?

Author response:
The details of the model architectures, presented in Table 1 and 2 of the supplementary materials, may provide two key explanations.

1, the ViT-Tiny model has a head number of 3, significantly smaller than the 12 in   
ViT-B. This limitation hampers ViT-Tiny's ability to capture diverse patterns in images. This can be supported by the paper ‘On the Relationship between Self-Attention and Convolutional Layers’ ICLR 2020.

2, with only 5.7 million parameters, ViT-Tiny falls short of the parameter count in  ResNet-18 by nearly half. This suggests that ViT-Tiny may struggle to capture the necessary complexity and hierarchical features as effectively as ResNet-18 in ImageNet classification tasks.

Reviewer comment (Evaluation):
Can the authors elaborate on this statement? "Besides, when the models are corrupted under brute force attack, the positive noise also can not work." Why is this the case?

Author response:
The paragraph on the moderate model assumption claims that positive noise functions effectively for a 'normal' or 'ordinary' model. However, for instance, if a model is compromised, as demonstrated in the 'Color Backdoor: A Robust Poisoning Attack in Color Space,' CVPR 2023, the positive noise may not work. If this statement makes readers confused, we will revise it.

Reviewer comment (Theory):
This point also requires more detailed explanation - "Second, injection to shallow layers obtain less entropy change gain because of trendy replacing Equation 8 with Equation 7." The explanation for why shallower layers don't provide as high accuracy gains as deeper layers can be improved.

Author response:
Thanks for the great suggestions. An additional explanation could be that deeper layers lead to better representations. Evidence from 'Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth' (ICLR 2021) suggests that as the depth or width of the model increases, there is an emergence of principal components that contribute to improved performance. This implies that a certain depth is necessary for the model to achieve satisfactory performance.

Reviewer comment (Reproducibility):
Given that this is a new perspective and the results are strong, will code be released for reproducibility?

Author response:
All members have already agreed that all the source code running CNNs and ViTs on ImageNet, ImageNet V2, Office-Home, and Visda2017 will be released on GitHub upon acceptance. We will also provide the pretrained models.

Reviewer comment (Experiments):
Can the authors give other examples of positive noise that they considered?

Author response:
This is a great question! Yes. We will explore more kinds of positive noises. Another team has recently achieved promising results by using uniform noise as positive noise in an NLP task; their related submission is already on ArXiv. 

The work by Xuelong Li, 'Positive-Incentive Noise,' published in IEEE Transactions on Neural Networks and Learning Systems in 2022, is a pioneering effort that introduces positive noise in machine learning. We also recommend another paper that explores positive noise in signal processing: 'Exploring Positive Noise in Estimation Theory' by Radnosrati, Kamiar, Gustaf Hendeby, and Fredrik Gustafsson, published in IEEE Transactions on Signal Processing in 2020. We strongly believe that there is a great potential for positive noise in AI community.

Reviewer comment (Experiments):
The range of tasks tackled remains relatively limited, lacking diversity and complexity in comparison to broader applications. To be specific, this paper only conducts experiments on classification tasks. More results on other tasks (e.g., regression tasks like Object Detection or generative tasks like language understanding) are lacking to validate its generalization ability.

Author response:
We appreciate your feedback and are dedicated to providing detailed answers to any questions.

Weakness: The range of tasks tackled remains relatively limited, lacking diversity and complexity in comparison to broader applications. (e.g., regression tasks like Object Detection or generative tasks like language understanding)

Our answer: We will certainly explore the tasks mentioned by the reviewer. For instance, the object detection task involves predicting both the coordinates of the bounding box and the label of the object. This differs from classification tasks, which only predict labels. Consequently, our plan includes conducting theoretical research on reducing information entropy in object detection tasks, followed by experimental validation.If the reviewer is an expert in object detection or related areas, there could be an opportunity for collaboration after the anonymous review period.

Reviewer comment (Evaluation):
For each type of noise, there will exist positive noises. What are their difference and influences?

Author response:
Questions: For each type of noise, there will exist positive noises. What are their difference and influences?

Our answer:  
According to the definition in formula (5), any noise that aids in reducing the entropy of the learning system is labeled as positive noise. The extent of performance improvement resulting from the addition of positive noise depends on the degree to which it decreases entropy. The greater the reduction in the system's entropy, the higher the expected increase in performance.

In our view, these types of noises represent potential ways to alter the entropy of the learning system and influence its performance. One significant distinction is that salt-and-pepper and Gaussian noises have their own distributions and are independent of the data samples, whereas linear transform noise utilizes features from other data samples, making it dependent on the data samples.