Q1. "The formulation in lines 185 and 192..."

Thanks for your correction, we have rewritten the formulas more formally (see Sec. 3.1).

Q2. High perceptual variability among participants

Both clustering analysis and behavioral analysis (e.g., Fig. 3 and A.8) indicate significant perceptual variability among participants on varMNIST. Factors such as demographic characteristics, experimental environments, or purely biological differences could potentially contribute to this variability, but these factors alone are unlikely to fully explain the complexity of perceptual behavior. For instance, two participants may consistently disagree on various stimuli across different digits, which cannot be attributed to a single factor. This is why we introduced individual models to align with specific participant behaviors. These models enable the generation of controversial stimuli between any two participants, providing an opportunity to explore differences in cognitive boundaries between individuals (see Fig. 5).

As for the choice of the number of clusters, it was primarily determined for visualization purposes without specific theoretical justification. Regardless of the exact number, the results consistently demonstrate meaningful intra-cluster and inter-cluster differences. Additionally, we found that analyzing the manipulation experiments offered a clearer explanation of perceptual variability among participants. Therefore, in the updated manuscript, we focused on a detailed analysis of the manipulation experiments (see Sec. 5) and moved the clustering analysis to the appendix. For further details, please refer to Global rebuttal 3.

Q3. Statistical significance

Thank you for raising this concern. In response, we re-ran the human experiments (Global rebuttal 4) and model fine-tuning to ensure statistical rigor. The updated results demonstrate that the individual fine-tuned model achieved an average accuracy improvement of nearly 5% compared to the group fine-tuned model (see Fig. 4b). Across all 246 participants, accuracy improved for 241 participants and decreased for only 5, yielding a p-value approaching 0 for this improvement. It is also worth noting that each participant completed experiments with only 500 samples, a small dataset compared to MNIST (70,000 samples) and varMNIST (20,000 samples). Despite this limitation, our findings demonstrate that even with a small sample size, we successfully captured perceptual variability among individuals.

In addition, we computed the statistical significance for our new manipulation experiments (Fig. 5c). With 18 participants, our manipulation results demonstrated statistical significance, further validating the effectiveness of our findings.

Q4. clarify uncertainty guidance and controversial guidance

Uncertainty guidance and controversial guidance are used separately to generate different subsets of images (see Table 2 and 3). We also conducted a quantitative analysis to compare their effectiveness in generating ambiguous samples for human perception (see Fig.3b, A.11, A.13, A.14).

Q5. Technical novelty

Yes, our work is applicable to cognitive studies and human-AI alignment. However, as noted in W1, the novelty of our work does not primarily lie in combining existing algorithms. Instead, it lies in proposing a systematic process from collection to prediction to manipulation to study human perceptual variability. Compared to exploring decision boundaries between AI models, investigating the differences in decision boundaries among humans is a far more challenging and significant problem.

The human brain is a black box, and we can only collect extremely limited data from individuals, making this task particularly complex. To address this challenge, we proposed methods tailored to generate stimuli with high perceptual variability for human participants (Sec. 3.1, 3.2), conducted extensive behavioral experiments (Sec. 3.3), and ultimately demonstrated the ability to manipulate human behavior effectively. Our results validate that it is possible to reveal human perceptual variability using limited individual data. Although this was achieved within the relatively simple context of digit recognition tasks, it represents a groundbreaking step in achieving precise behavioral manipulatio—something previously demonstrated only in AI systems.

We sincerely thank you for your thoughtful and detailed feedback on our work. Your comments have been instrumental in improving the quality of our manuscript. We have thoroughly addressed the points you raised and incorporated major revisions as detailed in the Global rebuttal section.

W1. Technical contribution

Thank you for pointing out this issue. We have revised the manuscript to better highlight our innovations (see Global rebuttal 3). As shown in our updated Introduction and Figure 1, the primary innovation of our work lies in constructing a systematic research paradigm. This paradigm leverages generated images to reveal human perceptual variability, achieves human-AI alignment at the individual level, and enables targeted modulation of specific participants’ behavior.

We proposed a systematic process from collection to prediction to manipulation, conducting groundbreaking and in-depth research into human perceptual variability. While the techniques of uncertainty and controversial guidance have been explored in prior studies, we are the first to apply these methods to the scientific problem of "human perceptual variability."

Additionally, we introduced new behavioral experiments (see Global rebuttal 1) to further validate our generative model. These experiments demonstrate that the stimuli generated by our model can elicit significant controversial behavior between participants (e.g., ensuring Participant A selects digit 4 while Participant B selects digit 5 on the same stimulus). This is the first time such precise cross-participant modulation has been achieved in visual perception tasks. We believe this work will provide significant insights for future research in human behavior and studies on AI-human alignment.

W2. The post-hoc analysis

Thank you for your valuable suggestions. We have made major revisions to the manuscript to address the issues you raised. Please refer to the Global rebuttal 2 section for details. Our analysis of human experiment on varMNIST now focuses on Fig. 3 and 4 in the updated manuscript, where we provide an in-depth discussion of experiment results and human-AI alignment.

Thank you for your constructive comments. We have made major revisions to the manuscript to address the issues you raised. The modifications can be found in the Global rebuttal.

We have optimized the structure of the paper and supplemented it with detailed experimental descriptions. Please refer to Global rebuttal 3 for more information.

W1&2. Dataset Construction

In the current version of the manuscript, we collected behavioral data from 400 participants, each completing 500 trials, resulting in a total of 200,000 trials across 20,000 stimuli. During data preprocessing, 154 participants were excluded based on control trials (also referred to as sentinel trials in the paper), leaving data from 246 participants, comprising 116,715 trials and 19,943 valid stimuli in varMNIST (Sec. 3.3.1). This means that each stimulus was seen by approximately six participants, providing roughly six labels per stimulus. Based on this labeling, we calculated the entropy of each stimulus and analyzed its variability, enabling a robust discussion of perceptual variability within the dataset. All relevant descriptions in the manuscript have been updated accordingly.

Additionally, we have updated the data collection process to improve the quality of the dataset. Please refer to Global rebuttal 4 for more details.

W3. Manipulate individual behavior

Thank you for your detailed comments. In response to the issues you raised, we have made the following updates and improvements:

We introduced new lab based behavioral experiments (see Global rebuttal 1) to further validate our generative model. These experiments demonstrate that the stimuli generated by our model can elicit significant controversial behavior between participants (e.g., Participant A selects digit 4 while Participant B selects digit 5 on the same stimulus). Notably, each participant labeled only about 500 samples in the first round of the experiment, yet their behavior was successfully manipulated in the second round. These results indicate that we were able to capture perceptual differences between individual participants even with a limited sample size.

Regarding your concern that "subject-finetuned models seem to have very low accuracy for quite a few subjects," we have resolved this issue through updated experiments and fine-tuning methods. Among the 246 participants, the majority of individual-finetuned models achieved accuracies between 0.7 and 0.9, with only two participants falling below 0.6 (see Fig. 4a and Sec 4.2).

W4&5. Naturalness of Images

Our emphasis on natural images stems from our experimental goal: identifying stimuli that evoke inter-participant variability. For example, presenting a noise image to participants and asking them to choose a digit from 0 to 9 may lead to different choices each time, reflecting intra-participant variability. In contrast, we aim to find stimuli (if they exist) that are clearly reasonable for each participant's choice but provoke differing decisions between participants. Such variability could indicate inter-participant differences rather than random intra-participant variability. While we lack a comprehensive understanding of which image features evoke inter-participant variability, reducing intra-participant variability is a logical first step. Generating more natural images becomes essential in this context (e.g., a digit resembling both "3" and "5" and looks like a natural handwritten digit, as shown in Sec. 3.2).

Gaziv et al.’s method, which constructs stimuli by adding perturbations to existing photographic images, generates results that are at least more natural than their baselines (based on adversarial examples), enabling stronger influences on human cognition. Similarly, the “naturalness” discussed here primarily refers to controlling image categories in a manner more aligned with human cognition (rather than introducing noise-like artifacts, as in adversarial examples), rather than focusing on whether the images belong to photorealistic domains. From this perspective, their method is comparatively “less natural” than newer adversarial example approaches based on diffusion models. To avoid misunderstanding, we have revised the description of Gaziv et al.’s work in the Related Works section.

W6. Visualization

Thank you for your suggestion. We have standardized the drawing style and labeling throughout the manuscript and modified the data visualization diagrams based on your feedback.

"W7. Controversial stimuli..."

We used the controversial guidance method described in Sec. 3.1 of the updated paper.

The authors have spent considerable effort on improving the weaknesses mentioned in the review. They have rerun their experiments with an improved focus on data quality, performed an additional experiment to manipulate individual behavior and improved the presentation of their results. I have therefore raised my score.

W1&2. Dataset construction My confusion about the dataset construction and the number of data points has been resolved.

My remaining concern is about the data filtering procedure. The data exclusion criterion resulted in 38.5% participants being excluded because they performed with less than 70% percent accuracy on standard MNIST images.

• How was this criterion for exclusion determined?
  • The proportion of participants that were excluded seems surprisingly high. Why did so many participants fail to classify simple handwritten digits? Recent work (e.g. Thomas et al., 2024) shows that dataset bias between large-scale online experiments and laboratory studies can affect the conclusions drawn from neural network models on online studies. I think this point warrants further discussion.

W3. Manipulate individual behavior

My concern that "subject-finetuned models seem to have very low accuracy for quite a few subjects" seems to be resolved, although it is not really clear to me which of the concrete steps taken by the authors ("novel directional sampling method", "digit judgment experiment", "updated experiments and fine-tuning methods") are responsible for this. Is it the due to the tweaks in the image generation and data collection or due to the substantial amount of data filtering (38.5% of participants)?

I really appreciate that the authors actually performed the kind of experiment I suggested. The effect of controversial guidance on behavior, although relatively small, is statistically significant and provides a more direct test of the proposed method.

W4&5. Naturalness of images

Thanks for the explanation, I now understand what you mean. Like some of the other reviewers, I still have reservations about the naturalness of the images and the validity of the conclusions drawn from artificially generated controversial digits.

W6. Visualization

Thank you for the greatly improved figures with a consistent color scheme.

Minor points:

• "As shown in Figure. 5 and ??" (l. 431)

Additional references: Thomas, T., Straub, D., Tatai, F., Shene, M., Tosik, T., Kersting, K., & Rothkopf, C. A. (2024). Modelling dataset bias in machine-learned theories of economic decision-making. Nature Human Behaviour, 8(4), 679-691.

We sincerely thank your detailed evaluation of our work. We have made major revisions to the manuscript to address the issues you raised. The modifications can be found in the Global rebuttal.

W1. Natural images as stimuli

Regarding the your concern about the focus on digit-like images rather than natural images, we acknowledge this limitation, which we also noted in the manuscript. While natural images are undoubtedly more relevant for many human perception studies, we chose to focus on digit recognition tasks to address a unique challenge: evoking perceptual variability in a domain where participants typically share consistent views. This makes digit recognition an effective and controlled test case for validating our methodology, while natural images often don't elicit such shared views across observers. Also in general, given the novelity of this research activities it seems sensible to start a simple challenge before moving on to more difficult tasks. We hope the reviewer agrees with this research strategy.

W2. Missing Implementation Details

We have updated the manuscript and the relevant appendix to ensure all technical details are clear and complete. Please refer to Global rebuttal 3 for more information.

• The diffusion model is not a pre-trained model but was trained by us. Thank you for pointing out this error, which we have now corrected. Details of the diffusion model have been added to Appendix A.3.1.
• The architectures of the classifiers are described in Appendix A.3.2. The performance of different classifiers in generating high variability images is thoroughly discussed in Fig. 3b, A.11.

W3. Balance of dataset

Your concern is highly relevant, and we have addressed it by improving the data generation algorithm and experimental process, followed by re-collecting the data. Please refer to Global rebuttal 4. We believe the issue you raised has been effectively resolved.

• In the original paper, reference digits were uniformly sampled from the standard MNIST dataset. The images used as experimental stimuli (20,000 in total) are detailed in Table 3 (distribution of different generation strategies), Fig. A.6 (distribution of guided digits). Sec. A.2, and Fig. A.3, A.4, and A.5 further analyze the effects of different methods on stimulus distribution and diversity.

• In the updated paper, our method ensures high uncertainty in the model's predictions for generated images (Appendix A.2.1). Regarding the entropy of human decisions, additional discussions can be found in Fig. A.10 (bottom left) and Fig. 4c, d.

• As detailed in Appendix A.2.1, A2.4 and Fig. A.6, the images viewed by each participant were sampled evenly from the generated dataset of 20,000 images.

W4. Details for finetuning

The details of the finetuning process have been supplemented in Sec. 4.1 and Appendix B.2.

• During the finetuning process, only participant choices were used as labels. For our task, there is no "correct" label, as different participants may make different choices for the same stimulus. This is why the individual model (IndivNet in the paper) is meaningful and necessary.
• The group model (GroupNet in the paper) was trained on the entire varMNIST dataset, which includes all participant choices. During training, the model encounters cases where the same stimulus is associated with multiple labels. However, the model's predictions ultimately align with the majority opinion (i.e., the choice made by most participants).

W5. Improve clarity and readability

See Global rebuttal: 3.

Q1. Why is the MSE loss important?

In the original paper, MSE loss was used to mitigate the bias of the diffusion model, which tended to generate a simpler images due to the imbalance in the prior distribution. Since the guidance method did not specify target digits, MSE loss was necessary to guide generation toward specific digits, ensuring balanced sampling. Reference digits were directly sampled from the standard MNIST dataset. In the revised paper, we addressed this issue more directly by specifying target digits for guidance (see Fig. A.3, A.4, A.5), eliminating the need for MSE loss.

Q2. Why is model entropy centered around 0?

This is because the classifiers trained on the MNIST dataset (base model) exhibits overfitting. When encountering out-of-distribution samples like varMNIST, the models tend to produce overconfident predictions, resulting in model entropy being centered around lower values.

Thank you for your valuable and insightful comments. We sincerely appreciate the time and effort you invested in reviewing our work. We have carefully considered your feedback and made significant revisions to the manuscript to address the issues you raised. Please refer to the Global rebuttal for detailed updates.

W1. Limitation the generalizability

Regarding the your concern about the focus on digit-like images rather than natural images, we acknowledge this limitation, which we also noted in the manuscript. While natural images are undoubtedly more relevant for many human perception studies, we chose to focus on digit recognition tasks to address a unique challenge: evoking perceptual variability in a domain where participants typically share consistent views. This makes digit recognition an effective and controlled test case for validating our methodolog, while natural images often don't elicit such shared views across observers. Also in general, given the novelity of this research activities it seems sensible to start a simple challenge before moving on to more difficult tasks. We hope the reviewer agrees with this research strategy.

W2. Lack of quantitative comparison

We sincerely thank your valuable suggestion. To enhance the reliability of our conclusions, we have supplemented our work with extensive experiments and analyses. Since systematic studies on human perceptual variability are still scarce, there are currently no existing methods that can be directly compared to ours (including those mentioned in the related works section). However, our behavioral analysis of varMNIST demonstrates that our generated dataset exhibits high entropy and guidance success rates, strongly indicating its ability to evoke human perceptual variability (see Figure 3 in the revised manuscript). Additionally, we conducted extensive experiments and analyses to compare human and model performance on perceptual variability. These results confirm that our models can effectively predict human perceptual variability. For further details, please refer to Global rebuttal 2.

Moreover, we introduced new behavioral experiments (see Global rebuttal 1) to further validate our generative model. These experiments demonstrate that the stimuli generated by our model can elicit significant controversial behavior between participants (e.g., ensuring Participant A selects digit 4 while Participant B selects digit 5 on the same stimulus). This is the first time such precise cross-participant modulation has been achieved in visual perception tasks. We believe this work will provide significant insights for future human behavior research and studies on AI-human alignment.

W3. Trade-off Between Alignment and Performance

The reviewer has raised an important point regarding the potential trade-off between perceptual alignment and performance on standard classification tasks. While this is a generally valid concern, our updated fine-tuned models (both group-level and individual-level) have demonstrated a surprising result: we improved perceptual variability alignment (i.e., prediction accuracy on varMNIST) while maintaining performance on standard classification tasks (i.e., prediction accuracy on MNIST)** (see Fig. 4b, A.13). A reasonable explanation for this phenomenon is that, for most participants, their predictions on the standard MNIST dataset are highly consistent. Therefore, even when the models learn participant-specific behaviors, their performance on MNIST remains unaffected.

Upon further analysis, we found that individual and group-level models tend to differ primarily on more challenging stimuli (those with high entropy levels) while showing similar performance on simpler stimuli (see Fig. 4d). Moreover, the difference between individual-level and group-level models becomes more pronounced as task difficulty increases, underscoring the importance of individual alignment. This finding highlights the significance of human perceptual variability in AI-human alignment studies and suggests that studying such variability has important implications for advancing personalized AI systems.

4. Improved data collection process to ensure high-quality experimental stimuli (Sec. 3)

Based on the suggestions from reviewer vTKk, Lgkn and vi4H, we improved our data collection process to ensure the acquisition of high-quality experimental stimuli. Unlike our orignal non-directional uncertainty guidance and controversial guidance methods (based on entropy and KL divergence), we introduced a novel directional sampling method (simultaneously guiding toward digits i and j) to sample more evenly from the ANN's decision boundaries. This resulted in a more diverse dataset (Sec. 3.1 and Appendix A.2.1&A.2.4).

Additionally, to ensure sample quality and avoid generating stimuli that participants would find impossible to classify, we conducted a digit judgment experiment where humans were asked to "is this picture a digit?". The data from this experiment were used to train a judgment surrogate model, which was then integrated into our method for image generation. This step helped preventing out-of-distribution samples and improved the quality of stimuli in varMNIST (Sec 3.2).

To further enhance the quality of the experimental data, we included control trials (also referred to as sentinel trials in paper) from the standard MNIST dataset. Only participants with an accuracy of 70% or higher on these control trials were included in the final dataset. This step eliminated 38.5% of participants. With this measure, we successfully constructed a higher-quality and more reliable varMNIST dataset (Sec. 3.3).

We have conducted new experiments in response to suggestions from reviewers vTKk, Lgkn, and SqUF.

Experiment Details

Given the lack of prior experiments with natural images, conducting a full-scale study within one week posed significant challenges, particularly due to the complexity of cognitive experiments and subsequent analyses. Nevertheless, we performed a small-scale experiment with a limited number of participants, and obtained preliminary results, which are summarized below. These figures will soon be available at the following link: https://anonymous.4open.science/r/HumanPerceptualVariability

Key Findings

1. Evoking Perceptual Variability

   • Sampling along ANN boundaries successfully evoked perceptual differences in humans using natural image stimuli.
   • Example stimuli generated by our method are shown in Fig. B.1, while behavioral results are presented in Fig. B.3.
   • Participant responses (success, bias, and failure) were analyzed, similar to Fig. 3 in the manuscript. The analysis and corresponding data are shown in Fig. B.4 and the table below:

   Guidance Outcome	Proportion
   Success	0.571104
   Bias	0.376564
   Failed	0.052332

   • Typical stimuli with the highest success rates are presented in Fig. B.2. Our findings indicate that stimuli generated from natural images can successfully influence participants' choices with high variability.

2. Capturing Human Perceptual Differences

   • Even with fine-tuning on an MLP head of CLIP, we demonstrated the ability to capture human perceptual differences. Results are detailed in Fig. B.5 and summarized in the tables below:

   Performance on the Group-Level Validation Set

   Model	Accuracy
   Base model	0.571319
   GroupNet	0.614264

   Performance on the Individual-Level Validation Set (noise ceiling is 66.48%)

   Model	Accuracy Mean	Accuracy Std
   GroupNet	0.613882	0.2327
   IndivNet	0.628444	0.24012

Experimental Setup

We followed the experimental paradigm of Gaziv et al. [1] and referenced methods from Chen et al. [2][3]. We introduced uncertainty guidance to generate stimuli using natural image datasets.

• Dataset:

  • Used 9 classes ('Dog', 'Cat', 'Frog', 'Turtle', 'Bird', 'Monkey', 'Fish', 'Crab', 'Insect') from Restricted ImageNet [1][4].
  • Filtered synthetic data yielded 879 images.

• Participants:

  • Recruited 30 participants, each completing 300 trials.
  • Excluded data from 8 participants based on response times, retaining data from 22 participants (6600 trials in total).

• Procedure:

  • A 200ms fixation cross was displayed before each stimulus, which was shown for 200ms.
  • Participants made their choices without time constraints.

References

1. Guy Gaziv, Michael Lee, and James J. DiCarlo. Strong and Precise Modulation of Human Percepts via Robustified ANNs. Advances in Neural Information Processing Systems, 36, 2024.
2. Chen Wei, Jiachen Zou, Dietmar Heinke, and Quanying Liu. Cocog: Controllable Visual Stimuli Generation Based on Human Concept Representations. IJCAI-24, 2024a.
3. Chen Wei, Jiachen Zou, Dietmar Heinke, and Quanying Liu. Cocog-2: Controllable Generation of Visual Stimuli for Understanding Human Concept Representation. arXiv:2407.14949, 2024b.
4. Logan Engstrom, Andrew Ilyas, et al. Robustness (Python Library), 2019.