Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper discussed some findings on the impact of data encoding in quantum NN
strengths_and_weaknesses: **Originality**:

* To my knowledge and understanding, this paper's findings seems original 

**Quality**:

* The paper technically sounds correct and claims well supported by theoretical analysis and experimental results.
* Related works and background knowledge are covered and discussed.
* Experiments are conducted extensively in comparing different aspects for different encoding strategies, experimental results are thoroughly discussed. 


**Clarity**:

* Structure wise, this paper is well written and organised.
* It would be easier to navigate if encoding strategies can have names instead of the one in F2 or F4.



**Significance**:
The finding suggests that different encoding strategies have impact on training accuracy as it affects feature preservation.

questions: * Figure 5 shows that the strategy in figure 4 would decay faster then the on in figure 2 as the qubit increases, is there any comparison on how would this affect training accuracy? Will strategy 4 also summer quick loss than strategy 2?
limitations: The authors have discussed the limitations of the proposed encoding method
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper raise an important issue for data encoding in PQC: concentration. The claim is theoretically and emprically verified. The paper is generaly well-written and the issue is indeed central in quantum machine learning.
strengths_and_weaknesses: Strengths: 
- it is a important issue
- both theoretical and empirical verification
- well-written

Weaknesses:
- no solution provided for the mentioned issue.
- it does not consider various data encoding strategies.
- relatively weak experiment (but it is fine to evidence the concentration issue)


questions: - How do you think about  learning a non-linear data encoding strategy if possiable?
- why specify ${\color{red} 3}nD$ for $\mathbf{x}$ in shape ?

limitations: not found
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This work analyzes the effect of classical data encoding for quantum machine learning models. Focusing on non-reuploading techniques, upper bounds are proved on the divergence between the encoded state and the maximally mixed state. These bounds show dramatic decreases in divergences with increases in number of qubits and depth. These bounds are then verified with a collection of numerical simulations. 

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Note: after author response, rating moved from 6 to 7
strengths_and_weaknesses: Pros:
- Understanding data encodings in quantum machine learning for classical data is critical to fully unlocking the potential of QML and this paper makes an important step in that direction
- The upper bounds proven show important limitations of certain encoding schemes and are practically relevant for QML with classical data
- The visual aids (figures and circuit diagrams) are helpful and make the information clearer
- The paper is generally well written and effective at conveying the point

Cons:
- Including some discussion of other encoding strategies would be beneficial. Understandably the focus is on one, but including other strategies in the empirical results would help practitioners make more informed decisions about encoding techniques.
- Defining cross entropy loss (eq. 8) seems unnecessary 
- Depth 10 is very hard to see in Figure 6(c)
- Experiment code is not released, the authors acknowledge that it should be easy to reproduce, but releasing code would only help to ensure this

questions: - A variety of gradient based optimizers have been used for QVCs, is there a reason why Adam was chosen over other methods?
- Based on the limitations presented in this work, is there any situation in which this style of angle embedding/encoding would be recommended?

limitations: The authors adequately addressed the potential negative societal impacts of their work.
review_title: null

Meta-review: metareview: This submission studies the effect of data encoding from quantum machine learning models. All reviewers agreed on the significance of this work and recommended acceptance.
confidence: Certain
Decision: Accept