Reviewer has chosen to be Anonymous

Overall Impression: Average

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes, but limited
Adequacy of the bibliography: Yes, but see detailed comments

Presentation:
Adequacy of the abstract: Yes
Introduction: background and motivation: Limited
Organization of the paper: Needs improvement
Level of English: Satisfactory
Overall presentation: Average

Detailed Comments:

Reviewer confidence: Medium, I've never worked with hyperdimensional computing before, but I'm pretty familiar with neural networks and some of the application domains shared in the paper.

Detailed Comments:
This paper seems like a decent introduction to hyperdimensional computing, and provides pointers that might be interesting to explore as research topics. However, this paper seems to rely heavily on its citations [31] and [32]. While it is a merit that they ground their work on another more robust survey, it transpires a lack of novelty in the paper -- even though I would rather use this paper as the 92 combined pages of the abovementioned survey.

This paper has a decent presentation that would be greatly improved if the authors fixed some of the issues I'll point below:
1. Add citations to many of the statements in the introduction. It is known that Deep Learning systems often lack transparency and a direct interpretation, and that they are power hungry, but please base your statements on a more solid footing.
2. Explain the purposed and structure of your paper at the end of the introduction, as its format is a bit nonstandard.
3. Proofread your paper better before submitting it to a journal. Although it is understandable, the paper has many small mistakes that make its reading less enjoyable (See non-exhaustive list of examples below).

An additional point that I believe would enrich the paper, but that I would not consider absolutely necessary for it in case the authors have a different vision, is having some of the commonly raised criticisms of HDC addressed in the paper, so that the readers can make a somewhat more informed decision on whether to spend more time to read about the area or not.

Non-exhaustive list of mistakes and specific comments:

"as they lack of transparency" -> "as they lack transparency"
"and, pairwise difficult to map the mechanisms to used by human brains to reason and learn using own symbols for objects, abstractions, and the relationships between them." confusing
"The sum-vector (and the mean-vector) has the property of being similar to the addend vectors." -> "The sum-vector (and the mean-vector) has the property of being similar to the added vectors."
"To produce a vector for the set that be dissimilar from those of its elements" -> "To produce a vector for the set that is dissimilar from those of its elements"
"This is a direction that is worth of further investigation." -> "This is a direction that is worthy of further investigation."
"HDC/VSA models have been used for analogical retrieval [51] and references therein)" -> "HDC/VSA models have been used for analogical retrieval [51] (and references therein)"
"It has been pointed out that conventional classifiers assuming that any component of the input vector can be interpreted on its own, a reasonable assumption when components are features endowed with meaningful interpretations, generally not holding for HD representations [31]." -> Very confusing, the sentence continuantion after the second comma does not seem to continue or complement the first sentence.
"generalized LVQ classifiers" -> undefined acronym (easily inferred from the citation, but still would be better to have the full name in the text)
"The approach presented in [37], showed that transforming 2D molecular structures it was possible to construct classifiers for drug discovery problems that outperformed the baseline methods on a collection of tasks." -> they outperformed D-MPNN on only a single dataset (Clintox), please re-check this citation.
"The transformation may be considered as another hyperparameter in a optimization problem which may be determined with the standard statistical approaches such as cross-validation on." -> on what?

Reviewer has chosen to be Anonymous

Overall Impression: Average

Content:
Technical Quality of the paper: Average
Originality of the paper: Yes, but limited
Adequacy of the bibliography: Yes, but see detailed comments

Presentation:
Adequacy of the abstract: No
Introduction: background and motivation: Limited
Organization of the paper: Needs improvement
Level of English: Unsatisfactory
Overall presentation: Average

Detailed Comments:

This manuscript provides a comprehensive survey of the literature on hyperdimensional computing (HDC) aka vector-symbolic architectures (VSA), with a focus on reasoning and learning. Although the significance of reasoning within HDC/VSA is well-justified given the current research interest, the presentation of the entire review paper requires significant improvement. Several technical issues, as well as minor corrections, should be carefully addressed.

The survey's potential contribution is obscured by writing issues. To enhance clarity and strengthen the logic, consider employing tables to showcase the authors’ work (e.g., listing the existing reasoning work in HDC) and comprehensively illustrating those reasoning strategies, including any proposed by the authors. The current version is plain and the logic is not as strong as expected. The following paper is recommended to be incorporated for the reasoning in HDC: “Reasoning with vectors: A continuous model for fast robust inference”.

Additionally, focus on improving readability. While the manuscript provides sufficient examples and cases, articulation is poor. Use simple language and provide necessary interpretations when introducing new strategies.

(Technical issues)

*Change the subtitle to “Perspectives of Learning and Reasoning with Hyperdimensional Computing aka Vector Symbolic Architectures”. Avoid adding a hyphen. If there is no specific reason, it would be more natural to introduce learning before reasoning. Hence in the main context, swap the content in Section 5 and Section 6.

*Enhance the quality of the abstract by incorporating the importance of learning and reasoning using HDC. Given the title, “The Blessing of Dimensionality”, elaborate more in the abstract on the “interesting” properties associated with dimensionality.

*Include figures in the paper to help illustrate ideas. Ensure clarity, especially in Example 4.6 (Page 8), where the absence of a referenced directed graph can confuse readers.

*(Page 4, Line 19-24) The authors' illustration is inspired by the work [26]. However, it is important to note that in [26], the terms “Replication” and “Error-correcting codes” are originally associated with the telecommunication field rather than HDC. The cited work employs these telecommunication concepts to illustrate the “HDC” idea. In essence, the robustness of HDC stems from its redundant representation, where information is encoded and equally distributed over high dimensions.

*(Page 6, Line 2) Clarify the reference of "it" – does it refer to "S," which has not been applied to the majority rule? Make this part clearer.

*(Page 6, Line 19) Provide necessary explanation or citations for the term “difference-vector”, which only appears once in this paper.

*(Page 6, Line 27) Correct the heading to “Multiplication” and remove the first sentence in this line. Addition, multiplication, and permutation are different types of mappings. It is not accurate to say “Mappings can be defined in terms of multiplications”.

*(Page 6, Line 32) The correct output after the XOR should be “0011…10”.

*(Page 6, Line 36) The definition of Hamming distance should be revised carefully. Hamming distance in information theory is exactly what the authors describe, which is integer values and could be higher than 1. In the field of HDC, the Hamming distance should be divided by the dimensionality of the hypervectors so that the distance will range from [0, 1]. Please double-check which definition should be written.

*(Page 7, Line 7-8) Add “, where n is the dimensionality of the hypervectors.” at the end of the first sentence. Reference [26] after “they can be shown”. Similarly, reference [26] at the end of the sentence on Page 6, Line 9.

*(Page 8, Line 17) Illustrate symbols “:”, “::”, and “?” to aid reader understanding.

*(Page 9, Line 51) Replace “smallest distance” with “highest similarity” so that this statement will also be true for non-binary HDC.

*(Page 10, Line 33) The statement “Related to this task, we will deal with…in the following” indicates that the authors propose some solutions. If the authors propose solutions, highlight their contributions in the abstract, main body, and conclusion.

*(Page 10, Line 50-51) Consider encoding triples as “Pht=P1*H + P2*T” for consistency.

*(Page 11, Line 9) Confirm whether it should be “” instead of “”.

*(Page 11, Line 44) I could not find “plethora of *2VEC” in [40]. Please provide the correct reference or terminology.

(Minor corrections)

*Ensure consistency in terminology usage. Introduce terms with full names and abbreviations and reference them consistently. This paper does not reference terms properly. For example, it should not have “hyperdimensional computing” (Page 2, Line 29) and “HD-computing” (Page 11, Line 51) since HDC has already been first introduced on Page 1, Line 42. Similarly, the terms, such as “hypervector”, “hyper-vectors”, “high-dimensional space”, and “hyperspace”, should be first introduced and later referenced consistently. Please fix similar issues for other terminologies throughout the entire paper.

*(Page 1, Line 45) Replace “AI” with “Artificial Intelligence (AI)” and later reference it as “AI”. Do the same for “Machine Learning” and “BSC”.

*Maintain consistency with “HDC/VSA” throughout the paper. Replace “HDC-VSAs” with “HDC/VSA” (Page 10) to align with the literature [31, 32].

*Add references [1-25] correctly. The current manuscript starts with reference [26].

*In modern American English, a comma should follow both “e.g.” and “i.e.”. Correct them in the entire paper.

*(Page 2, Line 41) Fix “ans”.

*(Page 3, Line 17) Revise the brackets for reference “[32”.

*(Page 3, Line 48) The use of “very” does not add much value. Additionally, it is used twice in the same sentence.

*(Page 3, Line 50) Add a reference after “deep learning” to allow readers to refer to the paper that illustrates the importance of hyperspaces.

*Eliminate unnecessary italics for terminologies such as “IoT,” “Edge Computing,” and “SVM.” Use full names with abbreviations for IoT and SVM in the first introduction and reference them using abbreviations later. Use lowercase for “edge computing.”

*(Page 4, Line 33) Avoid using “2E+3010” in a scientific paper.

*(Page 4, Line 38) Add necessary citations for the first sentence under “Basic Operations”.

*(Page 5, Line 15) Correct “th basic” to enhance clarity.

*(Page 6, Line 15-16) Revise to “that is dissimilar…before being stored it in memory”.

*(Page 6, Line 30) Specify that “ordinary bitwise multiplication is used” for precision.

*(Page 6, Line 46) Fix “as as”.

*(Page 6, Line 47-48) Replace the semicolon with a period at the end of the sentence for better structure.

*(Page 6, Line 51) Add a left parenthesis after “permutation matrix”.

*(Page 9, Line 15) Unexpected “)” appears after “therein”. Fix it.

*(Page 9, Line 29) Change to “An interesting…” for grammatical accuracy.

*(Page 9-11) Change to “an HD” and “an HDC/VSA”. Correct similar mistakes throughout the whole paper. For example, it is supposed to be “an autoassociative” memory on Page 5, Line 47.

*The usage of commas should be paid attention. For example, adding a comma on Page 12, Line 19 can enhance the readability. In this manuscript, there are a lot of sentences that may need the employment of a comma. Improve them.

*(Page 11, Line 26) Provide the full name for “FOL” and do the same for “XAI” on Page 12, Line 37.

*(Page 11, Line 41) It should be “is” instead of “are”.

*(Page 12, Line 22) It is supposed to be “extraction” rather than “exaction”.