**Summary:**
The paper addresses the challenges in Machine Learning (ML) for data with real values, specifically focusing on developing canonical representations that are complete, bi-continuous, and invariant under rigid motion. It introduces the concept of 'Nested Distributed Projection' (NDP), a new invariant for clouds of unordered points in Euclidean space, and formalizes conditions for application-driven ML. The paper discusses the significance of these conditions, the practical cases for dimensions and point counts, and the importance of distinguishing between different rigid classes of real objects. It also presents experimental results on large molecular databases, demonstrating the effectiveness of the proposed approach.

**Strengths:**
- The paper formulates a comprehensive problem (Problem 1.1) for complete and bi-continuous invariants, providing a clear framework for application-driven ML in the context of real objects with ambiguous representations.
- The development of the 'Nested Distributed Projection' (NDP) as a solution to Problem 1.1 for clouds of unordered points in 2D space is a significant contribution.
- The paper includes a detailed discussion of past work and how it relates to the proposed approach, highlighting the novelty and practical implications of the solution.
- The experimental results on large molecular databases demonstrate the effectiveness of the proposed method, validating the theoretical contributions.

**Weaknesses:**
- The paper lacks a detailed comparison with existing methods, making it difficult to fully appreciate the novelty and impact of the proposed approach.
- The explanations for some technical concepts, such as 'realizability' and 'bi-continuity', could be more accessible to a broader audience.
- The experimental section could benefit from more context and discussion regarding the limitations and assumptions of the method.

**Questions:**
- How does the proposed method compare to existing approaches in terms of computational efficiency and scalability?
- What are the limitations of the current method in higher dimensions (n > 2)?
- How does the method handle outliers or noise in the data?

**Soundness:**
Soundness result: **3 good**
The paper presents a well-structured and theoretically grounded approach to the problem of developing complete and bi-continuous invariants for ML on real objects. The problem formulation is clear and relevant, the proposed solution (NDP) is novel, and the experimental results support the effectiveness of the method. However, the lack of comparison with existing methods and some technical explanations could be improved.

**Presentation:**
Presentation result: **3 good**
The paper is well-organized, with a clear introduction to the problem, a detailed methodology, and a thorough discussion of the results. The use of bullet points in the abstract highlights the key contributions, and the sections are logically structured. However, some sections could benefit from more detailed explanations or examples to aid understanding.

**Contribution:**
Contribution result: **4 excellent**
The paper makes significant contributions to the field of ML by formalizing the necessary conditions for complete and bi-continuous invariants and providing a practical solution (NDP) for clouds of unordered points. The experimental validation on molecular databases demonstrates the method's practical utility and relevance.

**Rating:**
Rating result: **7 accept, but needs minor improvements**
The paper presents a strong contribution to the field of ML with a clear problem formulation, novel solution, and validation through experiments. However, the lack of comparison with existing methods and some technical explanations could be improved. These issues, while not critical, would benefit from further refinement to enhance the paper's overall impact and clarity.