Thank you for your careful assessment and recognition of our novel contributions, such as the semi-autoregressive architecture, part-wise decomposition, triplane projection guidance, and hierarchical KNN aggregation. We appreciate your acknowledgment of our technical soundness and clear ablation studies. Please find below our responses to your concerns, organized by weaknesses, questions, and limitations.

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W.1: Limited Scope of CAD Operations

While our experiments focus on sketch-extrusion operations (that constitute the majority of parametric CAD workflows), our framework is inherently operation-agnostic. The core contribution lies in projection-guided, part-aware geometry reasoning, which readily extends to other operations such as sweeping and lofting. Our approach introduces a learnable mapping from geometric features to modeling instructions that is not constrained to specific operation types. Extending to sweeps or lofts would require expanding the instruction vocabulary and incorporating additional primitives (guided curves, profiles), but the fundamental projection-guided reasoning and part-aware decomposition principles remain directly applicable.

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W.2 / L.2: One-to-Many Mapping and Ambiguity Resolution

You raised an insightful point about the inherent ambiguity in geometry-to-sequence mapping. As discussed in the Limitation section of the main paper, multiple valid construction paths often exist for the same geometry, reflecting different design philosophies and modeling preferences.

Our current deterministic decoding validates the proposed framework, but we recognize this limitation. In preliminary investigations, we found that resolving ambiguity requires defining optimization criteria (e.g., minimizing sequence length, the number of sketch-extrusion pairs, or the use of sketch primitives). However, these may not align with real-world practices, where experienced designers often prefer multiple simple operations over single complex ones for clarity and reusability.

We strongly agree with your suggestion on distributional outputs. Generating multiple plausible instruction paths represents a promising direction that could provide designers with meaningful alternatives while preserving semantic richness. This could involve variational architectures, mixture models, or beam search strategies to explore valid reconstruction sequences.

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W.3: Alternative Representation Exploration

Our work is strategically positioned within sequence modeling to reconstruct procedural CAD instructions from point clouds. Unlike neural B-Rep approaches (explicit surfaces/topology) or CSG methods (Boolean primitives), our sequential representation captures the temporal and logical structure of the modeling workflow itself.

This distinction is crucial, as we preserve not just geometric outcomes but procedural knowledge of how geometry was constructed. Sequential representations naturally support part-level modifications, constraint editing, and design iteration workflows fundamental to parametric CAD practice.

Our experiments also demonstrate competitive accuracy against recent fitting-based methods, further validating the practical effectiveness of our framework. Finally, the instruction representation can be straightforwardly compiled into B-Rep or CSG forms for compatibility with existing CAD engines, whereas the reverse conversion remains under-constrained and not directly attainable.

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Q.1: Alternative Input Modalities

While our current work focuses on point cloud inputs for implicit part decomposition and projection-guided decoding, the framework is flexible. Core ideas of part-wise decomposition and projection-guided reasoning can extend to sketch or image inputs through modality-specific encoder adaptations. In particular, the projection-based decoding design is well-suited for integration with 2D sketch or image features. Such extensions would significantly broaden practical applicability for reverse engineering and design digitization.

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L.1: Real-World Point Cloud Challenges

We acknowledge that noisy or incomplete point clouds are common in real-world applications. In our main paper (Section 4) and Appendix C.3, we evaluate the robustness of our method through real-scan experiments (using data from consumer-level 3D scanner), along with systematic tests involving surface perturbations (to simulate noise) and partial inputs (to simulate occlusion or incompleteness). The results show that our framework remains effective under such challenging conditions.

We greatly appreciate your detailed and thoughtful evaluation. Your positive assessment of our pipeline design, projection features, attention mechanisms, and comprehensive ablation studies is highly valued. Below we address your insightful concerns with additional clarifications.

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W.1: Technical Novelty and Integration

While individual modules do build upon established techniques, our main contribution lies in their thoughtful integration to address CAD-specific challenges. Our novelty centers on: (1) autoregressive part decomposition that produces interpretable, structure-aware latents as semantic anchors; (2) projection guidance that injects design-intent-aware features through rotation-guided triplane projections; and (3) non-autoregressive parameter decoding that efficiently generates sketch-extrusion instructions while preserving consistency. This cohesive design has demonstrated effectiveness and contributes to more interpretable CAD generation.

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W.2/W.3/Q.3: Model Generalization and Data Dependency

You raised excellent points about data dependency. We acknowledge that high-quality data plays an important role, as in most deep learning domains. However, our framework goes beyond template memorization through structured part-wise decomposition and projection-guided decoding, offering generalization beyond replicating training sequences. We performed careful deduplication to prevent data memorization and ensure that the model doesn't rely on near-identical examples. As shown in Figure 1 (main paper) and Figures 12-13 (Appendix C.2), our method successfully reconstructs diverse shapes with complex sketch structures and intricate topologies, demonstrating robustness across various design variations, though extremely complicated configurations remain challenging.

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W.3/Q.3: Construction Ambiguity and Modeling Diversity

We acknowledge that construction path ambiguity is a fundamental challenge in procedural CAD modeling, as the same geometry can often be constructed through different valid instruction sequences. Addressing such ambiguity often requires specifying some optimal criteria (e.g., minimizing sequence length, the number of sketch–extrusion pairs, or the use of curve primitives), which may diverge from natural human modeling habits. Rather than enforcing a single canonical path, our work focuses on how to effectively generate valid instruction sequences for the given shape. While our current framework employs a deterministic decoding strategy, future work will aim to model this ambiguity explicitly and explore criteria for defining optimal or human-aligned construction sequences.

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W.3/Q.1: Intermediate Representations and Structural Supervision

We appreciate your insightful comments regarding the intermediate representations. In our current design, we adopt an autoregressive implicit part decomposition strategy conditioned on both the 3D point cloud features and previously generated latents. This approach is inspired by the incremental nature of CAD modeling, where even operations like Cut or Intersect can be viewed as negative geometric increments. To guide the decomposition process, we employ a Part Discriminator that evaluates the validity of each generated latent and provides supervision during training. Beyond this core motivation, we would like to share two of our experiences.

First, for explicit intermediate representations, two common forms are part-level point cloud segments or part-specific point cloud features. We experimented with bypass tasks (e.g., part-level segmentation) to incorporate more structured intermediate cues. However, these efforts yielded only marginal gains in accuracy and came at the expense of increased computation and framework complexity. As a result, we opted for a more flexible implicit decomposition strategy coupled with part validity supervision, which has proven effective across a wide range of CAD modeling scenarios.

Second, regarding the autoregressive generation strategy, we also experimented with one-shot approaches that generate all part latents from the input point cloud in a single forward pass. However, we observed lower performance and frequent discontinuities in latent generation (e.g., premature invalid part latents).

Despite these experiences, we recognize the importance of intermediate representations and will continue to explore more effective and efficient mechanisms to incorporate them into future iterations of our PartCAD framework.

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W.3/Q.2: Autoregressive Generation and Error Accumulation

We agree that error accumulation or drifting is a common challenge in purely autoregressive frameworks. In our preliminary experiments, we observed this issue when extending the autoregressive formulation to the CAD instruction generation stage (i.e., directly generating the sequence tokens). As discussed in W.3/Q.1, introducing more explicit intermediate representations helps alleviate this issue by providing stronger geometric grounding. Beyond that, we also explored feature-level solutions, such as similarity-based mechanisms for distinguishing part latents, but they yielded limited gains.

In our current setup, where autoregression is applied only to the part decomposition stage, we did not observe significant drifting effects in our experiments, as evidenced by both quantitative results and visual reconstructions. In addition, several design choices help mitigate this issue. The Part Discriminator provides explicit supervision to guide the generation of valid parts and suppress the propagation of invalid latents. The rotation-guided projection introduces strong geometric priors during instruction decoding, while the localized and structured nature of sketch loops offers further geometric constraints across parts.

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Q.4: Cross-Part Operations and Decomposition Dependencies

We understand your concern regarding potential limitations of the decomposition and decoding strategy and would like to provide the following clarification.

First, in typical CAD modeling workflows, any cross-part operations (e.g., Join, Cut, or Intersect) are generally performed after a base body has been created. This modeling paradigm is also strictly followed in all CAD sequences within the DeepCAD dataset. Our framework explicitly models each CAD part as a sequence of sketch–extrusion pairs, with each part latent independently decoded into its corresponding instruction sequence. Each sketch–extrusion pair represents a complete and self-contained solid modeling operation (e.g., Newbody Creation, Cut, Join, Intersect). Importantly, these operations are executed incrementally and can only act on geometry that has already been constructed up to that point. No instruction is allowed to depend on future parts or not-yet-created geometry. This paradigm adheres to standard CAD modeling conventions and is consistent with the behavior of commercial CAD systems.

Second, while the final CAD instructions in our framework are generated in a single forward pass, the parameter decoder leverages both local 2D projections and global 3D context. The global context is encoded via autoregressively generated part latents, which inherently capture structural dependencies between each modeling step. This design enables geometry-aware and part-specific predictions by modeling both intra-part details and inter-part relationships.

We acknowledge the existence of certain scenarios (like lofting operations requiring simultaneous access to multiple parts) that fall beyond our current scope, and we're interested in developing hybrid formulations for more complex inter-part constraints in future work.

We sincerely appreciate the time and effort you devoted to reviewing our work. We are glad that you found the overall structure clear and that the figures and appendix supported the presentation effectively. Thank you for your positive comments on the design and evaluation of key components, including the part-aware decoding, projection guidance, and instruction generation, as well as your recognition of the real-world reconstruction results. Below please find the responses to the two points you raised for clarification.

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W.1: Part Latent Decomposition Process and Supervision

We respond to this question in three aspects:

(1) Part Latent Decomposition and Decoding: As described in the Autoregressive Implicit Part Decomposition part of Section 3, the input 3D point cloud is encoded and autoregressively decoded into several part latents via a part decoder (implemented as a four-layer Transformer). These part latents serve three purposes: (i) guiding final instruction generation, (ii) providing rotation cues for projection, and (iii) being supervised for part validity.

(2) Orientation Prediction and Supervision: Each part latent is fed into the Orientation Predictor (implemented as a single-layer MLP) to estimate its rotation parameters, which guide the subsequent projection onto canonical planes. The predicted rotations are supervised using a cross-entropy loss ($L_\text{rot}$) computed from the ground-truth orientation parameters (Euler angles).

(3) Validity Supervision: To supervise the implicit decomposition of the 3D point cloud, a Part Discriminator (implemented as a one-layer MLP) predicts the probability that each part latent corresponds to a valid part. A binary cross-entropy loss $L_\text{val}$ is computed between these predictions and the ground-truth validity labels.

The supervision details for both rotation and validity are described in the Optimization part of the Section 3 and all supervision signals (including rotation parameters and part validity one-hot labels) can be directly obtained from the dataset.

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W.2: Model Complexity and Scalability

Beyond the qualitative results presented in Figures 5–6 of the main paper, we also provide further examples in Figure 1 and Figures 12–13 (Appendix C.1), showcasing reconstruction results for CAD models with complex sketch structures and topologies. These examples highlight PartCAD’s capability to recover intricate sketch layouts and handle multi-body relationships and solid modeling operations. While longer instruction sequences may introduce greater prediction uncertainty, we have not observed significant error accumulation in practice. Empirically, modeling difficulty is influenced more by geometric complexity than by the number of part latents. For example, a geometrically complex single-part model can pose greater challenges than a multi-part assembly of simpler components.

As detailed in the Implementation Details part of Appendix A.1, our current experimental setup supports up to 10 part latents (i.e., sketch–extrusion pairs) per CAD model. Each part latent can include up to 6 sketch loops, with each loop consisting of at most 15 curve primitives. This configuration covers all modeling cases in the DeepCAD dataset.

We sincerely thank you for the thorough review and constructive feedback. We appreciate your thoughtful questions that will help improve our work. Below are our responses to your concerns, along with additional clarifications.

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W.1/W.4/Q.2: Structure, Parts, and CAD Modeling

We appreciate your point about 3D structural complexity. Our work specifically targets the procedural structure inherent to CAD modeling workflows, where part-wise decomposition provides a tractable abstraction that aligns well with standard CAD practices. Each "part" in our context represents a meaningful modeling step (sketch-extrusion pair) that captures design intent rather than purely geometric segmentation.

We perform implicit decomposition through autoregressive latent generation, allowing each part to naturally correspond to procedural modeling actions while avoiding the complexities of geometric partitioning. Through our experiments, we found this implicit formulation more effective and scalable than explicit segmentation approaches. We will revise the introduction to better articulate this CAD-specific scope and procedural focus.

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W.2/W.5: Related Work and Comparisons

Thank you for highlighting these important references that we missed. We will include them in the revision, as they provide valuable context for part-based latent modeling. Our work focuses specifically on procedural CAD sequence generation rather than static shape analysis or segmentation. Regarding Point2Cyl, our approach takes a different direction. We generate structured instruction sequences using discrete tokens aligned with formal grammar, ensuring syntactic validity and semantic interpretability. Point2Cyl, in contrast, fits continuous cylinders using implicit functions, without the symbolic structure needed for procedural modeling. We will include a more detailed comparison highlighting these complementary approaches.

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W.3: CAD Operation Coverage

You raised an important point about our current scope. We acknowledge that real CAD models typically involve more operations and primitives. Our current work focuses on sketch-extrusion operations that constitute the majority of parametric CAD workflows, but this is indeed a limitation we should discuss. We appreciate the pointer to CAD-Recode and will cite it along with a discussion on extending to broader CAD operations. Our framework is designed to be extensible to richer operations (sweeping, lofting) and sketch primitives (splines, complex curves) given appropriate training data, which we plan to pursue in future.

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W.6/Q.3: Autoregressive Design Choice

While global features are extracted in a single pass using a standard encoder, part latents are generated autoregressively to reflect the sequential nature of CAD modeling, allowing each part to condition on previous ones and capture inter-part dependencies consistent with real-world workflows. We did explore one-shot alternatives that generate all latents simultaneously, but observed reduced performance and less stable outputs, particularly with premature or invalid part generation. While autoregression does reduce parallelism and could potentially introduce error accumulation, we found minimal runtime overhead in practice and no significant output drift thanks to the supervision from our Part Discriminator. We will include a more detailed discussion of this design trade-off in our revision.

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W.7/W.8: Discretization and Datasets

Discretization does introduce quantization error, but we found this trade-off worthwhile as it significantly improves training stability compared to direct regression approaches. The discrete formulation also enables more structured supervision and token-based evaluation. Regarding datasets, we focused on current datasets to maintain consistency with prior work. They contain complex samples with long, hierarchical sequences, suitable for testing our method's robustness. We appreciate the suggestion about CC3D and are currently applying for access to include it in future evaluations.

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W.9: CAD-Aware Evaluation

We agree that CAD-aware evaluation is crucial. Our framework does integrate CAD-aware design in both training and evaluation. During training, we supervise both geometric parameters and structural/semantic tokens that encode high-level CAD concepts like boundary markers and Boolean operations using cross-entropy loss. Our evaluation goes beyond pure geometry through token-level F1-scores that assess both low-level parameters and high-level instruction structure.

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W.10/W.11: Point2Cyl Comparison and Real Scan Evaluation

We excluded Point2Cyl from instruction-level comparison because its outputs use continuous implicit representations rather than discrete symbolic primitives. While its 2D sketches may visually resemble our primitives, they're defined through fitted parameters rather than explicit modeling commands. Post-hoc parsing into symbolic tokens is possible but often unreliable. For real-world scans, our evaluation is primarily qualitative, as most real scan datasets unfortunately lack the high-quality parametric CAD annotations needed for rigorous quantitative comparison. We plan to curate more scan-CAD pairs with parametric labels for future research.

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W.12: Statistical Rigor and Error Reporting

We sincerely apologize for the mismatch in our checklist, which was our oversight. You’re absolutely right that empirical results should be supported by proper statistics. Since model parameters are fixed after training, variability primarily arises from inference randomness and stochastic point sampling in the Chamfer Distance computation. To address this concern, we conducted 10 independent inference runs without fixed random seeds and computed mean and standard deviation for the main metrics (see the following 2 tables). Our original experiments followed strict protocols: consistent data splits, fixed training seed, dataset deduplication, and full implementation details (see Section 4, Appendix A.2–A.3). We acknowledge the importance of reporting statistical variation. We will include error bars and statistical analysis in the final version and sincerely appreciate your attention to this crucial issue.

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Table: Experiments in DeepCAD Dataset

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Table: Experiments in Fusion360 Dataset

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Q.1: Instruction Format Details

CAD modeling instructions are structured as $C =${$c_n$}$_{n=1}^N$, where $N$ is the sketch–extrusion pairs. Each instruction consists of sketch and extrusion components, both quantized as 8-bit discrete sequences (see Section 3 and Appendix A.1). The sketch component has variable length depending on the number of 2D primitives and structural boundary tokens, while the extrusion component is fixed at 11 tokens covering orientation, position, scale, depth, and Boolean operations. For parallelization and efficient training, each instruction sequence is padded to a fixed length of 110 tokens, which covers all samples in our current dataset.

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Q.4: Hierarchical KNN Design Rationale

The hierarchical KNN aggregation serves as an intermediate step for selecting reliable neighborhoods among 2D projection points, which are then processed by learnable encoders (EdgeConv layers). This design augments learning with geometric priors rather than replacing it entirely. It is motivated by the observation that important CAD structures (sketch profiles, extrusion contours) exhibit locally coherent patterns in projection views. Our hierarchical KNN applies three-stage refinement considering spatial proximity, radial alignment, and surface normal similarity to identify geometrically consistent regions that correspond to underlying modeling processes. This helps the encoder learn more robust features for CAD instruction generation.