BrepEncoder: Neural CAD Encoding

• BrepEncoder is a module that converts CAD's B-Rep models—comprising faces, edges, and vertices—into compact latent codes while preserving geometric and topological details.
• It integrates methods like graph neural networks, autoencoders, and tokenization schemes to efficiently encode complex CAD structures for downstream machine learning tasks.
• Empirical studies show enhanced performance in memory efficiency, reconstruction speed, and watertight validity compared to traditional CAD representation methods.

A BrepEncoder is any module or architecture that processes Boundary Representation (B-Rep) models—parametric CAD solids represented as sets of faces, edges, vertices, and their precise topological adjacencies—into compact latent codes, feature vectors, or discrete sequences for downstream machine learning pipelines. BrepEncoders are central to nearly all modern neural approaches for CAD handling, enabling neural models to reason about 3D geometry and topology directly from native B-Rep data. The landscape of BrepEncoder designs is diverse, incorporating point/curve/surface feature extraction, graph neural networks, autoencoders, quantization, and diffusion or autoregressive tokenization, with each paradigm optimized for generative, discriminative, or multimodal interfaces.

1. Core Principles and Motivation

B-Rep models are the canonical representation in CAD, encoding both exact geometry (typically as NURBS, planes, cylinders, etc.) and an adjacency graph linking faces, edges, and vertices. BrepEncoders are designed to map these high-fidelity, variable-structure models into fixed-dimensional spaces or length-adaptable token streams, facilitating further processing by deep learning systems—e.g., generative models, neural editors, or LLMs—without lossy mesh or voxel conversion.

Key objectives in the design and adoption of BrepEncoders include:

• Preserving geometric and topological fidelity: Encodings must maintain both the precise surface/curve geometry and entity adjacencies to ensure downstream tasks respect original model validity, watertightness, and manufacturability.
• Data efficiency: Strategies such as direct NURBS parameter consumption, adaptive sampling, or quantized latent compression reduce storage, memory, and computation relative to UV-grids or naive point clouds.
• Compatibility with neural architectures: Output formats (dense vectors, token sequences, graphs) are tailored for transformers, GNNs, or diffusion models as required by the application context.

2. Representative Encoder Architectures

Recent works have converged on several major design archetypes for BrepEncoders. The following table summarizes salient properties of key published encoders:

Paper / Model	Input Features	Core Encoding Method	Output Format
HoLa-BRep, B-repLer (Liu et al., 19 Apr 2025, Liu et al., 13 Aug 2025)	Per-face surface/adjacency	MLP + GNN over face graph	32-d per-face vectors
NeuroNURBS (Fan et al., 2024)	Native NURBS params (control points, knots, weights)	Transformer over grid/padded features	48-d per-surface latent
BrepGen (Xu et al., 2024)	UV-grids for faces/edges, bounding boxes	VAE for geometry, tree structuring for topology	Latent tensors + tree
BrepLLM (Deng et al., 18 Dec 2025)	Area/length-adaptive point sampling on faces/edges	Multi-scale: PointTransformerV3, NNConv, EGAT	128-d per-face, global token
BRepNet (Lambourne et al., 2021)	Per-entity features, coedge adjacency	Topological walks, MLPs, message passing	Per-face/edge/coedge states
BrepGPT (Li et al., 27 Nov 2025)	Voronoi Half-Patch per half-edge	Dual VQ-VAE, vertex-centric tokens	11-token per vertex
BR-DF (Zhang et al., 18 Nov 2025)	Volumetric SDF+per-face UDF grids	3D VQ-VAE, U-Net latent diffusion	Scalar fields (latent volumes)
AutoBrep (Xu et al., 2 Dec 2025)	UV-grids for geo, adjacency graph	AE+FSQ, BFS tokenization, Transformer	Discrete token sequence

Each approach balances trade-offs between expressivity, computational efficiency, and architectural compatibility with generative or editing pipelines.

3. Detailed Workflows and Mathematical Formulations

BrepEncoder workflows typically comprise several computational stages:

1. Entity Extraction & Preprocessing: Faces, edges, and sometimes coedges are enumerated. For each, raw parameters (surface/control points, curve samples, adjacency indices) are aggregated. When applicable, area- or length-adaptive sampling ensures uniform feature richness across primitives of varying size (Deng et al., 18 Dec 2025).
2. Feature Mapping and Embedding:
   • Per-Primitive MLPs/Transformers: Raw attribute vectors for each entity are embedded via MLPs or transformers, often separately for faces and edges. For NURBS input (as in NeuroNURBS), surface parameters are directly embedded without recourse to surface re-sampling (Fan et al., 2024).
   • Graph Neural Refinement: Adjacency graphs connect surface nodes. GNN layers propagate context and refine local embeddings via message passing (Liu et al., 19 Apr 2025, Liu et al., 13 Aug 2025).
   • Topological Handling: Some architectures (e.g., BRepNet) operate at the coedge level, employing topological walks across entity types to aggregate neighbor context (Lambourne et al., 2021).
3. Latent Compression & Quantization:
   • (V)AEs and Quantizers: For generative models or tokenizers (e.g., BrepGen, AutoBrep), high-dimensional entity features are compressed via VAEs or quantized into discrete tokens using methods such as Finite-Scalar Quantization or VQ-VAE stacks (Xu et al., 2024, Xu et al., 2 Dec 2025, Li et al., 27 Nov 2025).
   • Tokenization Schemes: Output tokens maintain information on geometry, bounding boxes, and local/global topology, arranged for efficient transformer consumption—e.g., breadth-first face ordering (Xu et al., 2 Dec 2025), vertex-centric interleaving (Li et al., 27 Nov 2025).
4. Output Aggregation:
   • Per-Primitive Tokens: Most methods produce a fixed- or variable-length sequence of per-face/edge or per-vertex tokens, each containing sufficient information for geometry reconstruction.
   • Global Summary Vectors: For tasks such as retrieval or contrastive alignment, a global pooled vector is produced (e.g., in BrepLLM (Deng et al., 18 Dec 2025)).

4. Integration in Generative and Editing Pipelines

BrepEncoders are foundational components in a variety of neural CAD pipelines:

• Text/Multimodal Editing: In B-repLer, the HoLa-BRep encoder provides per-face vectors, which are lifted to transformer tokens and fused with image and text representations for semantic editing via multimodal LLMs (Liu et al., 13 Aug 2025). Cross-attention enables high-level, text-driven shape modification while enforcing geometric validity.
• Autoregressive Generation: BrepGPT and AutoBrep employ token-level generation strategies, where the encoder facilitates mapping of B-Rep structure into discrete tokens appropriate for sequence modeling, leading to scalable, watertight B-Rep synthesis (Li et al., 27 Nov 2025, Xu et al., 2 Dec 2025).
• Diffusion-based Modeling: In BrepGen, the encoder provides node embeddings for tree-structured denoising diffusion, while BR-DF leverages volumetric latent spaces to guarantee watertight faceted B-Rep reconstructions (Xu et al., 2024, Zhang et al., 18 Nov 2025).
• Language Integration: BrepLLM aligns B-Rep feature tokens with frozen text embeddings (e.g., CLIP), bridging natural language and CAD geometry for descriptive, reasoning, and QA tasks (Deng et al., 18 Dec 2025).

5. Empirical Results and Quantitative Comparisons

Extensive experimental studies demonstrate the efficacy of BrepEncoder designs in diverse generative and discriminative settings. Key performance findings include:

• AutoBrep achieves higher geometric coverage, lower MMD/JSD, and superior watertight validity rates (70.8%) versus BrepGen and HoLa on ABC-1M generation tasks (Xu et al., 2 Dec 2025).
• NeuroNURBS provides ~8× memory and storage savings and 13× reconstruction speedup over UV-grid baselines, with comparable or improved generative and segmentation quality (Fan et al., 2024).
• BR-DF achieves perfect (100%) watertight validity and identical topology recovery in round-trip conversion, unparalleled among prior methods (Zhang et al., 18 Nov 2025).
• BRepLLM demonstrates SOTA text-to-BRep alignment and downstream task scores by leveraging a hierarchical, multi-context encoder (Deng et al., 18 Dec 2025).
• BRepNet surpasses point cloud and mesh-based models for face segmentation accuracy and efficiency (92.52% accuracy, 359k parameters) (Lambourne et al., 2021).

Ablation studies consistently show that topological context propagation (via GNN/self-attention), spatial orientation information (e.g., UV-grid resolution), and properly quantized geometry tokens are all critical to maximizing downstream validity and fidelity (Liu et al., 19 Apr 2025, Xu et al., 2 Dec 2025).

6. Open Challenges and Future Directions

Despite substantial advances, several open challenges persist:

• Scalability and Variable Sizes: While tokenization schemes (AutoBrep, BrepGPT) have reduced generation complexity, there remains an inherent tension between fixed-length sequence designs and the unbounded structural variety of industrial B-Reps.
• Semantic Annotation and Construction History: Lack of annotated datasets with operation-level semantics constrains supervised learning of high-level editing and reasoning tools, as explicit in B-repLer’s data pipeline (Liu et al., 13 Aug 2025).
• Hybrid Representations: Emerging lines, such as BR-DF, indicate the utility of volumetric fields for guaranteeing topology, suggesting potential synergies with explicit-entity encodings for hybrid robust pipelines (Zhang et al., 18 Nov 2025).
• Integration with Symbolic and Human-Interpretable Graphs: While current encoders focus on geometric fidelity and connectivity, further work is needed to bridge to human-interpretable design semantics and construction workflows at scale.

• "B-repLer: Semantic B-rep Latent Editor using LLMs" (Liu et al., 13 Aug 2025)
• "HoLa: B-Rep Generation using a Holistic Latent Representation" (Liu et al., 19 Apr 2025)
• "BrepLLM: Native Boundary Representation Understanding with LLMs" (Deng et al., 18 Dec 2025)
• "NeuroNURBS: Learning Efficient Surface Representations for 3D Solids" (Fan et al., 2024)
• "BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry" (Xu et al., 2024)
• "BRepNet: A topological message passing system for solid models" (Lambourne et al., 2021)
• "BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch" (Li et al., 27 Nov 2025)
• "B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?" (Zhang et al., 18 Nov 2025)
• "AutoBrep: Autoregressive B-Rep Generation with Unified Topology and Geometry" (Xu et al., 2 Dec 2025)

These works define the current state of the art in geometric neural representation learning for CAD, with the BrepEncoder at the crux of nearly all advances in intelligent, data-driven 3D engineering workflows.