Masked BRep Autoencoder via Hierarchical Graph Transformer¶
Conference: ECCV2026
Paper: ECCV Paper
Area: 3D Vision / Self-Supervised Learning
Keywords: boundary representation, masked autoencoder, hierarchical graph Transformer, cross-scale attention, CAD representation learning
TL;DR¶
The method preserves CAD boundary-representation topology while masking raw face and edge geometry and attributes, reconstructing them through dual-resolution cross-scale attention and local message passing to learn transferable representations that reach 88.75% face-level accuracy on MFInstSeg with 0.1% labeled data.
Background & Motivation¶
Industrial CAD models describe not only appearance but also precise surfaces, curves, and connectivity needed for manufacturing and editing. Boundary representation (BRep) places continuous geometry and discrete topology within the same data structure. Consequently, identifying a face as a hole wall, chamfer, or modeling operation requires more than scattered sample points: its connections to other faces matter. Methods such as UVNet exploit this information through surface UV sampling and graph neural networks, but primarily rely on local neighborhood propagation. Meanwhile, intellectual-property restrictions on industrial CAD data make large, high-quality task annotations difficult to obtain.
Unlabeled pre-training can reduce annotation dependence, but its architecture and learning objective still matter. Purely local message passing struggles to capture distant geometric relationships directly, while a flat Transformer does not explicitly separate overall structure from small surface variations. For example, large planes and small fillets can coexist, and uniform dense sampling sends many similar planar signals into the representation alongside important details. Masking only already-encoded features can also allow the encoding stage to expose information about the geometry that should be recovered. The paper therefore changes both the pre-training input and the graph encoder rather than simply using a wider attention network.
Its approach lets coarse-resolution face representations extract global context, uses that context to guide fine-resolution representations, and finally returns to actual adjacency relationships. Here, the hierarchy primarily concerns dual-resolution geometry and global-to-local computation, not successive pooling of a CAD assembly tree. The task remains representation learning: masked reconstruction supplies a training signal and does not directly establish generation of complete, editable, topologically valid CAD files. Core Idea: mask raw geometry without deleting topological connections, infer missing information through cross-scale global interactions and local topology propagation, and transfer the encoder to limited-label tasks.
Method¶
Overall Architecture¶
The input is a BRep with known topology: faces become nodes in a geometric attributed adjacency graph (gAAG), and BRep edges become attributed graph edges. Pre-training begins with random masking of raw geometry and attributes, followed by dual-resolution encoding, cross-scale mutual attention, and local message passing. A two-stage decoder first recovers graph features and then explicit geometry and attributes, with the unmasked input providing reconstruction supervision. Downstream adaptation removes the reconstruction decoder, attaches a face-level or shape-level task head, and fine-tunes the entire encoder together with that head.
%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
Input["BRep geometry, attributes<br/>and fixed adjacency"] --> Mask["Input-Level Masking"]
Mask --> Embed["Dual-Resolution<br/>Geometry Encoding"]
Embed --> Global["Cross-Scale<br/>Mutual Attention"]
Global --> Local["Local Topology<br/>Propagation"]
Local -->|Pre-training| Decode["Two-Stage<br/>Reconstruction Supervision"]
Input -.->|Unmasked targets and stop-gradient| Decode
Local -->|Downstream: complete input| Head["Face-level or shape-level task head"]
Key Designs¶
1. Input-Level Masking: hide observations while preserving the relational structure
By default, the method randomly masks 70% of faces and edges in their raw geometry and attributes, rather than masking latent features after complete encoding. The model cannot directly read the hidden entities' original geometry and must infer it from surviving faces, edges, and global context. Masking does not delete graph nodes or edges; the original topology remains unchanged throughout pre-training. The task is therefore to recover geometry given connectivity, not to infer both graph structure and geometry simultaneously. The authors interpret this as a stricter information bottleneck: block the input first, then learn to aggregate context. The main paper does not specify the exact replacement values for masked raw channels, so neither zero filling nor a particular mask token should be assumed.
Compared with unmasked autoencoding, the model cannot simply learn an approximate identity mapping. Compared with latent gAAG masking, the hidden entities' original observations do not first pass through the BRep encoder of the corrupted-input branch. Table 4 tests these differences separately; they should not be collapsed into a generic claim that pre-training helps.
2. Dual-Resolution Geometry Encoding: retain coarse structure and fine detail for each surface
Each face is sampled in its UV parameter domain on \(3\times3\) and \(13\times13\) grids. Each sample contains 3 coordinate channels, 3 normal channels, and 1 trimming indicator, giving 7 geometry channels. The face attribute vector has 16 dimensions: type with 6, area with 1, centroid with 3, and bounding box with 6. The trimming indicator helps distinguish the actual surface region from the entire rectangular parameter domain. Each edge is uniformly sampled at 13 points, with coordinates, tangents, and normals of its two incident faces forming 12 geometry channels. Edge attributes have 9 dimensions: type with 5, length with 1, and convexity with 3.
Two 2D CNN branches separately encode coarse and fine face geometry into 256-dimensional vectors, while an attribute MLP produces a 128-dimensional vector. Each geometry vector is concatenated with the attribute vector and passed through an MLP to produce its own 256-dimensional node embedding. Edge geometry is encoded by a 1D CNN into 256 dimensions, and edge attributes by an MLP into 128 dimensions, before fusion into a 256-dimensional edge embedding. Thus, subsequent attention operates on dual-resolution features for each face rather than treating every UV sample as an individual attention token. The coarse and fine branches correspond to the same faces; this does not imply fewer face nodes in the coarse branch. The inductive bias separates geometric content at different sampling scales, rather than demonstrating a lower asymptotic attention complexity.
3. Cross-Scale Mutual Attention: aggregate global cues before refining high-resolution features
Cross-scale mutual attention (CSMA) separates face features into low-resolution and high-resolution groups. Low-resolution features query high-resolution features for detail and then aggregate global context through self-attention. The updated global context subsequently guides high-resolution refinement while incorporating explicit edge features. Two CSMA blocks are stacked, allowing overall information and local geometry to interact repeatedly. Unlike uniform single-level interactions across faces, this directed cross-scale route emphasizes extraction followed by feedback. The authors argue that it prevents redundant planar details from overwhelming important geometric changes; the single-resolution and wider-network controls in Table 4 support its task-level benefit.
Equations (1)–(2) are corrupted in the supplied text extraction, preventing reliable recovery of all nested attention operations. The description above follows the prose on pages 6–7 and the explanation of Figure 3, without presenting an inferred operator sequence as the authors' exact formula. The text states that edge features participate in high-resolution refinement, but their complete tensor organization requires the original equations or supplementary material.
4. Local Topology Propagation: emphasize actual adjacency after global context
High-resolution face features from the second CSMA block enter a message-passing neural network (MPNN) together with edge features. The MPNN aggregates information along the supplied adjacency graph, allowing geometric relationships and actual face-to-face connectivity to constrain the representation jointly. This is more than additional depth: global attention can connect distant faces, whereas local propagation explicitly identifies which faces share boundaries. The resulting latent face features support face-level prediction, while the latent graph representation can also feed a shape-level classification head. The main paper delegates specific task-head implementations to the supplementary material; no pooling method or layer-by-layer design is assumed here.
The ordering is itself a testable design choice. Moving the MPNN before the Transformer yields 76.39% accuracy on MFInstSeg with 0.1% labeled data, below the default 88.75%. This comparison supports global-before-local computation in this configuration, but does not imply that all graph tasks should use the same order.
5. Two-Stage Reconstruction Supervision: recover graph representations before explicit geometry
An MPNN graph decoder recovers intermediate graph features from latent face and edge features. The BRep decoder then uses FoldingNet branches to recover face and edge geometry, and two MLP branches to recover their attributes. Face geometry outputs correspond to 7-channel sampled signals and edge geometry to 12-channel signals; attribute outputs have 16 and 9 dimensions, respectively. For faces, the model reconstructs only high-resolution features and their geometry, without separately reconstructing the low-resolution grid; for edges, it reconstructs edge features and original information. High-resolution targets contain finer geometry, encouraging recovery of small structures rather than only approximate overall shape.
The complete, unmasked BRep passes through the BRep encoder to produce intermediate feature targets, with stop-gradient applied to this target branch. The network must therefore recover explicit geometry while aligning decoded graph features with features obtained from complete observations. The authors describe stop-gradient as a safeguard against representation collapse, but this branch should not be interpreted as an undocumented EMA teacher. The dotted edge in the diagram denotes training supervision, not access to complete answers at inference time.
A Worked Example¶
Consider a mechanical part containing planes, a hole wall, and a fillet; this is a conceptual walkthrough, not an additional quantitative experiment from the paper. The same large plane produces coarse and fine UV samples, and the fillet uses both resolutions as well. If pre-training masks the fillet's observations, the adjacency graph still specifies which faces connect to it. The coarse branch gathers overall shape cues from surviving fine-resolution features, and the fine branch updates using global context and edge information. The MPNN then propagates information along actual adjacency, and the decoder attempts to recover the hidden face's geometry and attributes. For machining feature recognition, random masking and reconstruction are no longer performed; a task head classifies faces directly from the encoded representation.
Loss & Training¶
Page 8 lists five supervision terms: latent feature alignment, face geometry reconstruction, face attribute reconstruction, edge geometry reconstruction, and edge attribute reconstruction. Supervision covers all faces and edges, not only masked entities. Exact loss definitions, weights, and attribute-regression details are delegated to unavailable supplementary material, so no total-loss formula is invented here. Pre-training uses AdamW, batch size 128, initial learning rate \(10^{-4}\), cosine decay, and 100 epochs. The default masking ratio is 70%, and experiments use a single NVIDIA A800. Machining-feature fine-tuning runs for 200 epochs, with learning rate \(10^{-4}\) for the task head and \(10^{-5}\) for the pre-trained encoder. The standard setting updates the entire network; Frozen encoder, which trains only the head, is a separate ablation rather than the default evaluation protocol.
Key Experimental Results¶
Main Results¶
Page 9 reports a pre-training candidate collection of 283,018 models, using only 25,000 SolidLetter samples rather than its complete 96,861-model dataset. According to the authors, merging only the training portions yields 198,113 unlabeled models, with downstream test sets excluded from both pre-training and fine-tuning. Machining feature recognition uses an 80%/10%/10% split, whereas modeling segmentation and classification use 70%/15%/15%. Acc is face-level accuracy for the first two tasks, and mIoU averages class intersection-over-union; classification Acc is measured per shape. All results below are percentages, and comparisons should remain within the same dataset and supervision setting.
The following excerpt is from Table 1 on page 11; each dataset has 25 machining-feature classes.
| Dataset | Labeled proportion | Method | Acc | mIoU |
|---|---|---|---|---|
| MFInstSeg | 0.1% | BRepFormer | 33.43 | 7.47 |
| MFInstSeg | 0.1% | BRepMAE | 87.93 | 66.53 |
| MFInstSeg | 0.1% | Ours | 88.75 | 66.38 |
| MFInstSeg | 0.5% | BRepMAE | 94.86 | 83.38 |
| MFInstSeg | 0.5% | Ours | 96.19 | 87.21 |
| MFCAD++ | 0.1% | BRepMAE | 86.38 | 65.75 |
| MFCAD++ | 0.1% | Ours | 89.19 | 67.29 |
| CADSynth | 0.1% | BRepMAE | 93.55 | 78.40 |
| CADSynth | 0.1% | Ours | 93.82 | 79.29 |
| MFInstSeg | 100% | BRepFormer | 99.62 | 98.75 |
| MFInstSeg | 100% | Ours | 99.53 | 98.47 |
The next excerpt is from Table 2 on page 12: 8-class modeling segmentation on Fusion 360 Gallery, where 10-shot means 10 labeled training samples in total, not 10 per class.
| Method | 10-shot Acc | 10-shot mIoU | Full-data Acc | Full-data mIoU |
|---|---|---|---|---|
| BRep-BERT | 59.26 | 19.02 | 95.14 | 82.88 |
| BRT | 54.98 | 13.54 | 94.48 | 79.23 |
| BRepFormer | 50.24 | 12.31 | 94.02 | 78.73 |
| Ours | 72.33 | 34.63 | 97.02 | 86.75 |
By contrast, SolidLetter classification in Table 3 on page 13 uses 10 or 20 examples per class across 26 classes, so its shot budget is not directly equivalent to the table above. Ours achieves 82.51%, 89.58%, and 97.91% Acc under 10-shot, 20-shot, and full-data settings; excluding SolidLetter from pre-training gives Ours* results of 81.83%, 88.47%, and 97.78%.
Ablation Study¶
The following excerpt is from Table 4 on page 14, reporting MFInstSeg face-level Acc (%); column labels denote downstream supervision proportions, while masking ratios describe pre-training configurations.
| Config | 0.1% labeled | 0.5% labeled | 100% labeled |
|---|---|---|---|
| Single resolution, \(13\times13\) only | 85.83 | 93.14 | 99.27 |
| Single resolution, 512 dimensions | 87.17 | 95.46 | 99.41 |
| Triple resolution, adding \(7\times7\) | 86.41 | 94.46 | 99.42 |
| MPNN first | 76.39 | 92.10 | 99.06 |
| No masking, 0% | 66.41 | 84.19 | 99.43 |
| Mask gAAG features | 78.63 | 92.98 | 99.16 |
| Frozen encoder | 82.01 | 92.71 | 98.64 |
| Ours, default 70% masking | 88.75 | 96.19 | 99.53 |
Key Findings¶
- With 0.1% labeled data, removing masking reduces Acc from 88.75% to 66.41%, a difference of 22.34 percentage points; the learning objective is not a minor accessory.
- Widening the single-resolution model to 512 dimensions still gives only 87.17%, but without variance or significance tests, small differences should not all be treated as stable advantages.
- Ours does not lead on every metric: MFInstSeg mIoU at 0.1% is 66.38%, slightly below BRepMAE's 66.53%, and full-supervision performance also trails BRepFormer.
- Table 5 on page 15 reports 6.09M parameters, 5.26G FLOPs, 10.42 ms latency, and 96.01 models/s for the downstream network on models averaging 30 faces; these numbers cannot be extrapolated to large assemblies.
Highlights & Insights¶
- Input-level masking works together with preserved topology: the model loses direct geometric answers but retains a relational structure for inference. This is more specific than merely applying MAE to CAD.
- Dual resolution is not simply an extra feature set concatenated to the original; directed cross-scale interactions organize information. Wider-network and triple-resolution ablations provide concrete comparisons for that choice.
- A frozen encoder still achieves 82.01% Acc with limited labels, suggesting that downstream end-to-end fitting does not explain all gains. However, this establishes representation utility only in the tested setting.
Limitations & Future Work¶
- The authors explicitly acknowledge increased preprocessing and storage costs from dual-resolution sampling, with memory and training-sequence-length bottlenecks for large industrial assemblies.
- Equations (1)–(4) are corrupted in the text extraction, and supplementary material is absent from the supplied source; exact attention equations, loss details, and task heads cannot be reproduced here.
- Page 9 describes pre-training on a 70% training portion of each dataset, while machining tasks use an 80% training split; their nesting should be checked against actual split manifests, rather than asserting leakage or independently verified isolation from prose alone.
- Classification results for BRep-BERT are taken from its original paper rather than rerun with the same code; this qualification matters when interpreting fairness.
- Table 4 does not report variance across random seeds; very limited-label sampling may fluctuate, motivating repeated trials and cost analysis on larger assemblies.
Related Work & Insights¶
- Compared with UVNet / AAGNet: the method retains face and edge geometry with graph adjacency, adding cross-scale global interactions and self-supervised pre-training rather than discarding topology for pure point clouds.
- Compared with BRepMAE: it masks raw inputs directly and adds hierarchical attention before local MPNN processing; limited-label gains in Table 1 coexist with individual mIoU exceptions.
- Compared with BRepFormer: the limited-label comparison changes both pre-training and architecture, so the entire gap against a from-scratch baseline cannot be attributed to CSMA alone.
- Research direction: selecting sampling density based on curvature or geometric complexity could address the reported storage bottleneck; this is a reader proposal, not an adaptive-sampling result validated by the paper.
Rating¶
- Novelty: 4/5. Input-level masking, dual-resolution interaction, and global-to-local organization form a clear combination, although the basic modules are not entirely new.
- Experimental Thoroughness: 4/5. Three task types, cross-dataset pre-training controls, and multiple ablations are covered, but repeated trials and complete reproducibility details are lacking.
- Writing Quality: 3/5. The main argument is clear, while important implementations rely on supplementary material; corruption in this extraction does not imply a typesetting error in the original.
- Value: 4/5. The approach has practical relevance for limited-label CAD representation learning, with applicability still constrained by large-assembly costs.