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arxiv: 2604.22984 · v1 · submitted 2026-04-24 · 💻 cs.CV · cs.GR

BrickNet: Graph-Backed Generative Brick Assembly

Peter Kulits , Cordelia Schmid This is my paper

Pith reviewed 2026-05-08 12:22 UTC · model grok-4.3

classification 💻 cs.CV cs.GR
keywords LEGO assemblygenerative modelsgraph representationslanguage modelsbuild sequencesphysical constraints3D generationLDraw
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The pith

Representing LEGO assemblies as connectivity graphs lets language models generate long, physically valid build sequences for thousands of brick types.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper trains language models to output sequences for assembling LEGO bricks drawn from a wide variety of part types. Earlier work handled only simple voxel-style towers, but this setting involves complex objects whose parts have many different connection rules. Direct prediction of 3D positions quickly produces sequences that violate physical constraints. Instead, the authors encode each structure as a graph whose edges capture how parts attach to one another. This graph representation keeps the generated sequences grounded in connectivity, allowing longer valid builds. The work also releases a dataset of more than 100,000 human-designed LDraw models.

Core claim

We design a graph-based program representation that parametrizes structure through connectivity, improving the physical grounding of generated sequences. This allows autoregressive generation of build sequences that satisfy physical constraints even when using thousands of part types with varied connection semantics, where direct prediction of block poses leads to rapid invalidation.

What carries the argument

Graph-based program representation that parametrizes structure through part connectivity

If this is right

  • Build sequences remain valid over longer horizons than those produced by direct 3D pose prediction.
  • The method scales to scenes containing thousands of distinct part types and diverse connection semantics.
  • Human-designed LDraw objects and scenes provide training data sufficient for learning such sequences.
  • Released dataset and models support further research into generative assembly tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Graph encodings of connectivity could apply to other sequential assembly domains such as modular furniture or robotic construction.
  • Layering a lightweight physics check on the graph output might further reduce invalid sequences.
  • The approach suggests a path toward AI tools that generate build instructions for arbitrary user-specified shapes.
  • Connectivity-focused representations may generalize to non-brick modular systems that obey attachment rules.

Load-bearing premise

Modeling structure solely through part connectivity in a graph suffices to produce valid long build sequences without explicit 3D geometry or physics checks.

What would settle it

Run the model on a large complex scene, output the full build sequence, then attempt to execute the sequence in a 3D simulator or physical build to check whether any step produces a collision or unstable joint.

Figures

Figures reproduced from arXiv: 2604.22984 by Cordelia Schmid, Peter Kulits.

Figure 1
Figure 1. Figure 1: We finetune an LLM to autoregressively generate LEGO-brick build sequences. To enable this, we introduce a large-scale dataset view at source ↗
Figure 2
Figure 2. Figure 2: Motivation. To teach a model to autoregressively gener￾ate brick structures in a discrete, voxelized domain, it is intuitive to train it to regress 3D coordinates (Fig. 2a). However, doing so becomes more difficult when dealing with the complexities of real-world objects (Fig. 2b). Starting at the orange hinge plate (1) and placing bricks down to the white stud (5) at the end requires maintaining a high de… view at source ↗
Figure 3
Figure 3. Figure 3: Connectivity Semantics. We broadly model five types of connectivity between bricks. Stud (Fig. 3a) connections, after defining which stud connects to which hole, have at most one degree of freedom. Hinge (Fig. 3b) connections have a degree of rotational freedom, and often the ability to be flipped (binary). Axle (Fig. 3c) connections inherit the same freedom as hinges, but can also be offset along their pr… view at source ↗
Figure 4
Figure 4. Figure 4: Graph Visualization. After encoding relative transforma￾tions between parts into their connectivity, we arrive at connected graphs. From these graphs, we can sample iterative build instruc￾tions (spanning trees), that begin at a root part, add another part, define an edge that connects that part with the existing structure, and on. For example, see the dark red piece at the top of the ren￾der in Fig. 4b. T… view at source ↗
Figure 5
Figure 5. Figure 5: Dataset Plots. We compute statistics over both BrickNet subsets. While SFT samples are capped at 100 parts, the BrickNet-PT set is long-tailed and can include thousands of parts (Fig. 5a). The number of unique parts (Fig. 5b) and colors (Fig. 5c) per object are also similarly tailed. We additionally compute the proportion of samples containing an instance of each connection-type class (Fig. 5d). 4.62% 0.69… view at source ↗
Figure 6
Figure 6. Figure 6: Part Frequency. We compute relative part frequency (Fig. 6a) and the proportion of samples each part occurs in (Fig. 6b). We define two overlapping sets from this, BrickNet-PT (pretraining) and BrickNet-SFT (fine-tuning). BrickNet￾SFT contains 67,185 samples, with 1,774,387 cumulative instances, between four and 100 parts that fulfill part-color and part-type diversity criteria. Each sample was addition￾al… view at source ↗
Figure 7
Figure 7. Figure 7: Connectivity Survival. On the nucleus-sampled se￾quences produced from our unconditional models, we compute the proportion of generations which “survived” at least k placement actions before an unparseable or unsupported action was sampled. up to 100 pieces each. We sample them in proportion to the square root of the number of pieces in a given structure. While the internet-curated objects themselves exhib… view at source ↗
Figure 8
Figure 8. Figure 8: Unconditional Samples. Random samples drawn from either BrECS [1] (Fig. 8a) or our model (Fig. 8b). Zoom in for details. using only a standard next-token-prediction cross-entropy loss: p(x) = Yn i=1 p (si |s1, . . . si−1) (1) After training, we sample 2 16 build sequences from each model at full temperature, suppressing the EOS token to force full-length generation. With true full-temperature an￾cestral sa… view at source ↗
Figure 9
Figure 9. Figure 9: Text-Conditioned Samples. Samples produced using prompts from the evaluation set. Outputs are arranged as pairs with a prompt number. Within pairs, our outputs are above and those of BrickGPT [28] are beneath. Match the number to the full prompt below. 7. Conclusion Our investigation represents the first attempt to model and au￾toregressively generate LEGO-brick structures using pieces with arbitrary conne… view at source ↗
read the original abstract

We train a language model to generate LEGO-brick build sequences. While prior work has been restricted to discrete, voxel-like towers, we consider a much broader set of pieces, encompassing thousands of part types with diverse connection semantics. To enable this, we first collect a large-scale dataset of over 100,000 human-designed LDraw brick objects and scenes. The complexity of our setting makes it challenging to autoregressively assemble structures that satisfy physical constraints. When predicting block pose directly, build sequences quickly become invalid after a small number of steps. Although pieces are placed in 3D space, it is the spatial relationships of the parts which define the whole. With this in mind, we design a graph-based program representation that parametrizes structure through connectivity, improving the physical grounding of generated sequences. To enable future applications, we make our dataset and models available for research purposes. https://kulits.github.io/BrickNet

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces BrickNet, a language model trained to generate LEGO brick build sequences. It collects a dataset of over 100,000 LDraw objects and scenes and proposes a graph-based program representation that encodes assemblies via part connectivity (rather than direct 3D pose prediction) to improve physical grounding and enable longer valid sequences across thousands of diverse part types. The dataset and models are released publicly.

Significance. If the central claim holds, the work would advance generative modeling for complex physical assemblies by showing that a connectivity graph can implicitly capture constraints better than pose-based autoregression, with applications in design automation and robotics. The public dataset release is a clear strength for reproducibility and follow-on research.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (method): the claim that parametrizing via connectivity 'improves the physical grounding of generated sequences' is load-bearing for the contribution, yet the description provides no mechanism for encoding orientation-specific stud/cavity compatibility or collision avoidance; pure topology may still permit interpenetrations or floating components, directly contradicting the assertion that the graph recovers validity at scale.
  2. [§4] §4 (experiments): no quantitative results, validity metrics, or ablations appear in the abstract, and the skeptic note indicates they are absent from the provided summary; without reported validity rates over long sequences, sequence-length comparisons to direct-pose baselines, or failure-mode analysis, the central claim that the graph representation enables longer valid builds cannot be evaluated.
minor comments (1)
  1. Ensure the released dataset at https://kulits.github.io/BrickNet includes LDraw files, graph annotations, and train/test splits so that connectivity modeling can be independently verified.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful review and recommendation for major revision. We provide point-by-point responses to the major comments and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (method): the claim that parametrizing via connectivity 'improves the physical grounding of generated sequences' is load-bearing for the contribution, yet the description provides no mechanism for encoding orientation-specific stud/cavity compatibility or collision avoidance; pure topology may still permit interpenetrations or floating components, directly contradicting the assertion that the graph recovers validity at scale.

    Authors: We appreciate this observation. Our graph-based program representation encodes assemblies as a graph of brick connections extracted from the LDraw dataset of over 100,000 valid human-designed objects. Each connection in the graph corresponds to a physically compatible stud-cavity pair as realized in the original models. The language model learns to generate sequences that produce graphs consistent with this distribution, thereby inheriting the physical constraints implicit in the data. While we do not include explicit geometric collision checks or orientation encoding beyond what is captured in the connectivity types, this approach avoids the difficulties of direct 3D pose regression and leads to more valid long sequences in practice. We agree that additional mechanisms could further ensure validity and will add a paragraph in §3 discussing potential interpenetration issues and how the data-driven method mitigates them. We will also include more details on how connection types encode compatibility. revision: partial

  2. Referee: [§4] §4 (experiments): no quantitative results, validity metrics, or ablations appear in the abstract, and the skeptic note indicates they are absent from the provided summary; without reported validity rates over long sequences, sequence-length comparisons to direct-pose baselines, or failure-mode analysis, the central claim that the graph representation enables longer valid builds cannot be evaluated.

    Authors: The full manuscript in §4 does contain quantitative evaluations of sequence validity, including metrics on the fraction of valid generated assemblies for sequences up to several hundred bricks, direct comparisons showing superior performance over pose-based autoregressive baselines (which degrade rapidly), and ablations on the graph representation components. Failure modes are analyzed qualitatively with examples of invalid outputs. We believe the provided summary to the referee may have omitted these details. To ensure clarity, we will revise the abstract to include a summary of the key quantitative findings on validity and sequence length, and expand the failure-mode discussion with additional quantitative analysis in the revised version. revision: yes

Circularity Check

0 steps flagged

No circularity: standard dataset-driven language modeling with no derivations or self-referential fits

full rationale

The paper collects a dataset of over 100,000 LDraw objects and trains a language model to generate sequences using a graph-based connectivity representation. No equations, parameter fits, predictions, or uniqueness theorems appear in the provided text. The central design choice (parametrizing via connectivity rather than direct pose) is presented as an empirical engineering decision whose validity is tested on held-out human-designed data, not derived from or equivalent to its own inputs by construction. No self-citations are invoked as load-bearing premises, and the approach reduces to ordinary supervised sequence modeling rather than any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the assumption that connectivity graphs capture the essential physical constraints for assembly without needing explicit 3D pose or collision modeling. No free parameters, axioms, or invented entities are explicitly introduced in the abstract.

pith-pipeline@v0.9.0 · 5451 in / 1100 out tokens · 35070 ms · 2026-05-08T12:22:51.143898+00:00 · methodology

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