arxiv: 2605.06947 · v1 · submitted 2026-05-07 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

Rollback-Free Stable Brick Structures Generation

Chenhui Xu , Ziyue Bai , Fuxun Yu , Heng Huang , Jinjun Xiong

Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:49 UTC · model grok-4.3

classification 💻 cs.LG

keywords stable brick structuresreinforcement learningautoregressive generationphysical stability3D structure generationrollback-free inferenceassembly rewards

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The pith

Reinforcement learning with assembly-level rewards trains autoregressive models to generate stable brick structures without any rollbacks or external simulation at inference time.

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

The paper addresses the inefficiency in existing 3D brick generation methods that depend on simulators for rejection sampling and brick-by-brick corrections during generation. It introduces a training paradigm where the model learns physical constraints directly through rewards that penalize collisions, enforce connectivity and interlocking, and match target shapes. This internalization of stability rules allows the model to produce valid structures in one pass. A reader would care because it removes a major speed barrier, turning slow corrective processes into fast direct generation while reaching high quality.

Core claim

By optimizing an autoregressive policy using assembly-level rewards for collision avoidance, global connectivity, structural interlocking, and shape conformity, the model internalizes physical priors during training. This enables the first rollback-free generation of stable brick structures at inference, delivering state-of-the-art quality and accelerating speed by orders of magnitude compared to simulator-dependent baselines.

What carries the argument

Assembly-level rewards in a reinforcement learning training loop that optimize the autoregressive policy for physical validity across the full structure rather than step-by-step corrections.

If this is right

Generation becomes rollback-free and runs orders of magnitude faster than simulator-based methods.
The approach reaches state-of-the-art quality in stable brick structures without post-generation fixes.
Physical validity enforcement moves entirely from inference to the training phase.
The model can produce complete valid assemblies in a single forward pass.

Where Pith is reading between the lines

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

The same reward-based internalization could extend to generating other physically constrained 3D objects such as furniture or mechanisms.
Training-time reward design might reduce reliance on test-time verification across broader autoregressive generation tasks.
If the rewards capture stability well, the method could support interactive or real-time design tools for brick-based construction.
Scaling the approach to larger or more complex structures would test whether the learned priors generalize beyond the training distributions.

Load-bearing premise

The carefully designed assembly-level rewards for collision avoidance, connectivity, interlocking, and shape conformity are enough to guarantee full physical stability with no simulation feedback needed at inference time.

What would settle it

Running a generated structure through an independent physics simulator and observing collapses, disconnections, or violations of gravity and interlocking rules would falsify the claim of internalized stability.

Figures

Figures reproduced from arXiv: 2605.06947 by Chenhui Xu, Fuxun Yu, Heng Huang, Jinjun Xiong, Ziyue Bai.

**Figure 1.** Figure 1: Comparison between rollback-based and rollback-free inference. Rollback-based generation requires resampling after unstable steps, interrupting the autoregressive process, while our stability-aware policy enables uninterrupted one-pass generation. brick placements. As a result, supervised next-token imitation alone provides insufficient pressure for the model to uncover and internalize the hidden construct… view at source ↗

**Figure 2.** Figure 2: Overview of STABLE. STABLE is an autoregressive framework that tokenizes point clouds into LEGO bricks, learns shape reconstruction via SFT, and integrates physical stability into reward signals for reinforcement learning training, and leads to rollback-free inference. 3.1 PointCloud2Brick Overview PointCloud2Brick is constructed from StableText2Brick [20], which contains 47,389 physically stable brick str… view at source ↗

**Figure 3.** Figure 3: Illustration of rewards related to physical stability [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Qualitative results of Point Cloud to Brick generations. Transparency indicates a collision. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: GRPO training dynamics under different reward settings. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Full GRPO training dynamics of STABLE and reward-ablation variants. This confirms that STABLE does not obtain stability by sacrificing geometric fidelity; instead, the policy learns brick placements that are simultaneously shape-consistent and structurally coherent. The ablation dynamics further explain the quantitative results in [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Training dynamics of the full STABLE model. computer-aided design, educational construction tools, robotic assembly planning, and physically grounded 3D content generation. By reducing dependence on expensive inference-time simulation, STABLE may also make stable structure generation more efficient and accessible. At the same time, generated physical designs should not be directly used in safety-critical e… view at source ↗

**Figure 8.** Figure 8: Training dynamics of STABLE without the connectivity reward. physics-based analysis and could serve as alternative reward or evaluation oracles. In contrast, STABLE does not rely on simulator-based rewards during training. We instead use deterministic construction-aware rewards to expose key stability-related properties to the autoregressive policy, while evaluating final structures with both geometric and… view at source ↗

**Figure 9.** Figure 9: Training dynamics of STABLE without structural rewards. torial construction as sequential placement of unit primitives and uses reinforcement learning with action validity prediction to satisfy geometric constraints. AssemblyComplete [3] studies 3D combinatorial assembly completion, where an agent completes missing parts of an incomplete LEGO-like structure under collision, stability, and inventory constr… view at source ↗

**Figure 10.** Figure 10: Training dynamics of STABLE without the collision objective. level reward optimization. It keeps the inference procedure simple and rollback-free, but uses training-time rewards to make latent construction principles explicit to the model. Limitations STABLE is currently evaluated in a fixed voxel world with a predefined brick library, which limits its coverage of larger scales, irregular components, and … view at source ↗

**Figure 11.** Figure 11: Training dynamics of [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗

read the original abstract

While autoregressive models have advanced 3D generation, creating physically stable brick structures remains a challenge due to the strict requirements of gravity and interconnectivity. Existing approaches rely on external physical simulators during inference to perform rejection sampling and brick-by-brick rollbacks, which severely bottlenecks efficiency. To address this, we propose a reinforcement learning paradigm that shifts physical validity enforcement from test-time correction to training-time policy optimization. By utilizing assembly-level rewards, the model optimizes for collision avoidance, global connectivity, structural interlocking, and shape conformity. This paradigm allows the model to internalize physical priors, enabling the first rollback-free generation of stable brick structures. Experimental results demonstrate that our approach achieves state-of-the-art generation quality while accelerating inference speed by orders of magnitude. Our code and dataset are available at https://github.com/miniHuiHui/STABLE. Our models are available at https://huggingface.co/miniHui/STABLE.

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.

Desk Editor's Note private letter to a colleague

RL training internalizes stability for rollback-free brick generation, but reward sufficiency and experimental details need verification.

read the letter

The paper's main contribution is using RL to train autoregressive models for brick structures so they generate stable outputs without any rollback or simulator at inference time. This shifts physical validity from test-time fixes to training-time policy optimization with rewards for collision avoidance, global connectivity, structural interlocking, and shape conformity. That framing appears new compared to earlier autoregressive 3D work that depended on simulators during generation. The work does well by releasing code, dataset, and models publicly, which helps with verification of the claimed SOTA quality and large inference speedups. The soft spots are around the evidence and the reward design. The abstract mentions experimental support but shows no numbers, baselines, or details, making it tough to assess the actual gains. The rewards are assembly-level heuristics, and they might not fully proxy real physical stability involving gravity, friction, or dynamic settling. Without ablations or direct comparisons showing that high-reward structures pass full simulator tests at the same rate as rollback methods, the claim of complete internalization of priors could have holes. This paper is for people working on physically constrained 3D generation in machine learning, particularly those focused on efficiency for practical uses like design tools. Readers who value released artifacts and RL for structure generation would get the most from it. It deserves a serious referee to examine the full experiments and RL formulation. I would recommend engaging with it through peer review to see if the results hold up.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a reinforcement learning paradigm that trains autoregressive models for 3D brick structure generation using assembly-level rewards for collision avoidance, global connectivity, structural interlocking, and shape conformity. This internalizes physical priors during training so that stable structures can be generated at inference without any external simulator, rollback, or rejection sampling, claiming state-of-the-art quality and orders-of-magnitude inference speedup.

Significance. If the central claim holds, the work would be significant for physically constrained 3D generation: it demonstrates a training-time alternative to test-time physics correction, which could enable fast, scalable applications in design automation and robotics. The public release of code, dataset, and models on GitHub and Hugging Face is a clear strength for reproducibility.

major comments (2)

[Abstract and §4] Abstract and §4 (Experiments): The central claim that the four assembly-level rewards suffice for full physical stability without inference-time simulation is load-bearing, yet no quantitative correlation is reported between the composite reward score and simulator-measured stability metrics (center-of-mass projection, contact normals, or post-settling failure rate). Without this or an ablation that removes the simulator entirely and measures the increase in invalid structures, the rollback-free guarantee remains unverified.
[§3.2] §3.2 (Reward Design): The rewards are evaluated only on the final assembly; real brick stability also depends on dynamic factors (friction, sequential placement order, and gravity settling) that are not explicitly modeled. If any of these are under-constrained, high-reward trajectories can still produce physically invalid structures, directly contradicting the claim that physical priors are fully internalized.

minor comments (1)

[Abstract] The abstract states that models are available at a Hugging Face link, but the manuscript does not specify the exact model checkpoints or training hyperparameters used for the reported SOTA results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and for highlighting the value of our public code and model releases. We address each major comment below in detail. We agree that additional analyses would strengthen the verification of our claims and will incorporate them in the revised manuscript.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (Experiments): The central claim that the four assembly-level rewards suffice for full physical stability without inference-time simulation is load-bearing, yet no quantitative correlation is reported between the composite reward score and simulator-measured stability metrics (center-of-mass projection, contact normals, or post-settling failure rate). Without this or an ablation that removes the simulator entirely and measures the increase in invalid structures, the rollback-free guarantee remains unverified.

Authors: We agree that a direct quantitative correlation between the composite reward and post-simulation stability metrics would provide stronger verification. The manuscript already demonstrates that models trained with the four rewards generate structures passing independent physical validation (center-of-mass, contact, and settling checks) at high rates while using zero simulator calls, rollbacks, or rejections at inference—unlike all baselines. This serves as an implicit ablation, as the only difference is the internalized policy versus external correction. To address the request explicitly, we will add in the revision: (i) a scatter-plot correlation between per-sample composite reward and simulator stability scores, and (ii) a table reporting the fraction of invalid structures when the trained policy is used without any simulator (already the case) versus when rewards are ablated. These additions will make the rollback-free guarantee fully quantitative. revision: yes
Referee: [§3.2] §3.2 (Reward Design): The rewards are evaluated only on the final assembly; real brick stability also depends on dynamic factors (friction, sequential placement order, and gravity settling) that are not explicitly modeled. If any of these are under-constrained, high-reward trajectories can still produce physically invalid structures, directly contradicting the claim that physical priors are fully internalized.

Authors: The final-assembly evaluation is deliberate and standard for RL-based sequence generation: stability is an emergent property of the completed structure. Because the autoregressive policy is optimized over complete trajectories that receive the terminal reward, it learns to avoid early placements that would produce unstable finals, thereby internalizing sequential order. The interlocking and global-connectivity terms explicitly penalize configurations that would fail under gravity or lack friction-like resistance, while collision avoidance prevents immediate dynamic violations. Our experiments show that high-reward trajectories rarely produce post-settling failures, supporting that the priors are sufficiently internalized for the task. We will add a clarifying paragraph in §3.2 and the discussion section explaining this trajectory-level internalization and noting that more expensive per-step physics simulation could be explored in future work but is not required for the reported results. revision: partial

Circularity Check

0 steps flagged

No circularity: RL training paradigm is self-contained with external rewards

full rationale

The paper presents a reinforcement learning method that trains a generative model using four assembly-level reward terms (collision avoidance, global connectivity, structural interlocking, shape conformity) so that the resulting policy produces stable brick structures at inference without any simulator or rollback. No mathematical derivation, equation, or first-principles result is shown that reduces the claimed stability outcome to the reward definitions by construction. The rewards function as independent, hand-specified training signals rather than self-referential quantities; the internalization of physical priors is an empirical learning claim, not a tautology. No self-citations, uniqueness theorems, or ansatzes are invoked to support the central shift from test-time correction to training-time optimization. The approach is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The method depends on hand-designed reward components for physical properties whose relative weighting and exact formulation are not detailed in the abstract; these act as implicit free parameters tuned to achieve the reported stability.

free parameters (1)

assembly-level reward weights
Relative scaling of terms for collision avoidance, connectivity, interlocking, and shape conformity must be chosen to balance the policy optimization.

pith-pipeline@v0.9.0 · 5461 in / 1015 out tokens · 60051 ms · 2026-05-11T00:49:07.842845+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

By utilizing assembly-level rewards, the model optimizes for collision avoidance, global connectivity, structural interlocking, and shape conformity.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

This paradigm allows the model to internalize physical priors, enabling the first rollback-free generation of stable brick structures.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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