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LAMP: Data-Efficient Linear Affine Weight-Space Models for Parameter-Controlled 3D Shape Generation and Extrapolation

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
3D Shape GenerationParametric ControlData Efficient LearningEngineering Design
Abstract:

Generating high-fidelity 3D geometries that satisfy specific parameter constraints has broad applications in design and engineering. However, current methods typically rely on large training datasets and struggle with controllability and generalization beyond the training distributions. To overcome these limitations, we introduce LAMP (Linear Affine Mixing of Parametric shapes), a data-efficient framework for controllable and interpretable 3D generation. LAMP first aligns signed distance function (SDF) decoders by overfitting each exemplar from a shared initialization, then synthesizes new geometries by solving a parameter-constrained mixing problem in the aligned weight space. To ensure robustness, we further propose a safety metric that detects geometry validity via linearity mismatch. We evaluate LAMP on two 3D parametric benchmarks: DrivAerNet++ and BlendedNet. We found that LAMP enables (i) controlled interpolation within bounds with as few as 100 samples, (ii) safe extrapolation by up to 100% parameter difference beyond training ranges, (iii) physics performance-guided optimization under fixed parameters. LAMP significantly outperforms conditional autoencoder and Deep Network Interpolation (DNI) baselines in both extrapolation and data efficiency. Our results demonstrate that LAMP advances controllable, data-efficient, and safe 3D generation for design exploration, dataset generation, and performance-driven optimization.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces LAMP, a framework for parameter-controlled 3D shape generation via weight-space mixing of aligned SDF decoders. It resides in the 'Neural Parametric Models for Deformable Shapes' leaf, which contains only three papers total (including LAMP itself). This is a relatively sparse research direction within the broader taxonomy of fifty papers, suggesting that neural parametric approaches emphasizing explicit parameter control and extrapolation remain less explored compared to generative synthesis or classical CAD modeling.

The taxonomy reveals that LAMP's immediate neighbors focus on learned shape spaces: sibling works NPMs and GNPM also encode shape variations via neural networks, while the parent branch includes parametric human body models (seven papers) that use anthropometric data. Adjacent branches cover generative models (diffusion, GANs) for 3D synthesis and classical parametric geometric modeling (PDE-based, CAD). LAMP diverges from generative approaches by prioritizing data efficiency and interpretable parameter mixing rather than large-scale learned distributions, and from classical methods by leveraging neural implicit representations instead of explicit splines or PDEs.

Among eighteen candidates examined, no contribution was clearly refuted by prior work. The core LAMP framework examined seven candidates with zero refutable overlaps; the safety metric examined one candidate with no refutation; and the engineering applications examined ten candidates, again with no refutable prior work. This suggests that within the limited search scope—top-K semantic matches plus citation expansion—LAMP's specific combination of weight-space alignment, parameter-constrained mixing, and linearity-mismatch validation appears distinct from existing methods, though the analysis does not claim exhaustive coverage of all related literature.

Based on the limited search of eighteen candidates, LAMP appears to occupy a relatively novel position combining data-efficient neural parametric modeling with explicit extrapolation guarantees. The sparse population of its taxonomy leaf and absence of refuting prior work within the examined set suggest meaningful differentiation, though a broader literature review would be needed to confirm novelty across all related subfields (e.g., CAD optimization, physics-guided design).

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
18
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: parameter-controlled 3D shape generation and extrapolation. The field encompasses diverse approaches to creating and manipulating three-dimensional geometry through explicit or learned parametric controls. At the highest level, the taxonomy distinguishes between purely generative models that synthesize novel shapes (often via diffusion or GANs), classical parametric geometric modeling rooted in CAD and spline-based representations, learned parametric shape spaces that encode deformations or variations in neural networks, surface fitting and deformable model techniques that adapt templates to data, and domain-specific applications ranging from medical anatomy to architectural elements. Works such as ShapeCrafter[8] and BlockFusion[2] illustrate generative synthesis, while methods like ReparamCAD[16] and Curved-Crease Folding[26] exemplify traditional parametric design. Meanwhile, neural parametric approaches—including NPMs[19], GNPM[12], and the original paper LAMP[0]—learn compact latent codes or parameter sets to drive shape variation, bridging classical geometry with modern deep learning. A particularly active line of research focuses on neural parametric models for deformable shapes, where the goal is to capture complex, continuous shape families (e.g., human bodies, anatomical structures) in a low-dimensional parameter space. LAMP[0] sits squarely within this cluster, emphasizing learned parametric control for extrapolation beyond observed training distributions. Nearby works such as NPMs[19] and GNPM[12] similarly encode shape variations via neural networks, but they differ in how they handle out-of-distribution generalization and the granularity of parameter semantics. In contrast, methods like Champ[3] and VolTeMorph[5] target specific deformation tasks (character animation, medical registration) with more specialized architectures. A central open question across these branches is how to balance expressiveness—capturing fine geometric detail—with robust extrapolation to novel parameter ranges, a trade-off that LAMP[0] addresses through its parametric design choices.

Claimed Contributions

LAMP framework for parameter-controlled 3D mesh generation

The authors introduce LAMP (Linear Affine Mixing of Parametric shapes), a method that aligns signed distance function decoders by overfitting each exemplar from a shared initialization, then synthesizes new geometries by solving a parameter-constrained mixing problem in the aligned weight space. This enables controllable interpolation and extrapolation with few training samples.

7 retrieved papers
Linearity-mismatch safety metric for geometry validity

The authors propose a safety metric that detects geometry validity by measuring the mismatch between the mixed decoder output and the linear combination of individual SDFs. This metric provides a data-independent safeguard to flag unsafe generations, especially in low-data regimes.

1 retrieved paper
Engineering applications demonstrating controlled generation and extrapolation

The authors validate LAMP on two parametric benchmarks for aerodynamic design, demonstrating three key capabilities: controlled interpolation within dataset bounds using as few as 100 samples, safe extrapolation up to 100% beyond training ranges, and physics performance-guided optimization under fixed parameters.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

LAMP framework for parameter-controlled 3D mesh generation

The authors introduce LAMP (Linear Affine Mixing of Parametric shapes), a method that aligns signed distance function decoders by overfitting each exemplar from a shared initialization, then synthesizes new geometries by solving a parameter-constrained mixing problem in the aligned weight space. This enables controllable interpolation and extrapolation with few training samples.

Contribution

Linearity-mismatch safety metric for geometry validity

The authors propose a safety metric that detects geometry validity by measuring the mismatch between the mixed decoder output and the linear combination of individual SDFs. This metric provides a data-independent safeguard to flag unsafe generations, especially in low-data regimes.

Contribution

Engineering applications demonstrating controlled generation and extrapolation

The authors validate LAMP on two parametric benchmarks for aerodynamic design, demonstrating three key capabilities: controlled interpolation within dataset bounds using as few as 100 samples, safe extrapolation up to 100% beyond training ranges, and physics performance-guided optimization under fixed parameters.

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