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

ICML 2026

Ghadi Nehme 1, Yanxia Zhang 2, Dule Shu 2, Matt Klenk 2, Faez Ahmed 1
1Massachusetts Institute of Technology    2Toyota Research Institute
Paper arXiv Code Video

LAMP mixes per-shape SDF decoders in their aligned weight space — yielding controllable, interpretable, and safely-extrapolated 3D geometries from as few as 50 training samples.

Abstract

Generating high-fidelity 3D geometries under explicit parameter constraints is central to engineering design, yet current methods often require large datasets and fail to provide reliable control beyond the training distribution.

We introduce LAMP (Linear Affine Mixing of Parametric shapes), a data-efficient framework for controllable and interpretable 3D generation. LAMP aligns signed distance function (SDF) decoders by overfitting each exemplar from a shared initialization, then generates new designs by solving a parameter-constrained affine mixing problem in the aligned weight space. To improve reliability, we propose a linearity-mismatch safety metric that detects when mixed decoders leave the valid local regime.

We evaluate LAMP on DrivAerNet++, BlendedNet, and additional industry-level vehicle families, including sports cars, SUVs, and convertibles. LAMP enables controlled interpolation with as few as 50 samples, safe extrapolation up to 100% beyond training ranges, and performance-guided optimization under fixed parameters. It significantly outperforms conditional autoencoder and Deep Network Interpolation (DNI) baselines in extrapolation, data efficiency, and parameter fidelity. These results show that LAMP supports low-data, parameter-driven design exploration where fast geometry generation and reliable extrapolation are essential.

Video

Method

LAMP method overview

LAMP has three stages: (I) aligned SDF weight space construction — a SIREN MLP is overfit to each exemplar mesh from a shared anchor initialization, producing a per-shape weight vector that lives close to all the others in parameter space. (II) parameter-constrained mixing — a target parameter vector is matched by solving an SLSQP affine combination problem in the aligned weight space; the resulting blend yields a synthetic SIREN whose decoded SDF satisfies the target parameters. (III) mesh extraction — marching cubes on the blended SDF field gives an editable surface mesh, which can be further constrained by symmetry and domain-specific decode grids.

Parameter Sweep Extrapolation

Trained on 50 samples per vehicle style, swept with ±100% extrapolation beyond the dataset range.

Dataset range Extrapolation

Front bumper curvature

C-HR Front Bumper Curvature sweep

C-HR

Porsche Front Bumper Curvature sweep

Porsche

Supra Front Bumper Curvature sweep

Supra

Ramp angle

C-HR Ramp Angle sweep

C-HR

Porsche Ramp Angle sweep

Porsche

Supra Ramp Angle sweep

Supra

Car roof height

C-HR Car Roof Height sweep

C-HR

Porsche Car Roof Height sweep

Porsche

Supra Car Roof Height sweep

Supra

Multi-View Inspection

The same Greenhouse Angle sweep on the C-HR mesh, viewed from three orthogonal cameras to highlight LAMP's structural consistency.

C-HR greenhouse 3/4

3/4 view

C-HR greenhouse front

Front

C-HR greenhouse side

Side

Physics-Guided Drag Optimization

Drag-optimized shapes

Performance-driven optimization on DrivAerNet++. Left: target vs. predicted drag reduction for LAMP, DNI, and AE-LPA. Right: error heatmaps relative to the reference mesh. LAMP achieves accurate prediction and a physically interpretable modification (a flattened windscreen), while DNI and AE-LPA fail to produce aerodynamically meaningful changes.

Safety Metric

Safety metric

LAMP's linearity-mismatch safety metric detects when an extrapolated parameter request has left the regime where the affine weight-space mixing remains valid. Geometries above the threshold are flagged, giving the designer an interpretable veto on visually degenerate outputs.

BibTeX

@article{nehme2025lamp,
  title={LAMP: Data-Efficient Linear Affine Weight-Space Models for Parameter-Controlled 3D Shape Generation and Extrapolation},
  author={Nehme, Ghadi and Zhang, Yanxia and Shu, Dule and Klenk, Matt and Ahmed, Faez},
  journal={arXiv preprint arXiv:2510.22491},
  year={2025}
}