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

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.

VideoCAD: A Large-Scale Video Dataset for Learning UI Interactions and 3D Reasoning from CAD Software

Computer-Aided Design (CAD) is a time-consuming and complex process, requiring precise, long-horizon user interactions with intricate 3D interfaces. While recent advances in AI-driven user interface (UI) agents show promise, most existing datasets and methods focus on short, low-complexity tasks in mobile or web applications, failing to capture the demands of professional engineering tools. In this work, we introduce VideoCAD, the first attempt at engineering UI interaction learning for precision tasks. Specifically, VideoCAD is a large-scale synthetic dataset consisting of over 41K annotated video recordings of CAD operations, generated using an automated framework for collecting high-fidelity UI action data from human-made CAD designs. Compared to existing datasets, VideoCAD offers an order of magnitude higher complexity in UI interaction learning for real-world engineering tasks, having up to a 20x longer time horizon than other datasets. We show two important downstream applications of VideoCAD: learning UI interactions from professional precision 3D CAD tools and a visual question-answering (VQA) benchmark designed to evaluate multimodal large language models' (LLM) spatial reasoning and video understanding abilities. To learn the UI interactions, we propose VideoCADFormer - a state-of-the-art model in learning CAD interactions directly from video, which outperforms multiple behavior cloning baselines. Both VideoCADFormer and the VQA benchmark derived from VideoCAD reveal key challenges in the current state of video-based UI understanding, including the need for precise action grounding, multi-modal and spatial reasoning, and long-horizon dependencies.