TL;DR
LAMP is a data-efficient, controllable 3D shape generation framework that enables safe extrapolation and outperforms existing methods, requiring fewer samples and providing interpretable parameter control.
Contribution
LAMP introduces a novel weight-space mixing approach for controllable 3D shape generation that is data-efficient and supports safe extrapolation beyond training ranges.
Findings
Enables controlled interpolation with as few as 100 samples
Achieves safe extrapolation up to 100% parameter difference beyond training
Outperforms autoencoder and DNI baselines in extrapolation and data efficiency
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…
Peer Reviews
Decision·ICLR 2026 Conference Desk Rejected Submission
Data-efficient and interpretable approach for parameter-controlled 3D generation. Clear problem motivation in engineering design, emphasizing low-data and extrapolation regimes. Practical safety check (linearity mismatch) that can identify unstable generations without ground truth. Demonstrates reasonable quantitative and visual improvements over strong baselines (DNI, AE-LPA). Readable and systematic experimental section, showing controlled interpolation, extrapolation, and performance optimiza
The main weakness of this paper lies in its limited conceptual novelty. The core idea of affine weight mixing closely follows earlier works like Deep Network Interpolation (DNI) and model interpolation methods, without introducing much theoretical advancement. The key assumptions behind the approach, especially (A1) and (A2), feel heuristic and are never really tested beyond small, local cases—there’s no solid evidence that SDF weights behave linearly when pushed far beyond the training range. T
1. The paper is well-written, with clear and coherent presentation. 2. LAMP enables precise parameter-controlled generation with limited training data.
1. For each example, is the weight w the flattened vector of all parameters of its trained SDF network? What is the dimensionality D of w? Storing such large vectors per example may impose substantial storage costs—how does the method scale as the dataset grows? 2. Training a separate SDF network per example could be time-consuming. Could you report the overall training cost and per-example training time, and compare both training and inference time against the baseline methods. 3. The selection
The proposed method provides a data-efficient framework for parameter-controlled 3D mesh generation. The paper demonstrates the effectiveness of the method on some benchmark datasets.
Although the safety metric is shown to be effective for the test case (when compared with human judgement), it lacks theoretical guarantee why a simple threshold is sufficient. The paper should discuss limitations/failure cases more clearly. The process from SDF to mesh may lead to changing mesh connectivity even when the parameters only change by a small amount.
- To my knowledge, existing work mainly focuses on generating network weights or latents, such as HyperDiffusion. The idea of interpolating network weights with shared initialization to obtain new generation results is both interesting and novel. - Despite its simplicity, the experimental results demonstrate that the framework achieves better performance on both DrivAerNet++ and BlendedNet datasets for interpolation and extrapolation. The framework also enables aerodynamic optimization and achie
The current manuscript has some minor concerns: - This work assumes generated 3D shapes are produced from an affine transformation of the input shapes (Theorem A(1)). The proposed framework is unlikely to work on datasets with heterogeneous topologies. It is recommended to discuss this assumption and limitation. - Theorem A(2) assumes that if the weight difference from initialization is small enough, the obtained mixed SDFs will be close to a linear combination of the original SDFs. While this
The strength of this paper lies in the novel idea of combining parameter vectors and neural SDF weights to generate new shapes under given constraints. The method offers some much-needed fine-grained control over the generated shapes. Furthermore, the proposed method does not rely on large datasets or compute for training. The method is conceptually simple and easy to implement, and the experiments demonstrate that the affine combination weights derived from the parameter vectors can (perhaps
One weakness of the paper is that the linearity of the SDF weights is only reasonable for very similar weights. This limits the variability of the generated shapes. Furthermore, it is not clear to me how sensitive the method is to the choice and number of known shapes. If the known shapes do not cover the parameter space well, it is unclear how well the method performs. On a more minor note Table 1 does not seem to be referenced in the text.
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