# LInK: Learning Joint Representations of Design and Performance Spaces through Contrastive Learning for Mechanism Synthesis

arXiv: https://arxiv.org/abs/2405.20592 · HTML: https://mlsanity.com/paper/2405.20592/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [A Survey on Contrastive Self-supervised Learning](https://mlsanity.com/paper/2011.00362/) (2020)
- [Multi-modal Molecule Structure-text Model for Text-based Retrieval and Editing](https://mlsanity.com/paper/2212.10789/) (2022)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [A Decade Survey of Content Based Image Retrieval using Deep Learning](https://mlsanity.com/paper/2012.00641/) (2020)
- [Deep Learning for Instance Retrieval: A Survey](https://mlsanity.com/paper/2101.11282/) (2021)
- [Video Corpus Moment Retrieval with Contrastive Learning](https://mlsanity.com/paper/2105.06247/) (2021)
- [Self-Supervised Adversarial Hashing Networks for Cross-Modal Retrieval](https://mlsanity.com/paper/1804.01223/) (2018)
- [LINKS: A dataset of a hundred million planar linkage mechanisms for data-driven kinematic design](https://mlsanity.com/paper/2208.14567/) (2022)
- [Joint Search of Optimal Topology and Trajectory for Planar Linkages](https://mlsanity.com/paper/2109.03392/) (2021)
- [Deep Binaries: Encoding Semantic-Rich Cues for Efficient Textual-Visual Cross Retrieval](https://mlsanity.com/paper/1708.02531/) (2017)

## Built on by (most cited first, 7 of 7)

- [BikeBench: A Bicycle Design Benchmark for Generative Models with Objectives and Constraints](https://mlsanity.com/paper/2508.00830/) (2025)
- [GIFT: Bootstrapping Image-to-CAD Program Synthesis via Geometric Feedback](https://mlsanity.com/paper/2603.27448/) (2026)
- [Symbolic Intermediaries as a Linguistic-Numerical Interface for LLM-Driven Geometric Reasoning](https://mlsanity.com/paper/2505.17607/) (2025)
- [Creative synthesis of kinematic mechanisms](https://mlsanity.com/paper/2510.03308/) (2025)
- [Intelligent Design 4.0: Paradigm Evolution Toward the Agentic AI Era](https://mlsanity.com/paper/2506.09755/) (2025)
- [LinkD: AutoRegressive Diffusion Model for Mechanical Linkage Synthesis](https://mlsanity.com/paper/2601.04054/) (2026)
- [Discrete Autoregressive Transformer for Generative Mechanism Synthesis](https://mlsanity.com/paper/2606.17409/) (2026)

## Abstract (arXiv)

In this paper, we introduce LInK, a novel framework that integrates contrastive learning of performance and design space with optimization techniques for solving complex inverse problems in engineering design with discrete and continuous variables. We focus on the path synthesis problem for planar linkage mechanisms. By leveraging a multimodal and transformation-invariant contrastive learning framework, LInK learns a joint representation that captures complex physics and design representations of mechanisms, enabling rapid retrieval from a vast dataset of over 10 million mechanisms. This approach improves precision through the warm start of a hierarchical unconstrained nonlinear optimization algorithm, combining the robustness of traditional optimization with the speed and adaptability of modern deep learning methods. Our results on an existing benchmark demonstrate that LInK outperforms existing methods with 28 times less error compared to a state of the art approach while taking 20 times less time on an existing benchmark. Moreover, we introduce a significantly more challenging benchmark, named LINK ABC, which involves synthesizing linkages that trace the trajectories of English capital alphabets, an inverse design benchmark task that existing methods struggle with due to large nonlinearities and tiny feasible space. Our results demonstrate that LInK not only advances the field of mechanism design but also broadens the applicability of contrastive learning and optimization to other areas of engineering. The code and data are publicly available at https://github.com/ahnobari/LInK.