The success of Transformer-based models has encouraged many researchers to learn CAD models using sequence-based approaches. However, learning CAD models is still a challenge, because they can be represented as complex shapes with long construction sequences. Furthermore, the same CAD model can be expressed using different CAD construction sequences. We propose a novel contrastive learning-based approach, named ContrastCAD, that effectively captures semantic information within the construction sequences of the CAD model. ContrastCAD generates augmented views using dropout techniques without altering the shape of the CAD model. We also propose a new CAD data augmentation method, called a Random Replace and Extrude (RRE) method, to enhance the learning performance of the model when training an imbalanced training CAD dataset. Experimental results show that the proposed RRE augmentation method significantly enhances the learning performance of Transformer-based autoencoders, even for complex CAD models having very long construction sequences. The proposed ContrastCAD model is shown to be robust to permutation changes of construction sequences and performs better representation learning by generating representation spaces where similar CAD models are more closely clustered. Our codes are available at https://github.com/cm8908/ContrastCAD.

Counting the number of linear extensions of a partial order was considered by Stanley about 50 years ago. For the partial order on the vertices and edges of a graph determined by inclusion, we call such linear extensions {\it construction sequences} for the graph as each edge follows both of its endpoints. The number of such sequences for paths, cycles, stars, double-stars, and complete graphs is found. For paths, we agree with Stanley (the Tangent numbers) and get formulas for the other classes. Structure and applications are also studied.

This paper presents a novel generative model for Computer Aided Design (CAD) that 1) represents high-level design concepts of a CAD model as a three-level hierarchical tree of neural codes, from global part arrangement down to local curve geometry; and 2) controls the generation or completion of CAD models by specifying the target design using a code tree. Concretely, a novel variant of a vector quantized VAE with "masked skip connection" extracts design variations as neural codebooks at three levels. Two-stage cascaded auto-regressive transformers learn to generate code trees from incomplete CAD models and then complete CAD models following the intended design. Extensive experiments demonstrate superior performance on conventional tasks such as unconditional generation while enabling novel interaction capabilities on conditional generation tasks.

Learning distributions of graphs can be used for automatic drug discovery, molecular design, complex network analysis, and much more. We present an improved framework for learning generative models of graphs based on the idea of deep state machines. To learn state transition decisions we use a set of graph and node embedding techniques as memory of the state machine. Our analysis is based on learning the distribution of random graph generators for which we provide statistical tests to determine which properties can be learned and how well the original distribution of graphs is represented. We show that the design of the state machine favors specific distributions. Models of graphs of size up to 150 vertices are learned. Code and parameters are publicly available to reproduce our results.