Inferring programs which generate 2D and 3D shapes is important for reverse engineering, editing, and more. Training such inference models is challenging due to the lack of paired (shape, program) data in most domains. A popular approach is to pre-train a model on synthetic data and then fine-tune on real shapes using slow, unstable reinforcement learning. In this paper, we argue that self-training is a viable alternative for fine-tuning such models. Self-training is a semi-supervised learning paradigm where a model assigns pseudo-labels to unlabeled data, and then retrains with (data, pseudo-label) pairs as the new ground truth. We show that for constructive solid geometry and assembly-based modeling, self-training outperforms state-of-the-art reinforcement learning approaches. Additionally, shape program inference has a unique property that circumvents a potential downside of self-training (incorrect pseudo-label assignment): inferred programs are executable. For a given shape from our distribution of interest $mathbf{x}^*$ and its predicted program $mathbf{z}$, one can execute $mathbf{z}$ to obtain a shape $mathbf{x}$ and train on $(mathbf{z}, mathbf{x})$ pairs, rather than $(mathbf{z}, mathbf{x}^*)$ pairs. We term this procedure latent execution self training (LEST). We demonstrate that self training infers shape programs with higher shape reconstruction accuracy and converges significantly faster than reinforcement learning approaches, and in some domains, LEST can further improve this performance.
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