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Learning the Geometry of Admissible Hypotheses through Inductive Bias in Training Distributions

arXiv · AI, language, vision and robotics · article · Aug 31, 2026 · UTC

Scientific discovery often requires reasoning over competing hypotheses that are consistent with experimental observations. For mixed-variable and combinatorial hypothesis spaces, however, constructing probabilistic representations remains challenging because both the active model components and their associated parameters are unknown. In this work, we present a framework for learning continuous latent representations of admissible partial differential equations (PDEs) by embedding a scientific inductive bias directly into the training distribution. Progressively richer structural principles (

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