The prior is that there's a space of symmetries the phenomenon being modeled may obey (e.g., affine), and the learning task is to discover which (e.g., only translations, or only some translations).
@pmddomingos
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Controlled Perturbation: Function Application as Risk Factor
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But in reality you may fail when you try to do f(X), so doing it is effectively just another perturbation, albeit under your control.
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Rung 3 Model: Conditioning on Evidence and Counterfactuals
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All rung 3 requires is a model that lets you condition on arbitrary evidence, including counterfactuals. To learn the model you need inductive biases / prior assumptions, which are necessary and sufficient for all rungs and may or may not include a theory of causality.
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Permutation Invariance: Operating on Unordered Sets
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Permutation invariance lets you operate on (unordered) sets. It's not a symbol manipulation apparatus per se.
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Algorithms for Learning Symmetries Save Data in Machine Learning
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We have algorithms for learning symmetries, and using them saves a lot of data. E.g.: https://
homes.cs.washington.edu/~pedrod/papers
/nips14.pdf
…