Minimal weight norm of fixed-precision looped neural networks equals Kolmogorov complexity of output string up to log factor, making weight decay match the optimal universal prior up to polynomial factor.
Grünwald.The Minimum Description Length Principle
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Binary acyclic SCMs can have observational distributions with constant description length while single-variable interventional oracles require Θ(n²) bits, with a further Θ(n) gap to counterfactuals.
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Neural Weight Norm = Kolmogorov Complexity
Minimal weight norm of fixed-precision looped neural networks equals Kolmogorov complexity of output string up to log factor, making weight decay match the optimal universal prior up to polynomial factor.
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The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy
Binary acyclic SCMs can have observational distributions with constant description length while single-variable interventional oracles require Θ(n²) bits, with a further Θ(n) gap to counterfactuals.