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DSLT 2. Why Neural Networks obey Occam's Razor — LessWrong

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TLDR; This is the second main post of Distilling Singular Learning Theory which is introduced in DSLT0. I synthesise why Watanabe's free energy formula explains why neural networks have the capacity to generalise well, since different regions of the loss landscape have different accuracy-complexity tradeoffs. I also provide some simple intuitive examples that visually demonstrate why true parameters (i.e. optimally accurate parameters) are preferred according to the RLCT as n → ∞ , and why non-true parameters can still be preferred at finite n if they have lower RLCT's, due to the accuracy-complexity tradeoff. (The RLCT is introduced and explained in DSLT1). It is an amazing fact that deep neural networks seem to have an inductive bias towards "simple" models, suggesting that they obey a kind of Occam's Razor: Plurality should not be posited without necessity. or in modern parlance, If two models of the world are similarly accurate, the simpler explanation should be preferred. This

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