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    High Dimensions Turn Boundary Generalization Into Volume Advantage

    Tweet from Tsinghua PhD student explains volume advantage for generalization in high-dimensional spaces.

    YJ
    1 Source, 32d ago, first seen 32d ago

    TLDR

    You Jiacheng posted that generalization and reinforcement learning operate on boundaries, which appears problematic. He noted that in high-dimensional space the boundary occupies most of the volume. The post gave an example of training on 10k samples from a unit ball and generalizing to a (1+δ) ball that contains at least (1+δ)^d times 10k cases. The message frames high dimension as a feature rather than a drawback for such tasks.

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    1 Source, first seen 32d ago

    Combined views

    6.6K

    1 Source, first seen 32d ago

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    2 comments
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    6 reposts
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    1 Source

    @YouJiachengHigh dimension is a feature? Generalization and RL work on the boundary, sounds bad. But in high dimensional space, the boundary occupies the most of volume! trained on 10k samples from an unit ball, generalize to a (1+δ) ball, which contains ≥(1+δ)^d * 10k cases.

    1 Source

    @YouJiachengHigh dimension is a feature? Generalization and RL work on the boundary, sounds bad. But in high dimensional space, the boundary occupies the most of volume! trained on 10k samples from an unit ball, generalize to a (1+δ) ball, which contains ≥(1+δ)^d * 10k cases.