A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
International Series in Pure and Applied Mathematics
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Under a block-wise contraction condition, spectral gaps of random-scan and deterministic-scan component-wise Markov chains are simultaneously positive or zero and differ by at most polynomial factors in the number of blocks.
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Any-Dimensional Invariant Universality
A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
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Solidarity of Spectral Gaps for Component-Wise Markov Chains
Under a block-wise contraction condition, spectral gaps of random-scan and deterministic-scan component-wise Markov chains are simultaneously positive or zero and differ by at most polynomial factors in the number of blocks.