Draft paper uses Markov-chain eigenfunctions to build partitions and speed up sampling
michaelchchoi · x · 2026-07-21
A work-in-progress paper proposes using the bottom eigenfunction of a Markov chain to build a partition that speeds up sampling.
Core idea
- The method partitions the state space into 4 blocks
- Same color means the same block in the animation
- The left chain in the demo is the original sampler, which has trouble moving to the right ring
Why it matters
The technique is aimed at improving mixing by structuring the chain around spectral information, rather than relying on the sampler to discover the partition on its own.
The author says a draft is available and that the work is still in progress, with feedback invited.
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