fcf5fb66c4
Both written before either has run on the board. Co-Authored-By: Claude Opus 5.5 <[email protected]>
38 lines
2.5 KiB
Text
38 lines
2.5 KiB
Text
Written 2026-11-06, before any board run of the joint test, and committed before it. Not edited
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after the data.
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WHAT IS TESTED. The sample kernel's joint law, not only its per-cell frequencies: a sampler that drew
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each cell from its right marginal, independently, would pass every per-cell test. Four cases, each a
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workload small enough that the exact law of a chain's final state can be enumerated over all 3^n
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states (src/exact.rs, `exact::cases`):
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ring 8, fixed T = 1.5, 4 sweeps 200,000 chains 6,561 states
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ring 8, the job's anneal from T = 2.5, 10 sweeps 200,000 chains 6,561 states
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dense 6, fixed T = 4, 2 sweeps 200,000 chains 729 states
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sparse 10, the job's anneal from T = 1.5, 8 sweeps 400,000 chains 59,049 states
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Chain r of a case has the seed chain_seed(2027, r). (Seed 2026 was used while writing the test, on
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the model; 2027 has not been run anywhere before this file was committed.) Every chain runs on the
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board through the AXI link's sequencer, and on the CPU reference.
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THE EXACT LAW. A probability vector over every state, pushed through each cell update of each sweep
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with the three probabilities a/2^53, (b-a)/2^53 and 1 - b/2^53 from the reference's cut points
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(a, b) = cuts(h, cost, beta), then through the synchronous sweep at temperature 0 where the job's
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anneal ends with one. It assumes ideal uniform 53-bit draws; nothing is sampled.
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STATISTICS AND THE RULE, per case:
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1. Pearson chi-square and the G-test over every state expected at least 5 times, the rest pooled
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into one bin: p >= 0.001 for both.
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2. Every cell's three marginal frequencies (z scores) and every pair of cells' nine joint
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frequencies: Bonferroni p >= 0.001 for each family.
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3. Every chain's final state on the board equals the CPU reference's.
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4. Control: the same histogram against the law with the exact marginals and independent cells
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must be rejected, chi-square p < 1e-6, while its cell family still passes. This shows the test
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sees the joint structure that per-cell statistics cannot.
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A case passes if 1-4 hold. Sixteen p values are taken at 0.001 each; the chance that a correct
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kernel fails one by chance is about 1.6%.
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WHAT IT DOES NOT SHOW. Because the board is bit-exact (rule 3), its histogram is the reference's:
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the test holds the shared kernel (the reference's algorithm and its counter-based draws) to exact
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enumeration on the board's own outputs; it is not an independent sample of a different machine.
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Board-level, one board.
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