预写: 给Ben信中的"请教K"段(用户08-03决定跑完135M后征询)

策略: 把可能的软肋转为对定理作者的真诚请教。要点=给全数据(K=1余弦0.9999/配对差3e-5/seed散布
大两个数量级)+主动指出我方round与其round非同一单位故不宣称与其K≥4矛盾+明说不愿悄悄改用K=1
+把成本收益(2.7→1.6×)摆出但声明不以描述失准为代价。

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

1 files changed, 21 insertions, 0 deletions

diff --git a/docs/audit/EP_READOUT_FLOOR_AUDIT.md b/docs/audit/EP_READOUT_FLOOR_AUDIT.md
index 7786b87..cc7a071 100644
--- a/docs/audit/EP_READOUT_FLOOR_AUDIT.md
+++ b/docs/audit/EP_READOUT_FLOOR_AUDIT.md
@@ -123,3 +123,24 @@ Hughes et al. Optica 2018、Kendall 2006.01981、2503.22810、2602.03670、Stoch
 > remedy there is to form it elementwise in higher precision rather than to substitute.
 >
 > A standalone checker is at [tools/contrast_floor_check.py], and it runs against any implementation.
+
+## 给 Ben 的信中"请教 K"段（预写, 用户 08-03 决定: 跑完 135M 后一并发出并征询他的意见）
+> One question I would rather ask you than decide on my own. In our layered setup the free phase is a
+> single forward pass, as it is for PCNs in your ImageNet paper, so the only thing that iterates is the
+> nudged equilibrium. We transmit the nudge down the whole stack analytically in one round, rather than
+> updating layers asynchronously, and with that transmission the number of rounds turns out not to
+> matter: at a fixed checkpoint the cosine to the backprop gradient is 0.9999 at one round, and over a
+> paired six thousand step comparison the final loss at one, two, and three rounds agrees to three parts
+> in a hundred thousand, against a seed to seed spread two orders of magnitude larger. So in this
+> architecture the equilibrium iteration appears to do no measurable work, and one round is the adjoint
+> up to a correction of order beta that sits only in the parameter Jacobian.
+>
+> Your sensitivity result gives K at least four, with the optimum near the depth of the network, which
+> makes sense for asynchronous updates where a round moves information about one layer. I do not think
+> our round and your round are the same unit, so I am reluctant to read our result as contradicting
+> yours, and equally reluctant to quietly report one round as though the iteration count were a free
+> parameter. How would you report this? Is the round count a meaningful axis at all for an architecture
+> whose free phase is exact by construction, or is the honest framing that the contribution sits in the
+> locality of the update and the finite beta behavior rather than in the equilibrium computation itself?
+> Dropping to one round would take our training cost from 2.7 times backprop to about 1.6, which is
+> worth having, but not at the price of describing the method inaccurately.