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authorYurenHao0426 <Blackhao0426@gmail.com>2026-04-08 18:59:33 -0500
committerYurenHao0426 <Blackhao0426@gmail.com>2026-04-08 18:59:33 -0500
commit6a057a379e58dc464f04e5208861699b01b5d477 (patch)
treef91ca912d69c3b887aabc0cb93c22dc10eafb65a /results/cifar10
parent7c3b3393ca2264c463296144461d2ce6c62e3657 (diff)
paper v2.31.14: §3 ¶1 local-loss formula sign-consistency
Original §3 ¶1: "reducing a local loss of the form -<f_l, a_l>" = minimizing -<f, a> = maximizing <f, a> = "alignment with credit target is rewarded" (matches prose) But "reducing a local loss of the form -X" reads awkwardly because the "-" sign in front of an inner product looks like a typo or extra negative. Replaced with the equivalent positive form: "maximizing a local objective of the form <f_l(h_l), a_l>" This is mathematically equivalent (both give optimizer direction ∇W in the direction that increases <f, a>) but reads more cleanly. The §3 ¶1 prose "any direction in which a larger block output improves inner-product alignment with the method's fixed or learned credit target is rewarded" now matches the formula directly: maximizing <f, a> = rewarding alignment. This relies on the convention e_T = one_hot - softmax (paper a_l is the negative of the script's a_dfa). The script's positive-sign minimization of local_loss = (f * a_dfa).sum() is the same operation under that convention. If the convention is unfamiliar to a reader, the actual direction (toward larger inner product with a fixed random direction) is unambiguously stated by the prose. Page layout preserved: 9 pages main, refs p10, 0 overfull boxes. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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