From 6a057a379e58dc464f04e5208861699b01b5d477 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Wed, 8 Apr 2026 18:59:33 -0500 Subject: =?UTF-8?q?paper=20v2.31.14:=20=C2=A73=20=C2=B61=20local-loss=20fo?= =?UTF-8?q?rmula=20sign-consistency?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Original §3 ¶1: "reducing a local loss of the form -" = minimizing - = maximizing = "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 " This is mathematically equivalent (both give optimizer direction ∇W in the direction that increases ) 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 = 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) --- paper/main.pdf | Bin 501154 -> 501164 bytes 1 file changed, 0 insertions(+), 0 deletions(-) (limited to 'paper/main.pdf') diff --git a/paper/main.pdf b/paper/main.pdf index 229f118..bd6fa77 100644 Binary files a/paper/main.pdf and b/paper/main.pdf differ -- cgit v1.2.3