From 3919f5a7db4abb699af150107bb1a2c587c14cfd Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Wed, 8 Apr 2026 12:53:00 -0500 Subject: Round 41 (Appendix L): add nudging-test functional evidence for cos-vs-acc dissociation MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The nudging test values were already in the round 38 JSON under diag['nudging']['0.01'] but never used. Extracted and added to Appendix L: SB+penalty: deep nudge delta = -1.78e-3 (per-layer, eta=0.01) CB+penalty: deep nudge delta = -0.45e-3 (per-layer, eta=0.01) A single step of size eta=0.01 in each method's credit direction decreases the test loss by 1.78e-3 (SB) vs 0.45e-3 (CB) — a 4x gap in functional loss decrease that EXACTLY INVERTS the 4x deep-cosine gap between the methods. This is the direct functional measurement for the 'angular agreement is not sufficient' claim. Combined with the drift diagnostic (larger CB updates), the cos-vs-acc mechanism hypothesis now has THREE independent pieces of support: 1. Test accuracy (headline: CB same as DFA, SB higher) 2. Parameter drift (CB larger updates than SB) 3. Nudging functional loss decrease (CB 4x smaller than SB) Zero new compute — all from existing round 38 JSON data. Main content still 9 pages exactly within E&D budget. Co-Authored-By: Claude Opus 4.6 (1M context) --- paper/main.pdf | Bin 483268 -> 484316 bytes 1 file changed, 0 insertions(+), 0 deletions(-) (limited to 'paper/main.pdf') diff --git a/paper/main.pdf b/paper/main.pdf index 0626715..814a77b 100644 Binary files a/paper/main.pdf and b/paper/main.pdf differ -- cgit v1.2.3