at-scale W_U row-norm check (GPT-2): geometric confound generalizes, r(log10)≈-0.45/-0.49; blog draft: drop 'Actually', log-freq lead, probe transparency, norm-vs-readout concessionmain

1 files changed, 6 insertions, 0 deletions

diff --git a/README.md b/README.md
index ae9ba86..de56776 100644
--- a/README.md
+++ b/README.md
@@ -20,6 +20,11 @@ Workspace in Language Models"* (2026,
 4. A causal loss-reweighting test (2x loss weight on 'q' targets vs two
    controls) tests whether effective frequency causally demotes a token's
    J-lens norm. See `results.md` for the latest numbers.
+5. The geometric half generalizes: GPT-2's unembedding row norms (V = 50,257,
+   wte == tied lm_head) anti-correlate with token log-frequency
+   (r ≈ -0.45/-0.49, gpt2/gpt2-medium; monotone across frequency deciles) —
+   the learned W_U geometry is not a 65-char vocabulary artifact
+   (`src/wu_row_norm_check.py`, CPU-only).
 
 See `docs/blog-jlens-frequency.md` for the write-up and `results.md` for the
 numbers. The three independent adversarial reviews that shaped the project
@@ -44,6 +49,7 @@ src/jlens_v3.py           FAITHFUL J-lens: rows of W_U * J_l (canonical)
 src/synthetic_pair.py     frequency-matched synthetic pair experiment
 src/loss_reweight.py      causal loss-reweighting experiment
 src/gpt2_jlens.py         GPT-2 scale test (under-powered; see results.md)
+src/wu_row_norm_check.py  at-scale W_U row-norm check (CPU-only; results.md §5)
 tests/                    unit tests (see scripts/test.sh)
 scripts/test.sh           canonical test command
 docs/blog-jlens-frequency.md  write-up (Feynman-style)