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Diffstat (limited to 'results.md')
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@@ -89,30 +89,6 @@ experiment + evaluation data) finds ZERO occurrences of frequency/unigram/ token-count terms. Their README confirms the fit corpus is "a generic web-text corpus" — no frequency balancing. -## 1c. Independent corroboration (willkn, GreaterWrong, GPT-2-medium) - -An independent engineering analysis of the paper (willkn, GreaterWrong, 24 Jul -2026; notebooks: github.com/willkn/jlens_re; full text: docs/willkn-jlens- -greaterwrong-analysis.md), on GPT-2-medium (355M, d=1024, L=24, V=50,257), -found: -- the raw fitted Jacobian "misweights structural tokens (grammar, punctuation) - over semantic content" — dominant spectral channels carry ~10x the gain of - the residual pathway. Structural tokens ARE the high-frequency tokens; this - is the same distortion we measure as frequency anti-correlation, at 30x our - model scale and via a different metric (next-token faithfulness of the - readout). -- the Jacobian is essentially full-rank: 562-858 dimensions capture 90% of - spectral variance, "leaving little room for compression" — corroborates our - dimensional-starvation / full-rank result at scale. -- a single-parameter shrinkage regularizer (J + lambda*I) monotonically - recovers next-token faithfulness (beats logit lens at layer 12: 0.294 vs - 0.275). Anthropic's released fitting code applies no such regularization. -- measured noise law rel_F(J_n) ~ c_l/sqrt(n), c_l growing ~4x from layer 20 - to layer 4; per-backward cost ~5ms + 9ms/layer on L4 at dim_batch=8. - -Untested (natural next experiment): does shrinkage also remove our frequency -correlation? - ## 2. Frequency-matched synthetic pair (`src/synthetic_pair.py`) Two new characters at identical 0.1% unigram frequency in Shakespeare: @@ -182,6 +158,40 @@ Reading: 4. Absolute norms differ across experiments (base L3 q = 0.0109 vs these 0.015-0.018) — only within-experiment comparisons are meaningful. +## 5. At-scale W_U row-norm check (GPT-2, V=50,257) — RESOLVED + +The geometric half of the confound generalizes. Correlating GPT-2 unembedding +row norms (wte == tied lm_head, so this is exactly W_U's rows) against token +unigram log-frequencies from wikitext-103-raw (117.9M tokens; 46,887/50,257 +vocab covered): + +``` + model r(raw) r(log10, all V) r(log10, seen) Spearman(seen) + gpt2 (d=768) -0.092 -0.451 -0.468 -0.462 + gpt2-medium -0.104 -0.493 -0.515 -0.498 +``` + +n = 46,887 seen tokens; 95% CIs [-0.475, -0.461] (gpt2) and +[-0.522, -0.508] (gpt2-medium). Log10-freq decile -> mean row norm is +monotone in both models (gpt2: 4.02 -> 3.42; medium: 3.93 -> 3.16): rare +tokens get bigger unembedding rows. Top-norm tokens are rare or zero-count +(SPONSORED, soDeliveryDate, Reviewer, advertisement). + +Reading: the learned W_U geometry finding from the 65-char model carries to +real LMs at V = 50,257 — present in two independently trained models, monotone +across the whole vocabulary — but it is WEAKER than at toy scale +(r(log10) -0.45/-0.49 vs -0.69; Spearman -0.46/-0.50 vs -0.81). So the +char-scale result was not a vocabulary-size artifact, and neither is the +at-scale effect as strong as the toy suggested. The layer-dynamics component +(partial r after regressing out W_U) at scale remains untested — that needs +the faithful J-lens on GPT-2 (future work). + +Reproduce, CPU-only, no training, no GPU: +``` +.venv/bin/python src/wu_row_norm_check.py --models gpt2,gpt2-medium +``` +Full log: `outputs/wu_row_norm_check.log`. + ## 4. Historical / do-not-copy - Original proxy finding (r = -0.65, `jlens_v2`): superseded by the faithful @@ -190,5 +200,6 @@ Reading: (`gpt2_jlens.py`) gave avg r = -0.18 across layers — UNDER-POWERED (96 token positions, n=100 sampled tokens) and a different quantity (norm-per-batch vs norm-of-mean). Kept here only as a reproducibility - warning: **do not cite the -0.18 as evidence**; the at-scale test with the - faithful lens is future work. + warning: **do not cite the -0.18 as evidence**; the at-scale W_U geometry + check (section 5) is the powered version of the geometric claim, and the + at-scale test with the faithful lens is future work. |