Residual analysis

Primary: drop-comparison encodes h and ĥ at the same L40 site so the site gap cancels — features strong in h but absent in ĥ are what the channel drops. Secondary: raw-residual enrichment is a labeled null (noise overlap 30/30).

substrate: 1000 gold + 021 AR reconstructions
sae: gemma-scope-2 L40 16k l0=60
primary method: drop-comparison (gap-cancelled)
experiment: 021_interp_combos

Caveat — site gap —The SAE is trained at layers.40 output (hidden_states[41]); the NLA reads hidden_states[42]. The drop-comparison method (§2) explicitly encodes both h and ĥ at the same L40 site, so the gap cancels and the primary result is valid. The raw-residual enrichment (§3) does not cancel the gap and is a labeled null.SAE trained at layers.40 output = hidden_states[41]; the NLA reads hidden_states[42], one block downstream. This gap is NOT corrected in 021 — it is the honest reason fvu_h is elevated (~0.44 in 020) and the residual methods are mushy.

§1

Sanity gate

four FVU measurements

The SAE was trained on full activations at layers.40. We hand it (a) gold activations one block later (h), (b) AR reconstructions (ĥ), (c) residuals r = h − ĥ, and (d) Gaussian noise norm-matched to those residuals. FVU on r and noise are both noise-level — confirming the raw-residual enrichment is an off-manifold artifact.

0.44

FVU on h

L0 64 (trained l0 60)

0.39

FVU on ĥ

L0 48

1554

FVU on r

L0 905

1453

FVU on noise

L0 886

Finding —FVU on h (~0.44) is elevated vs the paper's ~0.08 in-distribution number — expected from the one-block site gap. FVU on r and noise are both ~1400–1554 (noise-level), confirming the residual is entirely off-manifold for this SAE.

§2

Drop-comparison (primary)

gap cancels — real result

Method: encode h and ĥ separately at the same L40 site (passing each through the SAE directly, not via r = h − ĥ). The site gap applies equally to both encodings, so it cancels. Features present in the h encoding but absent or weak in the ĥ encoding are what the text channel drops during AR reconstruction.

separate-encode h vs h-hat at the same L40 site (gap cancels); PRIMARY residual method for 021

0.44

FVU encode(h)

same site as ĥ

0.39

FVU encode(ĥ)

510

features in h

min freq 0.02

top dropped

feature	label / logit-lens	freq h	freq ĥ	mean act h	mean act ĥ	drop ratio
f3726	operation finishes	0.075	0.000	46.5	0.0	76.0
f3023	lists followed by and/or to	0.039	0.000	22.8	0.0	40.0
f2384	上記の上記 उपरोक्त ছাড়াও	0.053	0.001	30.6	0.5	27.0
f8485	code or special characters	0.022	0.000	15.9	0.0	23.0
f8625	order status	0.028	0.001	17.7	0.5	14.5
f3819	again	0.037	0.002	15.9	0.6	12.7
f12505	complex numbers	0.023	0.002	12.3	1.4	8.0
f1632	closing punctuation marks	0.031	0.005	14.5	2.3	5.3
f15243	military alliances or problems	0.055	0.010	30.1	4.3	5.1
f13871	code snippets and multi-language keywords	0.029	0.005	15.4	3.0	5.0
f2303	hon'ble legal context	0.020	0.004	10.0	2.0	4.2
f4025	oxygen	0.020	0.004	10.8	1.8	4.2
f9263	foreign and multilingual references	0.056	0.013	41.3	8.7	4.1
f4120	personal and meaningful connection	0.029	0.007	13.3	3.1	3.8
f1248	yine again Again again	0.021	0.005	10.2	2.0	3.7
f2394	oretically 并不是 *, ,	0.042	0.011	24.5	6.4	3.6
f6169	lists of things like languages or services	0.023	0.006	12.9	4.4	3.4
f2186	various forms of likewise	0.025	0.007	12.4	2.8	3.3
f15222	the daycare	0.023	0.007	13.0	3.3	3.0
f2211	edge devices and entering hurricanes	0.045	0.015	24.1	7.5	2.9
f13181	DSP, CAP, acronyms	0.035	0.012	24.3	8.6	2.8
f2714	React hooks and technologies	0.032	0.011	18.7	6.6	2.8
f4151	technical terms and diverse languages	0.021	0.007	12.1	5.5	2.8
f3265	goodness	0.048	0.017	24.8	8.7	2.7
f3360	start of critical or related phrases	0.026	0.009	13.3	4.6	2.7
f12830	called or so-called	0.023	0.008	14.0	4.8	2.7
f15301	month, form, threat	0.028	0.010	13.3	3.8	2.6
f2862	typical Typical typical Typical	0.020	0.007	12.8	4.9	2.6
f9517	. \n	0.022	0.008	9.1	3.6	2.6
f6727	other languages	0.027	0.010	15.4	5.9	2.5

Features strong in h (freq ≥ min_freq_h) but absent/weak in ĥ. drop_ratio = mean_act_h / max(mean_act_hhat, ε). High ratio = strongly dropped by the channel.

§3

Raw-residual enrichment (labeled null)

noise overlap 30/30 — artifact

This is a negative result. NEGATIVE RESULT / labeled null: SAE-encode(h-hat) of the raw residual. The SAE is not linear over differences, so this is semi-baked regardless of site; kept for the record. The drop_compare method (separate-encode) is the primary one.

30/30

noise overlap

top-30 'enriched' features shared with noise arm

5192

active in r

11153

active in h

4432

active in noise

Finding —Noise overlap is 30/30 — the top-30 “enriched” features all fire on the noise arm too. The enrichment table below is measuring off-manifold breakage, not what the channel drops. Use §2 (drop-comparison) for the actual result.

feature	label / logit-lens	enrich	freq r	freq h	freq noise	mean act
f169	official/original sources	48	1.00	0.02	1.00	986
f39	numbers and units	46	1.00	0.02	1.00	1881
f507	camaraderie социа музей disgraced	46	1.00	0.02	1.00	3441
f86	't or '2	46	1.00	0.02	1.00	1507
f826	wired charging and plots	45	1.00	0.02	1.00	1266
f711	which and which valamint	43	0.99	0.02	0.99	1558
f527	code, numbers, ````	43	0.98	0.02	0.97	904
f403	وغيرها 等等 इत्यादी 以及	42	1.00	0.02	1.00	1424
f400	multitude plethora lot Vielzahl	42	1.00	0.02	1.00	5096
f439	K H G the	42	1.00	0.02	1.00	1436
f1082	generate revenue or transmit information	40	1.00	0.02	1.00	1280
f348	`` čne とはいえ izinsuku	38	1.00	0.03	1.00	3829
f504	ibid https formerly http	37	1.00	0.03	1.00	1237
f21	breakdown of why/how/what	36	0.80	0.02	0.70	544
f7513	code following punctuation	36	0.79	0.02	0.76	353
f1643	instructions and constraints	35	0.73	0.02	0.70	411
f541	numbers and ranges	35	1.00	0.03	1.00	2327
f5251	special, unique, or distinct concepts	34	0.77	0.02	0.76	508
f489	* <ul> Саша	33	1.00	0.03	1.00	1950
f318	patitth pabbaj entusiasmo ettha	33	1.00	0.03	1.00	1931
f9517	. \n	33	0.76	0.02	0.70	333
f5444	restrictive lung disease, surnames	32	0.68	0.02	0.72	324
f352	<unused541> abbanti <unused284> <unused291>	32	1.00	0.03	1.00	2936
f322	gahet sajana pona iha	32	1.00	0.03	1.00	1473
f346	aka S iaz others	31	1.00	0.03	0.99	1120
f269	<unused437> saddhim niektor <unused218>	30	1.00	0.03	1.00	6018
f631	government agreements and announcements	30	0.81	0.03	0.78	354
f30	the followed by a noun	29	1.00	0.03	1.00	4969
f37	ending lists or explanations	28	0.90	0.03	0.86	648
f79	Context, What, Progress	28	0.98	0.03	0.99	607

Caption: artifact table. freq_noise ≈ 1.0 throughout confirms these are off-manifold threshold activations, not content. Reported for completeness only.

§4

Per-example drill-down

top-5 in r vs top-5 in h

Raw-residual top features per example (top_r) alongside gold-h top features (top_h). Same caveats as §3 apply to top_r — these are off-manifold activations. Top_h is on-distribution and meaningful.

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