The fresh turn-averaged SAE's indeterminate tier verdict is floor-local: every looser alive floor reads coarse-over-specific because newly admitted specific-tier features are poorly predicted (MODERATE confidence)

Methodology: docs/methodology/issue_2476.md · gist

Takeaways

• The indeterminate verdict is floor-local. At the plan-fixed 1%-of-rows alive floor the fresh-arm decision rule still returns indeterminate (tier medians 0.625/0.131/0.670 on 788/88/3 alive features), but at every swept looser floor — 0.5%, 0.25%, 0.2% — both rule conditions agree coarse-better: the permutation read sits below its whole null band and the coarse-minus-finest contrast flips from −0.04 to at least +0.52, with intervals clear of zero. The looser-floor rule readings are reported, not re-fixed; the reported lattice is floor-sensitive.
• Doubling the sparsity budget does not populate the specific tier. Retrained at k = 200 with everything else held (width 65,536, data, recipe, splits, estimators), the manipulation landed cleanly — realized validation L0 200.39 vs the parent's 98.96, variance-FVE 0.9304 vs 0.9093 — yet the finest tier counts 4 alive features at the plan-fixed 1% floor against the round's declared budget-limited threshold of 10, so the round's declared verdict is budget-discharged. The 3 → 4 change is deep inside single-training-seed noise; the verdict rests on the count sitting far below 10, not on that delta.
• The attrition apportionment now reads: floor convention settled by the floor sweep, sparsity budget discharged by this round — attribution covering the total k intervention, its induced top-k competition, threshold, and allocation dynamics included — and matryoshka allocation (plus residual undertraining at fixed budget) the remaining untested contributor. Doubling k halves dead-feature fractions (finest 0.356 → 0.177), yet finest candidates clearing the loosest floor fall 130 → 90 of 49,152 and 1%-floor middle counts fall 88 → 35 while coarse counts rise 788 → 1,239: the added budget flows to coarse features and sub-floor firing.
• Newly admitted finest-tier features are poorly predicted at both budgets — pooled finest medians fall 0.670 → 0.046 across the k = 100 sweep (newly-alive-only 0.044, 34% at or below zero) and 0.494 → 0.072 across the k = 200 sweep (newly-alive-only 0.070, 36% at or below zero) — and each instrument's plan-fixed-floor survivors are an unrepresentative elite. Every k = 200 floor reads coarse-over-specific on both rule conditions; those are reported labels, and the gradient verdict of record stays the parent's k = 100 plan-fixed cell.
• The instrument reads are budget-stable: retrieval stays coarse-concentrated (fresh coarse acc@1 0.708 at k = 100 and 0.727 at k = 200 against middle-tier map rates at or below 0.009, chance 5.0e-5, with the identity+bias middle-tier advantage persisting), the token-level dictionary on turn averages stays reversed at all its floors, the map beats identity+bias on median R² in every tier-floor cell at both budgets, and per-feature predictability rank-correlates 0.767 across grain while the tier profile inverts.
• Scope limits: one SAE training seed per budget; each instrument's floors share seeds and nested alive sets, so per-instrument floor patterns are one dependent read; the k = 200 counts gate halted its first production pass on a slice bug in the gate's own recount arm, whose sweep also quantified a 2.34% holdout-row spill in the parent's banked fresh-arm (arm-c) train-mean numerator (constant baseline only; no promoted number moves — Methodology); open review residuals consumer-contract-g4-residual, g2b-reuse-verdict-schema, retrieval-device-pin-residual, g2a-min-cross-machine-headroom, unpinned-q1-source-revision, a13-demotion-scope-drift, result-commit-invalidates-resume, and, from the k = 200 round, production-r7-unexercised and sibling-drivers-accept-nonpass-gate-state are detailed in Methodology.

Goal

Determine whether the context-to-answer map's high-level-over-low-level predictability gradient — the coarse-over-specific gradient, in the parent's terms — holds in a turn-averaged SAE basis: per-tier held-out R² and retrieval accuracy versus an identity+bias baseline, for turn-averaged SAE features of true and map-predicted answer summaries.

This experiment in context: #779 fit the map — a ridge from the last-prompt-token activation to the whole-answer mean activation (layer 19, Qwen-2.5-7B-Instruct, ~963k real chat contexts, held-out R² 0.72–0.75). #1482 found at token-level-SAE grain that this map predicts coarse matryoshka features far better than specific ones (tier medians 0.435/0.174/0.043). A token-level basis pools per-token codes, one step removed from the map's actual target; an SAE trained directly on whole-answer means decomposes that target itself, so this run asks whether the coarse-over-specific gradient is a fact about the map or about the token-level basis.

Broader narrative: the paper's limits-of-the-mapping section claims the map predicts high-level, identity-adjacent content and not low-level, topic-level content. This run rescopes that claim at the map's own grain: the specific tier mostly fails to clear any swept alive floor, the features admitted at looser floors are poorly predicted, and the retrieval read keeps a pronounced coarse-over-specific profile — the fresh-basis evidence now leans the paper claim's way, with the plan-fixed cell itself still indeterminate. A doubled sparsity budget does not move this picture: the specific tier stays starved at the plan-fixed floor and its floor-admitted features stay poorly predicted.

Methodology

Design: One manipulated variable — the grain of the SAE basis (per-token activations vs whole-answer turn averages) — read through two instruments. The fresh-SAE arm (headline) trains a matryoshka BatchTopK sparse autoencoder (SAE) directly on banked layer-19 whole-answer mean activations and scores 20,000 held-out conversations; the bridge arm applies the token-level matryoshka dictionary from the prior token-level round to turn averages at layer 20 on that round's exact 6,000 score rows, giving the only same-dictionary, same-rows grain contrast. Matryoshka nesting makes feature id a training-imposed granularity label: ids below 2,048 are trained under every nested-prefix reconstruction loss (coarsest tier), ids 2,048–16,383 the middle tier, ids 16,384–65,535 only under the full-width loss (finest tier). Controls: identity+bias (predict the answer summary as the context state plus a learned constant shift), train-mean null, a dense-input companion ridge (context state → each SAE feature directly, separating "the map loses tier-t content" from "tier-t content is linearly unreachable at all"), a 20-draw row-shuffle floor, a within-activity-quintile tier-label permutation, a corpus-transfer fold (fit on LMSYS rows, score on the 9,017 WildChat holdout rows), a pile-trained dictionary twin, and an inlier-masked pooling twin. One SAE training seed (2476). Config slugs, matching the plan roster: arm_c_map / arm_c_ib, arm_b_map / arm_b_ib, dense_in_c / dense_in_b, trainmean_null, shuffle_null, tier_perm, corpus_fold, arm_b_pile, arm_b_inlier. The verdict rule is defined on the fresh-SAE arm:

Outcome	Rule (both conditions required)
gradient holds	permutation percentile ≤ 2.5 (coarse-better side) and coarse-minus-finest median contrast above 0
gradient reversed	permutation percentile ≥ 97.5 (fine-better side) and contrast below 0
indeterminate	any other combination, including the two conditions disagreeing

Same-issue follow-up round (floor-sensitivity-sweep, one variable): the alive-floor convention becomes a swept analysis parameter — 1% (the plan-fixed convention), 0.5%, 0.25%, and an absolute 240 rows (0.2%) of the 120,000 fit rows on the fresh arm; 240/120/60 rows (1%/0.5%/0.25%) on the bridge arm, whose absolute point coincides with its 1%. Nothing is retrained or refit: the banked SAE, the banked dense map and identity+bias predictions, splits, score rows, seeds, and draw counts are the parent's, identical across floors, so cross-floor differences are never resampling noise. The rule above binds at the 1% floor only — the verdict of record — and is evaluated descriptively at the looser floors. The demotion convention reports census-only, with no rule label, any floor where over half of a populated tier's alive features return undefined R²; it never triggered (zero undefined reads at every floor, tier, and arm). The round's hypothesis convention compares the finest-tier median at the 240-row floor against the middle tier's interquartile range computed on the same floor's alive middle features. The pile-dictionary leg is exploratory; its census uses recomputed counts (no banked reference exists for it). Round config slugs, matching the follow-up plan roster: fs_c_map_f1200 / fs_c_map_f600 / fs_c_map_f300 / fs_c_map_f240 with identity+bias twins fs_c_ib_f*; bridge fs_b_map_f240 / fs_b_map_f120 / fs_b_map_f60 with fs_b_ib_f*; fs_b_pile_f*; gates gate_repro, gate_counts, gate_rows; nulls fs_trainmean, fs_shuffle, fs_tierperm; firing census fs_firing_ecdf.

Second same-issue follow-up round (k200-instrument-census, one variable): the fresh instrument's sparsity budget k doubles from 100 to 200 at fixed width, tier bounds, training data, recipe, splits, score rows, seeds, and estimator constants — a fresh SAE is trained (init seed 2476) and the full per-floor battery re-runs on it. The round's declared claim is a two-outcome budget rule evaluated once, at the plan-fixed 1% floor: budget-limited if at least 10 finest-tier features are alive there, budget-discharged otherwise, conditional on a manipulation check (realized validation L0 at or above 150, the concrete form of “materially exceeds the parent's 98.96”). The parent's gradient rule is evaluated on the k = 200 cells as reported labels only, and the k = 100 comparison is census-level, never feature-paired (two different instruments). Round config slugs, matching the round plan roster: k200_map / k200_ib, dense-input companion k200_densein (also the third retrieval source), nulls k200_trainmean / k200_shuffle / k200_tierperm, swept companions k200_f600 / k200_f300 / k200_f240, comparison arm k100_committed, gates gate_g4_k200 / gate_rows / gate_splits / gate_counts_self.

Training: the only models trained are the fresh turn-averaged SAEs — the parent round's k = 100 instrument and the budget round's k = 200 retrain; the map itself is refit (never retrained): a shared-Gram ridge from context state to answer summary, with the regularizer selected by whole-map validation R² over a 23-value logarithmic grid from 1e-3 to 1e8 on the pinned 400-row validation split — selected value 1e-3, the grid's low edge, for both refits, seed 0 (the corpus-transfer refit runs the same grid and selection rule). Every value below is copied from the committed run artifacts.

Hyperparameter	Value	Source
SAE architecture	matryoshka BatchTopK; nested prefix reconstruction losses, mean reduction; threshold EMA 0.999	train_log.json cfg
SAE dimensions	input 3,584; dictionary 65,536; k = 100; tier bounds 2,048 / 16,384 / 65,536	train_log.json cfg; tier bounds match the bridge dictionary for tier parity
SAE optimizer	Adam, betas 0.9 / 0.999, lr 2e-4, batch 256, 3 epochs (10,941 steps), init seed 2476	train_log.json cfg; recipe from arXiv 2606.28548 (same model, layer, corpus, object)
SAE training rows	933,444 train + 10,000 validation carve (seed 2476) from the 943,444-row pool (963,444 banked contexts minus holdout and pinned val/test)	train_log.json pools
Realized training state	final validation variance-FVE 0.9093 (FVE = fraction of variance explained; training-sanity halt floor 0.5) at L0 98.96 (mean active features per row); per-tier dead-feature fractions 0.095 / 0.291 / 0.356 after epoch 3	train_log.json epochs; floor from gates_p4.json
Map refits	shared-Gram ridge, grid and selection rule as stated above; selected regularizer 1e-3 (grid low edge) at validation R² 0.754 for both the full-train and holdout-excluded refits, seed 0; both reproduce the committed whole-map R² (deltas 3.5e-7 and 2.1e-7 against tolerances 0.002 / 0.003)	parent refit records (refit_full__ridge__seed0.json, refit_holdout__ridge__seed0.json), reproduced per recon_gate.json
Bridge-arm map	ridge fit on 24,000 rows, scored on 6,000 (selected λ 3.16e3, validation R² 0.671); dense-input companion λ 1.0e3	preds_meta.json
Bridge dictionary	chanind/qwen2.5-7B-it-layer-20-saes revision db8c88b4…, sae_id lmsys/matryoshka/k-100 (pile twin pile/matryoshka/k-100), k = 100, width 65,536	the prior round's pin, re-listed live
Alive floor + panel	active on ≥ 1% of fit-side true-summary encodes (1,200 of 120,000 fresh; 240 of 24,000 bridge); panel cap 16,384, seed 14824	tier_tests_c.json / tier_tests_b.json alive-mask provenance
Statistics constants	10,000 permutation draws; 10,000 bootstrap draws (seeds 24761 / 24762); 20 row-shuffle draws; retrieval at k = 1 / 5 / 10, euclidean + cosine; acc@1 uncertainty: 95% Wilson intervals; matched-activity interval recompute 10,000 bootstrap draws, seed 42, estimators imported from the run scripts	tier_tests_*.json, retrieval_*.json, matched_tier_ci.json
Answer generation	none this run; the measured answers are the banked on-policy rollouts (Qwen-2.5-7B-Instruct, single stochastic sample per prompt, engine seed 42, at most 1,024 new tokens)	capture-run record (provenance in footer)
Floor grid (follow-up round)	fresh 1,200 / 600 / 300 / 240 fit rows (1% / 0.5% / 0.25% / 0.2%); bridge 240 / 120 / 60 (1% / 0.5% / 0.25%)	follow-up plan v7 §11 (1% inherited; halvings bracket the mean firing rate k/width ≈ 0.15%; 240 = the token-level round's absolute floor)
Follow-up round statistics	no training and no fits; every estimator parameter, seed, and draw count identical to the Statistics-constants row above, applied per floor	floor_sweep_c.json / floor_sweep_b.json provenance fields
k = 200 SAE (budget round)	identical architecture, recipe, and pool at k = 200: width 65,536, Adam 0.9 / 0.999, lr 2e-4, batch 256, 3 epochs (10,941 steps), init seed 2476, 933,444 train + 10,000 validation rows; realized validation variance-FVE 0.9304 at L0 200.39; per-tier dead fractions 0.009 / 0.131 / 0.177 after epoch 3	k = 200 cfg.json + train_log.json (HF sae_c_k200/); realized FVE and L0 from gates_k200.json
Budget-round statistics	every estimator parameter, seed, and draw count identical to the Statistics-constants row above, applied per floor; one new fit — the dense-input companion ridge refit on the k = 200 union-alive columns (same grid and selection rule; 120,000 rows against 3,584 inputs; selected λ 1.0e3 at validation R² 0.675)	tier_sweep_k200.json / retrieval_k200.json provenance fields; realized selection from densein_meta_k200.json

Evaluation: No text is generated and no judge is called; every dependent variable is a per-feature or per-row statistic over banked activations, so validity rests on the gates tabled below rather than on-policy or judged-instrument checks. DV1 (primary): per-feature held-out R² of the SAE-encoded map prediction against the SAE-encoded true answer summary — median over alive features per tier; the construct is preservation of tier-t answer content by the pre-generation map. DV2 (companion): retrieval accuracy at k — whether the predicted tier-t feature vector picks the right conversation out of the held-out pool (chance = k over pool size).

Gate (run)	Predicate	Outcome
Reconciliation (parent)	the refit map reproduces the committed whole-map validation R² within tolerances 0.002 / 0.003	PASS — deltas 3.5e-7 / 2.1e-7 (Training table)
Recapture identity, version 2 (parent)	30,000 row-matched cosines of the recaptured context state vs the banked store: min ≥ 0.995, 0.1st percentile ≥ 0.999, median ≥ 0.9995	PASS — 0.9954 / 0.99956 / 0.999933; the version-1 flat bar (every row ≥ 0.999) refused with 4 rows below it — recalibration disclosed below
Encoder fitness, bridge dictionary (parent)	turn-average variance-FVE ≥ 0.35, else the off-domain bridge read is demoted	PASS — 0.659 at L0 26.5 on the 30,000 turn averages; degraded from its native token-level regime exactly as the recipe paper's measurement predicts, so the bridge read is kept
SAE training sanity (parent)	held-out variance-FVE at or above the plan expectation of ~0.85 (halt floor 0.5)	PASS — 0.909 at L0 99.0
Row alignment (floor round)	banked prediction row ids match the assembled holdout order and the bridge score rows	PASS — all six identity checks
Split reproduction (floor round)	all six split sha256 digests equal the banked records	PASS — delta exactly 0
Counts reconciliation (floor round)	recomputed full-width firing counts equal the banked census; no alive-set flips at any floor	PASS — max per-feature delta 0 over all 65,536 features; zero flips
Instrument reproduction, v6 max predicate (floor round)	every per-feature R² within 2e-3 of its committed value	HALT — one of 879 features (56641) at delta 2.83e-3; the production run stopped here and relaunched under v7
Instrument reproduction, v7 quantile predicate (floor round)	at least 99% of features within 2e-3, max 1e-2; per-tier median agreement within 1e-3, binding on tiers with at least 10 features; per-feature deltas reported verbatim below that	PASS — fresh arm 99.886% share with the single 2.83e-3 near-tie; bridge arm zero violators, max delta 3.6e-5
Training sanity, identity, and counts (budget round)	validation variance-FVE at or above 0.5; banked-prediction row alignment; all six split sha256 digests; counts self-consistency — within-pass accounting identity exact, union-column recount within ±3 per feature with alive-set flips confined to floor boundaries, fit-row count 120,000; and a strict phase-entry predicate: each later phase refuses to start on any recorded non-PASS gate verdict	PASS — FVE 0.9304 at L0 200.39; all identities and digests exact; recount max per-feature delta 0, zero alive-set flips

The fresh SAE is trained on exactly the map's target distribution, and encoding the prediction is near-distribution (encoder reconstruction FVE 0.937 on predictions); the bridge encoder is declared off-domain and rides the encoder-fitness gate above. Bootstrap intervals are conditional on the realized score rows.

The recapture identity gate carries a recalibration made after seeing production data: following the version-1 refusal, a worst-16-row re-probe at fp32 improved 13 of 16 rows against the bank (worst fp32 row 0.99595) — consistent with single-position deep-layer numerical jitter rather than a mapping bug (known mapping bugs read 0.39–0.84). The version-2 bars were set from the same production distribution they pass — chosen after seeing that distribution, not before it. Margin on the flat bar is 4.0e-4.

The instrument-reproduction recalibration is post hoc in the same sense: the v7 quantile predicate was recorded as a plan amendment before relaunch but chosen after seeing the halted run's delta distribution (percentile-50 2.5e-6, percentile-99 2.15e-4), and it still hard-fails any systematic shift or order-of-magnitude excursion. The single violator is a cross-pod floating-point near-tie 1.4 times over a bar measured on a different recompute class — and, being one of the three finest-tier survivors, it is itself the 1%-floor finest median at n = 3: 0.6696 committed, 0.6667 recomputed. Prose quoting 0.670 uses the committed parent value; prose quoting 0.667 uses this round's recompute.

Two-SHA phase provenance: the recapture phase ran at code a51057beaf (before the crash-fix relaunch that recalibrated the gate), all later phases at 064462df4d68.

The budget round's counts gate halted its first production pass: the recount's final chunk slice ran past the 120,000 fit rows into 2,880 held-out rows (numpy clamps a past-the-end slice at the array end, not the loop bound), inflating near-saturated features' recounts by up to +2,832. This was a bug in the gate's own recount arm, not in the measurement: a read-only re-probe with the slice clamped reproduces the banked counts with delta exactly 0 over all 2,659 union features, so the banked census and encode artifacts were never wrong; after the one-line fix and same-pod relaunch the gate passed with delta 0. A whole-chain sweep found one sibling of the same slice pattern: the parent round's banked arm-c train-mean numerator includes the same 2,880-row spill (2.34% of summed rows), touching only that constant-baseline anchor. The budget round recomputes train-mean from clamped sums, and the promoted anchor claim — per-tier train-mean medians within 2e-4 of zero — holds on both the spilled and the corrected bases, so no promoted number or verdict moves.

The 1%-of-rows alive floor is inherited for comparability, and the attrition finding depends on where it sits: mean per-feature firing under k = 100 at width 65,536 is ~0.15% of rows, ~6.5 times below the floor. Under k = 200 the realized mean firing (~0.31% of rows) sits inside the swept bracket, between the 0.5% and 0.25% floors, and ~3.3 times below the plan-fixed floor — which still admits only 4 finest-tier features.

Smoke-run markers on this task (24-row composed smokes in each round; the k = 200 smoke legs read FVE 0.41 at L0 42.9) are not production results and must never be cited.

Four parent-round code-review residuals stay open as concerns, named here and in the Takeaways scope bullet. consumer-contract-g4-residual: the firing-census consumer looks rows up via searchsorted on staged row_idx arrays with no early strict-sortedness assertion — searchsorted presumes a sorted array, so an unsorted staged array would silently mis-map rows; the interpretation boundary is that the counts-reconciliation and row-alignment gates certify this run's delivered census downstream (max per-feature delta 0, zero alive-set flips), leaving an unguarded code path rather than an observed data defect. g2b-reuse-verdict-schema: the stale-gate recompute keys on record schema rather than verdict; retrieval-device-pin-residual: retrieval ran on the GPU fp32 backend, whose near-tie rank parity against the fp64 reference helper is unproved — immaterial at the orders-of-magnitude contrasts reported here; g2a-min-cross-machine-headroom: the 4.0e-4 flat-bar margin above, with repeat-machine tail spread unmeasured.

Three review residuals from the floor round stay open as concerns: unpinned-q1-source-revision (the chunk re-assembly delegates some fetches without per-call revision pins, so content equality with the parent instrument is certified downstream — by the split-digest, counts, and reproduction gates — rather than at fetch time), a13-demotion-scope-drift (the census-only demotion was implemented on any populated tier, broader than the plan's finest-tier trigger; it never fired — zero undefined reads — so no lattice label was withheld), and result-commit-invalidates-resume (the result-publishing commit advances the code sha that keys phase resume, so a hypothetical post-publish retry would recompute the analysis phases; no retry occurred).

Two review residuals from the budget round stay open as concerns: production-r7-unexercised (the composed smoke exercised the result-publishing legs only in stub form, so the git and HF finalization paths first ran in production — they completed, and their outputs are the committed artifacts in the footer) and sibling-drivers-accept-nonpass-gate-state (the parent and floor-round drivers' resume paths key on gate-record presence rather than verdict — an unguarded path; the budget round's strict phase-entry predicate closes it for this round's phases only).

Conciseness acknowledgment: the total skim-prose budget, the 120-word per-result band, and Takeaways bullet lengths are exceeded — the eleven results carry verdict tables and companion reads, and the scope bullet carries the named review-residual ids; every hard cap is met.

Data extraction: Tier-1 real-world data: first-turn LMSYS / WildChat user conversations with the banked on-policy model answers (no new generation; the teacher-forced re-read consumes persisted text and stores only reduced means). The fresh arm streams the 1,920 banked capture chunks and assembles layer-19 context-state and answer-mean matrices for 963,444 conversations (fp16, ~6.9 GB each), re-asserting the pinned splits by sha (val 400 / test 1,000 / holdout 20,000 / SAE-fit 120,000). The bridge arm re-captures the prior round's exact 30,000 rows with the same tokenization convention, accumulating answer-span means at layers 19 and 20 in a streaming reduction (per-token activations never materialized beyond the batch). Encodes: fresh SAE on layer-19 objects (20,000 held-out rows); bridge dictionary on layer-20 turn averages (6,000 score rows). Artifact-name convention: file suffix _c marks the fresh-SAE arm, _b the bridge arm. The floor-sensitivity round re-assembles the answer-mean matrix from the same 1,920 banked chunks (splits re-asserted by sha), recomputes full-width firing counts over the fit rows, and encodes the score rows once at the union of all floors' alive columns — 2,150 (fresh), 800 (bridge), 697 (pile) — from which every per-floor read is a subset; no new text, no generation. The budget round re-assembles the answer-mean matrix from the same 1,920 banked chunks (splits re-asserted by sha), re-stages the banked map and identity+bias predictions at the pinned revision, trains the k = 200 SAE on the same 933,444-row pool, recomputes full-width firing counts over the fit rows from raw threshold counts, and encodes the 20,000 score rows once at the union of the k = 200 floors' alive columns — 2,659 — from which every per-floor read is a subset; again no new text and no generation.

Sample training/evaluation data + completions: this task produces no completions and calls no judge; the end-to-end unit is context state → map prediction → SAE encode → per-feature held-out R². Below, first the underlying conversation rows, then the per-feature evaluation rows. 3 of 19,967 labeled holdout rows (the fresh arm's score rows), random sample, seed 2476 — sanitized for context hygiene: real-user-corpus rows, so each cell carries only a mechanically truncated 12-word excerpt standing in as [truncated — sanitized row; verify at the pinned judge-labels tree, rows ci471286 / ci264094 / ci558155]; full text lives in the pinned judge-labels tree, keyed by row id.

Row id	Corpus	Prompt excerpt (truncated)	Model answer excerpt (truncated)
ci471286	lmsys	"Please start a dialogue, with the aim of naturally leading me to …"	"Sure! Let's start with a light topic. How's your day going so …"
ci264094	lmsys	"Do humans have anal glands?"	"Humans do not have anal glands. Anal glands are a characteristic found …"
ci558155	wildchat	"授权委托书 关键词：甲方是我们，乙方是租客 …" (a Chinese rent-collection authorization-letter request)	"授权委托书 甲方：……" (the drafted template letter, in Chinese)

Per-feature evaluation rows: 5 of 879 (fresh arm) and 5 of 412 (bridge arm) alive-feature rows, random sample, seed 42, plus — from the floor-sensitivity round — 3 of 127 newly-alive finest-tier features (fresh arm, 0.2% floor), random sample, seed 42, plus — from the budget round — all 4 finest-tier features of the k = 200 instrument alive at the plan-fixed floor (the full population, not a sample); full arrays in the committed perfeature_c_encodepred.npz, perfeature_b_encodepred.npz, perfeature_union_c.npz, and perfeature_union_k200.npz.

Arm	Feature id	Tier	Held-out R²	Active fit rows
fresh	1771	coarsest	0.650	100,372 of 120,000
fresh	1033	coarsest	0.342	13,587
fresh	1537	coarsest	0.651	2,329
fresh	195	coarsest	0.635	49,858
fresh	1014	coarsest	0.481	3,309
bridge	11376	middle	0.651	519 of 24,000
bridge	171	coarsest	0.864	24,000
bridge	1123	coarsest	0.099	310
bridge	1641	coarsest	0.205	767
bridge	1573	coarsest	0.117	432
fresh, newly alive at the 0.2% floor	54134	finest	0.382	752
fresh, newly alive at the 0.2% floor	22864	finest	0.200	394
fresh, newly alive at the 0.2% floor	50045	finest	0.091	386
fresh k = 200, finest alive at the plan-fixed floor	21581	finest	0.382	1,218 of 120,000
fresh k = 200, finest alive at the plan-fixed floor	36205	finest	0.740	1,573
fresh k = 200, finest alive at the plan-fixed floor	53272	finest	0.395	1,514
fresh k = 200, finest alive at the plan-fixed floor	62588	finest	0.592	1,405

Worked example: for fresh-arm feature 1537 (coarsest tier), the map's predicted answer summary is encoded for each of the 20,000 held-out conversations, and the predicted feature value tracks the true one with held-out R² 0.651 — despite the feature firing on only 2,329 of 120,000 fit rows.

Results

The verdict is indeterminate on the headline arm: the permutation criterion fires coarse-better while the endpoint contrast lands negative

Plotted: per-tier median held-out per-feature R² of encoded map predictions against encoded true summaries; four bars per tier — fresh turn-averaged SAE (20,000 rows, 879 features) and token-level dictionary on turn averages (6,000 rows, 412 features), each vs identity+bias; black dashes: token-level reference medians (different grain, layer, dictionary, and rows — not a matched contrast).

Figure. Neither turn-averaged basis reproduces the token-level round's monotone coarse-over-specific decline. Median held-out per-feature R² per matryoshka tier: fresh turn-averaged SAE (blue) vs its identity+bias baseline (orange), token-level dictionary on turn averages (green) vs its baseline (pink); black dashes = token-level reference medians. Whiskers: 10,000-draw bootstrap intervals.

Arm	Tier medians (n alive)	Coarse-minus-finest contrast (95% interval)	Permutation percentile (observed pooled rank correlation vs null band)	Rule outcome
Fresh turn-averaged SAE, layer 19	0.625 / 0.131 / 0.670 (788 / 88 / 3)	−0.044 (−0.264 to −0.013)	0.0, coarse-better side (−0.449 vs −0.190 to −0.069; achievable magnitude ceiling 0.528)	indeterminate — the two conditions disagree
Token-level dictionary on turn averages, layer 20	0.420 / 0.553 / 0.601 (387 / 21 / 4)	−0.181 (−0.325 to +0.105; crosses zero)	99.42, fine-better side (+0.113 vs −0.103 to +0.086)	reversed — a secondary read; the rule is defined on the fresh arm
Token-grain reference (its own round: token level, layer 20, 6,000 rows)	0.435 / 0.174 / 0.043 (16,384-feature panel)	+0.392	coarse-better (−0.395 vs −0.250 to −0.228)	gradient holds

The two rule conditions read different populations: the permutation pools all 879 features and is dominated by coarse-vs-middle (876 of 879), while the endpoint contrast is decided by the 3 finest-tier survivors — indeterminate is the honest cell at this floor (shown floor-local below). The bridge-arm reversal is marginal: its endpoint interval crosses zero. An inlier-masked pooling twin matches the plain mean to four decimals, so outlier tokens do not drive the inversion.

The map beats identity+bias on per-feature R² at every tier; fresh-arm deltas exceed 1 because the baseline's held-out R² goes deeply negative.

Tier	Paired R² delta, fresh (95% interval)	Paired R² delta, bridge
coarsest	+1.39 (+1.28 to +1.49)	+0.45 (+0.42 to +0.49)
middle	+5.26 (+3.90 to +6.91)	+0.56 (+0.46 to +0.76)
finest	+1.15 (+1.15 to +6.49)	+0.50 (+0.13 to +0.74)

Per-unit exemption: the per-feature scatter behind these medians is embedded two results below.

Alive-feature attrition, not a gradient, is the dominant turn-averaged phenomenon

Plotted: the fraction of each tier's candidate features clearing the alive floor (active on at least 1% of fit rows), log y-axis, one bar per tier and arm, then the per-candidate firing-fraction distribution behind the census.

Figure. Above 99.9% of finest-tier candidates fall below the alive floor in both turn-averaged instruments. Fraction of candidate features per matryoshka tier clearing the 1%-of-fit-rows floor (1,200 of 120,000 rows, fresh arm; 240 of 24,000, bridge arm), log scale.

Figure. Per-candidate companion to the census bars. Cumulative share of each tier's candidates at or below a given firing fraction (log x); each curve enters at its never-fires share (fresh instrument 19%/61%/77% across coarsest/middle/finest, bridge 31%/79%/96%); the dashed line is the 1% alive floor.

Tier (candidates)	Fresh SAE	Bridge dictionary	Pile twin
coarsest (2,048)	788 (38%)	387 (19%)	261 (13%)
middle (14,336)	88 (0.6%)	21 (0.15%)	39 (0.27%)
finest (49,152)	3 (0.006%)	4 (0.008%)	14 (0.03%)

The token-level panel carried 16,384 alive features; the same dictionary on turn averages retains 412. The counts say almost no specific-tier feature clears the inherited floor under these k = 100, width-65,536 instruments.

Mean firing (k over width, ~0.15% of rows) sits ~6.5 times below the floor; the floor sweep below apportions the contributions. Under the plan-fixed floor turn-averaging removes specific features from the alive panel; the floor sweep shows they return poorly predicted at looser floors — the map's target object carries little well-predicted specific-tier structure, which rescopes the paper claim rather than contradicting it. The per-candidate curves sharpen this: most specific-tier candidates never fire at all, and the floor cuts each surviving tail far above its bulk.

Surviving finest-tier features match coarse features of similar firing frequency — a survivor-conditioned read; the middle-tier dip is instrument-dependent

Plotted: every alive feature's held-out R² against log10 of its active fit rows, tier-colored, one panel per arm — the per-unit view behind every median above.

Figure. Fresh-arm middle-tier features cluster at low activity and low R²; the bridge arm's middle tier does not. Each point is one alive feature: held-out R² vs log10 active fit rows, colored by tier (fresh arm n = 879, bridge arm n = 412).

Read	Values	Note
Matched-activity coarse median, fresh (1,400–2,400 active rows)	0.525 (0.491 to 0.565), n = 197	finest-tier survivors read 0.880 / 0.670 / 0.648
Matched-activity middle median, fresh (same band)	0.132 (0.104 to 0.180), n = 41	matched coarse-minus-middle +0.393 (+0.333 to +0.442) — the dip holds at matched activity with the interval clear of zero
Matched coarse-minus-finest contrast, fresh	−0.145 (−0.381 to −0.097)	excludes zero on the negative side, but the finest side is the 3 survivors — survivor-conditioned, not population evidence
Matched-activity coarse median, bridge (390–552 active rows)	0.393 (0.343 to 0.452), n = 83	finest survivors 0.745 / 0.626 / 0.576 / 0.318; fresh band applied instead: 0.509 (0.303 to 0.577), n = 22
Matched contrasts, bridge (same band)	coarse-minus-middle −0.126 (−0.410 to +0.394), middle-tier n = 5; coarse-minus-finest −0.208 (−0.354 to +0.076), finest n = 4	both cross zero; coarse-minus-finest agrees with the unmatched endpoint contrast in the first results table
Matched-activity reads, pile twin (250–1,922 active rows — its own middle-tier survivor range, derived by the bridge-arm rule)	coarse 0.416 (0.381 to 0.444), n = 192; middle 0.557 (0.429 to 0.634), n = 35; coarse-minus-middle −0.141 (−0.200 to −0.035)	middle above coarse with the interval clear of zero — opposite sign to the fresh arm's +0.393
Identity+bias coarse-minus-finest contrast	fresh −0.287 (−0.416 to +5.146, crosses zero); bridge −0.126 (−0.337 to −0.008)	a map-free predictor reproduces the endpoint inversion at the point estimates
Dense-input companion medians	0.533 / 0.159 / 0.719 (fresh); 0.391 / 0.544 / 0.598 (bridge)	survivors are also more linearly predictable from context at all
Corpus-transfer fold (fit LMSYS, score 9,017 WildChat rows)	0.522 / 0.075 / no finite finest values	18 of 86 finite middle-tier transfer values negative; coarse tail reaches −6.83
Pile-twin medians	0.457 / 0.557 / 0.413 (n = 261 / 39 / 14)	non-monotone, but a small positive coarse-minus-finest endpoint (+0.044)

Survivors read as at least as predictable as coarse features of comparable firing frequency in both instruments — a survivor-only description at n = 3–4, not a population inference; survival is itself activity selection no within-panel control can undo, and the floor sweep below identifies these survivors as the elite tail of a poorly predicted population. The middle-tier dip survives corpus transfer and activity matching in the fresh instrument, and the matched contrasts separate: fresh coarse-better, pile twin middle-better, both intervals clear of zero, while the bridge arm leans the pile twin's way at matched activity on 5 middle-tier features without separating. Identity+bias and the dense-input companion reproduce the survivor-profile shape without the map, so map-specific content loss is not necessary for the endpoint inversion — a survivor-panel effect and shared dictionary geometry are indistinguishable here.

Retrieval concentrates in the coarsest tier: acc@1 0.708 coarsest vs 0.001 middle

Plotted: per-tier retrieval accuracy at k = 1 (euclidean; pool = held-out rows, 20,000 fresh, 6,000 bridge; chance = 1 over pool size), map vs identity+bias per arm; inset: middle and finest tiers. Below it, the per-row rank distributions behind these cells.

Figure. Coarse-tier features identify the held-out conversation at 0.708; middle- and finest-tier rates sit orders of magnitude lower. Retrieval accuracy at k = 1 per tier, map vs identity+bias, fresh arm (chance 5.0e-5) and bridge arm (chance 1.67e-4); inset: middle and finest tiers. Black whiskers: 95% Wilson intervals.

Figure. Per-row companion: the coarse tier's retrieval advantage holds across the whole rank distribution, not only at rank 1. Share of held-out rows whose true conversation ranks at or below x (euclidean, log x), per tier; solid = map, dashed = identity+bias.

Diagnostic	Fresh arm	Bridge arm
Encoder reconstruction FVE of the input being scored (map prediction vs identity+bias guess)	0.937 at L0 88 vs 0.305 at L0 955	gate values in Methodology
Alive features beating the 20-draw row-shuffle floor (map vs identity+bias)	100% vs 29.6%	100% vs 47.8%
Dense-space anchor (before encoding)	acc@1 0.705; pooled R² 0.724	—
Retrieval cells favoring the baseline (of 12 total)	middle tier, both metrics — systematic at k = 1, 5, 10	finest-tier cosine cell

Encoding an identity+bias guess lands off the feature manifold (fresh-arm middle-tier median −5.13; diagnostics table). Middle-tier map cells sit at 21x and 39x chance yet roughly 670x and 50x below their coarse-tier rates, and 3 of 12 map-vs-baseline cells favor the baseline.

Tier-restricted vectors have 788/88/3 dimensions, so low-tier cells are dimension-confounded — coarse-concentrated is the supportable read, not a content-loss quantification. The two dependent variables disagree in profile; the headline is scoped to the R² profile. The per-row ranks were recomputed after the run, which persisted only the aggregate cells; every accuracy-at-1 cell reproduces exactly, all cells within two rows in 20,000 (deltas: footer).

Per-feature predictability transfers across grain (rank correlation 0.767) while the tier profile inverts

Plotted: each intersection feature's held-out R² at turn-averaged grain (bridge arm) against the same feature's committed token-level R² — same dictionary, same rows; 409 features, tier-colored, identity diagonal; every point is one feature, so this is its own per-unit view.

Figure. Feature ranking is basis-stable; the level shifts down and the tier profile inverts. Held-out per-feature R², turn-averaged vs token grain, on the 409-feature intersection (same dictionary, same 6,000 score rows); points below the diagonal lose predictability at the turn-averaged grain.

Pooled rank correlation 0.767 (per tier 0.754/0.893/0.5 at n = 387/19/3) clears the plan's 0.5 expectation — the ranking clause of the bridge hypothesis passes. The level shifts down for most features (median delta −0.152; 337 of 409 points below the diagonal, 72 above — dominant but heterogeneous), and the gradient-preservation clause is refuted: the per-tier profile inverts (0.420/0.553/0.601 vs the token-level 0.435/0.174/0.043). The token-level gradient ran through thousands of low-activity specific features that do not exist as alive features at this grain — 15,975 of its 16,384 panel features fall out of the intersection.

The indeterminate cell is floor-local: every swept looser floor reads coarse-over-specific on the fresh arm, while the bridge instrument stays reversed

Plotted: per-tier median held-out R² against the alive floor (fresh arm, map vs identity+bias); the table adds each floor's within-activity permutation read for both instruments — observed pooled rank correlation of tier index against per-feature R² vs its 10,000-draw null band (more negative means coarse-better).

Figure. The finest-tier median collapses once the floor admits a real population. Median held-out per-feature R² per matryoshka tier vs alive floor, fresh turn-averaged SAE: map (solid) vs identity+bias (dashed); shaded bands are 10,000-draw bootstrap intervals. Per-tier alive counts per floor are in the table below.

Arm, floor	Alive by tier	Tier medians (map)	Coarse-minus-finest (95% interval)	Permutation: observed vs null band	Rule reading
Fresh, 1% (plan-fixed)	788 / 88 / 3	0.625 / 0.131 / 0.667	−0.042 (−0.263 to −0.013)	−0.449 vs (−0.190, −0.069), coarse-better	indeterminate
Fresh, 0.5%	992 / 314 / 26	0.607 / 0.172 / 0.087	+0.520 (+0.373 to +0.594)	−0.641 vs (−0.300, −0.217), coarse-better	gradient holds (reported)
Fresh, 0.25%	1,137 / 696 / 80	0.592 / 0.166 / 0.049	+0.543 (+0.485 to +0.579)	−0.691 vs (−0.349, −0.287), coarse-better	gradient holds (reported)
Fresh, 0.2%	1,178 / 842 / 130	0.588 / 0.163 / 0.046	+0.542 (+0.517 to +0.568)	−0.699 vs (−0.377, −0.320), coarse-better	gradient holds (reported)
Bridge, 1% (its plan-fixed cell)	387 / 21 / 4	0.420 / 0.553 / 0.601	−0.181 (−0.325 to +0.105)	+0.113 vs (−0.103, +0.086), fine-better	reversed
Bridge, 0.5%	529 / 56 / 7	0.377 / 0.471 / 0.626	−0.249 (−0.399 to +0.069)	+0.118 vs (−0.150, +0.001), fine-better	reversed
Bridge, 0.25%	657 / 130 / 13	0.307 / 0.319 / 0.576	−0.269 (−0.438 to +0.010)	+0.020 vs (−0.221, −0.104), fine-better	reversed

The full reported vector, ordered 1% → 0.2%: indeterminate at the plan-fixed cell, then gradient holds at every looser floor (fresh); the bridge reads reversed throughout. The reported lattice is floor-sensitive — the plan-fixed cell stays the verdict of record; looser-floor labels are descriptive.

The looser floors share seeds and nested alive sets with the 1% cell — one dependent pattern, not independent replications — and cross-floor permutation values are descriptive too (activity quintiles are recomputed per floor); within a floor the permutation controls activity composition. The 1%-row values are the sweep's recomputations — hence finest median 0.667 here vs the committed 0.670 (the near-tie feature; gate bars in Methodology). Per-unit exemption: the per-feature curves behind these medians are the next result's figure.

Newly admitted finest-tier features collapse toward zero: the three 1%-floor survivors are an unrepresentative elite

Plotted: the cumulative distribution of per-feature held-out R² per tier, one panel per floor (fresh arm) — the per-unit view behind the medians above.

Figure. At every floor below 1% the finest tier's distribution sits far to the left of the coarse tier's. Cumulative share of alive features at or below a given held-out R², per tier and floor, fresh arm; per-tier n per floor in the previous result's table.

Read (fresh arm; loosest floor unless stated)	Value
Pooled finest median by floor, 1% → 0.2%	0.667 → 0.087 → 0.049 → 0.046 (n = 3 / 26 / 80 / 130)
Newly-alive-only finest median at 0.2%	0.044 (n = 127); 34% at or below zero; 69% below 0.1
Finest median 95% interval vs same-floor middle-tier interquartile range	0.020–0.067 vs 0.062–0.306 (middle median 0.163, n = 842)
Newly admitted vs previously-alive medians at 0.2%	coarse 0.475 vs 0.625; middle 0.172 vs 0.131
Alive features beating the 20-draw row-shuffle floor (map read)	100% at 1% → 97.0% at 0.2%
Corpus halves, finest median at 0.2%	0.040 LMSYS / 0.030 WildChat
Undefined per-feature R²	0 at every floor, tier, and arm

The round's hypothesis convention compares the finest-tier median at the 240-row floor against the same floor's middle-tier interquartile range. The hypothesis fails: the newly-admitted finest median (0.044) sits at roughly a quarter of the middle median and below the middle interquartile range — though the bootstrap interval's upper end grazes the range's lower edge.

Every cross-floor median move is composition: previously-alive features keep their values exactly (same rows, same encodes), and the newly admitted cohorts read lower (coarse) or comparable (middle). The 3% shuffle-floor failures at the loosest floor sit among the newly admitted low-activity features, consistent with the collapse read; the train-mean null anchors the scale: per-tier medians within 2e-4 of zero at every floor. A bookkeeping spill in the banked fresh-arm train-mean numerator (2.34% held-out rows; Methodology) touches only this anchor and leaves it within that bound.

Attrition stays above 99.7% of finest-tier candidates at every swept floor: the floor convention explains the verdict, not the census

Plotted: alive-feature counts per tier against the floor for all three dictionaries (log y), then the per-candidate firing-fraction distributions with the swept floors and the instrument's mean firing rate marked.

Figure. The finest tier gains features 43-fold across the sweep yet stays under 0.3% of its candidates. Alive features per matryoshka tier vs alive floor: fresh turn-averaged SAE, the token-level dictionary on turn averages, and the pile-trained twin (exploratory).

Figure. Per-candidate companion to the census counts: most specific-tier candidates never fire, and every swept floor cuts each tail far above its bulk. Cumulative share of candidate features at or below a firing fraction (log x), per tier and dictionary; dash-dot line marks the mean firing rate (k over width), dashed lines the swept floors.

Floor (% of fit rows)	Fresh finest alive (of 49,152)	Bridge finest	Pile twin finest
1%	3	4	14
0.5%	26	7	21
0.25%	80	13	42
0.2% (fresh grid only)	130	—	—

Within the swept 0.2%–1% bracket the apportionment is two-way: the floor convention carries the verdict's indeterminacy (previous results) and a 43-fold finest census change, while the attrition bulk — over 99.7% of finest candidates below even the loosest floor — stayed, at that round's close, with the joint matryoshka-allocation-plus-undertraining residual; the budget round, two results below, discharges its sparsity-budget half. Floors below the bracket, including any below the mean firing rate (~0.15% of rows), were not swept and stay unresolved. The pile twin is exploratory: its census rests on recomputed counts and its tier medians move non-monotonically with the floor.

Retrieval is coarse-concentrated at the plan-fixed floor; the looser-floor cells are aggregate-only descriptive reads

Plotted: per-tier retrieval accuracy at k = 1 (euclidean) against the floor, map vs identity+bias, fresh arm, log y with the chance line; only the 1% column has a per-row companion.

Figure. At the plan-fixed floor retrieval is coarse-concentrated; the three looser floors' cells, aggregate-only descriptive reads, sit the same way. Retrieval accuracy at k = 1 per tier vs alive floor, fresh arm, map vs identity+bias (pool 20,000; chance 5.0e-5, dotted).

Tier, predictor (looser floors aggregate-only)	1%	0.5%	0.25%	0.2%
Coarsest, map	0.708	0.706	0.706	0.706
Middle, map	0.0011	0.0041	0.0081	0.0088
Middle, identity+bias	0.0035	0.0134	0.0224	0.0252
Finest, map	0.0001	0.0003	0.0004	0.0007

The claim of record sits at the plan-fixed floor, where the parent's committed per-row rank arrays (embedded two results above) back the aggregate: coarse map acc@1 0.708 vs middle 0.0011. The looser-floor cells are aggregate-only descriptive reads — their per-row ranks cannot be recomputed, because the union encode matrices behind them are among the plan's declared discards and the pod is terminated. Descriptively those cells move the same way: the coarse map rate stays flat, middle- and finest-tier rates grow roughly with dimension yet remain 80-fold or more below it, the baseline's middle-tier advantage strengthens — the dimension confound carries through — and bridge cells match (coarse 0.331–0.335).

A per-floor per-row recompute, re-encoding the held-out rows at each floor's alive panel, is a needs-gpu follow-up candidate.

Doubling the sparsity budget to k = 200 leaves the finest tier starved: 4 alive features at the plan-fixed floor against a declared threshold of 10

Plotted: alive-feature counts per matryoshka tier (log y), the k = 200 retrain beside the committed k = 100 census — four bar pairs per tier, one per swept floor, ordered 1% to 0.2%; counts are raw threshold firing counts over the 120,000 fit rows. Below it, the per-candidate firing distribution behind the counts.

Figure. The plan-fixed finest-tier counts are 3 and 4 at one training seed per budget — within single-seed noise and both far below the threshold of 10. Alive features per matryoshka tier: k = 200 (colored) beside the committed k = 100 census (gray); four floor pairs per tier (1%, 0.5%, 0.25%, 0.2%, left to right); log scale.

Figure. Per-candidate companion: the k = 200 finest tier still concentrates far below every swept floor. Cumulative share of each tier's candidates at or below a firing fraction (log x), k = 200 instrument; dashed and dotted verticals mark the k = 200 and k = 100 mean firing rates, light verticals the swept floors.

Read	k = 100 (committed)	k = 200 (this round)
Validation L0 / variance-FVE (manipulation check)	98.96 / 0.9093	200.39 / 0.9304 — both clean-manipulation preconditions held
Mean realized firing (share of fit rows)	~0.15%, below the whole swept bracket	~0.31%, inside the bracket
Dead-feature fraction after epoch 3 (coarsest / middle / finest)	0.095 / 0.291 / 0.356	0.009 / 0.131 / 0.177
Alive at the 1% floor (coarsest / middle / finest)	788 / 88 / 3	1,239 / 35 / 4
Alive at the 0.2% floor	1,178 / 842 / 130	1,687 / 882 / 90
Finest candidates clearing the loosest floor	130 of 49,152 (0.26%)	90 of 49,152 (0.18%)
Encoder reconstruction FVE of the map prediction being scored	0.937	0.956 at mean L0 186

The round's two-outcome rule — budget-limited if at least 10 finest-tier features clear the plan-fixed floor, budget-discharged otherwise — returns budget-discharged at 4 of 49,152. Both manipulation preconditions held, so the discharge covers the total k intervention, its induced top-k competition, threshold, and allocation dynamics included. Dead fractions halve, but no middle or finest count multiplies at any floor, so the added budget flows to coarse features and sub-floor firing.

The 3 → 4 change is deep inside single-seed noise; the verdict is the count sitting far below 10. Matryoshka allocation, with residual undertraining at fixed budget, remains the untested contributor.

The doubled-budget instrument repeats the survivor-elite pattern: newly admitted finest features collapse while every reported floor reads coarse-over-specific

Plotted: median held-out per-feature R² per tier against the alive floor, k = 200 instrument, map versus identity+bias, with the committed k = 100 map medians overlaid as crosses; below, the per-feature distributions behind every plotted series.

Figure. The k = 200 finest-tier map median falls from 0.49 at the plan-fixed floor toward 0.07 at the loosest while identity+bias goes deeply negative. Median held-out R² per tier vs alive floor, k = 200: map (solid) vs identity+bias (dashed); gray crosses are the committed k = 100 map medians (a different instrument — census-level comparison only).

Figure. Per-feature companion to every plotted series: each looser floor's finest cohort piles up near zero. Cumulative share of alive features at or below a held-out R² (x clipped at −1), per tier (rows) and floor (columns): k = 200 map (solid), identity+bias (dashed), k = 100 map reference (dotted); per-tier n in the table below.

Floor	Alive by tier	Tier medians (map)	Coarse-minus-finest (95% interval)	Permutation: observed vs null band	Reported label
1% (plan-fixed)	1,239 / 35 / 4	0.590 / 0.155 / 0.494	+0.096 (−0.150 to +0.211; crosses zero)	−0.232 vs (−0.113, −0.006), coarse-better; achievable magnitude ceiling 0.298	coarse-over-specific
0.5%	1,483 / 244 / 21	0.585 / 0.149 / 0.323	+0.262 (+0.185 to +0.478)	−0.526 vs (−0.261, −0.185), coarse-better	coarse-over-specific
0.25%	1,645 / 702 / 53	0.576 / 0.126 / 0.087	+0.489 (+0.422 to +0.539)	−0.698 vs (−0.410, −0.357), coarse-better	coarse-over-specific
0.2%	1,687 / 882 / 90	0.574 / 0.127 / 0.072	+0.502 (+0.472 to +0.555)	−0.715 vs (−0.440, −0.392), coarse-better	coarse-over-specific

Companion read (k = 200)	Value
Plan-fixed-floor finest survivors (all 4)	R² 0.382 / 0.395 / 0.592 / 0.740, median 0.494 — above the same-floor middle-tier interquartile range 0.097–0.262
Newly-alive finest at the 0.2% floor	median 0.070 (n = 86); 36% at or below zero; 63% below 0.1
Map-vs-identity+bias paired deltas at the plan-fixed floor	+1.80 / +7.65 / +1.02 across tiers, intervals clear of zero
Retrieval acc@1 at the plan-fixed floor (euclidean; aggregate-only cells)	map coarsest 0.727 vs middle 0.0006 and finest 5.0e-5 (chance 5.0e-5); identity+bias coarsest 0.289; the baseline's middle-tier advantage reappears at looser floors (0.019 vs 0.005 at 0.2%)
Dense-input companion medians at the plan-fixed floor	0.523 / 0.190 / 0.562
Share of alive map features beating the 20-draw shuffle floor	100% / 100% / 99.2% / 98.2% across floors (identity+bias 22.5% / 19.3% / 15.6% / 15.0%)
Train-mean anchor (recomputed from clamped sums)	per-tier medians within 1.3e-4 of zero at every floor
Corpus halves, finest median at the 0.2% floor	0.012 LMSYS / 0.029 WildChat
Undefined per-feature R²	0 at every floor and tier

All four k = 200 floors read coarse-over-specific on both parent rule conditions — reported labels; the gradient verdict of record stays the parent's k = 100 plan-fixed cell. The plan-fixed label is fragile in the parent's way: it rests on 4 elite survivors whose contrast interval crosses zero and who read above the middle tier's interquartile range, like the parent's 3. The feature-splitting alternative never arises: it required a multiplied census with a well-predicted newly-populated tier.

Newly admitted finest features collapse toward zero as at k = 100, the dense-input companion tracks the survivor profile, and retrieval keeps its coarse-concentrated shape; its per-row companions are not recomputable (the union encode matrices are declared discards).

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Repro: ~7.3 h wall on 1× H100-80 (RunPod pod-2476), zero LLM-API calls. Workload: scripts/issue2476_turnavg_sae.py @ 064462df4d (--phase all); two-SHA phase provenance — the bridge-row recapture ran at a51057beaf (its gate record carries that commit), all later phases (SAE training / maps / eval / figures) at 064462df4d68. Eval artifacts (git, branch issue-2476): eval_results/issue_2476/turnavg tree — 28 files: tier_tests_c.json / tier_tests_b.json (medians, permutation, bootstrap, verdict inputs), retrieval_c.json / retrieval_b.json plus the per-row rank arrays behind every retrieval cell (perrow_retrieval_ranks.npz, with per-cell reproduction deltas and provenance in perrow_retrieval_ranks_meta.json — recomputed post-run by scripts/issue2476_perrow_views.py @ a3338b6ec57855d03531d5c81b1bd6d59f61c32a from the uploaded SAE weights and prediction stores; the fresh arm's dense map predictions come from the parent round's committed copy of the same ridge refit, issue1482_error_analysis/analysis_tensors/percontext/refit_holdout__ridge__seed0.npz @ 89cfa76cdc, this run's own refit store having not been uploaded — the recompute fetched that file at the then-current unpinned default branch, and the pinned revision serves identical content (its last touching commit is dated 2026-07-18, before the 2026-08-23 recompute); row set asserted identical and the committed per-feature R² arrays reproduced, verification deltas in perrow_retrieval_ranks_meta.json), panel_c.json / panel_b.json, per-feature npz for the map / identity+bias / dense-input / transfer / pile / inlier reads, bridge_b.npz, train_log.json, recon_gate.json, preds_meta.json, regime.json (split shas), and the recapture gate record gates_p2.json; recapture-gate recalibration evidence at eval_results/issue_2476/g2a_recalibration tree. A follow-up analysis round (no new compute) added bootstrap intervals for every matched-activity read: matched_tier_ci.json in the turnavg tree @ 179a7b69aa, produced by scripts/issue2476_matched_tier_ci.py @ 179a7b69aa (10,000 draws, seed 42; point medians re-derived from the committed per-feature npz files and checked against every committed matched read before any interval was computed; branch issue-2476). Figures: hero pair figures/paper/c3_turnavg_tier_gradient + c3_turnavg_tier_acc1 (png, pdf, data sidecars) and exploratory panels under figures/issue_2476 @ a3338b6ec57855d03531d5c81b1bd6d59f61c32a; the gradient hero and the bridge scatter were re-rendered for label fixes (internal arm tokens, then a bare issue token) by scripts/issue2476_fig_relabel.py @ a3338b6ec57855d03531d5c81b1bd6d59f61c32a, sidecar numeric data asserted identical to the first renders each time; the two per-unit companions (i2476_candidate_firing_ecdf, i2476_retrieval_rank_ecdf) are new in this revision round (same script as the rank arrays); other panels unchanged at 8dac0f576f and 8d0d7d545c. HF (listed live at write time, 99 files): issue2476_turnavg/analysis_tensors — recapture_store/ (68 files: the 30,000-row mean store + the gate record source), eval/ (21), split_meta/ (7), sae_c/ (3: SAE weights 1.88 GB safetensors, cfg, train log). Artifact-suffix legend: _c = fresh turn-averaged SAE arm, _b = bridge arm, _ib = identity+bias, _densein = dense-input companion. Reuse provenance: capture chunks + rollout text from #779 at HF issue779_monitoring/fitter-fair-comparison-n1m/{final_token_capture,raw_completions} @ revision 89cfa76cdc… (the run read both prefixes at the then-current unpinned default branch; the pinned revision serves identical content — the last commits touching them are dated 2026-07-15 for the capture chunks and 2026-08-17 for the rollout text, both before the run's 2026-08-22/23 assemble and recapture reads) — the map's own training capture, fitness by construction; pinned splits, the 30,000-row subsample, the committed token-level per-feature panel, and the layer-20 dense store from #1482 at HF issue1482_error_analysis/analysis_tensors/matryoshka_tier/store revision 8b82eb9753… — same-lineage products, shas re-asserted in-run; token-level dictionaries chanind/qwen2.5-7B-it-layer-20-saes — that round's own pin, fitness gate passed at FVE 0.659; sample-row text from #1482's committed judge-labels file (pinned above) — the same holdout rows this run scores. Plan: plans/plan.md (v4) in the task directory; production results marker posted 2026-08-23T11:44Z. Discarded per plan: per-token recapture activations, assembled fp16 matrices, and SAE optimizer state (regeneration recipes in the plan's reproducibility card); no rollout text, judge output, metric, or config discarded. Floor-sensitivity round (same-issue follow-up round floor-sensitivity-sweep, cheap band): ~3.1 GPU-h on 1× H100-80 (RunPod pod-2476, fresh pod), zero LLM-API calls; workload scripts/issue2476_floor_sweep.py @ a1e18f25d1 (parent kernels imported by file path; one production halt at the first instrument-reproduction predicate, relaunched after the plan-v7 re-calibration narrated in Methodology). Round eval artifacts (git, branch issue-2476, result commit 23eb255f10ca…): eval_results/issue_2476/floor_sweep tree — 8 files: floor_sweep_c.json, floor_sweep_b.json, floor_sweep_b_pile.json (per-floor medians, permutation, contrasts, lattice vectors), floor_retrieval_c.json, floor_retrieval_b.json, gates_floor_sweep.json (all six gate records), perfeature_union_c.npz, perfeature_union_b.npz (union per-feature arrays + per-floor alive masks; the source of every newly-alive decomposition above). Round figures: nine floor-sweep panels under figures/issue_2476 @ 23eb255f10 (stems i2476_floor_sweep_hero_r2, i2476_floor_sweep_hero_acc1, i2476_floor_hero_b_r2, i2476_floor_alive_counts, i2476_floor_r2_ecdf, i2476_floor_perm_summary, i2476_floor_firing_ecdf, i2476_floor_corpus_split, i2476_floor_shuffle_null; png, pdf, and data sidecar each); the acc@1 hero was re-rendered for a legend label fix (the internal predictor token ib spelled out as identity+bias) by scripts/issue2476_fig_relabel.py @ 86bf3d56db --floor-acc1, sidecar numeric data asserted identical to the first render, and is pinned at 86bf3d56db. Round HF artifacts (listed live at write time, 5 files): issue2476_turnavg/analysis_tensors/floor_sweep — firing_census_c.npz, firing_census_b.npz, firing_census_b_pile.npz plus the two union npz twins. Round plan: plans/plan.md (v7, self-contained); round upload-verification pass posted 2026-08-24T06:50Z. Budget round (same-issue follow-up round k200-instrument-census, cheap band): ~3.9 h wall on 1× H100-80 (RunPod pod-2476; planned 3.7 h, one crash-fix round included), zero LLM-API calls; workload scripts/issue2476_k200_census.py @ 8360a1d72d (--phase all; parent kernels imported by file path), landed across commits 1b93837e92 (budget seam + revision-pin threading), 0bbb76d7cc (round driver + failure-semantics test pins), dba08c36b7 (review-round fixes), 5b94a13c67 (strict gate-verdict phase-entry predicate), and 8360a1d72d (the chunk-slice clamp narrated in Methodology). Round eval artifacts (git, branch issue-2476, result commit 3d9c2ea588…): eval_results/issue_2476/k200_census tree — 6 files: census_k200.json (census + the budget-rule record + manipulation check), gates_k200.json (gate records + the prediction-encode fidelity read), tier_sweep_k200.json (per-floor medians, permutation, contrasts, nulls, corpus splits), retrieval_k200.json (per-floor per-tier cells, three sources), perfeature_union_k200.npz (union per-feature arrays + per-floor alive masks), and — landed after the result commit, at its own pin — densein_meta_k200.json @ 36e6ca5c5d (the dense-input companion's fit diagnostics: selected λ 1.0e3 at validation R² 0.675). Round figures: eleven k = 200 panels under figures/issue_2476 @ 3d9c2ea588 (stems i2476_k200_census_hero, i2476_k200_tier_r2_hero, i2476_k200_firing_ecdf, i2476_k200_finest_r2_ecdf, i2476_k200_retrieval_acc1, i2476_k200_dead_frac_epochs, i2476_k200_loss_fve, i2476_k200_perm_summary, i2476_k200_shuffle_null, i2476_k200_corpus_split, i2476_k200_densein_profile; png, pdf, and data sidecar each); the tier-R² result's per-feature companion was later regenerated with full series coverage (all tiers and floors, k = 200 map and identity+bias, plus the k = 100 map reference) as i2476_k200_tier_r2_percell_ecdf by scripts/issue2476_k200_percell_ecdf.py @ 0f8103a19f from the two committed union npz files (alive counts asserted against the body tables before rendering), superseding the finest-only i2476_k200_finest_r2_ecdf panel in the body. Round HF artifacts (listed live at write time, 3 + 3 files): issue2476_turnavg/analysis_tensors/sae_c_k200 — the k = 200 SAE weights (1.88 GB safetensors), cfg, and train log — and issue2476_turnavg/analysis_tensors/k200_census — firing_census_k200.npz, perfeature_k200_densein.npz, perfeature_union_k200.npz. Round plan: plans/plan.md (v11, self-contained); round results marker posted 2026-08-24T18:56Z. Discarded per plan: the re-assembled fp16 matrices, the k = 200 optimizer states and per-epoch checkpoint, and the union-restricted encode matrices (regeneration recipes in the plan's discard slot); no rollout text, judge output, metric, or config discarded.

Context: Origin prompt (verbatim): Paper outline 2026-08-22: 'SAE experiments — try turn averaged SAEs'. Lineage: #1482 — the token-level tier-gradient round this run re-tests at turn-averaged grain, itself an error-analysis child of the #779 map. Created 2026-08-22; production run 2026-08-23 (one crash-fix relaunch after the recapture identity gate refusal narrated in Methodology); interpretation passed both critics 2026-08-23; matched-activity interval round folded 2026-08-23. Follow-up round floor-sensitivity-sweep (source: the automatic follow-up proposer, cheap band; scope marker posted 2026-08-24T00:35Z), originating proposal title (verbatim): ### 1. Alive-floor sensitivity sweep of the tier profile — Diagnostic; run 2026-08-24 (one halt at the instrument-reproduction gate, plan-v7 re-calibration, relaunch), folded 2026-08-24. Follow-up round k200-instrument-census (source: the automatic follow-up proposer, cheap band; scope marker posted 2026-08-24T08:52Z), originating proposal title (verbatim): ### 3. k-budget census: retrain the fresh SAE at k = 200 — Ablation; run 2026-08-24 (one crash-fix relaunch after the counts-gate halt narrated in Methodology), folded 2026-08-24.