Structure is not mechanism: high-gain gated-FFN rows across text and genomic foundation models

• The central question is whether properties of recurring activation-derived high-gain structures determine functional importance, beyond detecting extreme parameters.Source: §1 · p. 2
• Genomic models provide a cross-domain setting spanning decoder-only, bidirectional, and hybrid architectures operating on nucleotide sequences.Source: §1 · p. 2
• The study computes each candidate row’s bilinear operator exactly and uses its norm and singular spectrum as weight-space descriptors, then tests interventions against native loss.Multi-row case studies compare additive response models with richer calibration and pairwise-interaction models.Source: §1 · p. 2
• Across text and genomic models, high-gain gated-FFN rows recur, but structural prominence is an enrichment signal rather than a calibrated measure of functional importance.Source: §1 · p. 2
• Activation-derived candidates were generally more consequential than same-layer controls, yet operator magnitude and spectral concentration did not calibrate causal severity.Focused cases showed a pretrained pair interaction in DNABERT-2 and a beginning-of-sequence-mediated native-loss effect in GENERator.Source: §1 · p. 2

Magnitude-matched controls

• Candidates exceeded the median top-norm control in 20 of 22 models under partial suppression and 19 of 22 under full ablation, while q1 did not predict full-ablation effects.Across the 22-model cohort, q1 versus full-ablation effect had Spearman ρ = 0.074 (p = 0.744); both q1 and Frobenius-magnitude associations disappeared within text decoders. Some candidates were less concentrated than high-norm neighbours yet caused one to three orders of magnitude more loss damage.Source: Magnitude-matched controls · pp. 4, 6

2.1 Structural properties

• Across 23 models, q1 ranged from 0.389 in NTv3 to 0.9996 in EuroBERT-610M, and candidates were more concentrated than all five random controls in every census model.The median random-control gap was 0.935, but the median top-norm margin was only 0.014; in 7 of 22 models, a high-norm neighbour was more concentrated. Thus, concentration was recurrent but not universal or generally distinctive from the strongest same-layer alternatives.Source: §2.1 · pp. 3–4, Figure 1 · p. 5

2.2 Functional enrichment

• At full ablation, candidates exceeded the median random same-layer control in 20 of 22 models, with a median candidate-minus-control gap of +0.88%.The 95% model-bootstrap interval was +0.61% to +111.78%, reflecting a highly right-skewed distribution; effects ranged from −0.79% to +698.87%. At partial suppression, candidates exceeded the control median in 18 of 22 models, with a median gap of +0.60%.Source: §2.2 · p. 4, Figure 2 · p. 7

2.3 Within-layer sweep: detection versus severity

• Among 15 rows at or above the ratio threshold of 5.0, ratio strongly ordered damage in GENERator and SmolLM2, whereas 21 below threshold carried no usable damage information.Above threshold, correlations were ρ = 0.639 and ρ = 0.975, respectively; the frozen candidates caused 6.1 × 10^4 and 5.4 × 10^5 times the median sub-threshold damage. The exploratory split supports detection and ordering, not a dose-response measure of severity.Source: Figure 3 · p. 8, §2.3 · p. 8

2.4 Two critical rows in one layer

• In SmolLM2-1.7B layer 7, r161 caused +287.2% loss despite rank 4 by ratio, while rank-2 r749 caused only +2.2%; paired effects were non-additive.The r161–r749 pair caused only +2.1% versus +289.4% summed singles, while r227–r749 was super-additive and r227–r161 mildly sub-additive. The cancelling rows were positively aligned, but the measurements do not establish why the interaction occurs.Source: §2.4 · pp. 8–9

2.6 GENERator: position-localized dependence

• For GENERator-EUK row 2371, ablating only its BOS contribution reproduced nearly all native-loss damage, while preserving or restoring BOS yielded a rescue fraction of 0.9996.The row’s full ablation reduced mean GC fraction from approximately 0.420 to 0.307; preserving or restoring BOS raised it to approximately 0.412, while matched non-BOS restoration did not rescue. Random-direction replacement reproduced the low-GC phenotype at matched damage, and ablation also modestly degraded other generation-quality measures while preserving valid nucleotide output.Source: §2.6 · pp. 10, 12

2.5 DNABERT-2: a pairwise interaction

• In DNABERT-2, L9/r264 and L9/r294 increased loss by only +0.0218 and +0.0064 alone but +2.0400 jointly, with +2.0118 full-ablation epistasis.The pairwise model F3 outperformed the fitted additive model F2 on held-out predictions at both intervention strengths, reducing MAE by 54.7% at ε = 0.5 and 24.4% at ε = 1.0; F3 was better in all 100 resplits, and this pair ranked first by absolute interaction coefficient at both strengths.Source: §2.5 · pp. 9–10, Figure 4 · p. 11

2.6 GENERator: position-localized dependence

• The longest homopolymer accounted for only 3.9% of the GC decrease; non-ACGT output remained absent, supporting a genuine composition shift rather than repetitive or invalid-output collapse.Ablation also produced broader but milder changes in entropy and sequence diversity, and enriched short motifs were broadly AT-rich.Source: §2.6 · p. 12
• The random-direction experiment showed that the associated compositional phenotype did not require preserving the learned row direction under comparably severe damage.This further distinguishes structural prominence from a specification of causal organization.Source: §2.6 · p. 12
• In GENERator, BOS-only ablation reproduced nearly all native-loss damage, while preserving or restoring the BOS contribution nearly fully rescued it; DNABERT-2 instead showed strong pairwise dependence.Restoration at a matched non-BOS position provided essentially no rescue; in DNABERT-2, individually weak rows became consequential when jointly perturbed.Source: §2.6 · p. 12, Figure 5 · p. 13

• Activation-derived candidates were generally more consequential than same-layer controls, but structurally similar rows had widely different ablation effects and weight magnitude alone did not recover causal ordering.Structural geometry is an enrichment signal, not a direct readout of mechanism.Source: §3 · p. 14
• Above the activation-ratio acceptance threshold, the criterion ordered rows but did not grade severity; below it, the ratio was uninformative, and it could miss the most consequential coordinate.In SmolLM2-1.7B, a row ranked fourth was 130-fold more damaging than the second-ranked row; in OLMo-7B, the selected coordinate was 47-fold less damaging than the published coordinate it missed.Source: §3 · p. 14
• DNABERT-2 showed interaction-dependent damage between rows with weak singleton effects, whereas GENERator's L4/r2371 native-loss effect was mediated through its BOS contribution.Preserving or restoring the BOS contribution produced near-complete rescue; the co-localized attention-sink phenotype remained observational because attention was not causally manipulated.Source: §3 · p. 14
• The model panel is heterogeneous and not randomly sampled, the census tests one frozen primary row per model, and full ablation can enter nonlinear failure regimes.The GENERator BOS result concerns one model and one coordinate; conclusions concern pretrained native objectives rather than downstream biological or linguistic tasks.Source: §3 · pp. 14–15
• The evidence supports cohort-scale enrichment across 22 models, within-layer ordering in two decoders, and single-model existence proofs—not a causal organization that generalizes across models.The case studies illustrate model-specific mechanistic realizations rather than a shared mechanism.Source: §3 · p. 15
• Weight-space analysis can prioritize candidate components, but functional criticality requires intervention, and multi-component response complexity should be tested separately from singleton effects.Held-out observer comparisons offer one way to test whether richer interaction models are needed.Source: §3 · p. 15

4.1 Model panel and checkpoints

• The 23-model panel includes text decoders and encoders plus genomic decoders and encoders, with Evo2-7B tested but lacking an accepted candidate.The text-decoder panel includes Llama-7B, Mistral-7B, OLMo-7B, Phi-3-mini, Qwen2.5 variants, and SmolLM2 variants; genomic models include GENERator variants, GenomeOcean-4B, DNABERT-2, and NTv3.Source: §4.1 · p. 15
• Checkpoint revisions were recorded where available, but the original NTv3 model-weight revision was not recorded exactly.For models originally evaluated without an explicit revision, the resolved Hub commit is reported when recoverable.Source: §4.1 · p. 15
• The 22-model singleton causal cohort excludes Phi-3-mini, which was represented structurally by a pre-frozen six-row basis rather than one comparable primary row.Figure 1B reports the median q1 across those six rows.Source: §4.1 · p. 15

4.2 Row-associated bilinear weight operator and structural metrics

• For output row k, the associated bilinear operator uses the gate and up rows for each hidden unit, weighted by that unit’s down-projection coefficient.Its squared Frobenius norm can be computed without explicitly materializing all cross terms, using a Gram identity.Source: §4.2 · p. 15
• The leading-singular-direction energy fraction q1 measures spectral concentration, whereas the Frobenius norm measures operator magnitude.The within-layer magnitude comparison divides a candidate’s exact Frobenius norm by the same-layer median.Source: §4.2 · p. 16
• The diagonal proxy omits interactions between distinct hidden units and was used only for retrospective calibration, not cross-model structural comparisons.The authors identify it as unsuitable for cross-model dimensionality claims.Source: §4.2 · p. 16

4.3 Candidate provenance

• The activation-ratio protocol accepted coordinates with a same-layer activation ratio of at least 5.0, while six earlier activation-magnitude candidates were retained rather than reselected.The 16 ratio-selected and six retained coordinates formed the stated provenance breakdown; Phi-3 was handled separately.Source: §4.3 · p. 16
• The ratio maximum recovered published coordinates in Llama-7B and Mistral-7B, but OLMo-7B’s published row index recurred at different depths.Across 24 WikiText-2 windows, ratio maxima matched in 100% of Llama-7B and Mistral-7B windows and 83% of OLMo-7B windows.Source: §4.3 · p. 16
• DNABERT-2’s frozen activation-maximum coordinate was L5/r603, while its global ratio maximum was L8/r603, and the two selection rules were not uniformly closer to causal importance.In OLMo-7B, ablating the published coordinate increased native loss by 111.8%, versus 2.4% for the ratio maximum; DNABERT-2 showed the opposite direction.Source: §4.3 · pp. 16–17
• The DNABERT-2 activation-ratio result depended on tokenizer special-token handling, while structural metrics for a coordinate remained unchanged across tested combinations.The canonical discovery preprocessing used tokenizer-default special tokens; the structural census path disabled them.Source: §4.3 · p. 17
• Resolved Hub commits were available for 21 of 22 models, but NTv3’s original model-weight revision was not recorded exactly and could not be recovered.Frozen coordinates were also evaluated on 24 additional domain-matched inputs in 20 models without reselection.Source: §4.3 · p. 17

4.4 Structural statistical analysis

• The random q1 gap compares a candidate with the mean of five random same-layer controls, while the top-norm margin compares it with the maximum among five highest-norm alternatives.Structure–function analyses used the absolute value of the top-norm q1 margin.Source: §4.4 · p. 17
• The architecture-and-scale regression covered 23 models with accepted candidates, but its heterogeneous panel was not treated as a random sample of foundation models.Coefficient tests were interpreted descriptively rather than as population-level architectural laws.Source: §4.4 · p. 17
• Descriptor–effect correlations were computed across the full panel and within architecture classes, with panels smaller than eight reported as underpowered.Those smaller panels were not used to support claims.Source: §4.4 · p. 17

4.5 Cross-model singleton functional-criticality census

• The census included one frozen candidate per model across 10 text decoders, six text encoders, four genomic decoders, and two genomic encoders, alongside five same-layer controls.Candidate selection preceded causal evaluation; random and top-norm controls were defined without reference to causal measurements.Source: §4.5 · pp. 17–18

4.5.1 Row intervention

• Each targeted down-projection row was tested individually by scaling it to 50% or setting it to zero, then restoring the original row.The two intervention strengths corresponded to ε=0.5 and ε=1.0.Source: §4.5.1 · p. 18

4.5.2 Native-objective evaluation endpoints

• Text models used native token or masked-token NLL endpoints, while genomic models used causal token NLL for decoders and masked-nucleotide loss for encoders.Evaluation used WikiText-2 for text models and hg38-derived sequence windows for genomic models, with fixed masking realizations for encoder objectives.Source: §4.5.2 · p. 18

4.5.3 Effect definitions and control comparison

• Baseline and perturbed losses are token-weighted means computed from each evaluation unit’s summed loss and contributing-token count.The section reports the signed relative effect as 100Rε percent.Source: §4.5.3 · p. 19
• The control gap Gε is the candidate’s signed relative effect minus the median effect of five independently measured same-layer controls.Positive relative effects indicate degradation after suppression; negative effects indicate lower loss after suppression.Source: §4.5.3 · p. 19
• 18/22 models at ε=0.5 and 20/22 at ε=1.0 had positive candidate-minus-control gaps, whose cohort medians were +0.60% and +0.88%, respectively.Figure 2A–B show signed candidate and individual-control relative effects; Figure 2C shows the signed full-ablation candidate effect.Source: §4.5.3 · p. 19

4.5.4 Finite-intervention tomography

• The tomography tested four observer families, from summed singleton effects to calibrated, additive, and pairwise-product models, using calibration-selected ridge strength and disjoint held-out evaluation.Performance included held-out R2, MAE, root-mean-square error, and normalized MAE; pair-dependence evidence relied on held-out prediction, bootstrap uncertainty, and design identifiability.Source: §4.5.4 · p. 19
• F3 outperformed F2 on held-out MAE in all 100 resplits at both ε=0.5 and ε=1.0.At ε=0.5, median held-out R2 was 0.92 for F3 and 0.55 for F2; at ε=1.0, it was 0.76 for F3 and 0.56 for F2.Source: §4.5.4 · p. 19

4.5.5 DNABERT-2 pretrained masked-language-model experiment

• The DNABERT-2 experiment defined pair epistasis as joint loss change minus the sum of singleton changes, and measured the L9/r264 × L9/r294 pair in a separate direct-ablation assay.The evaluation used 256 hg38 windows of 600 bp with a fixed 15% mask realization; candidate selection for L5/r603 used a distinct ACTB discovery probe and preprocessing.Source: §4.5.5 · pp. 19–20

4.5.6 GENERator GC-composition and BOS analyses

• The GENERator analysis compared row-2371 scale sweeps with non-2371 controls and a fixed random-direction replacement, measuring generated GC fraction and native-loss damage.A position-specific mediation experiment compared BOS-only removal and restoration conditions with full ablation, using rescue fraction relative to intact and ablated effects; BOS attention and activation measurements were interpreted as co-occurrence only.Source: §4.5.6 · p. 20

4.5.7 Statistical analysis

• The analysis reports effect sizes and held-out predictive performance rather than formal population tests because the model panel is small and heterogeneous, and applies no multiple-comparison correction.Operator spectra are deterministic single-checkpoint calculations; tomography intervals use 5,000 paired bootstrap resamples.Source: §4.5.7 · p. 21
• Intervention-effect intervals use paired bootstrap resampling of evaluation units, while cohort gaps and the q1–full-ablation association use model-level resampling.The reported Spearman test uses SciPy’s default asymptotic two-sided p value, and bootstrap limits resample the 22 model rows.Source: §4.5.7 · p. 21

4.5.8 Data and code availability

• The repository contains analysis code, measurement scripts, and result artifacts, but hg38 and WikiText-2 must be obtained independently and the census requires pinned model checkpoints.Source: §4.5.8 · p. 21

Supplementary material

• Supplementary Figure S1 presents Phi-3 candidate q1 values, same-layer random-control effects for five decoder models, and cohort q1-gap versus model-size data.Source: Figure S1 · p. 25
• The Phi-3 full-ablation response is treated as unresolved rather than modeled with higher-order terms, and its tomography is not used for a main-text cohort claim.Source: Supplementary material · p. 25
• Supplementary Figure S2 compares generated GC fraction and native-loss damage across row-2371 scales, non-2371 controls, and a fixed random-direction replacement; the largest random replacement remains substantially damaging.Source: Figure S2 · p. 25