Before Attention Sinks Form: Hidden-State Geometry Reveals and Modulates Their Formation

Fan Yang; Yue Song

cs.LGOct 12, 2026

Before Attention Sinks Form: Hidden-State Geometry Reveals and Modulates Their Formation

Authors: Fan Yang, Yue Song

Organizations: College of AI, Tsinghua University

Abstract

Attention sinks are usually studied after they have formed. We ask whether a measurable hidden-state change appears beforehand and whether changing that geometry alters what happens later. To remove network depth as a shortcut, we compare prompts in the same model and at the same layer. When sink timing varies across prompts, simple spectral summaries of the hidden states add information beyond current attention, with the clearest prompt-specific signal in a short window about two to three layers before sink formation. The predictive strength varies across cohorts, so we treat the spectrum as a readout of a pre-sink state change rather than a universal warning statistic. The signal is broader than one measured extreme activation. We then modify only the singular values of the post-layer hidden states after current attention has already been computed. These interventions change later sink behavior in Qwen2.5, GLM-Z1, and GPT-OSS relative to norm-matched random spectral perturbations. In Qwen2.5, the immediate suppressive effect is accompanied by a reduction in next-layer query--key preference for position~0, and the learned spectral directions remain stable when estimated from substantially less training data. Together, the results show that attention sinks are preceded by a short spectral reorganization of hidden states, and directly perturbing this geometry can causally alter subsequent sink formation.

Figures & tables

Figure 1: Overview of the observational and causal analyses. (A) We compare prompts in the same model and at the same layer before either has formed a sink, and ask whether their hidden-state spectra already differ before their later sink timing diverges. (B) After the source-layer attention has been computed, we modify only the singular values of the post-layer hidden state while keeping the token mean and singular subspaces fixed; current attention is therefore unchanged, and we measure how later sink behavior responds. (C) In Qwen2.5, the immediate effect of the spectral edit is associated with a change in the next layer’s relative QK preference for position 0 and a corresponding change in position-0 attention. (D) Tracking the perturbation across layers shows that its norm can survive while its full hidden-state direction rotates and its targeted spectral component may either persist or weaken, helping explain why the downstream effect depends on where the edit is introduced.

Question	What is compared	Main result	What it means
Does the spectrum add information before a sink forms?	Current attention only ( $\mathcal{A}$ ) vs. current attention plus spectrum ( $\mathcal{A}+\mathcal{S}$ ), with model and layer matched.	Exact 1: AP $.857\rightarrow.913$ ( $\Delta$ AP $=+.056$ , $[.028,.087]$ ). Strict within-cell: Within 2 $+.107$ $[.048,.155]$ ; Within 3 $+.053$ $[.002,.101]$ ; Within 4 $-.021$ $[-.037,.029]$ .	The extra information is clearest about two to three layers before the sink.
Does changing the spectrum change later sink behavior?	For the learned direction, opposite signs ( $+d$ vs. $-d$ ) are compared at the same perturbation size. That directional gap is then tested against gaps from norm-matched random spectral directions.	Later-sink directional gap: Qwen2.5: $-.00833$ , $p=.0308$ ; GLM-Z1: $-.01525$ , $p=.0308$ ; GPT-OSS: $+.05625$ , two-sided $p=.0462$ ; 30/30 fresh prompts have the same positive sign.	Yes, but the direction and size of the effect depend on model and state.
What changes immediately after the Qwen2.5 edit?	Opposite signs of the learned spectral direction are compared at the same perturbation size; source-layer attention is unchanged.	Next-layer position-0 attention changes by $-.0214$ . The QK-preference change tracks the attention change: $r=.544$ , with 97.7% sign agreement.	The immediate suppressive effect is associated with lower next-layer preference for position 0.
Can the edit direction be estimated from less data?	Directions estimated from reduced training sets are compared with the full-data direction or with an independently estimated half-sample direction.	Qwen2.5: disjoint-half direction cosine $.979$ . GPT-OSS: half-data effect $+.05634$ vs. full-data effect $+.05625$ (effect ratio $1.002$ ).	The learned direction and its downstream effect are stable under substantial data reduction.

Table 1: Key results and their reference points. For observational rows, AP is the prompt-grouped out-of-fold average precision for predicting future sink formation at the specified horizon. We report the attention-only baseline

\mathrm{AP}(\mathcal{A})

and the gain from adding hidden-state spectral features,

\Delta\mathrm{AP}=\mathrm{AP}(\mathcal{A}+\mathcal{S})-\mathrm{AP}(\mathcal{A})

. Comparisons are made within the same model and current layer. Intervention rows instead report changes in later sink strength under controlled post-layer spectral edits and therefore do not use AP.

Figure 2: The spectral increment is concentrated in a short pre-sink window. (A) In the primary pooled matched-depth analysis, adding spectral features to current attention improves prediction over several short horizons but not at six layers. (B) The pattern remains after removing model–layer spectral means using training-fold statistics. (C) When ranking is evaluated entirely within matched model–layer cells, the clearest prompt-specific gains occur at Within 2 and Within 3, while the Within 4 estimate is near zero. Points show

\Delta

AP and horizontal bars show prompt-bootstrap

95\%

confidence intervals; the vertical dashed line marks

\Delta

=0

Question	What is compared	Main result	Takeaway
Does the spectrum add information?	Attention only vs. attention + spectrum, with model and layer matched.	Exact 1: AP $.857\rightarrow.913$ ; $\Delta$ AP $=+.056$ $[.028,.087]$ .	Spectrum adds information beyond current attention.
When is the clearest prompt-specific signal?	Ranking is evaluated only among prompts in the same model and current layer.	Within 2: $+.107$ $[.048,.155]$ ; Within 3: $+.053$ $[.002,.101]$ ; Within 4: $-.021$ $[-.037,.029]$ .	The clearest signal is about two to three layers before the sink.
Does the result depend on threshold-derived attention features?	Continuous attention only vs. continuous attention + spectrum.	Exact 1: AP $.833\rightarrow.918$ ; Within 2: $.793\rightarrow.889$ ; Within 6: $.899\rightarrow.912$ , with CI including zero.	The short-range result does not come from reusing the onset threshold.
Is the effect size stable across prompt cohorts?	The same frozen Qwen3 analysis is evaluated on the expanded cohort and on the unseen post-audit subset.	$N=500$ , Exact 2: $\Delta$ AP $=+.232$ $[.117,.340]$ ; unseen $N=372$ : $+.102$ $[-.035,.223]$ .	The short transition persists as a pattern, but predictive strength is cohort dependent.

Table 2: Main observational results. Each row states the comparison before the spectral gain is reported. The strict same-model, same-layer result localizes the clearest prompt-specific signal to the next two to three layers.

Test	What is compared	Main result	Takeaway
Qwen2.5 intervention	Opposite signs of the learned direction at $\rho=.05$ ; the resulting gap is tested against matched random directions.	Future sink-strength gap $=-.00833$ ; empirical $p=.0308$ .	Changing the spectrum suppresses later sink strength in this setting.
GLM-Z1 intervention	Opposite signs of the learned direction at $\rho=.025$ ; the same matched-random test is used.	Future sink-strength gap $=-.01525$ ; empirical $p=.0308$ .	Independent cross-model support; the sign is again suppressive.
GPT-OSS frozen test	Frozen L10 learned direction at $\rho=.025$ ; later sink strength is averaged over full-attention layers 11, 13, and 15.	Gap $=+.05625$ $[.04983,.06267]$ ; two-sided $p=.0462$ ; 30/30 prompts positive.	Fresh-cohort confirmation with the opposite sign.
Qwen2.5 next-layer trace	Opposite signs of the learned direction at the same budget, inspected at the next attention layer.	Position-0 attention: $-.0214$ ; QK–attention correlation: $r=.544$ ; 97.7% sign agreement.	The immediate suppressive effect tracks lower position-0 QK preference.
Direction stability	Directions estimated from reduced data vs. full-data or independent half-sample estimates.	Qwen2.5 disjoint-half cosine $.979$ ; GPT-OSS: half-data effect $.05634$ vs. full-data $.05625$ .	The learned direction is not fragile to training-set reduction.
Cross-layer change	Upstream edits propagated to the same hidden state vs. a direct local edit.	GPT-OSS: 96–100% spectral projection retained, hidden cosine $.65$ – $.81$ ; Qwen2.5: 24% retained, cosine $.18$ .	Later blocks can preserve perturbation size while changing its direction and downstream effect.

Table 3: Main causal and cross-layer results. Intervention effects are directional contrasts between opposite signs of the learned spectral direction at matched perturbation size; their empirical

p

values are computed against norm-matched random spectral directions.

Setting	Boundary	Consequence
Gemma / Llama	Sink appears very early or is present at the first measured layer.	Little or no ordinary pre-sink interval is available.
Qwen3, $T=256$	499/500 prompts first cross at layer 7.	Prompt-specific matched-depth timing is effectively non-identifiable.
Qwen2.5, $T=256$	All 429 crossing prompts first cross at layer 4.	No onset-depth variation exists among crossing prompts.
GLM-Z1, $T=256$	Onset remains spread across several layers.	The strict same-layer analysis remains estimable and again localizes to Within 2–3.
Fresh GLM-4 / Qwen3 causal preparation	The pre-specified near/far support required by the frozen direction rule is absent.	The planned comparison is not replaced post hoc with a different grouping.
GPT-OSS / Qwen3.6	Position-0 visibility depends on attention type / sink-like states can disappear and reappear.	The ordinary single persistent-onset target is not architecture invariant.

Table 4: Main boundary conditions. Lack of an estimable comparison is not treated as negative evidence for the underlying spectral phenomenon.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Family	Variables / operational definition
QK preference	Sink log-probability mean/max, sink-versus-best-competitor log-probability margin mean/max, and attention entropy mean/min.
Value magnitude	Sink-position value-vector norm mean/max across attention heads.
Attention–value	Sink attention-weighted value contribution mean/max and its ratio to the total attention-output norm mean/max.
Branch scales	Attention-output/input Frobenius-norm ratio, MLP-output/input ratio, and block-update/input ratio.
Compact hidden outlier	Hidden maximum absolute activation, hidden max/RMS ratio, and sink hidden-token norm ratio.
Hidden outlier + concentration	Compact hidden-outlier family plus hidden top-1 and top-5 elementwise squared-energy ratios.

Appendix

Table 5: Activation-state families used to interpret the pre-sink transition. The distributed family contains 18 amplitude/outlier variables and is intentionally broader than the compact hidden-state controls.

Model	Prompts	$T$	Observed sink behavior	Role
Qwen2.5-7B	50	64	sinks often form near layer 4, with prompt variation	main
Qwen3-8B	50	64	sinks form mainly near layers 3 or 7	main
GLM-4-32B	50	64	delayed formation with limited timing variation	main
GLM-Z1-32B	50	64	sink timing varies substantially across prompts	main
Gemma 3-12B	20	64	sinks appear early and strengthen later	boundary
Llama 3.1-8B	20	64	sinks are present at the first measured layer	boundary

Appendix

Table 6: Sink-formation patterns across the evaluated models. The first four provide the main same-layer comparison; the remaining models show settings where the same target is difficult to define or estimate.

Target	$h$	$\mathcal{A}$	$\mathcal{A}+\mathcal{S}$	$\Delta$ AP	$95\%$ CI
Exact	1	.857	.913	+.056	[.028,.087]
Exact	2	.826	.867	+.042	[.011,.073]
Exact	3	.691	.799	+.108	[.034,.162]
Exact	4	.754	.824	+.070	[.010,.135]
Exact	6	.850	.854	+.005	[ $-.022$ ,.040]
Within	1	.857	.913	+.056	[.026,.088]

Appendix

Table 7: The pooled spectral gain is visible through horizon 4 and is absent by horizon 6. Complete pooled matched-depth results for the pre-sink transition. AP is reported for current attention (

\mathcal{A}

) and current attention plus hidden-state spectral geometry (

\mathcal{A}+\mathcal{S}

), followed by paired

\Delta

AP and prompt-bootstrap

95\%

confidence intervals.

Target	$\mathcal{A}_{\rm cont}$	$\mathcal{A}_{\rm cont}+\mathcal{S}$	$\Delta$ AP	$95\%$ CI
Exact 1	.833	.918	+.085	[.051,.123]
Within 2	.793	.889	+.096	[.055,.137]
Within 3	.787	.867	+.080	[.042,.121]
Within 4	.802	.896	+.094	[.045,.141]
Within 6	.899	.912	+.013	[ $-.003$ ,.031]

Appendix

Table 8: The short-range spectral gain remains after threshold-derived attention features are removed. The baseline retains continuous attention, enrichment, depth, fixed effects, and the original nested-CV procedure.

Model	Exact 1	Within 2	Within 3	Within 4	Exact-1 $\Delta$ AP [CI]
GLM-4	1/3	1/3	1/3	1/3	$+.203$ [ $-.033,.951$ ]
GLM-Z1	5/43	7/84	8/118	9/151	$+.032$ [ $-.018,.097$ ]
Qwen2.5	1/36	2/72	3/108	4/144	$+.007$ [ $0,.020$ ]
Qwen3	1/10	2/20	3/30	3/30	$-.094$ [ $-.288,.025$ ]

Appendix

Table 9: Matched support by model and horizon. Entries in the four middle columns are matched layers / positive rows. The final column reports the model-level Exact 1

\Delta

AP and

95\%

confidence interval.

Target	Centered pooled	Z-scored pooled	Cell macro	Cell row-weighted
Exact 1	$+.057$ $[.017,.098]$	$+.040$ $[.001,.078]$	$+.169$ $[-.002,.217]$	$+.096$ $[-.023,.151]$
Within 2	$+.068$ $[.029,.109]$	$+.022$ $[-.018,.065]$	$+.107$ $[.048,.155]$	$+.102$ $[.048,.149]$
Within 3	$+.054$ $[.024,.088]$	$+.018$ $[-.010,.046]$	$+.053$ $[.002,.101]$	$+.053$ $[.006,.105]$
Within 4	$+.068$ $[.034,.102]$	$+.014$ $[-.028,.055]$	$-.021$ $[-.037,.029]$	$-.003$ $[-.016,.019]$

Appendix

Table 10: The strict prompt-specific signal is clearest at Within 2 and Within 3 and is not evident at Within 4. Entries are

\Delta

AP with prompt-bootstrap

95\%

confidence intervals. “Centered” and “z-scored” are pooled predictions after fold-local model–layer transformation of spectral features. Cell-stratified columns aggregate AP differences evaluated entirely within matched cells.

Figure 3: Spectral gains survive a nonlinear attention baseline and depend on prompt-specific alignment. (A) Adding spectral features improves average precision under both the logistic attention baseline and a nonlinear HistGradientBoosting baseline, showing that the spectral increment is not specific to the linear classifier. (B) In the layer-preserving permutation test, complete spectral-feature rows are shuffled across prompts within each matched model–layer cell, preserving cell-level spectral distributions and class prevalence while destroying prompt-specific alignment. The observed

A+S

performance (

\mathrm{AP}=0.9160

) exceeds the maximum of all 1000 shuffled replicates (

0.8933

); the permutation mean is

0.8524

, the

95

th percentile is

0.8675

, and the add-one Monte-Carlo value is

p=1/1001

Excluded model	Exact 1	Within 2	Within 3	Within 4
GLM-4	$+.061$ $[.028,.095]$	$+.130$ $[.074,.187]$	$+.053$ $[.022,.085]$	$+.049$ $[-.008,.101]$
GLM-Z1	$+.155$ $[.047,.262]$	$+.021$ $[.006,.039]$	$+.038$ $[.008,.067]$	$+.074$ $[.035,.115]$
Qwen2.5	$+.165$ $[.078,.264]$	$+.229$ $[.138,.314]$	$+.166$ $[.082,.241]$	$+.152$ $[.074,.221]$
Qwen3	$+.030$ $[.006,.056]$	$+.043$ $[.018,.072]$	$+.057$ $[.025,.092]$	$+.072$ $[.031,.116]$

Appendix

Table 11: No single model is required for the pooled Exact 1 effect. Leave-one-model-out

\Delta

AP with prompt-bootstrap

95\%

confidence intervals.

Target	Mean	Median	Range	Positive
Exact 1	+.150	.000	[ $-.052,.760$ ]	2/5
Within 2	+.122	+.009	[ $-.001,.547$ ]	3/5
Within 3	+.087	+.040	[ $0,.316$ ]	4/5
Within 4	$-.005$	+.019	[ $-.096,.027$ ]	3/5

Appendix

Table 12: Prompt-family transfer is heterogeneous, with Within 3 the most consistently positive horizon. GLM-Z1 five-family leave-one-family-out spectral increments. “Positive” counts held-out families with

\Delta

>0

Model	Onset fraction range	Median-onset range	Label counts across 24 cells
Qwen2.5	[.72,1.00]	4–4	fixed-depth partial 19; clustered 5
Qwen3	[1.00,1.00]	7–7	deterministic 14; clustered 10
GLM-4	[1.00,1.00]	5–8	deterministic 15; clustered 9
GLM-Z1	[.98,1.00]	6–11	dispersed 15; deterministic 5; clustered 4

Appendix

Table 13: Median onset is stable for Qwen2.5 and Qwen3 but more threshold-dependent for the GLM models. Threshold and late-query sensitivity over 24 configurations. “Label counts” report operational regime assignments across the grid.

Onset definition	Within 2	Within 3	Within 4	Within 6
K1	$+.124$ $[.056,.241]$	$+.066$ $[.038,.094]$	$-.005$ $[-.026,.014]$	$-.001$ $[-.012,.009]$
K2	$+.201$ $[.172,.244]$	$+.079$ $[.063,.096]$	$-.047$ $[-.097,.014]$	$+.005$ $[-.005,.015]$

Appendix

Table 14: At

T=256

, the strict GLM-Z1 signal again concentrates at Within 2–3 and is near zero at longer horizons. Results use the frozen 500-source cohort. K1 is the first crossing; K2 requires two consecutive sink-like blocks. Macro within-cell

\Delta

AP is reported with prompt-bootstrap

95\%

confidence intervals.

Figure 4: Broader activation-state controls contain more of the predictive information carried by the spectrum. (A) Compact hidden-state amplitude and concentration controls leave a substantial positive spectral increment, whereas broader activation-state descriptions reduce the remaining increment toward zero. (B) In the nested pooled-GLM Exact 1 analysis, local computational families—including query–key preference, value magnitude, attention–value statistics, and branch scales—also leave a positive spectral increment, while conditioning on the distributed activation state leaves little additional spectral value. Points show the remaining

\Delta

AP after adding spectral features, horizontal bars show prompt-bootstrap

95\%

confidence intervals, and the vertical dashed line marks

\Delta

=0

. These comparisons measure predictive redundancy, not causal mediation.

Figure 5: Qwen3 sink timing varies across prompts while the stringent extreme-activation event remains depth-locked. (A) Median maximum-to-median hidden-activation ratio, with interquartile bands, for prompts whose sinks form at block 3 versus block 7. Under the

10^{4}

criterion, both groups exhibit the same abrupt extreme-activation event at block 6, after the early-onset group has already formed a sink and one block before the dominant late-onset group does. (B) Sweeping the extreme-activation criterion shows that this shared event depth is not specific to the single

10^{4}

threshold. Across stringent thresholds from

2\times 10^{3}

2\times 10^{4}

, both onset groups first cross at block 6 even though their sink onsets remain at blocks 3 and 7. The figure therefore shows a timing mismatch: the stringent extreme-event depth does not encode the prompt-specific difference in sink onset.

Budget	Natural gap	Random 95% interval	Empirical $p$
.025	$-.01525$	$[-.01205,.00946]$	.0308
.050	$-.02976$	$[-.02773,.02174]$	.0308
.100	$-.05022$	$[-.04574,.03433]$	.0462

Appendix

Table 15: GLM-Z1 separates from the matched random-direction null across the tested budgets, with the smallest budget giving the cleanest functional-damage profile. Natural gap is near-state minus far-state later sink strength. Random intervals are the empirical

2.5

–

97.5

percentile ranges over 64 realized-norm-matched spectral directions. The reported

p

values use the stored matched random-direction empirical test.

Quantity	Value
Prompts	30
Natural high-minus-low effect	$+.05625$
Bootstrap 95% CI	$[.04983,.06267]$
Prompt sign consistency	30 positive / 0 zero / 0 negative
Random median	$-.00269$
Random 2.5–97.5 percentile range	$[-.05538,.05548]$

Appendix

Table 16: The frozen GPT-OSS intervention gives a positive fresh-cohort effect on all 30 prompts. The test is run at layer 10 with

\rho=.025

and uses mean sink strength over full-attention layers 11, 13, and 15 as the endpoint.

Figure 6: GPT-OSS requires an architecture-aware sink measure because position-0 visibility depends on attention type. (A) Full-attention layers can attend to position 0 from arbitrarily late queries, whereas in a sliding-attention layer position 0 becomes structurally inaccessible once it leaves the local window; zero attention in that regime is therefore enforced by the architecture rather than evidence that a sink-like state has disappeared. (B) The measured position-0 attention follows this visibility boundary: full-attention layers retain nonzero mass, while sliding-attention layers approach structural zero once position 0 is outside the local window. This motivates evaluating the GPT-OSS causal intervention at subsequent full-attention checkpoints rather than defining a single persistent position-0 sink onset across all layers.

Figure 7: Qwen3.6 hybrid-attention boundary. Accepted sink-state fractions are shown only at the 16 full-attention checkpoints. The recurrent peak–collapse–reappearance pattern persists across context length and query-window choices, whereas the location and prevalence of the first threshold crossing vary substantially. This behavior supports treating Qwen3.6 as a recurrent, architecture-gated sink regime rather than an ordinary persistent-onset process.

Setting	Eligible prompts	Any crossing	First-crossing raw layers (counts)	Next-checkpoint persistence
$T=64,\ q_{\min}=16$	50	45	15 (41), 47 (2), 55 (1), 59 (1)	—
$T=256,\ q_{\min}=16$	50	27	15 (11), 47 (6), 55 (5), 59 (5)	5/27
$T=256,\ q_{\min}=64$	45	17	47 (2), 55 (5), 59 (10)	5/17

Appendix

Table 17: Qwen3.6 first crossings are often non-persistent and shift with context length and query window. “Next-checkpoint persistence” is evaluated only for prompts with a first crossing and an observed subsequent full-attention checkpoint.

Figure 8: Route-to-spectrum regression with nonlinear depth control. Jacobian route variables explain spectral-

\alpha

shifts under prompt-grouped out-of-fold evaluation, but most of this explanatory power is shared with flexible model-specific nonlinear depth. Adding route variables to the polynomial-depth baseline yields only a marginal improvement (

R^{2}_{\mathrm{OOF}}:0.846\rightarrow 0.850

;

\Delta R^{2}=0.004

Analysis	Comparison / setting	Main quantitative result	Role in the paper
Observational evidence
Primary pooled horizon grid	Current attention $\mathcal{A}$ vs. attention plus spectrum $\mathcal{A}+\mathcal{S}$ , matched by model and current layer	Exact 1–6 $\Delta$ AP: $+.056$ , $+.042$ , $+.108$ , $+.070$ , $+.005$ . Within 1–6: $+.056$ , $+.073$ , $+.052$ , $+.078$ , $+.002$ . The Exact/Within intervals exclude zero through horizon 4 and include zero at horizon 6.	Shows a short-range spectral increment beyond current attention.
Strict within-cell timing	AP is computed only among prompts in the same model and current layer	Exact 1: $+.169$ $[-.002,.217]$ ; Within 2: $+.107$ $[.048,.155]$ ; Within 3: $+.053$ $[.002,.101]$ ; Within 4: $-.021$ $[-.037,.029]$ .	Localizes the clearest prompt-specific signal to roughly two to three layers.
Continuous-attention control	Remove all threshold-derived sink-score features from the attention baseline	Exact 1: $.833\rightarrow.918$ ( $+.085$ $[.051,.123]$ ); Within 2: $.793\rightarrow.889$ ( $+.096$ $[.055,.137]$ ); Within 3: $+.080$ $[.042,.121]$ ; Within 4: $+.094$ $[.045,.141]$ ; Within 6: $+.013$ $[-.003,.031]$ .	Rules out reuse of the onset threshold as the explanation for the short-range gain.
Expanded Qwen3 cohort	Frozen $T=64$ analysis on 500 prompts, followed by an unseen 372-prompt post-audit subset	$N=500$ , Exact 2: $+.232$ $[.117,.340]$ ; continuous-attention-only: $+.195$ $[.062,.322]$ . Unseen $N=372$ , Exact 2: $+.102$ $[-.035,.223]$ ; continuous-only: $+.020$ $[-.108,.132]$ .	Shows a strong short-window result in the expanded cohort but weaker out-of-audit predictive strength.
Sustained-onset sensitivity	Require two consecutive sink-like layers instead of first crossing	Strict within-cell: Exact 1 $+.165$ $[.031,.275]$ ; Within 2 $+.217$ $[.105,.258]$ ; Within 3 $+.079$ $[.032,.135]$ ; Within 4 $+.045$ $[-.017,.108]$ ; Within 6 $-.022$ $[-.088,.029]$ .	Shows that the two–three-layer localization is not specific to first crossing.

Appendix

Table 18: Complete quantitative summary of the main empirical evidence. The table consolidates the results used to support or delimit the paper’s claims; experiment-specific tables and figures provide the full context.

Claim	Main evidence	Limitation
The hidden-state spectrum changes before a sink forms	Same-layer $\mathcal{A}$ versus $\mathcal{A}+\mathcal{S}$ prediction; removal of threshold-derived attention features; prompt shuffling; nonlinear attention baselines; expanded Qwen3 cohort	The primary estimate is pooled, model-level support is uneven, and the stricter Qwen3 post-audit holdout shows weaker cohort-dependent prediction.
The clearest prompt-specific signal appears about two to three layers before sink formation	Full horizon grid; removal of model–layer means; evaluation inside matched groups; sustained-sink definitions; $T=256$ GLM-Z1 result	The pooled signal extends farther, and two to three layers is not a universal causal window.
The spectral change is broader than one measured extreme activation	Compact outlier controls; capacity-matched activation measurements; random projections; Qwen3 timing experiment	These prediction tests do not identify a unique causal mechanism.
Changing the spectrum can change later sink formation	Post-layer singular-value edits; norm-matched random directions; Qwen2.5 and GLM-Z1 results; frozen 30-prompt GPT-OSS confirmation; half-data direction stability	The sign and size depend on model and state, and larger edits can cause broader functional changes.
The immediate Qwen2.5 suppression enters the next attention computation through a lower position-0 QK preference	Layer-1 post-block edit; layer-2 prompt–head QK-margin trace; source-attention invariance	This is a local diagnostic in one model and does not establish a universal QK mechanism.
Later transformer layers change the perturbation	GPT-OSS layer-8/9/10 propagation; Qwen2.5 layer-0-to-1 propagation	The cross-layer experiment covers two model families and is not claimed as a universal law.

Appendix

Table 19: Summary of the main claims, the experiments that support them, and the limits of those conclusions.

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May 7, 2026

The Structural Origin of Attention Sink: Variance Discrepancy, Super Neurons, and Dimension Disparity

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a mechanistic explanation for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose head-wise RMSNorm, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

Siquan Li, Kaiqi Jiang, Jiacheng Sun +1

1The Chinese University of Hong Kong, Shenzhen · 2Huawei

Self-Attention Attention Sinks Attention Mechanisms

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Abstract

Attention Sinks

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The Structural Origin of Attention Sink: Variance Discrepancy, Super Neurons, and Dimension Disparity