Gluing Local Contexts into Global Meaning: A Sheaf-Theoretic Decomposition of Transformer Representations

Bryce Grant; Peng Wang

cs.CLOct 12, 2026

Gluing Local Contexts into Global Meaning: A Sheaf-Theoretic Decomposition of Transformer Representations

Authors: Bryce Grant, Peng Wang

Organizations: Case Western Reserve University

Abstract

Existing interpretability tools do not test whether a representation keeps the same content when only the phrasing changes. We treat each paraphrase pair as a local witness that two activations should agree and build a cellular sheaf over the paraphrase graph; its Laplacian $L_\mathcal{F}$ answers the question on a frozen model with no training. The kernel $H^0$ is a content subspace: at 20 dimensions it beats the preserved subspace of the concept eraser LEACE on held-out CounterFact fact retrieval across eight architectures by a mean $+17.1$ ,pp, and constraining all paraphrases of a fact jointly adds a further $+6.5$ ,pp. The spectral complement concentrates causal influence: ablating the most paraphrase-variable coordinates, a coordinate-wise proxy for it, changes model outputs $5.6$ to $26.5\times$ more than ablating coordinates of matched per-coordinate variability, across nine models from 124M to 13B parameters. Stacking layers into a grid creates $b_1 = N(L-1)$ algebraic 1-cycles, and the resulting model-derived harmonic mass varies by nearly three orders of magnitude across six architectures and ranks them as their steering fragility does (Spearman $ρ= 0.90$ , exact one-sided permutation $p = 0.014$ ). The same paraphrase graph yields the content subspace, the influence directions, and the fragility measure. Project page: https://cwru-aism.github.io/gluing-lc-page/

Figures & tables

Figure 1: Sheaf decomposition of a paraphrase pair. Hidden states

h_{a},h_{b}

pass through

P^{\top}

into the edge stalk

\mathbb{R}^{k}

, where the coboundary measures their disagreement,

(\delta^{0}h)_{e}=P^{\top}(h_{b}-h_{a})

. The bottom and top eigenspaces of the sheaf Laplacian

L_{\mathcal{F}}

split the edge stalk

\mathbb{R}^{k}

into

H^{0}

(blue, content stable across phrasing) and the

H^{1}

directions (red, context-dependent variation).

Architecture	$L=2$	$L=4$	$L=8$	$L=16$	Pres. (%)
Mistral-7B	$0.0001$	$0.0001$	$0.0004$	$0.0008$	$39.4$
Qwen-2.5-7B	$0.0001$	$0.018$	$0.016$	$0.096$	$34.3$
Llama-3-8B	$0.001$	$0.002$	$0.003$	$0.004$	$36.0$
Phi-2	$0.033$	$0.126$	$0.109$	$0.067$	$27.5$
GPT-2 (124M)	$0.036$	$0.107$	$0.083$	–	$9.1$
Llama-2-7B	$0.079$	$0.071$	$0.047$	$0.028$	$4.2$

Table 1: Multi-layer matching grid,

b_{1}=N(L{-}1)

from depth alone. Hodge harmonic mass of model-derived edge cochains varies by nearly three orders of magnitude. Every row shares the same graph (

b_{1}=30

L=2

), so the variation comes from the model’s layer transitions.

30

MRPC pairs with joint-PCA per layer at shared

k=8

. The last column is steering fragility: CounterFact fact preservation (%) under random steering (§ 5.4 , Appendix A.3 ).

Figure 2: Per-architecture ratio of the output change from ablating the

H^{1}

coordinates to that from ablating control coordinates of matched per-coordinate variability (Table 3 ). Hatched bars use protocol

a

(one layer,

64

coordinates, effect on logits) and solid bars protocol

b

(three depths,

20

coordinates, effect on the final hidden state). Every architecture exceeds the dashed unit baseline, by

5.6\times

26.5\times

Model	Full	$H^{0}$ (20D)	LEACE-full	LEACE-20D	PCA-20	Rand-20	$\Delta$
GPT-2	43.1	85.3	43.1	28.9	24.6	39.1	+42.2
Mistral-7B	77.7	87.1	77.7	36.8	34.5	59.2	+9.4
OLMo-2-7B	81.3	82.8	81.3	40.9	35.7	62.3	+1.5
Phi-2	69.1	87.1	69.1	38.8	37.2	55.1	+18.0
Qwen-2.5-7B	49.4	64.1	49.4	36.8	37.5	43.7	+14.7
Gemma-2-9B	54.4	77.9	54.4	32.3	27.5	43.5	+23.5

Table 2: Held-out CounterFact retrieval (top-1 accuracy, hard same-relation distractors,

k=20

dims, 70/30 train/test split,

n_{\text{test}}=150

facts). Sheaf

H^{0}

basis and LEACE eraser are fit on training facts only, and evaluation is on held-out facts not seen during fitting. Across eight architectures sheaf

H^{0}

at 20 dimensions beats LEACE preserved at full hidden dimension, with gaps ranging from

+1.5

pp (OLMo-2) to

+42.2

pp (GPT-2).

Model	Ratio	Layer	95% CI	Cohen’s $d$
GPT-2 (124M) a	18.2 $\times$	L6	[17.2, 19.3]	2.34
Phi-2 b	14.48 $\times$	L8	[14.0, 15.0]	13.98
Mistral-7B b	19.71 $\times$	L8	[19.1, 20.3]	18.45
Qwen-2.5-7B b	5.76 $\times$	L7	[5.38, 6.12]	6.63
OLMo-2-7B b	9.17 $\times$	L16	[8.85, 9.49]	12.93
Gemma-2-9B b	9.24 $\times$	L21	[8.94, 9.54]	22.02

Table 3: Functional validation: output change from ablating the

H^{1}

coordinates over that from ablating control coordinates of matched per-coordinate variability. a

1000

sentences (

666

MRPC,

334

PAWS),

64

coordinates, one layer (

L/2

), effect on final-position logits. b

100

sentences,

20

coordinates, three layers (

L/4

L/2

3L/4

), effect on the mean-pooled final hidden state, best of the three depths shown. CIs are bootstrap

95\%

. Cohen’s

d

uses the pooled standard deviation of the two effect distributions.

Model	Method	Fact%	95% CI	McNemar $p$
Llama-2-7B	Contrastive sheaf ( $H^{1}$ dims)	31.0	[28.2, 33.9]	–
	PIXEL [ 66 ]	21.1	[18.6, 23.9]	$<10^{-16}$
	Full style (CAA)	13.7	[11.7, 15.9]	$<10^{-31}$
	$H^{0}$ -removed (sheaf)	13.7	[11.6, 15.9]	$<10^{-31}$
	$H^{1}$ dims (sheaf PCA)	12.1	[10.0, 14.1]	$<10^{-38}$
	Random	4.2	[3.0, 5.4]	$<10^{-70}$

Table 4: Steering on CounterFact (

\alpha=0.3

n=1000

per model). Fact preservation (%) with 95% bootstrap CIs. McNemar

p

is paired against the best method in each block (bold). Style saturates at 100% for all methods on all models.

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Topology	$H^{0}$	$H^{1}$ (algebraic)	$H^{2}$	$\ker(\delta^{0})^{\top}$ frac.	Harmonic frac.
Matching (acyclic)	180	0	0	0.000	0.000
Clique (filled)	60	0	240	0.600	0.000
Relation hypergraph	6	66	0	0.184	0.184

Appendix

Table 5: Genuine cohomology and Hodge harmonic fraction across architectures and topologies.

Model	Full	$H^{0}$ (20D)	LEACE preserved	LEACE erased	PCA-20	Random-20
GPT-2	85.3%	95.7 %	85.0%	2.0%	22.7%	53.7%
Phi-2	97.3%	93.0%	97.3%	3.3%	38.0%	64.3%
Qwen-2.5-7B	73.3%	82.0 %	75.0%	1.0%	30.3%	50.0%
OLMo-2-7B	100%	97.0%	100%	2.3%	36.7%	77.3%
Mistral-7B	100%	80.7%	100%	2.0%	50.0%	71.3%
Gemma-2-9B	99.3%	83.7%	99.3%	1.3%	26.7%	68.3%

Appendix

Table 6: LEACE vs sheaf

H^{0}

on 60-fact retrieval (20 dimensions, top-1 against all 60 facts). LEACE is fitted on paraphrase versus non-paraphrase fact prompts, and sheaf

H^{0}

uses the joint-PCA restriction map.

	$L=2$		$L=4$		$L=8$
Architecture	coexact	$\\|\delta^{1}\omega\\|^{2}$	coexact	$\\|\delta^{1}\omega\\|^{2}$	coexact	$\\|\delta^{1}\omega\\|^{2}$
Mistral-7B	$0.0000$	$1.4\!\times\!10^{2}$	$0.0002$	$8.6\!\times\!10^{2}$	$0.0006$	$2.5\!\times\!10^{3}$
Llama-3-8B	$0.0005$	$4.7\!\times\!10^{2}$	$0.0026$	$1.8\!\times\!10^{3}$	$0.0075$	$5.1\!\times\!10^{3}$
Qwen-2.5-7B	$0.0003$	$9.8\!\times\!10^{2}$	$0.0255$	$6.0\!\times\!10^{5}$	$0.0247$	$9.7\!\times\!10^{5}$
GPT-2 (124M)	$0.0544$	$6.7\!\times\!10^{3}$	$0.1219$	$1.4\!\times\!10^{5}$	$0.1014$	$2.2\!\times\!10^{5}$
Phi-2	$0.0572$	$5.1\!\times\!10^{3}$	$0.1895$	$7.9\!\times\!10^{4}$	$0.1970$	$2.0\!\times\!10^{5}$

Appendix

Table 7: Triangulated multi-layer grid (each square filled with two triangles sharing a diagonal). Edge dim

k=64

30

MRPC paraphrase pairs.

b_{1}=b_{2}=0

for every architecture and every

L

, so

\omega

has no harmonic component (Hodge harmonic mass collapses to machine precision). Reported quantities: model-derived

\omega

norm squared, coexact fraction (energy explained by the 2-skeleton), and face-cochain norm squared

\|\delta^{1}\omega\|^{2}

. Mistral-7B and Llama-3-8B place under

1\%

on the 2-skeleton and Qwen-2.5-7B under

3\%

, while GPT-2, Phi-2 and Llama-2-7B place 5–20%.

	$k=64$ ( $N=30$ )			$k=128$ ( $N=80$ )
Architecture	$L\!=\!2$	$L\!=\!4$	$L\!=\!8$	$L\!=\!2$	$L\!=\!4$	$L\!=\!8$
Mistral-7B	$0.00003$	$0.0002$	$0.0005$	$0.00002$	$0.0002$	$0.0005$
Llama-3-8B	$0.0005$	$0.0022$	$0.0061$	$0.0004$	$0.0017$	$0.0049$
Qwen-2.5-7B	$0.0003$	$0.0234$	$0.0248$	$0.0003$	$0.0191$	$0.0215$
GPT-2 (124M)	$0.050$	$0.112$	$0.101$	$0.041$	$0.081$	$0.084$
Phi-2	$0.054$	$0.180$	$0.197$	$0.053$	$0.156$	$0.180$

Appendix

Table 8: Multi-layer matching grid Hodge harmonic mass across edge dimensions. The body Table 1 reports

k=8

. Increasing

k

keeps the three robust architectures below the three fragile ones at every

L\leq 8

and widens the span to more than three orders of magnitude. The

k=128

row uses

N=80

paraphrase pairs to make the requested

k

admissible (otherwise

k

is capped at

\min(2N,k_{\text{req}})=60

Figure 3: Schematic of the multi-layer matching sheaf, a frame from an animation. Each slab is one layer $l$ , and struts join the same sentence at adjacent layers through the Procrustes transport $R_{l\to l+1}$ . A path up one strut, across layer $l+1$ , and down another strut closes an inter-layer square. These squares give the grid its $b_{1}=N(L-1)$ independent cycles and carry the harmonic mass. The slab shapes are illustrative and carry no topology of their own.

Model	$H^{0}$ CF (in-domain)	$H^{0}$ MRPC	$H^{0}$ PAWS	$H^{0}$ QQP	PCA-20	Random-20
GPT-2	85.3	55.1	63.9	59.1	24.6	39.1
Phi-2	87.1	57.3	61.6	57.6	37.2	55.1
Mistral-7B	87.1	57.8	65.9	61.2	34.5	59.2
OLMo-2-7B	82.8	64.1	60.5	57.6	35.7	62.3
Qwen-2.5-7B	64.1	47.0	53.3	56.7	37.5	43.7
Gemma-2-9B	77.9	48.3	47.9	51.0	27.5	43.5

Appendix

Table 9: Cross-dataset restriction-map transfer (held-out CounterFact, hard same-relation retrieval,

k=20

H^{0}

is fit with

P

from the source on the left and evaluated on the same CounterFact test set. Out-of-domain

P

retains

+5

+30

pp over no-kernel baselines but loses

\sim

25

pp relative to in-domain

P

Model	$H^{0}$ pair ( $b_{1}{=}0$ )	$H^{0}$ ring ( $b_{1}{=}N$ )	$H^{0}$ clique ( $b_{1}{\gg}N$ )	$\Delta_{\text{ring}}$	$\Delta_{\text{clique}}$
GPT-2	87.4	90.7	89.2	$+3.4$	$+1.8$
Phi-2	83.1	89.6	90.5	$+6.5$	$+7.4$
Mistral-7B	86.7	89.8	91.4	$+3.2$	$+4.7$
OLMo-2-7B	84.4	91.4	91.4	$+7.0$	$+7.0$
Qwen-2.5-7B	62.3	71.8	70.7	$+9.5$	$+8.4$
Gemma-2-9B	75.2	84.0	84.7	$+8.8$	$+9.5$

Appendix

Table 10: Cycle-aware

H^{0}

for hard-CounterFact retrieval. Both multi-paraphrase rings (

b_{1}=N

) and full paraphrase cliques (

b_{1}=N(K{-}1)(K{-}2)/2

) beat the pair-only acyclic forest (

b_{1}=0

) on all eight architectures, mean

+6.5

pp. Ring and clique perform within

0.1

pp of each other.

Model	$H^{0}$ PCA- $P$	$H^{0}$ random- $P$	$H^{0}$ identity- $P$	PCA-20 (no kernel)	Random-20
GPT-2	85.3	$77.1\pm 0.8$	79.0	24.6	39.1
Phi-2	87.1	$73.0\pm 2.0$	78.8	37.2	55.1
Mistral-7B	87.1	$80.6\pm 1.6$	83.3	34.5	59.2
OLMo-2-7B	82.8	$76.4\pm 1.6$	79.7	35.7	62.3
Qwen-2.5-7B	64.1	$61.4\pm 1.3$	62.3	37.5	43.7
Gemma-2-9B	77.9	$69.2\pm 1.5$	76.5	27.5	43.5

Appendix

Table 11: Restriction-map ablation (8 architectures, hard-CounterFact retrieval).

H^{0}

from

\ker L_{\mathcal{F}}

recovers content directions whether

P

is joint-PCA, a random orthonormal projection, or absent.

Model	Sheaf $H^{0}$	LDA	NCA	CCA	PLS	PCA-20	W-PCA	Full
GPT-2	84.9	87.4	88.3	47.9	49.0	24.4	39.5	43.1
Phi-2	87.6	84.9	83.3	58.9	64.1	37.9	42.7	69.1
Mistral-7B	86.9	90.1	88.3	60.7	63.7	34.3	45.1	77.4
OLMo-2-7B	82.6	88.5	86.9	62.8	67.5	36.6	37.2	81.3
Qwen-2.5-7B	64.8	72.5	72.9	50.8	56.0	36.6	38.1	50.3
Gemma-2-9B	77.4	76.1	76.3	51.2	50.1	27.3	37.2	54.4

Appendix

Table 12: Retrieval baseline comparison (held-out hard-CounterFact, top-1 %,

k=20

, same protocol as Table 2 ). Label-free: sheaf

H^{0}

, CCA, PLS, PCA-20 (top-20 principal components without kernel selection, as in Table 2 ), W-PCA (the same 20 components whitened, each scaled by

1/\sqrt{\lambda}

on centred activations). Label-requiring: LDA, NCA. Sheaf

H^{0}

bold where it beats both LDA and NCA.

Figure 4: Steering on CounterFact at

\alpha=0.3

(

n=1000

per model) for the three architectures with a PIXEL run. The hatched bar on Llama-3-8B repeats the PCA

H^{1}

value, since that model has no CCA or contrastive run. On fragile Llama-2-7B, random steering collapses to

4.2\%

and the contrastive sheaf leads at

31.0\%

. On robust Mistral-7B, the CCA sheaf and random tie (

41.6\%

vs.

39.4\%

). On Llama-3-8B, PIXEL and random lead. Same data as Table 4 and Appendix B.11 .

Model	Layers	$H^{1}$ /random, median	Range	Prompts	$H^{0}$ /random, median
GPT-2 (124M)	6	$17.8\times$	13.7–53.5	99%	$0.19$
Phi-2	16	$84.1\times$	18.4–122	97%	$0.56$
Mistral-7B	16	$398\times$	70.0–3075	100%	$0.54$
Qwen-2.5-7B	14	$127\times$	78.7–293	99%	$0.45$
OLMo-2-7B	16	$182\times$	112–1048	100%	$2.21$
Gemma-2-9B	21	$240\times$	75.8–1211	100%	$0.74$

Appendix

Table 13: Sheaf eigenbasis ablation: ratio of mean next-token KL from projecting out

H^{1}

(top

20

eigenvectors of

L_{\mathcal{F}}

) to that from

20

random

20

-dimensional subspaces at every other layer. Median and range are over layers. The prompts column is the smallest fraction over layers of held-out prompts on which

H^{1}

exceeds all

20

draws.

Model	Dormancy ratio ( $H^{1}$ /random)	Recall, no ablation	$H^{1}$ ablated	Random ablated
GPT-2	$2.5\times$	15.0%	2.0%	7.5%
Mistral-7B	$6.6\times$	46.7%	0.0%	47.0%
Llama-2-7B	$5.6\times$	47.3%	4.7%	48.7%

Appendix

Table 14: Dormancy and behavioural ablation. Dormancy ratio is the on-distribution projection spread of

H^{1}

divided by the mean spread of variance-matched random subspaces. Recall is the fraction of greedy continuations of the bare prompt that contain the target entity. Layer

\ell\approx 2L/3

k=20

, five random draws, seed 42.

Subspace	FR $\to$ EN	EN $\to$ FR
$H^{0}$ kernel (20-dim)	76	78
$H^{1}$ complement	6	3
Full hidden state (4096-dim)	82	59

Appendix

Table 15: Held-out cross-lingual retrieval on Llama-3-8B (top-1 %,

100

test pairs,

H^{0}

fit on

100

disjoint training pairs).

Figure 5:

H^{1}

-to-control effect ratio (protocol

b

of Table 3 ) at three depths per architecture,

L/4

L/2

and

3L/4

, plotted against normalized depth (layer index over number of layers). Stars mark each architecture’s largest measured ratio, and points are offset slightly in depth so overlapping peaks stay visible. Only measured points are shown. The GPT-2 and Llama values here come from protocol

b

and differ from their protocol-

a

rows in Table 3 .

	Observed	Shuffled	$p$	$N{=}2$	$N{=}3$	$N{=}4$	$N{=}6$
GPT-2 (124M)	$2.92$	$2.78$	$0.24$	$3.09$	$3.15$	$2.55$	$2.43$
Mistral-7B	$2.52$	$2.42$	$0.33$	$3.20$	$3.31$	$2.64$	$2.18$
Qwen-2.5-7B	$3.13$	$2.84$	$0.10$	$3.82$	$3.43$	$2.90$	$2.78$
Phi-2	$3.01$	$2.76$	$0.24$	$4.37$	$3.37$	$3.28$	$2.36$

Appendix

Table 16: Holonomy null calibration on the relation hypergraph. “Observed” = real paraphrase assignments. “Shuffled null” = mean over

20

within-relation paraphrase shuffles.

p

is the one-sided permutation

p

-value for

P(\text{shuffled}\geq\text{observed})

, smaller meaning observed obstruction exceeds null. Bootstrap-

N

obstructions are mean

\pm

std over

11

cycles at the listed token count.

Embedding	Loss	Top-1 $\sigma^{2}$ frac.	Effective rank	Feature var.	Pair MSE
GPT-2 (768D)	Naive MSE	$0.149$	$16.0/64$	$0.006$	$0.0000$
	$\mathrm{tr}(L_{\mathcal{F}})$ only	$0.151$	$16.6/64$	$0.008$	$0.0000$
	$\mathrm{tr}(L_{\mathcal{F}})-\beta\log\det\mathrm{Cov}$	$0.109$	$\mathbf{58.5/64}$	$\mathbf{4991}$	$0.0149$
Mistral-7B (4096D)	Naive MSE	$0.134$	$34.4/64$	$0.005$	$0.0000$
	$\mathrm{tr}(L_{\mathcal{F}})$ only	$0.121$	$33.1/64$	$0.006$	$0.0000$
	$\mathrm{tr}(L_{\mathcal{F}})-\beta\log\det\mathrm{Cov}$	$0.094$	$\mathbf{58.0/64}$	$\mathbf{8418}$	$0.0186$

Appendix

Table 17: Collapse prevention per architecture: top-1 variance fraction, effective rank (of 64), feature variance and paraphrase-pair MSE under naive MSE, the Laplacian energy

\mathrm{tr}(L_{\mathcal{F}})

alone, and the Laplacian energy with a log-determinant covariance term.

	GPT-2 ( $n=10$ )		Mistral-7B ( $n=5$ )
Method	Spearman $\uparrow$	Pearson $\uparrow$	Spearman $\uparrow$	Pearson $\uparrow$
Vanilla (no training)	$0.428$	$0.312$	$0.533$	$0.498$
SimCSE (final-layer, InfoNCE)	$0.578\pm 0.014$	$0.567$	$0.566\pm 0.016$	$0.549$
VICReg (final-layer, inv + var + cov)	$0.623\pm 0.006$	$0.602$	$\mathbf{0.645\pm 0.025}$	$\mathbf{0.635}$
MLST nosheaf (final)	$0.621\pm 0.005$	$0.598$	$0.634\pm 0.025$	$0.626$
MLST nosheaf (concat)	$\mathbf{0.668\pm 0.005}$	$\mathbf{0.650}$	$0.644\pm 0.009$	$0.630$

Appendix

Table 18: Multi-layer sheaf consistency training (MLST) on STS-B with frozen encoders: Spearman and Pearson correlation, mean

\pm

s.d. over seeds. nosheaf drops the transitions and the cycle term.

Model	$m{=}5$	$m{=}10$	$m{=}20$	$m{=}40$	$m{=}80$	$m{=}128$	Full
GPT-2	63.7	74.3	85.3	91.2	87.8	35.9	43.1
Phi-2	67.3	75.8	87.1	90.3	85.3	52.8	69.1
Mistral-7B	70.9	82.4	87.1	90.3	86.7	48.5	77.7
Llama-2-7B	62.8	74.0	80.4	85.3	85.1	35.2	68.2

Appendix

Table 19:

H^{0}

subspace dimension

m

sweep (hard CounterFact retrieval, edge dim

k=128

). Results are stable across

m\in\{20,40,80\}

. At

m=128=k

no kernel is selected and retrieval collapses.

	Mean (default)		Last token		First token
Model	Full	$H^{0}$	Full	$H^{0}$	Full	$H^{0}$
GPT-2	43.1	85.3	25.5	74.3	41.8	42.7
Phi-2	69.1	87.1	26.9	65.9	30.5	43.8
Mistral-7B	77.7	87.1	40.4	72.2	20.5	14.2
Llama-2-7B	68.2	80.4	21.4	47.0	19.6	23.0

Appendix

Table 20: Pooling sensitivity (hard CounterFact retrieval). Mean pooling is best for all architectures, and sheaf

H^{0}

beats the full hidden state under every pooling choice except first-token pooling on Mistral-7B.

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May 2, 2026Pratyush Acharya, Nuraj Rimal, Habish DhakalTransformer Interpretability Representation Learning
You Didn't Have to Say It like That: Subliminal Learning from Faithful Paraphrases
Mar 10, 2026Isaia Gisler, Zhonghao He, Tianyi QiuSubliminal Learning LLM Training
ETH Zürich · University of Cambridge · Peking University

Apr 7, 2026J/K move · Enter open · S save

LAG-XAI: A Lie-Inspired Affine Geometric Framework for Interpretable Paraphrasing in Transformer Latent Spaces

Olexander Mazurets, Olexander Barmak, Leonid Bedratyuk, Iurii Krak

Department of Computer Science, Khmelnytskyi National University, Khmelnytskyi, 29016, Ukraine · Department of Theoretical Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, 03187, Ukraine · Laboratory of Communicative Information Technologies, V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv, 03187, Ukraine

Transformer Interpretability Representation Geometry in Language Models

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Modern Transformer-based language models achieve strong performance in natural language processing tasks, yet their latent semantic spaces remain largely uninterpretable black boxes. This paper introduces LAG-XAI (Lie Affine Geometry for Explainable AI), a novel geometric framework that models paraphrasing not as discrete word substitutions, but as a structured affine transformation within the embedding space. By conceptualizing paraphrasing as a continuous geometric flow on a semantic manifold, we propose a computationally efficient mean-field approximation, inspired by local Lie group actions. This allows us to decompose paraphrase transitions into geometrically interpretable components: rotation, deformation, and translation. Experiments on the noisy PIT-2015 Twitter corpus, encoded with Sentence-BERT, reveal a "linear transparency" phenomenon. The proposed affine operator achieves an AUC of 0.7713. By normalizing against random chance (AUC 0.5), the model captures approximately 80% of the non-linear baseline's effective classification capacity (AUC 0.8405), offering explicit parametric interpretability in exchange for a marginal drop in absolute accuracy. The model identifies fundamental geometric invariants, including a stable matrix reconfiguration angle (~27.84°) and near-zero deformation, indicating local isometry. Cross-domain generalization is confirmed via direct cross-corpus validation on an independent TURL dataset. Furthermore, the practical utility of LAG-XAI is demonstrated in LLM hallucination detection: using a "cheap geometric check," the model automatically detected 95.3% of factual distortions on the HaluEval dataset by registering deviations beyond the permissible semantic corridor. This approach provides a mathematically grounded, resource-efficient path toward the mechanistic interpretability of Transformers.

Abstract

Transformer Interpretability

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