Thinking Leakage: A Causal Audit of NoThink Post-Training in Hybrid Reasoning Models

Zehao Liu; Vasant G. Honavar

cs.LGSep 23, 2026

Thinking Leakage: A Causal Audit of NoThink Post-Training in Hybrid Reasoning Models

Authors: Zehao Liu, Vasant G. Honavar

Organizations: College of Information Sciences and Technology Pennsylvania State University

Abstract

Post-training hybrid reasoning models in NoThink mode has attracted growing interest as a way to improve performance while keeping inference fast. However, these gains may draw on thinking behavior already accessible through the base model's Think mode. We formulate this thinking leakage in a causal mediation framework and audit its contribution using bidirectional interventions along a simple base-derived activation direction. Across three models and three post-training methods on competition math benchmarks, we find that leakage is real, causal, and substantial: behavioral and representational analyses reveal shifts toward Think, steering the base model along this direction reproduces most of the post-training accuracy gain, and counter-steering a checkpoint removes a substantial share of what it gains. Across nine aligned checkpoints with positive NoThink gains, the resulting leakage ratio ranges from 42% to 79%. These interventions support a substantial causal contribution of thinking leakage. Our findings show that a post-training method's apparent advantage can therefore reflect greater drift toward Think, obscuring whether it improves capability within NoThink or more effectively re-invokes existing Think behavior.

Figures & tables

Panel of Figure 1 — Figure 1: Causal structure of a NoThink forward pass. (a) Observationally, thinking engagement $\pi$ is generated by the input $x$ and weights $\theta$ ; accuracy $Y$ mixes the direct path $\theta{\to}Y$ with the mediated path $\theta{\to}\pi{\to}Y$ . (b) Steering and counter-steering intervene on $\pi$ , changing its natural value while leaving $\theta{\to}Y$ and $x{\to}Y$ intact: outcomes under intervention still depend on the weights.

Figure 2: Thinking leakage tracks NoThink accuracy across checkpoints of different training methods and model scales. Each point is one checkpoint; marker shape denotes the training method and color the base model.

\times

and

\star

are the base model in NoThink and Think . (a) Drift alignment to the leakage axis

\hat{v}_{\mathrm{leak}}

. (b) Paired projection drift (Cohen’s

d

) along

\hat{v}_{\mathrm{leak}}

. (c) Reasoning-marker density in the NoThink rollouts. More experiments and analysis are given in appendix D

Figure 3: GRPO collapses the mode gap. Layer-20 geometry of Qwen3-8B at GRPO steps

0

200

500

\bar{h}_{\mathcal{T}}

\bar{h}_{\mathcal{N}}

(dashed), and

v_{\mathrm{leak}}=\bar{h}_{\mathcal{T}}-\bar{h}_{\mathcal{N}}

(solid) are recomputed within each checkpoint. Both

\bar{h}_{\mathcal{T}}

\bar{h}_{\mathcal{N}}

keep their norms to within a few percent, yet the angle between them closes from

11.31^{\circ}

5.48^{\circ}

and

\|v_{\mathrm{leak}}\|

falls

15.43\to 8.81\to 7.18

. The panel is an approximate embedding rather than an orthogonal projection of

4096

-d quantities; embedding errors are reported in section D.3 .

Figure 4: Steering along

\hat{v}_{\mathrm{leak}}

recovers the Think performance without training. Reasoning-marker density versus NoThink accuracy, coloured by base model. Diamonds trace the layer-

20

induction sweep over five doses;

\times

and

\star

are the unsteered base model in NoThink and Think , and the circle is each model’s best post-training checkpoint.

Figure 5: Counter-steering along

\hat{v}_{\mathrm{leak}}

removes the post-training gains. Reasoning-marker density versus NoThink accuracy, coloured by base model. Each checkpoint is a before

\to

after pair joined by an arrow;

\times

and

\star

are the unsteered base model in NoThink and Think .

Figure 6: The two decompositions of the total gain. Left: the algebraic decomposition of

\Delta

into two paths,

(L_{\mathrm{trained}},R_{0})

and

(L_{\mathrm{base}},R_{1})

. Right: a schematic illustration of the same decomposition.

Figure 7: NoThink accuracy against the engagement , at layer 20, one panel per model. Blue: the base model under steering, tracing

Y_{0,0}\!\to\!Y_{0,1}

. Red: each post-trained checkpoint and its counter-steered counterpart, tracing

Y_{1,1}\!\to\!Y_{1,0}

. Arrows show the direction of the intervention, not of the decomposition.

L_{\mathrm{trained}}=Y_{1,1}-Y_{1,0}

is the height the checkpoint loses along the red arrow, and

R_{0}=Y_{1,0}-Y_{0,0}

compares the counter-steered checkpoint with the untreated base.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	GRPO	SFT	OPSD
General
Backbones	Qwen3-8B, Qwen3-4B, MiniCPM4.1-8B
Training data	DAPO-Math	OpenThoughts-Math	OpenThoughts-Math
Data
Max. prompt length	2048	2048	2048
Max. response length	8192	16000	1024

Appendix

Table 1: Training and evaluation hyperparameters for the three fine-tuning recipes. Dashes denote parameters that do not apply to a given method.

Figure 8: The drift is specific to

\hat{v}^{(\ell)}_{\text{leak}}

(layer

\ell=20

). Each point is one checkpoint; marker shape denotes the training method, colour the base model.

\star

is the base model in Think . (a), (c) Drift alignment on

\hat{v}_{\mathrm{leak}}

and

\hat{v}^{(\ell)}_{\text{ref}}

respectively. (b), (d) Cohen’s

d

of the same drift along each axis. The gray placebo band marks the null in each panel: in (a) and (c), the alignment obtained by splitting the base model’s own NoThink rollouts in half, so that the drift carries sampling noise only; in (b) and (d), Cohen’s

d

recomputed for the same checkpoint pair along a random unit direction. Both are drawn at the 90th percentile of the null’s absolute value.

Figure 9: The leakage happens across depth. Rows are (measure, axis), columns are depth. Each point is one checkpoint; marker shape denotes the training method, colour the base model. The legend is the same as in fig. 8 .

Quantity	Checkpoint	True	Drawn	Abs. err.	Rel. err.
$\\|v_{\mathrm{leak}}\\|$	base	$15.426$	$15.426$	$-0.000$	$-0.00\%$
	GRPO@200	$8.810$	$8.777$	$-0.034$	$-0.38\%$
	GRPO@500	$7.178$	$7.142$	$-0.037$	$-0.51\%$
rotation vs. base	GRPO@200	$20.270\degree$	$19.555\degree$	$-0.715\degree$	$-3.53\%$
	GRPO@500	$26.354\degree$	$25.844\degree$	$-0.510\degree$	$-1.94\%$
$\\|\bar{h}_{\mathcal{T}}\\|$	base	$72.318$	$73.525$	$+1.207$	$+1.67\%$

Appendix

Table 2: Fidelity of fig. 3 . Drawn is measured from the final two-dimensional coordinates; true is recomputed in

\mathbb{R}^{4096}

from the raw activations. Abs. err. means absolute error and Rel. err. is the corresponding relative error.

Figure 10: The closing gap is a property of training, not of the probe layer. Mode angle

\phi^{(\ell)}

between

\bar{h}_{\mathcal{T}}^{(\ell)}

and

\bar{h}_{\mathcal{N}}^{(\ell)}

across all

16

probed layers of Qwen3-8B. Dashed line marks layer

20

, used throughout the paper.

Corpus	$M_{\mathrm{Qwen}}$	$M_{\mathrm{MiniCPM}}$	Ratio
OpenThoughts-Math(SFT, OPSD)	$17.93$	$10.43$	$1.72$
Qwen3-8B Think	$18.81$	$12.58$	$1.49$
Qwen3-4B Think	$19.83$	$11.35$	$1.75$
MiniCPM4.1-8B Think	$5.13$	$18.73$	$0.27$

Appendix

Table 3: Style-token density per

1000

words, counted per word so that the three tokenizers are comparable.

	steering, $v_{\mathrm{leak}}$ at $\ell{=}20$
Model	Configuration	Acc.	Density	Trunc.	Loop	Len.
			( $\times 10^{-3}$ )	(%)	(%)	(tok)
Qwen3-8B	base, NoThink	0.178	3.08	3.1	7.9	4,268
	base, Think	0.557	18.30	12.4	1.1	17,782
	GRPO@500 (best ckpt)	0.472	11.85	1.6	2.2	9,293
	$\alpha=0.5$	0.231	5.57	1.3	6.0	4,940

Appendix

Table 4: Full steering sweep results. Density is the reasoning-marker density of section 3 . Trunc. is the share of rollouts that reach the generation cap and Loop the share whose word-level

12

-gram repetition ratio exceeds

0.3

; the caps and the repetition threshold are those of appendix C .

Model	Configuration	Acc.	Density	Trunc.	Loop	Len.
			( $\times 10^{-3}$ )	(%)	(%)	(tok)
Qwen3-8B	base, NoThink	0.178	3.08	3.1	7.9	4,268
	steer along $v_{\mathrm{leak}}$	0.335	10.26	0.8	2.9	6,850
	steer along $v_{\text{ref}}$	0.159	3.10	0.1	1.9	2,057
Qwen3-4B	base, NoThink	0.160	3.23	2.3	7.8	4,069
	steer along $v_{\mathrm{leak}}$	0.299	11.62	0.3	2.9	6,570

Appendix

Table 5: Steering along the reference axis instead of the leakage axis (

\alpha{=}1

\ell{=}20

Injection layer	Acc.	Density	Trunc.	Loop	Len.
		( $\times 10^{-3}$ )	(%)	(%)	(tok)
base, NoThink	0.178	3.08	3.1	7.9	4,268
$\ell=12$	0.254	4.25	2.1	5.6	6,527
$\ell=16$	0.233	4.27	1.3	7.3	5,358
$\ell=20$ †	0.335	10.26	0.8	2.9	6,850
$\ell=24$	0.224	6.68	0.5	4.2	4,260

Appendix

Table 6: Steering the same direction at different depths (Qwen3-8B,

\alpha{=}1

v^{(\ell)}_{\text{leak}}

is injected at one layer at a time; † marks

\ell{=}20

, the layer used everywhere else in the paper.

Configuration	Acc.	Density	Trunc.	Loop	Len.
		( $\times 10^{-3}$ )	(%)	(%)	(tok)
base, NoThink	0.178	3.08	3.1	7.9	4,268
base, Think	0.557	18.30	12.4	1.1	17,782
GRPO@500	0.472	11.85	1.6	2.2	9,293
$+$ steering, $\alpha{=}0.5$	0.545	16.42	1.3	1.8	12,179
$+$ steering, $\alpha{=}1$	0.553	18.31	3.8	1.0	15,033

Appendix

Table 7: Comparison of steered checkpoint with the base model. The steered row adds

\alpha{=}0.5,1,1.5

v_{\mathrm{leak}}

to the best GRPO checkpoint of Qwen3-8B.

Figure 11: Depth profile of steering (

\alpha=0.5,1,1.25,1.5,2

\pi^{(\ell)}

across probe depths, relative to each model’s bare NoThink run and divided by

\|v_{\mathrm{leak}}^{(\ell)}\|

. Colour is the steering dose. Total drift (

\pi^{(\ell)}_{\mathrm{tot}}

, solid) is measured during steered generation; behavioral drift (

\pi^{(\ell)}_{\mathrm{beh}}

, dashed) re-forwards the same text without the intervention. The dashed vertical line marks the injection layer

\ell{=}20

			Accuracy		Density		Loop (%)		Len. (tok)
Model	Checkpoint	$c$	bare	c.-s.	bare	c.-s.	bare	c.-s.	bare	c.-s.
Qwen3-8B	GRPO@500	+0.95	0.472	0.349	11.85	6.51	2.2	4.5	9,293	6,991
	GRPO@200	+0.95	0.447	0.315	9.47	4.55	4.3	13.9	12,583	9,936
	SFT@50	+0.91	0.417	0.267	13.91	9.72	2.4	14.2	13,745	12,337
	OPSD@25	+0.77	0.331	0.210	6.59	2.70	4.8	28.2	13,847	9,244
	OPSD@100	+0.46	0.150	0.131	2.33	1.90	23.3	28.0	8,613	6,088

Appendix

Table 8: Full counter-steering result (

\ell{=}20

\gamma{=}1

). bare is the original checkpoint, c.-s. the same checkpoint under counter-steering.

c=\cos(\delta_{s},\hat{v}_{\mathrm{leak}})

as defined in eq. 6 . Rows are grouped as described in section F.1 : unshaded, the nine aligned checkpoints; grey, the four with no usable gain ; blue, the two reverse-drift checkpoints.

	counter-steering
Model	Configuration	Acc.	Density	Trunc.	Loop	Len.
			( $\times 10^{-3}$ )	(%)	(%)	(tok)
Qwen3-8B	GRPO@500	0.472	11.85	1.6	2.2	9,293
	$v_{\mathrm{leak}}$	0.349	6.51	1.2	4.5	6,991
	$v_{\text{ref}}$	0.459	12.06	0.5	2.1	9,090
	random	0.455	12.05	0.9	1.9	9,325

Appendix

Table 9: Counter-steering along the leakage axis and two control axes (

\ell{=}20

\gamma{=}1

, best checkpoint per model).

		Accuracy		Density		Loop (%)		Len. (tok)
Model	Checkpoint	$\times 1$	$\times 2$	$\times 1$	$\times 2$	$\times 1$	$\times 2$	$\times 1$	$\times 2$
Qwen3-8B	GRPO@500	0.349	0.212	6.51	3.43	4.5	13.3	6,991	6,078
	GRPO@200	0.315	0.191	4.55	2.40	13.9	22.6	9,936	7,696
	SFT@50	0.267	0.131	9.72	4.79	14.2	30.1	12,337	9,587
	OPSD@25	0.210	0.087	2.70	1.21	28.2	59.6	9,244	6,154
	OPSD@100	0.131	0.076	1.90	1.53	28.0	41.4	6,088	5,353

Appendix

Table 10: Comparison of counter-steering at

\times 1

and

\times 2

dose (

\gamma{=}1,2

Configuration	Acc.	Density	Trunc.	Loop	Len.
		( $\times 10^{-3}$ )	(%)	(%)	(tok)
GRPO@500	0.472	11.85	1.6	2.2	9,293
$-$ $\hat{v}_{\mathrm{leak}}$	0.349	6.51	1.2	4.5	6,991
$-$ $\delta_{s}$	0.325	6.18	1.6	5.6	6,571
GRPO@200	0.447	9.47	6.2	4.3	12,583
$-$ $\hat{v}_{\mathrm{leak}}$	0.315	4.55	5.2	13.9	9,936

Appendix

Table 11: Removing the

\hat{v}_{\mathrm{leak}}

component of the drift against removing the whole drift (Qwen3-8B,

\ell{=}20

). The

\hat{v}_{\mathrm{leak}}

arm is the counter-steering used throughout the paper, which removes

\Delta\pi\,v_{\mathrm{leak}}

with

\gamma=1

; the

\delta_{s}

arm removes the drift in full.

Configuration	Acc.	Density	Trunc.	Loop	Len.
		( $\times 10^{-3}$ )	(%)	(%)	(tok)
base, NoThink	0.173	3.36	3.5	15.8	6,202
post-trained checkpoint	0.304	7.22	4.9	14.7	10,391
+ counter-steering	0.226	4.77	3.7	21.7	8,963
+ projection clamp	0.240	5.84	3.6	24.5	9,220

Appendix

Table 12: Counter-steering versus the projection clamp , averaged over the

15

checkpoints of section 5 . Both set

\gamma{=}1

Model	Configuration	Acc.	Density	Trunc.	Loop	Len.
			( $\times 10^{-3}$ )	(%)	(%)	(tok)
Qwen3-8B	base, NoThink	0.178	3.08	3.1	7.9	4,268
	$\gamma=0.5$	0.151	1.99	1.3	8.6	3,322
	$\gamma=1$	0.111	1.33	1.9	9.5	3,233
Qwen3-4B	base, NoThink	0.160	3.24	2.3	7.8	4,069
	$\gamma=0.5$	0.129	2.02	1.0	10.4	3,270

Appendix

Table 13: Counter-steering the base model (

\ell{=}20

). The magnitude is set as

\gamma\|v_{\mathrm{leak}}\|

since there is no drift for a base model.

Figure 12: Depth profile of counter-steering, checkpoint by checkpoint (

\gamma=1,2

). Columns are models, rows their five checkpoints. In each panel,

\pi^{\ell}

across probe depths, relative to that checkpoint’s original run and divided by

\|v_{\mathrm{leak}}^{(\ell)}\|

. Blue is

\gamma{=}1

, red

\gamma{=}2

; Total drift (

\pi^{(\ell)}_{\mathrm{tot}}

, solid) is measured during counter-steered generation; behavioral drift (

\pi^{(\ell)}_{\mathrm{beh}}

, dashed) re-forwards the same text without the intervention. The dashed vertical line marks the injection layer

\ell{=}20

Model	Checkpoint	$L_{\mathrm{base}}$	$R_{1}$	$L_{\mathrm{trained}}$	$R_{0}$	$\mathcal{A}$	$\lambda$
		via the base sweep		via counter-steering
Qwen3-8B	GRPO@500	+0.095	+0.199	+0.123	+0.171	+0.028	0.418
	GRPO@200	+0.084	+0.185	+0.132	+0.136	+0.049	0.492
	SFT@50	+0.132	+0.107	+0.150	+0.089	+0.018	0.627
	OPSD@25	+0.112	+0.041	+0.121	+0.032	+0.009	0.789
	OPSD@100	+0.070	-0.098	+0.019	-0.047	-0.051	-0.667

Appendix

Table 14: Per-checkpoint gain decompositions (

\ell=20

). Notation follows section 6 .

Model	Checkpoint	$\rho(g_{\mathrm{S}},\Delta)$	$\rho(\Delta,L_{\mathrm{trained}})$	$\rho(g_{\mathrm{T}},\Delta)$	$\rho(g_{\mathrm{T}},g_{\mathrm{S}})$
Qwen3-8B	GRPO@500	+0.772	+0.766	+0.836	+0.677
	GRPO@200	+0.792	+0.806	+0.852
	SFT@50	+0.754	+0.752	+0.882
	OPSD@25	+0.572	+0.643	+0.677
	OPSD@100	+0.341	+0.510	+0.349
Qwen3-4B	GRPO@450	+0.741	+0.820	+0.874	+0.613

Appendix

Table 15: Question-level alignment of gains and intervention effects. Spearman correlations across

120

questions. The base-only correlation

\rho(g_{\mathrm{T}},g_{\mathrm{S}})

is identical within each model. Shading follows table 8 .

Figure 13: A schematic showing that the response along

\hat{v}_{\text{leak}}

is asymmetric about the base model’s position, and post-training moves the model along it.

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