Evaluating the Semantic Specificity of Representation Steering in Language Models

Zhangdie Yuan; Andreas Vlachos

cs.CLAug 29, 2026

Evaluating the Semantic Specificity of Representation Steering in Language Models

Authors: Zhangdie Yuan, Andreas Vlachos

Organizations: University of Cambridge

Abstract

Localized Representation Steering (LRS) is widely used to correct reasoning pathologies in large language models. However, standard benchmark evaluations can easily be fooled by superficial label overrides, creating a false impression of reasoning circuit repairs. In this work, we propose Cross-Rule Transfer (CRT), a diagnostic framework that audits representational interventions by evaluating them on rule families where the model is natively competent. Evaluating late-layer LRS for a widespread logical failure, contradiction blindness, reveals that the intervention merely injects a global label bias: applying the steering vector to rules the model already handles correctly (99.6% baseline) degrades performance to 40.4% by forcing false contradiction predictions. We support this diagnosis with four complementary controls (direct logit bias equivalence, control vector label-flipping, cross-model grafting, and early-layer steering checks), providing a rigorous methodology to distinguish genuine reasoning repairs from superficial label overrides.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of the Cross-Rule Transfer (CRT) diagnostic audit and mechanistic explanation. Panel A: Mechanistic late-layer logit bottleneck showing how representation steering vectors $\mathbf{v}$ injected at late layers directly project through the unembedding matrix $W_{U}$ to shift logits, acting as a global output bias. Panel B: The CRT audit evaluates the steering vector on rule families where the model is natively competent (Rule A) alongside the target failing family (Rule B). A true reasoning circuit repair would preserve native competence, whereas the observed intervention collapses Rule A to $40.4\%$ accuracy, demonstrating a superficial label override.

Dimension	Locality Audit	Cross-Rule Transfer
Task Domain	Unrelated domains	Within-domain competent rules
Label Space	Disjoint label space	Shared label space
Failure Target	Collateral damage	Global label override
Validation Goal	Preservation of facts	Falsification of circuit repair

Table 1: Comparison between standard locality audits and Cross-Rule Transfer (CRT).

Rule Family	Example (Premise $\to$ Hypothesis)	Truth	Anchor
swap_sym	Alice is a friend of Bob. $\to$ Bob is a friend of Alice.	Entail	Entail ✓
trans_chain	A is taller than B. B is taller than C. $\to$ A is taller than C.	Entail	Entail ✓
sym_nonrefl	Alice is married to Bob. $\to$ Alice is married to Alice.	Contra	Entail ×
sym_nontrans	A is next to B. B is next to C. $\to$ A is next to C.	Contra	Entail ×

Table 2: Illustrative examples and anchor model baseline predictions across core rule families in Asymmetricity-2.0. The anchor model predicts entailment universally, succeeding on forward rules while completely failing on contradiction detection.

Rule Family	Test Inst. ( $N$ )	Anchor Acc [95% CI]	Failure Characteristics
swap_symmetry	9,374	$0.9967\pm 0.0012$	Near-perfect forward entailment
transitivity_chain	2,053	1.0000 [0.9981, 1.0000]	Perfect forward relational tracking
symmetric_nonreflexive	2,869	0.0000 [0.0000, 0.0013]	Complete collapse on contradiction
symmetry_not_transitive	2,088	0.0000 [0.0000, 0.0018]	Complete collapse on contradiction

Table 3: Rule-family accuracy breakdown for the Llama-1B Instruct anchor. The failure is strictly localized to rule families requiring contradiction detection.

Tier	Contradiction Recall	Count
Complete Failure	$R_{c}=0.0$	7
Near-Zero	$0.0<R_{c}<0.01$	5
Partial Recall	$0.01\leq R_{c}<0.5$	4
High Recall	$R_{c}\geq 0.5$	2

Table 4: Contradiction-recall pathology tiers for all 18 models at scale 65,536. See Appendix E for the full per-model breakdown.

Family	Model Checkpoint Anchor	Obs.	Late Err [95% CI]	Early Err [95% CI]	Localization
Llama	Llama-3.2-1B-Instruct	145k	$86.1\%\pm 0.18\%$	$0.75\%\pm 0.04\%$	Probe Degradation
Gemma	Gemma-4-E4B-It	145k	$86.3\%\pm 0.18\%$	$3.2\%\pm 0.09\%$	Probe Degradation
Qwen	Qwen-3.5-9B-Instruct	222k	$58.5\%\pm 0.20\%$	$33.7\%\pm 0.19\%$	Moderate late dominance
DeepSeek	DeepSeek-R1-Distill-Qwen3-8B	222k	$96.5\%\pm 0.07\%$	$97.3\%\pm 0.07\%$	Near-total failure

Table 5: Late-region vs. early-region linear probe error rates. Late-layer probes are trained on early-layer activations (where decodability is high) and evaluated on late-layer activations to trace representation shift.

Figure 2: Late-vs-early proxy-localization contrast. Llama and Gemma show the clearest late-region concentration of failure; Qwen remains late-dominant with more leakage; DeepSeek is cautionary because failure is nearly uniform across layers.

Model	Base	Steer	$\Delta$	Injected
Llama-1B-It	0.996	0.404	$-0.592$	298 false contr.
Qwen-9B-It *	0.452	0.742	$+0.290$	$-141$ contr. $\dagger$

Table 6: Cross-rule transfer metrics on entailment rules. * Presented for directional comparison (Qwen does not meet competence threshold).

\dagger

Qwen’s baseline includes 4 unparsed predictions that resolve to entailment under steering.

$\alpha$	Source Post-Acc	Downstream CLUTRR Post-Acc
0.00 (Baseline)	0.696	0.500
0.25	1.000	1.000
0.50	1.000	1.000
1.00	1.000	1.000
1.50 (Selected)	0.683	0.500
2.00	0.683	0.500

Table 7: Llama-3.2-1B-Instruct steering strength sweep. A sharp performance cliff appears between

\alpha=1.0

and

\alpha=1.5

for the unconditional (ungated) intervention.

Model	Method	Src	CLUTRR	SpartQA	ProntoQA
Llama	LRS (gated)	1.0000	0.50	0.29	0.46
	DLB (gated)	1.0000	0.50	0.29	0.46
	DLB (ungated)	0.6829	0.50	0.29	0.46
Qwen	LRS (gated)	1.0000	0.56	0.60	0.22
	DLB (gated)	1.0000	0.56	0.60	0.22
	DLB (ungated)	0.7394	0.56	0.60	0.22

Table 8: LRS vs. DLB comparison (

N=100

downstream, greedy decoding). Src is evaluated on the full balanced source dataset. All downstream columns show identical accuracy between LRS and DLB under greedy decoding (temperature

=0

), confirming functional equivalence once activated.

Control	Description	Pre $\rightarrow$ Post ( $\Delta$ )	Side Eff.
Early-layer	Steer L2 not L13	0.634 $\rightarrow$ 0.789 ( $+$ 0.154)	3,465
Shuffle	Randomized labels	0.000 $\rightarrow$ 1.000 $\ddagger$	0
Cross graft	Llama $\rightarrow$ Qwen	0.062 $\rightarrow$ 0.966 ( $+$ 0.904)	17

Table 9: Diagnostic control experiments.

\ddagger

The shuffle evaluation split consists of contradiction-only items; the vector flips predictions from all-entailment to all-contradiction, representing a label flip rather than a reasoning fix.

Validation Checklist for Representation Steering
1. Cross-Rule Transfer Audit: Evaluate the learned vector unconditionally on tasks where the model achieves native baseline competence ( $\geq 95\%$ ). Confirm native accuracy does not collapse.
2. Gated vs. Ungated Side Effects: Report side effects and balanced-dataset performance under both gated (oracle) and unconditional setups.
3. Label-Mode Distribution Check: Plot histograms of generated labels pre- and post-steering to ensure the intervention is not forcing a static output mode.
4. Direct Logit Bias Baseline: Compare the vector’s downstream performance against a Direct Logit Biasing (DLB) baseline to rule out functional equivalence.
5. Parameter-Level Cosine Audit: For open-weight models, report the cosine similarity between the learned steering vector $\mathbf{v}$ and the unembedding label directions $\mathbf{W}_{U}$ across layers.

Table 10: Checklist for evaluating and validating representation steering claims.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Rule Family	Premise	Hypothesis	Ground Truth
swap_symmetry	Alice is a friend of Bob.	Bob is a friend of Alice.	Entailment
transitivity_chain	Alice is taller than Bob. Bob is taller than Charlie.	Alice is taller than Charlie.	Entailment
symmetric_nonreflexive	Alice is married to Bob.	Alice is married to Alice.	Contradiction
symmetry_not_transitive	Alice is next to Bob. Bob is next to Charlie.	Alice is next to Charlie.	Contradiction

Appendix

Table 11: Concrete premise, hypothesis, and ground-truth NLI labels for the rule families in Asymmetricity-2.0. Entailment families require forward logical tracking, whereas contradiction families require detecting structural/relational violations.

Scale	$N$	Accuracy	F1-macro	Ent-Recall	Con-TP
1,024	1,024	0.6494	0.3937	0.9940	0
4,096	4,096	0.6577	0.3968	0.9963	0
16,384	16,384	0.6956	0.4102	0.9973	0
65,536	65,536	0.5262	0.3448	0.9989	1

Appendix

Table 12: Performance metrics for the Llama-1B Instruct anchor across dataset sizes.

Figure 3: Anchor across scales. Anchor accuracy and chain-length-2 accuracy shift with scale.

Model	Accuracy	F1-macro	Ent-R	Con-R	NonR	NonT
Qwen-3.5-4B-It	0.6362	0.6231	0.7830	0.4729	0.6310	0.0159
Qwen-3.5-4B	0.5472	0.5455	0.4590	0.6454	0.8524	0.0467
Llama-3.2-1B-It	0.5262	0.3448	0.9989	0.0000	0.0000	0.0000
Llama-3.2-1B	0.5254	0.3451	0.9970	0.0006	0.0007	0.0001
Gemma-4-E4B-It	0.5216	0.3446	0.9886	0.0020	0.0023	0.0009
Llama-3.2-3B-It	0.5064	0.3381	0.9595	0.0022	0.0020	0.0026

Appendix

Table 13: Behavioral metrics for all 18 models evaluated at dataset size of 65,536 instances. Ent-R and Con-R denote entailment and contradiction recall, respectively. NonR and NonT represent accuracy on the symmetric_nonreflexive and symmetry_not_transitive rule families, respectively.

Split Family	Example Count ( $N$ )	Anchor Accuracy
iid	3,125	0.6515
entity_disjoint_drop	2,321	0.6812
entity_disjoint_generate	3,126	0.4987
length_ood	1,562	0.9949
pair_disjoint	3,125	0.4982
property_disjoint	3,125	0.9949

Appendix

Table 14: Performance across dataset splits for the anchor model.

Metric	Median	Maximum
Accuracy	0.4041	0.6956
F1-macro	0.3382	0.6231
Contradiction Recall	0.0044	0.9352

Appendix

Table 15: Aggregate statistics across all 72 behavioral runs.

Protocol: Cross-Rule Transfer Diagnostic Audit
Inputs: Target model $M$ , evaluation suite $D$ containing multiple logical/semantic rule families, steering vector $\mathbf{v}$ constructed to repair a failing target rule family $F_{\text{fail}}$ (where baseline recall is low).
Step 1: Identify Native Competence. Evaluate the unsteered model $M$ on all rule families in $D$ . Identify a subset of rule families $F_{\text{comp}}\subset D$ where $M$ achieves high native baseline competence (accuracy $\geq\theta$ , where we define the default competence threshold $\theta=95\%$ ).
Step 2: Unconditional Intervention. Apply the steering vector $\mathbf{v}$ unconditionally (without oracle task-level gating) to all evaluation instances in the competent splits $F_{\text{comp}}$ during autoregressive inference.
Step 3: Measure Competence Loss. Calculate the post-steering accuracy on $F_{\text{comp}}$ and quantify the count of false target label injections. Perform a McNemar’s test for significance on discordant pairs.
Step 4: Classification. • If accuracy remains high ( $Acc\geq\theta$ ), classify the intervention as a generalized reasoning circuit repair . • If accuracy degrades significantly ( $Acc<\theta$ ) and errors are dominated by the target label token, classify the intervention as a superficial label bias override .

Appendix

Table 16: Step-by-step diagnostic recipe for the Cross-Rule Transfer audit protocol.

Threshold $\theta$	Selected Families	Baseline Acc	Steered Acc	Audit Result
$90\%$	swap_symmetry , transitivity_chain	$99.6\%$	$40.4\%$	Collapse
$95\%$	swap_symmetry , transitivity_chain	$99.6\%$	$40.4\%$	Collapse
$98\%$	swap_symmetry , transitivity_chain	$99.6\%$	$40.4\%$	Collapse

Appendix

Table 17: Sensitivity of CRT selection and audit to threshold

\theta

	Pred Entailment	Pred Contradiction
True Entailment (Pre)	498	2
True Entailment (Post)	202	298

Appendix

Table 18: Pre- and post-steering confusion matrices (N=500).

Label Format	Entailment Acc	Contradiction Recall	Collinearity
Entailment/Contradiction	$99.6\%$	$0.00\%$	High
Yes/No	$99.4\%$	$0.00\%$	High
A/B	$99.6\%$	$0.00\%$	High

Appendix

Table 19: Pathology metrics under alternative NLI label formats.

Model Checkpoint	Pre-Acc	Post-Acc	Recoveries
Llama-3.2-1B-Instruct	0.1503	1.0000	123,998
Qwen-3.5-9B-Instruct	0.4108	1.0000	131,290
DeepSeek-R1-Distill-Qwen3-8B	0.0349	1.0000	215,070
Gemma-4-E4B-It	0.5430	1.0000	117

Appendix

Table 20: Targeted steering results on contradiction splits under oracle-gated LRS. Recoveries = number of individual predictions flipped from incorrect to correct. All models achieve perfect recovery with zero side effects on non-target rule families. Gemma’s evaluation represents a bounded retry on 256 instances due to a missing full-scale mechanistic manifest.

Model	Task	Pre-Acc	Post-Acc	$\Delta$	Recoveries	Side Effects	Pre Label Mode	Post Label Mode
Llama-1B-It	CLUTRR	0.500	0.500	0.000	50	50	All-entailment	All-contradiction
Llama-1B-It	SpartQA	0.710	0.290	$-0.420$	29	71	All-entailment	All-contradiction
Llama-1B-It	ProntoQA	0.540	0.460	$-0.080$	46	54	All-entailment	All-contradiction
Qwen-9B-It	CLUTRR	0.440	0.560	$+0.120$	56	44	Mostly-contradiction	Mostly-entailment
Qwen-9B-It	SpartQA	0.400	0.600	$+0.200$	60	40	Mostly-contradiction	Mostly-entailment
Qwen-9B-It	ProntoQA	0.780	0.220	$-0.560$	22	78	Mixed	Mostly-entailment

Appendix

Table 21: Full downstream transfer results (

N=100

per task, balanced 50/50 splits). Recoveries = predictions flipped from incorrect to correct; Side Effects = predictions flipped from correct to incorrect. Pre and Post Label Mode columns reveal that steering systematically inverts the dominant label prediction.

Figure 4: Downstream accuracy after repair. All downstream probes complete, but performance remains weak, chance-like, or near-floor, indicating that the steering intervention does not generalize beyond the source benchmark. The label mode columns in Table 21 confirm that accuracy changes are driven by systematic label flips rather than improved reasoning.

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Large Reasoning Models (LRMs) exhibit backtracking and self-verification mechanisms that enable them to revise intermediate steps and reach correct solutions, yielding strong performance on complex logical benchmarks. We hypothesize that such behaviors are beneficial only when the model has sufficiently strong ``critique'' ability to detect its own mistakes. This work systematically investigates how current LRMs recover from errors by inserting arithmetic mistakes in their intermediate reasoning steps. Notably, we discover a peculiar yet important phenomenon: despite the error propagating throughout the entire chain-of-thought (CoT) without any verbalized correction, the model still reaches the correct final answer after the thinking process finishes. This recovery implies the existence of an internal mechanism helping the model to detect errors and trigger self-correction, which we refer to as the hidden critique ability. Building on feature space analysis, we identify a highly interpretable critique vector representing this behavior. Extensive experiments across multiple model scales and families demonstrate that steering latent representations with this vector improves the model's error detection capability and enhances the performance of test-time scaling at no extra training cost. Our findings provide a valuable understanding of LRMs' critique behavior, suggesting a promising direction to control and improve their self-verification mechanism. Our code is available at: https://github.com/mail-research/lrm-critique-vectors.

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