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
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 v injected at late layers directly project through the unembedding matrix WU 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 → Hypothesis)
Truth
Anchor
swap_sym
Alice is a friend of Bob. → Bob is a friend of Alice.
Entail
Entail ✓
trans_chain
A is taller than B. B is taller than C. → A is taller than C.
Entail
Entail ✓
sym_nonrefl
Alice is married to Bob. → Alice is married to Alice.
Contra
Entail ×
sym_nontrans
A is next to B. B is next to C. → 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±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
Rc=0.0
7
Near-Zero
0.0<Rc<0.01
5
Partial Recall
0.01≤Rc<0.5
4
High Recall
Rc≥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%±0.18%
0.75%±0.04%
Probe Degradation
Gemma
Gemma-4-E4B-It
145k
86.3%±0.18%
3.2%±0.09%
Probe Degradation
Qwen
Qwen-3.5-9B-Instruct
222k
58.5%±0.20%
33.7%±0.19%
Moderate late dominance
DeepSeek
DeepSeek-R1-Distill-Qwen3-8B
222k
96.5%±0.07%
97.3%±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
Δ
Injected
Llama-1B-It
0.996
0.404
−0.592
298 false contr.
Qwen-9B-It *
0.452
0.742
+0.290
−141 contr. †
Table 6: Cross-rule transfer metrics on entailment rules. * Presented for directional comparison (Qwen does not meet competence threshold). † Qwen’s baseline includes 4 unparsed predictions that resolve to entailment under steering.
α
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 α=1.0 and α=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 → Post ( Δ )
Side Eff.
Early-layer
Steer L2 not L13
0.634 → 0.789 ( + 0.154)
3,465
Shuffle
Randomized labels
0.000 → 1.000 ‡
0
Cross graft
Llama → Qwen
0.062 → 0.966 ( + 0.904)
17
Table 9: Diagnostic control experiments. ‡ 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 ( ≥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 v and the unembedding label directions WU 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-Recall
Con-TP
1,024
1,024
0.6494
0.3937
0.9940
0.0000
0
4,096
4,096
0.6577
0.3968
0.9963
0.0000
0
16,384
16,384
0.6956
0.4102
0.9973
0.0000
0
65,536
65,536
0.5262
0.3448
0.9989
0.0000
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
Minimum
Median
Maximum
Accuracy
0.0000
0.4041
0.6956
F1-macro
0.0000
0.3382
0.6231
Contradiction Recall
0.0000
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 v constructed to repair a failing target rule family Ffail (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 Fcomp⊂D where M achieves high native baseline competence (accuracy ≥θ , where we define the default competence threshold θ=95% ).
Step 2: Unconditional Intervention. Apply the steering vector v unconditionally (without oracle task-level gating) to all evaluation instances in the competent splits Fcomp during autoregressive inference.
Step 3: Measure Competence Loss. Calculate the post-steering accuracy on Fcomp 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≥θ ), classify the intervention as a generalized reasoning circuit repair . • If accuracy degrades significantly ( Acc<θ ) 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 θ
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 θ .
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
Δ
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.
Large language model (LLM) interpretability studies how internal representations and computations produce outputs, and how they can be explained or controlled.
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.
Hoang Phan, Quang H. Nguyen, Hung T. Q. Le +3
VinUni-Illinois Smart Health Center, VinUniversity · University of Illinois Urbana-Champaign
Applying steering vectors to large language models (LLMs) is an efficient and effective model alignment technique, but we lack an interpretable explanation for how it works--specifically, what internal mechanisms steering vectors affect and how this results in different model outputs. To investigate the causal mechanisms underlying the effectiveness of steering vectors, we conduct a comprehensive case study on refusal. We propose a multi-token activation patching framework and discover that different steering methodologies leverage functionally interchangeable circuits when applied at the same layer. These circuits reveal that steering vectors primarily interact with the attention mechanism through the OV circuit while largely ignoring the QK circuit. Freezing all attention scores during steering drops performance by only 8.83% across three model families. A mathematical decomposition of the steered OV circuit further reveals semantically interpretable concepts, even in cases where the steering vector itself does not. Leveraging the activation patching results, we show that steering vectors can be sparsified by up to 85-96% while retaining most performance, and that different steering methodologies agree on a subset of important dimensions.
This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.