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Spurious Rewards Paradox: Mechanistically Understanding How RLVR Activates Memorization Shortcuts in LLMs

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Spurious RLVR works by flipping on a memorization circuit already latent in the model, not by improving reasoning.

desk verdict Perplexity Paradox is new and useful, but the L18-20 'Anchor' may be an artifact of the wrong→right vs stable contrast. read the letter →

arxiv 2601.11061 v2 pith:5BBE4O53 submitted 2026-01-16 cs.LG cs.CL

Lecheng Yan , Ruizhe Li , Guanhua Chen , Qing Li , Jiahui Geng , Wenxi Li , Longyue Wang , Chenyang Lyu This is my paper · ORCID
classification cs.LGcs.CL
keywords RLVRmemorizationshortcutmechanisticinterpretabilityPerplexityParadoxFunctionalAnchordatacontaminationcausalsteeringneuralODE
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that RLVR trained with spurious (random or incorrect) rewards improves benchmark scores by activating memorized answers the base model already contains, not by improving reasoning. It identifies a 'Perplexity Paradox' — answer-token perplexity drops while prompt-side perplexity rises — as a macroscopic fingerprint of this shortcut. Mechanistically, it localizes a Functional Anchor in the middle layers (L18–L20) that causally triggers retrieval of a memorized answer, and Structural Adapters in later layers (L21+) that reorganize representations to carry that signal. Ablations and causal steering of specific MLP keys support the circuit's necessity and sufficiency, and control models without prior contamination show no such effect. This matters because it explains why RLVR gains can be illusionary and opens a route to detect and suppress data-contamination-driven performance.

What carries the argument

Anchor-Adapter circuit: the division of the model's depth into a Functional Anchor (layers 18–20), where the decision to retrieve a memorized answer is causally made and a high-probability trigger token is injected, and Structural Adapters (layers 21+), which perform representational rotation rather than storing new knowledge. The detection toolbox includes path patching (swapping activations between 'leakage' and 'stable' samples to find causal edges), counterfactual JSD on MLP sub-components to locate weight-reorganization peaks, Logit Lens to trace token emergence, and a Neural ODE fit to residual updates whose 'separation force' metric pinpoints trajectory bifurcation.

What would settle it

Run path-patching and NDE separation-force analyses on a leakage/stable split where each pair shares the same problem stem and differs only in the memorized answer; if the L18–20 peak and L21–22 JSD peak disappear, the Anchor-Adapter circuit is an artifact of question confounds rather than a memorization trigger.

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Extended reading notes

Core claim

Spurious RLVR tunes a two-part circuit in Qwen2.5-Math-7B: a Functional Anchor at layers 18–20 causally decides to retrieve a memorized answer and injects a high-probability trigger token, while Structural Adapters at layers 21+ rotate the feature space to carry that signal. Evidence: path patching recovers accuracy only when anchor layers are patched; counterfactual JSD peaks at L21–22; Logit Lens shows Layer 19 priming and Layer 23 injection; NDE separation force peaks at L18–20; ablations resetting the anchor drop leakage accuracy >10% while stable accuracy is unchanged; scaling top MLP keys bidirectionally steers contamination-driven accuracy.

Load-bearing premise

The entire localization rests on the claim that 'leakage' and 'stable' question sets are matched in difficulty, domain, and length; the paper states they are matched but never specifies the matching procedure, so content differences could confound the circuit attribution.

Editorial extensions

If this is right

  • Accuracy on a benchmark that can be gamed by this circuit is not evidence of reasoning; evaluation suites must screen for contamination.
  • The divergence of answer vs prompt perplexity can serve as a cheap, training-time fingerprint for shortcut formation.
  • Resetting or steering anchor-layer weights offers a post-hoc decontamination method that reveals baseline performance without retraining.
  • The circuit is dataset-specific, so layer manipulation can identify which benchmark items are leaked and which are genuinely solved.
  • The effect appears in Qwen-family models but not in the tested control models, suggesting architecture-dependent susceptibility to spurious RLVR.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the Anchor-Adapter circuit is a general property of pretrained models that have seen the test data, then contamination detection could be done by probing for a middle-layer trigger, complementing corpus-level string matching.
  • The same steering mechanism could be used adversarially to inflate benchmark scores, so releasing steering weights calls for safeguards.
  • The Perplexity Paradox might be exploited as an early-stopping or reward-shaping signal during RLVR to prevent memorization from dominating.
  • The NDE separation-force metric could be applied to any residual-stream model to locate the decision point for behaviors other than memorization.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper studies Qwen2.5-Math-7B before and after RLVR with incorrect/spurious rewards. It reports a 'Perplexity Paradox' (answer-token perplexity falls while prompt/full-text perplexity rises), and uses path patching, counterfactual JSD, logit-lens heatmaps, NDE trajectory analysis, layer ablations, and MLP-key scaling to localize the memorization shortcut. The central claim is that middle layers L18–L20 act as a 'Functional Anchor' that injects a high-probability trigger token for a memorized answer, while layers L21+ act as 'Structural Adapters' that rotate representations; scaling specific MLP keys in these layers is claimed to bidirectionally amplify or suppress contamination-driven accuracy. Comparisons against LLaMA-3.1-8B and OLMo-2-1124-7B (and Qwen3-8B) are used to argue the effect is contamination-specific.

Significance. Mechanistic localization of RLVR contamination effects would be valuable: it could explain why spurious rewards produce benchmark gains and suggest post-hoc mitigation. The paper has strengths: it combines several complementary probes, uses multiple control models, ships code, and its partial-prompt evaluation (Appendix A) is an independent behavioral label for memorization. However, the central evidence is currently undercut by an unspecified 'matched questions' design, a partly circular NDE analysis, and a steering-neuron selection rule that uses the ground-truth answer. With these fixed, the paper could be a useful contribution; in the current form the claims outrun the evidence.

major comments (4)
  1. [§4.1] Section 4.1 says every mechanistic probe 'is executed by contrasting the internal activations of these two groups on matched questions,' and that this 'cancels out difficulty, domain, and length confounds.' No matching procedure is described, and no balance table appears in the main text or appendices. This is load-bearing: leakage (wrong→right) and stable (always-right) groups are defined by base-model correctness, so they are not matched on the model's own difficulty axis. Path Patching (§4.3) is also biased because stable questions are at ceiling for base accuracy, so accuracy recovery can only be large for previously-wrong questions. The JSD, NDE, linear-probing, and ablation results inherit the same contrast. Please specify the matching algorithm and report covariate balance; alternatively, define groups using the Partial Prompt Evaluation label from Appendix A, which is an independ
  2. [§4.4] Section 4.4 models discrete residual updates with f_phi and then defines Separation Force as ||dh_leak/dt − dh_gen/dt||. Since the same fitted f_phi is a function of the observed layer-wise activations, the peak at L18–L20 is a smoothed restatement of the raw update differences, not an independent confirmation. The claim that NDE 'mathematically confirms' the causal anchor is overstated. Please show that the NDE fits are validated (e.g., prediction of held-out intermediate states), compare the separation force against raw Δx differences, and provide a null/permutation baseline to establish that the peak is not an artifact of the MLP fit. Also report training/regularization details for the two-layer MLP on 28 discrete steps.
  3. [§5, Appendix E] Section 5 and Figure 9 report that stable samples are robust to anchor/adapter reset. This is largely by construction: stable samples are correct in the base model, so replacing tuned weights with base weights should not destroy their accuracy. Therefore the asymmetry between leakage and stable sensitivity does not by itself show that L18–L20 are specialized memorization layers. Appendix E additionally states that on LiveMathBench the same leakage/stable partition produces an inverted pattern, 'attributed to distributional differences between the two subsets rather than memorization effects.' This admission undercuts the interpretation of the same partition on contaminated datasets. Please provide a group definition not based on base-model correctness, or at minimum demonstrate that the LiveMathBench inversion does not also apply to MATH-500/MinervaMath.
  4. [§6, Eq. (3)] Eq. (3) selects the top-k neurons using |Top-10(v_i) ∩ Tokens(y)|, where y is the ground-truth answer. Thus the 'task-relevant' neurons are chosen precisely because their output overlaps the answer token; scaling them by α will mechanically change the answer probability. Figures 13 and 14 therefore demonstrate that the selected neurons can modulate the answer, but do not independently confirm that the Anchor-Adapter circuit is the contamination mechanism. Please select neurons using leakage-vs-stable activation differences without access to y (or on a held-out answer set), and report sensitivity to k and λ.
minor comments (6)
  1. [Appendix A] Appendix A refers to Section 3.1 but the partial-prompt evaluation is described in Section 4.1; the cross-reference should be corrected.
  2. [§4.3, Figure 7] The Logit Lens conclusion is based on two stochastic trajectories of a single sample. Please add aggregate evidence across many leakage samples, ideally with confidence intervals, because the 'weaker precursor signal' in the failed run could be decoding stochasticity.
  3. [§4.1, Figure 1] The choice of MATH-500 and MinervaMath as the primary contaminated datasets is made after observing the accuracy gaps. Please state prespecified inclusion criteria or report all six datasets in every mechanistic probe to reduce post hoc selection concerns.
  4. [§6.1–6.2] Several hyperparameters are free: λ in Eq. (3), k=10, and the scaling factor α. Please include sensitivity analyses and clarify whether α is applied uniformly to all selected neurons at all generation steps.
  5. [§4.2, Figure 3] Define 'full-text' vs 'answer-only' perplexity precisely, including tokenization and whether the prompt is scored in full-text PPL. A declining answer-only PPL could partly reflect shorter or more templated answers, so a length-controlled comparison would strengthen the Perplexity Paradox.
  6. [Appendix F] Appendix F describes 'ablating (zeroing out)' factors at layers 22/23, but Section 6.2 defines only multiplicative scaling. Please clarify whether zeroing is α=0 and whether it is applied to selected neurons or all neurons.

Circularity Check

2 steps flagged · score 5.0 of 10

The NDE 'confirmation' is a re-expression of the same layer-wise updates, and the steering neurons are selected by ground-truth answer overlap, so two pieces of 'validation' reduce partly to their inputs.

  1. renaming known result [Section 4.4 (Dynamic Analysis), NDE implementation and Separation Force definition]
    "In our implementation, we approximate Fθ using a two-layer MLP fitted to the discrete layer-wise updates ∆xℓ = xℓ+1 − xℓ. ... Separation Force: Defined as || dh_leak/dt − dh_gen/dt ||, measuring the instantaneous divergence in update directions between leakage and stable samples; ... Figure 10 (Left) shows that the Separation Force peaks precisely at Layers 18, 19, and 20. This mathematically confirms that these layers exert the strongest directional influence to steer leakage samples onto the memorization trajectory."

    The NDE vector field is fitted to the observed layer updates ∆xℓ, so the 'separation force' at layer ℓ is approximately ||∆x_leak,ℓ − ∆x_gen,ℓ||. The peak at L18–L20 is therefore inherited from the same leakage-vs-stable activation differences used in the rest of the paper; it is a re-description of the input, not an independent mathematical confirmation of the Functional Anchor.

  2. self definitional [Section 6.1, Eq. (3) and Section 6.3, Figure 13]
    "We then compute a relevance score combining key activation magnitude and semantic overlap with answer tokens: s_i = |k^(i)_ℓ| · (1 + λ· |Top-10(vi)∩Tokens(y)| / |Tokens(y)|), (3) ... We select the top-k neurons (k=10) ranked by these scores as the intervention target set N^task_ℓ. ... Figure 13 presents the accuracy change when applying neuron-level steering ... Layer 18 exhibits maximal sensitivity (−3.8% under suppression, +4.4% under amplification), consistent with its role as the Functional Anchor."

    The 'task-relevant' neurons are selected partly by how strongly their unembedding projection overlaps the ground-truth answer tokens y. Scaling those same neurons and then reporting changes in answer accuracy is partly a restatement of the selection criterion: neurons are deemed relevant because they decode to the answer, and intervening on them moves the answer. The layer specificity retains some independent content, but the steering 'prediction' is substantially built into Eq. (3).

full rationale

The paper's central localization claim (L18–L20 Functional Anchor) is not wholly circular: Path Patching (Section 4.3) is a causal swap experiment, and the Ablation Study (Section 5) directly resets L18–20 and observes accuracy drops, which are external, falsifiable interventions. The self-citations (Li et al. 2025a/b) are methodological and not load-bearing uniqueness claims. However, two pieces of 'confirmation' reduce partly to their inputs. First, the NDE analysis fits a neural ODE to the exact layer-wise differences and then presents the resulting 'separation force' peak at L18–20 as a mathematical confirmation; this is essentially the same information re-expressed in continuous coordinates. Second, the causal-steering neurons are selected using ground-truth answer-token overlap (Eq. 3), so demonstrating that they modulate answer accuracy is partially tautological. The unspecified 'matched questions' protocol (Section 4.1) is a real confound risk but is a correctness/design concern rather than circularity. Overall, the independent causal evidence keeps the paper from being fully circular, but the NDE and steering validations inflate the support for the central claim, warranting a moderate score.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The mechanistic claims lean on two labeled constructs (Anchor/Adapter) that are extracted from the same data that defines them, plus a fitted NDE and a ground-truth-dependent neuron selector. No entity has an independent falsifiable signature outside this paper.

free parameters (4)
  • λ (semantic alignment weight) = not reported
    In Eq. (3), controls how strongly Top-10(v_i)∩Tokens(y) contributes to neuron relevance; no value or sensitivity analysis given.
  • top-k neurons per layer = k=10
    Neuron intervention set N_task^ℓ selected as top 10 by relevance score; no ablation of k.
  • steering scaling factors α = 3.0 (amplify), 0.2 (suppress)
    Chosen by hand for Figure 13/14; no grid or guideline reported.
  • NDE MLP hyperparameters = not specified
    Two-layer MLP approximating layer updates; hidden size, training epochs, and regularization not given.
assumptions (5)
  • domain assumption Transformer MLP layers act as key-value memories that store and retrieve parametric knowledge.
    Inherited from Geva et al. (2021); used to justify focusing on MLPs as the storage/retrieval site.
  • ad hoc to paper The residual stream can be modeled as a continuous ODE whose vector field is well-approximated by a two-layer MLP trained on discrete layer updates.
    Section 4.4; the fitted dynamics are then used to compute 'separation force' and locate the bifurcation.
  • domain assumption Logit Lens projection of intermediate hidden states via the unembedding matrix gives a faithful readout of the model's evolving distribution.
    Preliminaries; standard but unproven in this context.
  • domain assumption Questions that flip from wrong-before to right-after RLVR ('leakage') activate memorization, while questions right-before and right-after ('stable') reflect genuine reasoning.
    Section 4.1; the entire contrast is built on this labeling, which is itself the hypothesis under test.
  • ad hoc to paper The leakage and stable question sets are matched on difficulty, domain, and length so that activation contrasts isolate mechanism rather than content.
    Section 4.1 states matching but gives no procedure or verification.
invented entities (2)
  • Functional Anchor (L18-L20)
    purpose: Causal trigger that injects the memorized answer token into the residual stream.
    Defined by the paper's own path-patching peak and NDE separation force; no out-of-sample handle or prior independent measurement.
  • Structural Adapters (L21+)
    purpose: Reorganize representations to accommodate the anchor's injected signal.
    Label for layers with high JSD and velocity difference; they are a summary of the observed weight changes, not independently established components.

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Cite this review

Pith. "Pith review of Spurious Rewards Paradox: Mechanistically Understanding How RLVR Activates Memorization Shortcuts in LLMs." pith.science (2026). https://pith.science/paper/5BBE4O53

@misc{pith2026260111061,
  author       = {Pith},
  title        = {Pith review of: Spurious Rewards Paradox: Mechanistically Understanding How RLVR Activates Memorization Shortcuts in LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5BBE4O53}},
  note         = {Machine review of arXiv:2601.11061}
}
read the original abstract

Reinforcement Learning with Verifiable Rewards (RLVR) is highly effective for enhancing LLM reasoning, yet recent evidence shows models like Qwen 2.5 achieve significant gains even with spurious or incorrect rewards. We investigate this phenomenon and identify a "Perplexity Paradox": spurious RLVR triggers a divergence where answer-token perplexity drops while prompt-side coherence degrades, suggesting the model is bypassing reasoning in favor of memorization. Using Path Patching, Logit Lens, JSD analysis, and Neural Differential Equations, we uncover a hidden Anchor-Adapter circuit that facilitates this shortcut. We localize a Functional Anchor in the middle layers (L18-20) that triggers the retrieval of memorized solutions, followed by Structural Adapters in later layers (L21+) that transform representations to accommodate the shortcut signal. Finally, we demonstrate that scaling specific MLP keys within this circuit allows for bidirectional causal steering-artificially amplifying or suppressing contamination-driven performance. Our results provide a mechanistic roadmap for identifying and mitigating data contamination in RLVR-tuned models. Code is available at https://github.com/idwts/How-RLVR-Activates-Memorization-Shortcuts.

Figures

Figures reproduced from arXiv: 2601.11061 by the authors.

Figure 1
Figure 1. Left: Overall accuracy of four models on six benchmarks. Right: Dataset-selection rationale. Based on the accuracy gap, we retain MATH500, MinervaMath and LiveMathBench as our principal evaluation suites. Questions that are wrong before RLVR but correct after are treated as leaked and are the focus of subsequent mechanistic tests. ing datasets: AIME2024, AIME2025 (Li et al., 2024), MATH500 (Lightman et al., 2023), A… view at source ↗
Figure 2
Figure 2. Partial Prompt Evaluation for Qwen2.5-Math-7B. ROUGE-L scores (a) and completion accuracy (b) before (dashed) and after (solid) spurious RLVR. We analyze the “Wrong→Right” group (green), representing initially incorrect questions that be￾came correct post-RLVR. In contrast to MATH-500, LiveMath￾Bench shows no discernible improvement after RLVR, confirming its accuracy has no significant relationship with spurious RL… view at source ↗
Figure 3
Figure 3. Perplexity Analysis With Accuracy. Full-text (top) and answer-only (bottom) perplexity heatmaps. Heatmaps display full-text and answer-only perplexity across checkpoints (step 0, 50, 100, 150) under spurious RLVR with incorrect rewards. Percentage annotations under each block show base model accuracy and accuracy improvement after RL training [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: The Perplexity Paradox. While answer-only perplexity decreases (orange), full-text perplexity increases (blue), suggesting a trade-off between memorization and general language modeling capability. progressively as training proceeds, while full-text perplexity increase…
Figure 5
Figure 5. Figure 5: Path Patching Accuracy Recovery Comparison. Left: Qwen exhibits a sustained peak at L18–L20 (marking the final injection of the correct answer) followed by a sudden drop at L21 (revealing a critical feature space divergence). Right: LLaMA shows no comparable recovery p…
Figure 7
Figure 7. Figure 7: Logit Lens Analysis. (Top) In successful case, the Functional Anchor (L19) primes the stream, and after structural adaptation (L21-22), the MLP at L23 successfully injects the correct answer “4”. (Bottom) In the failure case, despite the MLP still attempting to inject …
Figure 8
Figure 8. Figure 8: Latent Space Trajectory (PCA Projection). The average trajectories of Leakage (red) and Generalization (blue) samples bifurcate significantly after the middle layers. directional influence to steer leakage samples onto the mem￾orization trajectory. Conversely, [PITH_F…
Figure 9
Figure 9. Figure 9: Ablation study results. Leakage samples from contaminated datasets exhibit higher sensitivity to layer manipulation than stable samples. The leakage-free LiveMathBench shows a different pattern, which are provided in Appendix E [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: NDE Dynamics Metrics. Left: Separation Force peaks at L18–L20, identifying the causal origin of trajectory divergence. Right: Velocity Difference increases in later layers, reflecting signal amplification by the Structural Adapter layers [PITH_FULL_IMAGE:figures/full…
Figure 11
Figure 11. Figure 11: Layer-wise Probing AUC. The distinguishability be￾tween leakage and stable samples peaks at Layer 20, corroborating the NDE and Path Patching results. Functional Anchor layers. Linear Probing Validation. As an independent validation, we train linear probes on each lay…
Figure 13
Figure 13. Figure 13: Dataset-Level Steering: Accuracy Change. (Left) On the leakage datasets, Layer 18 exhibits maximal sensitivity (±4%). (Right) On the leakage-free dataset, steering produces no systematic pattern, confirming that the intervention specifically targets contamination-depe…
Figure 14
Figure 14. Figure 14: Two Patterns of Sample-Level Steering Effects. Top: Gradual probability modulation in partially memorized samples. Bottom: Binary pathway activation in failed-retrieval samples, where amplification uniquely unlocks a dormant memorization circuit. (−3.8% under suppress…
Figure 15
Figure 15. Figure 15: Accuracy Comparison Across Models and Datasets. Qwen3-8B shows high baseline accuracy and dramatic improvement under spurious RLVR, while LLaMA-3.1-8B and OLMo-2-1124-7B remain at a low level performance regardless of training. This appendix provides the complete resu…
Figure 16
Figure 16. Figure 16: Qwen2.5-Math-7B Partial Prompt Results. The sharp rise in the ”Wrong→Right” group (green) on contaminated datasets signals the activation of memorized answers. (a) Qwen3-8B: ROUGE-L Scores (b) Qwen3-8B: Completion Accuracy [PITH_FULL_IMAGE:figures/full_fig_p014_16.png]
Figure 17
Figure 17. Figure 17: Qwen3-8B Partial Prompt Results. Qwen3-8B shows the expected increase in ROUGE-L and completion accuracy as prompt ratios increase, but the separation between pre- and post-RLVR is less pronounced compared to Qwen2.5-Math-7B, suggesting weaker memory activation under …
Figure 18
Figure 18. Figure 18: Control Models Partial Prompt Results. Neither LLaMA (top) nor OLMo (bottom) shows significant improvement in completion capability under spurious RLVR, confirming no memorization activation occurred. Note that for OLMo-2-1124-7B, there are no samples categorized as “…
Figure 19
Figure 19. Figure 19: Path Patching Recovery for Additional Models. (a) Consistent with LLaMA, OLMo does not display the middle-layer signal injection pattern observed in Qwen2.5-Math-7B. (b) Similarly, Qwen3-8B has a weaker contamination effects compared to Qwen2.5-Math-7B. C. Additional …
Figure 20
Figure 20. Figure 20: Layer-wise MLP Sub-component JSD Scores for Additional Models. (a) OLMo exhibits monotonic increase across all components, consistent with non-contaminated control models. (b) Qwen3-8B replicates the peak-and-decline pattern at Layer 33, confirming the generalizabilit…
Figure 21
Figure 21. Figure 21: Logit Lens Analysis for Control Models. Unlike Qwen2.5-Math, both LLaMA and OLMo show a flat probability trajectory where the answer token only emerges in the final layers. There is no evidence of intermediate MLP injection or leakage in the middle layers, regardless …
Figure 22
Figure 22. Figure 22: Additional Qwen2.5-Math Leakage Cases. Analysis of two additional samples from the contaminated set. Both examples replicate the distinct activation signature: strong signal priming at L18–L20, a transitional valley, and decisive answer token injection starting at Lay…
Figure 23
Figure 23. Figure 23: Logit Lens Analysis for Qwen3-8B. Consistent with Qwen2.5-Math-7B, Qwen3-8B exhibits a single decisive peak-valley-rise trajectory in successful retrieval (Left), while failed cases display oscillatory multi-peak patterns (Right), confirming that the singular peak sig…
Figure 24
Figure 24. Figure 24: Comprehensive Ablation Results. (Left) Overall accuracy trends show that Leakage samples (Top) are highly sensitive to Anchor/Adapter resetting, while Stable samples (Bottom) remain robust. (Right) Heatmaps of three datasets for different ablation conditions [PITH_FU…
Figure 25
Figure 25. Figure 25: Mechanistic intervention results across all 28 layers. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_25.png]

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.