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Robust Reward Modeling via Causal Rubrics

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Pith's one-line read Training a reward model on LLM-generated causal counterfactuals and tie-labeled neutral pairs makes it track genuine quality drivers and ignore unknown spurious attributes, improving RewardBench accuracy by up to 5.4% over baselines.

desk verdict A genuinely useful augmentation recipe for reward-model robustness, but the causal theory oversells its scope and the reproducibility is incomplete. read the letter →

arxiv 2506.16507 v1 pith:WNPNOAWM submitted 2025-06-19 cs.LG

classification cs.LG
keywords rewardhackingmodelrobustnesscounterfactualdataaugmentationspuriouscorrelationscausalattributesRLHFirrelevantqueryneutralsBench
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

Reward models used to align large language models with human feedback tend to reward superficial cues such as length and formatting, because standard preference training cannot separate those cues from genuine quality. Crome adds two kinds of synthetic training pairs: causal augmentations, where an oracle LLM rewrites an answer to upgrade or degrade a single quality attribute such as factuality, and neutral augmentations, where answer pairs are shown under an irrelevant query with a tie label. The paper claims this teaches a reward model sensitivity to true quality drivers and invariance to unknown spurious attributes, improving average RewardBench accuracy by up to 5.4% over baselines, with the largest gains in safety (up to 13.2%) and reasoning (up to 7.2%). If correct, Crome is a practical recipe for reducing reward hacking without knowing in advance which spurious features will be exploited.

What carries the argument

The load-bearing device is a causal graph in which the true reward $R^*$ depends only on the query $Q$ and causal attributes $C(A)$, while spurious attributes $SP(A)$ are unknown, high-dimensional, and merely correlated with preferences in the training data. Training combines a preference loss on original and causally augmented pairs (one attribute upgraded or degraded at a time, teaching sensitivity to each quality driver) with a neutral tie loss that forces the score difference toward zero on pairs shown under an irrelevant query, where the original causal signal is null and only spurious differences remain. This 'irrelevant query neutral' construction is what delivers invariance without ever naming or intervening on spurious factors; the composite objective is the preference loss plus $\lambda$ times the tie loss, with $\lambda = 1$ in the reported experiments.

What would settle it

Evaluate a Crome-trained model on a test set where a genuinely novel cosmetic feature (for example, a fixed decorative prefix appended to every chosen answer) has been injected to correlate with preference. If the preference-accuracy drop is as large for Crome as for a standard reward model, the claimed invariance to unknown spurious attributes fails. A complementary check is to randomly flip a fraction of the causal augmentation labels during training: if the RewardBench gains survive the scrambling, the causal-sensitivity mechanism is not what carries the result.

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Extended reading notes

Core claim

The paper's central claim is that a reward model trained on preference pairs plus LLM-written counterfactual pairs that differ along exactly one causal quality attribute, plus tie-labeled pairs of the same answers under an irrelevant query, learns to make its score depend on the stable causal attributes $C(A)$ and to be independent of the unknown, unstable spurious attributes $SP(A)$. The empirical statement is that Crome 'significantly outperforms standard baselines on RewardBench, improving average accuracy by up to 5.4% and achieving gains of up to 13.2% and 7.2% in specific categories,' with consistently smaller accuracy drops under meaning-preserving transformations on reWordBench and better Best-of-N selection across RewardBench, WildGuardTest, and GSM8K. A supporting theoretical result says that $\ell^1$-constrained regression on causally augmented examples recovers the true reward coefficients with error depending mainly on the number of causal attributes $k$ and the number of augmentations $m$, with only a logarithmic dependence on the spurious dimension $\ell$.

Load-bearing premise

Everything rests on the oracle LLM's rewrites being faithful counterfactuals, changing exactly the intended quality attribute while leaving all other attributes, especially causal content, intact, and the paper's own limitations section concedes that perfect attribute isolation in causal augmentations and complete causal content preservation in neutral pairs are not guaranteed.

Editorial extensions

If this is right

  • Models trained with Crome keep their edge under out-of-distribution transformations: aggregate reWordBench accuracy rises by up to 9.1% over baselines, and the accuracy drop from RewardBench to reWordBench is the smallest among compared methods.
  • Best-of-N selection with Crome beats selection with either baseline at every N tested, and on WildGuardTest it lowers the attack-success rate by up to about 2.7% at N=32 without increasing refusals of benign prompts.
  • Because no spurious attribute is ever specified or intervened upon, the recipe covers a far wider class of spurious cues than methods that target known biases like length or formatting.
  • The theoretical result implies the learned reward coefficients concentrate on causal drivers, with recovery error only logarithmic in the number of unknown spurious attributes, so the method does not need to know in advance what to be invariant to.
  • Gains reproduce across base models (Gemma-2-2B, Gemma-2-9B-IT, Qwen2.5-7B), both pairwise-preference and Bradley-Terry formulations, and with a weaker oracle LLM, indicating that the augmentation design rather than oracle strength drives the improvement.

Reading between the lines

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

  • The irrelevant-query neutral is the most transferable idea in the paper: it turns unknown spurious attributes into provably irrelevant ones by swapping the conditioning query, a trick that could apply beyond reward models to any classifier or embedding that must ignore style.
  • If the mechanism claim is right, Crome's advantage should widen as test-time spurious variation increases; an explicit stress test that scales the number of injected cosmetic cues and measures the accuracy-drop gap over baselines would sharpen this prediction.
  • The paper's own future-work sketch, using causal rubrics to generate synthetic data for base-model training, is the natural frontier: the same upgrade, degrade, and tie machinery would teach the quality attributes themselves rather than only a reward model's sensitivity to them.
  • The theory ties recovery error to the causal dimension $k$, which suggests a testable knob: shrinking the rubric from five attributes to fewer should measurably degrade robustness, matching the predicted trade-off.
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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

5 major / 5 minor

Summary. The paper proposes Crome, a data augmentation framework for training reward models against reward hacking. Crome prompts an oracle LLM (Gemini 2.0 Flash) to (i) identify five causal quality attributes for a query-answer pair; (ii) generate counterfactual upgraded/degraded answers intended to isolate one causal attribute (causal augmentations); and (iii) build tie-labeled neutral pairs by pairing answers with irrelevant queries (IQN) or by causally aligning answers (CAN). The RM is trained on original preferences plus filtered augmentations using a composite preference-plus-tie loss (Eq. 2). Empirical sections report RewardBench gains up to 5.4%, robustness gains on a reimplemented reWordBench, and Best-of-N improvements on RewardBench, WildGuardTest, and GSM8K. A theoretical section (Appendix I) analyzes an idealized boolean quadratic setting and claims that L1-constrained regression on causal augmentations recovers true causal coefficients with error depending weakly on the spurious dimension.

Significance. Conditional on the empirical claims and on the availability of reproducible artifacts, Crome would be a practically useful, spurious-factor-agnostic augmentation recipe for reward modeling: it requires no prior specification of spurious attributes, gives consistent gains across three base models and two RM formulations, includes multiple-run variance for the 9B model, and the paper is unusually honest about its limitations. The ablations comparing IQN, CAN, PARA, and causal-only variants and the oracle-LLM robustness check with Gemma-3-27B-IT are definite strengths. However, the central claim that augmentations isolate causal attributes and preserve causal content in neutrals rests on oracle counterfactual fidelity that is not independently verified, and the printed training loss in Eq. (2) appears to have the wrong sign for tie pairs. The robustness results additionally rely on a reimplemented benchmark, and the Best-of-N tables lack error bars. The current evidence therefore does not yet justify acceptance, although the identified issues appear fixable within the scope of the paper.

major comments (5)
  1. [§4.2, Eq. (2) and Appendix H.4 Eq. (3)] As printed, the neutral tie term has the wrong sign. The second term in Eq. (2) is -lambda * sum [ -1/2 (log sigma(Delta12) + log sigma(-Delta12)) ] = +lambda/2 * sum (log sigma(Delta12) + log sigma(-Delta12)). Since log sigma(Delta) <= 0, this term is negative and is minimized by making the tie pair's scores as different as possible, which is the opposite of the stated invariance objective. Appendix I.1 instead defines Ltie = -E[-1/2(log sigma + log sigma(-))] = 1/2 E(log sigma + log sigma(-)) and adds lambda * Ltie as a penalty, so the definition in Eq. (2) is internally inconsistent with the definition used in the theoretical section. Please fix the sign and confirm that all reported results were obtained with the intended tie loss, or correct the presentation and rerun affected experiments.
  2. [§3.3, Remark 1, Appendix A, Appendix K.6] The load-bearing premise is that LLM-generated counterfactuals modify exactly one causal attribute and that neutral rewrites preserve causal content. The paper itself states in Appendix A that "ensuring perfect attribute isolation in causal augmentations or complete causal content preservation in neutral pairs is challenging." The verification step in Appendix K.6 is an LLM-based evaluator, but the paper does not report whether the verifier is the same model as the generator, and it provides no human-annotated error rates or per-attribute off-target statistics. Without such an audit, off-target edits or imperfect neutrals could teach the reward model a mixture of attributes instead of the targeted one, and the observed gains could be attributable to extra training data or generic regularization. Please add an independent (human or differently-modeled) audit of a random sample of causal and neutral pairs, and report off-target rates per attribute and per neutral strategy.
  3. [Appendix I.2, Assumption 1.2 vs §3.2, Figure 19, Appendix G] The theoretical analysis assumes that all spurious variables are non-descendants of all causal variables (Assumption 1.2), so a causal intervention leaves Delta S_j = 0 for all spurious features. This is what produces the 4/k column-incoherence bound in Theorem 2. Yet Appendix G and Figure 19 explicitly model a subset SP2(A) of spurious attributes that co-move when causal attributes change, and the paper motivates IQN precisely as a way to provide invariance to SP2. The theorem therefore does not cover the mechanism that the paper identifies as central. Please extend the analysis to allow SP2 to be a descendant of C, or state explicitly that Theorem 2 applies only to the idealized case without SP2 and that the empirical SP2-related gains are supported only by experiments.
  4. [Appendix D, reWordBench reproduction; Figures 5-6] The reWordBench results are computed on the authors' independently reproduced version of the benchmark, not on the official release. The reproduction uses different generation models (e.g., gpt-4o for paraphrasing and back-translation) than those described for the original reWordBench, and the paper reports no per-transformation agreement analysis and does not release the reproduced data. Because the robustness claims in Figures 5, 6, and 9 hinge on this benchmark, please release the reimplementation and code, and if feasible compare a subset against the official reWordBench to establish comparability.
  5. [Table 3, Figures 7-8, Appendix C.1] The Best-of-N results are reported without error bars or statistical significance tests, even though the Gemma-2-9B setting admits multiple training runs as done for RewardBench in Table 5. The ASR reductions in Figure 7 range from about 0.3 to 2.7 percentage points, and the GSM8K gaps in Figure 8 are shown as point curves only. Without repeated Best-of-N runs or bootstrap confidence intervals, the claim of "consistent gains across increasing N" in the abstract and Section 6.2 is not fully supported. Please report means and variances over at least three seeds for the BoN evaluations, or provide intervals on the win-rate tables.
minor comments (5)
  1. [Abstract and §1] The abstract states average accuracy gains "up to 5.4%" and Safety/Reasoning gains of 13.2%/7.2%, while the introduction says "up to 4.5%" with substantial Safety and Reasoning gains. These should be aligned with the numbers in Table 2.
  2. [§4.2 and Appendix H.3] The loss hyperparameter lambda is fixed at 1 and the filtering threshold tau is fixed at 0.2, with no sensitivity analysis. Since the tie loss is the mechanism for spurious invariance, please report at least a small sweep over lambda and tau, or state why these values are robust.
  3. [Appendix J] The qualitative example contains stray newlines, misrendered JSON, and irregular indentation (e.g., the causal elements block and the chosen-response edits block). Please format this appendix as clean code blocks so that the example is readable.
  4. [Appendix E.5] Typo: "mdoels" should be "models" in the sentence describing base transformer architectures.
  5. [Figure 2 caption] The caption states "dim(C(A)) << dim(SP(A)) for all A" but does not define the dimension of an attribute set; please clarify whether this refers to the number of attributes or to a latent dimension of the attribute representation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are empirical comparisons on external benchmarks, and the theoretical analysis is an explicitly idealized model whose assumptions do not restate the target result.

full rationale

The paper's load-bearing claim is that training a reward model on LLM-generated causal and neutral augmentations yields better RewardBench, reWordBench, and Best-of-N results than baselines. This is an empirical claim evaluated on external benchmarks (RewardBench, reWordBench, GSM8K, WildGuardTest), not a quantity that is definitionally equal to the augmentation labels. The augmentation pipeline (Section 4.1 and Appendix H) uses an oracle LLM to identify attributes, generate counterfactual upgrades/degradations, and create tie-labeled irrelevant-query neutrals; the resulting supervision is then used to train the RM, but the reported accuracy numbers are measured on held-out benchmark data. No equation in the paper defines the benchmark accuracy as a function of the training labels, and no fitted parameter is renamed as a prediction. The theoretical result in Appendix I is an idealized recovery bound proved under explicit assumptions (Boolean causal and spurious attributes, sparse quadratic true reward, spurious attributes not descendants of causal attributes, ideal single-attribute counterfactual interventions). Those assumptions do not include the conclusion; they define a stylized setting in which the proof is carried out. The paper also explicitly acknowledges the gap between the idealization and practice in Appendix A: 'ensuring perfect attribute isolation in causal augmentations or complete causal content preservation in neutral pairs is challenging.' That is a validity/fidelity limitation, not a circularity. Self-citations are not load-bearing: the only notable overlap is a contextual reference to Carmo (Gupta et al., 2025), which shares an author but is used for positioning, not as the justification of Crome's correctness. There is no uniqueness theorem imported from the authors' prior work and no ansatz smuggled in via citation. Therefore the derivation chain is self-contained in the relevant sense, and the correct finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

Crome introduces no new physical or architectural entities; the key constructs (causal attributes, spurious attributes, IQN) are methodological labels over existing text. The load-bearing assumptions are the domain assumptions above and the reliability of the oracle LLM, which the paper itself flags as imperfect.

free parameters (4)
  • neutral loss weight lambda = 1
    Set by hand; main text says lambda=1 while Appendix H.4 says it is tuned on a validation set, an internal inconsistency.
  • baseline confidence filter threshold tau = 0.2
    Pairs are kept only if the baseline RM's probability deviates from the target label by more than 0.2; chosen without reported sensitivity analysis.
  • number of causal attributes l = 5
    Oracle LLM is prompted to output exactly five attributes per query, with importance scores summing to 1.
  • augmentation amplification factor = 10x causal, 1x neutral
    Approximately 10x causal pairs (5 attributes x 2 versions) and 1x neutral pairs are generated per original response, with no ablation of these ratios.
assumptions (5)
  • domain assumption True reward R*(Q,A)=f*(Q,C(A)) depends only on causal attributes; R* is independent of SP(A) given Q and C(A).
    Section 3.2, Figure 2. The entire method's objective (sensitive to C, invariant to SP) is only meaningful under this premise.
  • domain assumption The relationship (Q,C(A)) to R* is stable across labelers and answer generators, while correlations involving SP(A) are unstable.
    Section 3.2, stability property. Justifies why invariance to SP is desirable; if SP correlations were stable, ignoring them could discard useful signal.
  • ad hoc to paper Oracle LLM (Gemini 2.0 Flash) identifies reliable causal attributes and generates counterfactuals that modify only the targeted attribute.
    Section 3.3 and 4.1; acknowledged as imperfect in Appendix A. The training signal quality depends on this.
  • domain assumption For an irrelevant query Q_irrelevant, C(B1|Q_irrelevant) is approximately equal to C(B2|Q_irrelevant), approximately 0, so answer differences are spurious.
    Section 3.4.2 (IQN). If the irrelevant query still activates causal differences, the tie label may be wrong.
  • standard math Theoretical analysis assumes boolean attributes, sparse quadratic reward, spurious variables non-descendants of causal variables, and ideal single-attribute interventions.
    Appendix I, Assumptions 1-2 and Theorem 2. These are explicitly stated idealized tractability assumptions.

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Cite this review

Pith. "Pith review of Robust Reward Modeling via Causal Rubrics." pith.science (2026). https://pith.science/paper/WNPNOAWM

@misc{pith2026250616507,
  author       = {Pith},
  title        = {Pith review of: Robust Reward Modeling via Causal Rubrics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WNPNOAWM}},
  note         = {Machine review of arXiv:2506.16507}
}
read the original abstract

Reward models (RMs) are fundamental to aligning Large Language Models (LLMs) via human feedback, yet they often suffer from reward hacking. They tend to latch on to superficial or spurious attributes, such as response length or formatting, mistaking these cues learned from correlations in training data for the true causal drivers of quality (e.g., factuality, relevance). This occurs because standard training objectives struggle to disentangle these factors, leading to brittle RMs and misaligned policies. We introduce Crome (Causally Robust Reward Modeling), a novel framework grounded in an explicit causal model designed to mitigate reward hacking. Crome employs the following synthetic targeted augmentations during training: (1) Causal Augmentations, which are pairs that differ along specific causal attributes, to enforce sensitivity along each causal attribute individually, and (2) Neutral Augmentations, which are tie-label pairs varying primarily in spurious attributes, to enforce invariance along spurious attributes. Notably, our augmentations are produced without any knowledge of spurious factors, via answer interventions only along causal rubrics, that are identified by querying an oracle LLM. Empirically, Crome significantly outperforms standard baselines on RewardBench, improving average accuracy by up to 5.4% and achieving gains of up to 13.2% and 7.2% in specific categories. The robustness of Crome is further testified by the consistent gains obtained in a Best-of-N inference setting across increasing N, across various benchmarks, including the popular RewardBench (covering chat, chat-hard, safety, and reasoning tasks), the safety-focused WildGuardTest, and the reasoning-specific GSM8k.

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · cited by 1 Pith paper

  1. [1]

    and true is true

    Controlled Transformations: These are template-based edits that guarantee semantic equivalence by construction. They include: a. Add Quotes: Surrounding the entire prompt and responses with a fixed number of quotation marks. b. Punctuation Spaces: Inserting spaces around each punctuation mark. c. Twitter Handle/URL: Appending a randomly generated (harmles...

  2. [2]

    gpt-4o-2024-08-06

    use data augmentation for robustness andCromeis distinguished by its explicit grounding in a causal graph model of answer attributes. It systematically generates attribute-specific counterfactual and neutral examples via guided LLM prompting to directly train the RM to distinguish causal quality drivers (𝐶) from spurious correlates (𝑆𝑃). This allowsCromet...

  3. [3]

    minifying

    Domain-Targeted Transformations: These focus on specialized subsets of RewardBench—code, mathematics, and safety prompts—where specific artifacts may bias reward models: a. Code Minification: Automatically renaming variables, removing whitespace, and otherwise “minifying” Python snippets without changing functionality. b. Add Comment: Inserting “# bad” an...

  4. [4]

    in the wild

    Naturalistic Transformations: These simulate the kinds of noise and variation that occur “in the wild” and may not perfectly preserve meaning, but reflect realistic robustness challenges: a. Paraphrase: Rewriting prompt and response via a strong LLM (Llama-3-70B-instruct) under a paraphrasing instruction. b. Back-translation: Translating English→Spanish→E...

  5. [5]

    c a u s a l _ e l e m e n t s

    Δ𝐶𝑖,𝑗 Δ𝐶𝑖𝑆𝑗 = 0with probability1 − 1/𝑘. 6) Δ𝐶𝑖,𝑖′ Δ𝐶𝑗𝑆𝑘 = 0always if all four indices not equal. 7) Δ𝐶𝑖Δ𝐶𝑗𝑆𝑘 =0always. 8)Δ𝐶 𝑖Δ𝐶𝑖𝑆𝑘 =0with probability 1-1/k. If any of the these products is non zero, conditioned on that event, they equal the correlation on the preference training dataset (every correlation between features is bounded by at most4). Therefor...

  6. [6]

    Were there any specific aspects of the visual design that you particularly liked or disliked? (Open-ended text response)

  7. [7]

    ABase RM, trained solely on the originalDpref

  8. [8]

    non-contextuals

    TheRRM Baseline(Liu et al., 2024), which employs a distinct augmentation strategy using non- contextual examples and responses from different queries, not specifically aligned with identified causal or spurious attributes. Evaluation Benchmarks:RM quality is assessed by accuracy onRewardBench(Lambert et al., 2024) (overall and per category: Chat, Chat-Har...

Show all 50 references
  1. [9]

    The pair(A, ˜A(𝑆𝑃←𝑠𝑝′)) is labeled as a tie

    Direct Spurious Feature Perturbation (e.g., Paraphrasing, Formatting Changes):This involves taking an answerAand generating ˜A(𝑆𝑃←𝑠𝑝′) by applying meaning-preserving transformations (e.g., paraphrasing) intended to alter onlySP(A) while preservingC(A). The pair(A, ˜A(𝑆𝑃←𝑠𝑝′)) ...

  2. [10]

    spurious

    Rewrites of Rewrites (e.g., RATE (Reber et al., 2024)):RATE uses sequential rewrites for robust causal effect estimation. Adapted for augmentation, multiple causally-equivalent rewrites of an answer could form neutral pairs. Challenges with these General Methods: • Unknown/Uns...

  3. [11]

    Irrelevant Query Neutrals (IQN):Cromegenerates these neutral pairs efficiently by leveraging its existing pool of answers (original or causally augmented). Given two answers,B1 andB 2, that were 33 Robust Reward Modeling via Causal Rubrics generated or selected for a specific ...

  4. [12]

    off-target attributes

    Causally-Aligned Neutrals (CAN):This method directly leverages the original preference pairs or the outputs of causal augmentation. • Given an original preference pair fromDpref, say(A1, A2) whereA 1≻ A2, we generate˜A(𝐶←𝐶(𝐴 1)) 2 by rewritingA 2 to match the causal attribute ...

  5. [13]

    Causal attributes{𝐶𝑖(𝑄,𝐴)} 𝑘 𝑖=1 and spurious attributes{𝑆𝑗(𝐴)} ℓ 𝑗=1 are all boolean variables taking values in{+1,−1}

  6. [14]

    All spurious variables are non-descendants of all causal variables

  7. [15]

    ˆ𝑅= ∑︁ 𝑖 𝛼𝑖𝐶𝑖(𝑄,𝐴)+ ∑︁ 𝑗 𝛽𝑗𝑆𝑗(𝐴)+ ∑︁ 𝑖≠𝑖′ 𝛼𝑖,𝑖′𝐶𝑖(𝑄,𝐴)𝐶 𝑖′(𝑄,𝐴)+ ∑︁ 𝑗≠𝑗′ 𝛽𝑗,𝑗′𝑆𝑗(𝐴)𝑆 𝑗′(𝐴)+ ∑︁ 𝑖≠𝑗 𝛾𝑖,𝑗𝐶𝑖(𝑄,𝐴)𝑆 𝑗(𝐴).(4)

    Reward function is trying to fit a quadratic polynomial in causal and spurious attributes, i.e. ˆ𝑅= ∑︁ 𝑖 𝛼𝑖𝐶𝑖(𝑄,𝐴)+ ∑︁ 𝑗 𝛽𝑗𝑆𝑗(𝐴)+ ∑︁ 𝑖≠𝑖′ 𝛼𝑖,𝑖′𝐶𝑖(𝑄,𝐴)𝐶 𝑖′(𝑄,𝐴)+ ∑︁ 𝑗≠𝑗′ 𝛽𝑗,𝑗′𝑆𝑗(𝐴)𝑆 𝑗′(𝐴)+ ∑︁ 𝑖≠𝑗 𝛾𝑖,𝑗𝐶𝑖(𝑄,𝐴)𝑆 𝑗(𝐴).(4)

  8. [16]

    𝑅∗ = ∑︁ 𝑖 𝜃𝑖𝐶𝑖(𝑄,𝐴)+ ∑︁ 𝑖≠𝑖′ 𝜃𝑖,𝑖′𝐶𝑖(𝑄,𝐴)𝐶 𝑖′(𝑄,𝐴)(5) Here,∥𝜃∥ 0≤𝑠 << 𝑘2 and 𝜃𝑖 and 𝜃𝑖,𝑖′ variables form the vector𝜃

    Assume that the true reward function is a sparse quadratic polynomial depend on only the causal attributes. 𝑅∗ = ∑︁ 𝑖 𝜃𝑖𝐶𝑖(𝑄,𝐴)+ ∑︁ 𝑖≠𝑖′ 𝜃𝑖,𝑖′𝐶𝑖(𝑄,𝐴)𝐶 𝑖′(𝑄,𝐴)(5) Here,∥𝜃∥ 0≤𝑠 << 𝑘2 and 𝜃𝑖 and 𝜃𝑖,𝑖′ variables form the vector𝜃. All other coefficients for other features that invo...

  9. [17]

    Consider two types of triplets, one drawn from the natural distribution of the preference training dataset 𝐷pref and the others drawn from augmented distribution𝐷aug

    be the boolean vector with features {Δ𝐶𝑖},{Δ𝑆 𝑗},{Δ𝐶 𝑖,𝑖′},{Δ𝑆 𝑗,𝑗′},{Δ(𝐶 𝑖𝑆𝑗)}stacked row wise for the triplet𝑞,𝑎1,𝑎 2. Consider two types of triplets, one drawn from the natural distribution of the preference training dataset 𝐷pref and the others drawn from augmented distrib...

  10. [18]

    Let us assume that we have𝑚 augmentations where a triplet is randomly sampled from the training preference data distributionDpref and then augmented using the above counterfactual with a randomly chosen causal attribute negated. 38 Robust Reward Modeling via Causal Rubrics Rem...

  11. [19]

    This occurs with probability1− 1/𝑘

    Δ𝐶𝑖 = 0if is 𝐶𝑖 is not intervened. This occurs with probability1− 1/𝑘. 2) Δ𝐶𝑖Δ𝐶𝑗 = 0with probability 1− 2/𝑘. 3) Δ𝐶𝑖,𝑖′ Δ𝐶𝑗,𝑗′ = 0if all 𝑖,𝑖′, 𝑗, 𝑗′ are distinct indices. 4)Δ𝐶𝑖,𝑗 Δ𝐶𝑗,𝑘 = 0, with probability1− 1/𝑘

  12. [23]

    Ensure that the improvement is **significant but isolated** to {ATTRIBUTE} leaving the other attributes intact

    **Improve the Response:** Modify the causal elements to significantly improve {ATTRIBUTE}. Ensure that the improvement is **significant but isolated** to {ATTRIBUTE} leaving the other attributes intact

  13. [24]

    Confirm that all **other attributes remain unchanged**

    **Verify the New Response:** Reassess whether {ATTRIBUTE} has been significantly im- proved. Confirm that all **other attributes remain unchanged**. If necessary, improve the response further to better meet the improvement goal for {ATTRIBUTE}

  14. [25]

    Format your response according to the format given below and in no other format

    **Return the New Response:** Provide the final modified response with a significantly improved {ATTRIBUTE} score. Format your response according to the format given below and in no other format. 52 Robust Reward Modeling via Causal Rubrics ### **Output Format:** Chain of Thoug...

  15. [26]

    **Understand the Context:** Carefully read the question and original response and ex- amine the provided causal elements that influence {ATTRIBUTE}

  16. [27]

    **Identify the strength of {ATTRIBUTE}:** Determine which causal elements are **present** and their **direction of effect** (i.e., whether they increase or decrease {ATTRIBUTE})

  17. [28]

    Ensure that the degradation is **significant but isolated** to {ATTRIBUTE} leaving the other attributes intact

    **Degrade the Response:** Distort the causal elements to significantly degrade {ATTRIBUTE}. Ensure that the degradation is **significant but isolated** to {ATTRIBUTE} leaving the other attributes intact

  18. [29]

    Confirm that all **other attributes remain unchanged**

    **Verify the New Response:** Reassess whether {ATTRIBUTE} has been significantly de- graded. Confirm that all **other attributes remain unchanged**. If necessary, degrade the response 53 Robust Reward Modeling via Causal Rubrics further to better meet the degradation goal for ...

  19. [30]

    question

    **Return the New Response:** Provide the final modified response with a significantly degraded {ATTRIBUTE} score. Format your response according to the format given below and in no other format. ### **Output Format:** Chain of Thoughts: <Your analysis of the original response,...

  20. [31]

    Final Response

    Do not introduce changes beyond the specified elements. 5. Ensure the new response fully reflects the target causal profile across all attributes. Output Format: {{ "Final Response": "<Write the transformed response here>" }} Return only the final response JSON. Do not include...

  21. [33]

    Ensure Significant Degradation: Confirm that {ATTRIBUTE} is noticeably weakened, not subtly reduced

  22. [34]

    Check for Unintended Changes: Verify that the degradation is done by distorting the causal elements for {ATTRIBUTE} alone while keeping the other attributes unaffected

  23. [35]

    *Strictly* adhere to the provided format

    Determine Verdict: If only {ATTRIBUTE} is degraded significantly while all else remains unchanged, return **Pass**; otherwise, return **Fail**. *Strictly* adhere to the provided format. ### Output Format - If the modified response meets all requirements, return: Verdict: Pass ...

  24. [36]

    Identify Changes: Compare the original and modified responses to determine which causal elements were altered

  25. [37]

    Ensure Significant Improvement: Confirm that {ATTRIBUTE} is noticeably improved, not subtly improved

  26. [38]

    58 Robust Reward Modeling via Causal Rubrics

    Check for Unintended Changes: Verify that the improvement is done by modifying the causal elements for {ATTRIBUTE} alone while keeping the other attributes unaffected. 58 Robust Reward Modeling via Causal Rubrics

  27. [39]

    i n s t r u c t i o n

    Determine Verdict: If only {ATTRIBUTE} is improved significantly while all else remains unchanged, return **Pass**; otherwise, return **Fail**. *Strictly* adhere to the provided format. ### Output Format - If the modified response meets all requirements, return: Verdict: Pass ...

  28. [40]

    Overall, how would you rate your experience with the user interface? (Scale of 1-5, with 1 being poor and 5 being excellent)

  29. [41]

    Which specific features of the user interface did you find most useful or intuitive? (Open-ended text response)

  30. [42]

    (Open-ended text response)

    Were there any features of the user interface that you found confusing or difficult to use? If yes, please provide details. (Open-ended text response)

  31. [43]

    (Open-ended text response)

    Did you encounter any technical issues or bugs while using the user interface? If yes, please describe the issue(s) you faced. (Open-ended text response)

  32. [44]

    How would you rate the visual design and aesthetics of the user interface? (Scale of 1-5, with 1 being poor and 5 being excellent)

  33. [46]

    Did you find the user interface responsive and fast? (Yes/No)

  34. [47]

    (Open-ended text response)

    Were there any specific areas where you experienced slow loading times or delays? If yes, please specify. (Open-ended text response)

  35. [48]

    How would you rate the organization and layout of the user interface? (Scale of 1-5, with 1 being poor and 5 being excellent)

  36. [49]

    (Open-ended text response)

    Were there any specific areas where you felt the organization or layout could be improved? If yes, please provide details. (Open-ended text response)

  37. [50]

    Did you find the user interface easy to navigate and find what you were looking for? (Yes/No)

  38. [51]

    (Open-ended text response)

    Were there any specific areas where you had difficulty navigating or finding information? If yes, please specify. (Open-ended text response)

  39. [52]

    How likely are you to recommend the user interface to others? (Scale of 1-5, with 1 being not likely at all and 5 being very likely)

  40. [53]

    Sure!",

    Do you have any additional comments or suggestions for improving the user interface? (Open-ended text response) Thank you for taking the time to provide your feedback! Remarks The rejected response fails to follow the instruction (provide a single question) and instead provide...

  41. [2024]

    rewrites of rewrites

    or process supervision (Khalifa et al., 2025). Significant effort focuses on improving specific RM 21 Robust Reward Modeling via Causal Rubrics properties like calibration (Zhao et al., 2023; Zhu et al., 2025), training efficiency (Tunstall et al., 2023), uncertainty quantific...

  42. [2025]

    We useGemma-2-9B-IT as the base model and sample N responses for each prompt in this set

    and use all 2985 prompts from RewardBench (Lambert et al., 2024). We useGemma-2-9B-IT as the base model and sample N responses for each prompt in this set. Following this, we use the PairPM reward models (RM, RRM andCrome) to select the best response among the N responses, as ...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.