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REVIEW 5 major objections 5 minor 59 references

GRAIT: Gradient-Driven Refusal-Aware Instruction Tuning for Effective Hallucination Mitigation

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

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Pith's one-line read This paper claims that gradient-driven sample selection and adaptive weighting of refusal samples during instruction tuning reduces hallucinations while curbing over-refusal, outperforming prior refusal-aware tuning methods.

desk verdict GRAIT has a plausible gradient-based data-selection idea and positive in-domain numbers, but the theoretical derivation for the over-refusal weighting rests on a false assumption about cross-entropy, and the experiments lack error bars and have an unresolved OOD contradiction. read the letter →

arxiv 2502.05911 v1 pith:TBEAAFIA submitted 2025-02-09 cs.CL

Runchuan Zhu , Zinco Jiang , Jiang Wu , Zhipeng Ma , Jiahe Song , Fengshuo Bai , Dahua Lin , Lijun Wu
show 1 more author
Conghui He
This is my paper · ORCID
classification cs.CL
keywords refusal-awareinstructiontuninghallucinationmitigationover-refusalgradientinfluencedataselectionsampleweightinglargelanguagemodelstruthfulness-helpfulnesstradeoff
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

Refusal-aware instruction tuning trains LLMs to answer "I don't know" when a question falls outside their knowledge, but tuned models tend to refuse questions they could answer correctly. This paper proposes GRAIT, a framework that uses gradient information to pick which "unknown" training samples to keep and how much to weight each one during fine-tuning. The claim is that this gradient-driven selection and weighting reduces hallucination rates while keeping accuracy higher than existing refusal-tuning methods. If right, it gives a practical recipe for making LLMs more honest about their limits without losing helpfulness.

What carries the argument

The load-bearing machinery is the first-order influence formula $I(x_o, y_o, x_u, y_u; \theta) = \eta_t \langle \nabla L(x_o, y_o; \theta), \nabla L(x_u, y_u; \theta) \rangle$, which approximates how much training on one sample changes the loss on another. From it the paper derives two selection and weighting signals: the refusal influence $I_{\mathrm{ref}}(x)$, an inner product of a sample's gradient with the mean idk gradient, used to distill the idk set; and the stable influence $I_{\mathrm{sta}}(x)$, an inner product with the difference between the mean idk and mean ik-with-refusal-label gradients, exponentiated and normalized into a weight $\omega(x)$ for the idk loss during SFT. The derivation of $I_{\mathrm{sta}}$ relies on the symmetric-loss assumption that for an I-know input, the loss change under the correct label is approximately the negative of the loss change under the refusal label, which converts the over-refusal term into a difference of gradient inner products.

What would settle it

Measure, for the training samples the model answers correctly, the actual sign and magnitude of $\Delta L(x_{\mathrm{ik}}, y_{\mathrm{ik}}) + \Delta L(x_{\mathrm{ik}}, y_{\mathrm{idk}})$ after a single gradient step; if the sum is not near zero for the samples whose stable influence drives large weights, the derivation of the over-refusal correction fails. One could also train with the stable-influence weights negated: if over-refusal is still reduced, the mechanism is not the claimed one.

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Extended reading notes

Core claim

The paper's central claim is that the two goals of refusal-aware tuning—reducing wrong answers (C1) and avoiding over-refusal (C2)—can both be expressed in terms of gradient inner products, and that optimizing these expressions yields better results than prior RAIT methods. For C1, it derives that the expected loss reduction on unknown test samples is approximately the negative of the refusal influence $I_{\mathrm{ref}}(x) = \langle \nabla L(x;\theta), \mathbb{E}_{x_o \sim D_{\mathrm{idk}}}[\nabla L(x_o, y_{\mathrm{idk}};\theta)] \rangle$, so the idk training samples most parallel to the average idk gradient are the ones worth keeping. For C2, using a symmetric-loss assumption, it rewrites the over-refusal term as a difference of two influences and defines the stable influence $I_{\mathrm{sta}}(x) = \langle \nabla L(x;\theta), \mathbb{E}[\nabla L(\mathrm{idk};y_{\mathrm{idk}})] - \mathbb{E}[\nabla L(\mathrm{ik};y_{\mathrm{idk}})] \rangle$, which becomes a softmax weight $\omega(x)$ applied to the idk loss during SFT. The paper reports that on MMLU, ARC-c, TriviaQA, and NQ, GRAIT surpasses baselines including R-Tuning and CRaFT on the Truthful Helpfulness Score, e.g., 36.4 versus 34.0 on MMLU with LLaMA3-8B-Instruct.

Load-bearing premise

The whole over-refusal correction rests on the assumption that, for an answerable question, the effect of training the correct answer on the loss is roughly the exact opposite of the effect of training an 'I don't know' response—an equality that is not guaranteed for the loss function used.

Editorial extensions

If this is right

  • Using fewer idk samples selected by refusal influence reaches comparable or better hallucination reduction than training on the full refusal set.
  • Weighting idk samples by stable influence reduces over-refusal without increasing the hallucination rate, compared to unweighted refusal-aware tuning.
  • The method transfers out-of-domain: on ARC-c with LLaMA3-8B-Instruct, GRAIT reaches a Truthful Helpfulness Score of 34.3 versus 21.4 for CRaFT.
  • Selecting the ik samples with the highest correctness (ik-top strategy) preserves accuracy by keeping the two supervision signals well separated.
  • Gradient-based influence selection makes the data-construction step computationally cheaper because it requires only gradient computations on candidate samples rather than repeated retraining.

Reading between the lines

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

  • The symmetric-loss assumption could be replaced by a measured, per-sample correction factor, turning the stable-influence weight from a heuristic into a calibrated quantity; this is testable without changing the rest of the pipeline.
  • The same gradient-influence view could be used to decide not just how much to weight refusals, but when to update the refusal data during training, since the gradient directions change as the model learns.
  • The near-orthogonality of ik and idk gradients (reported as an inner product of 0.008 versus 0.513 for idk with itself) suggests the two supervision signals update largely separate parameter regions; if that holds, curriculum or adversarial schedules could exploit the separation more directly.
  • Applying the selection to a continuously updated knowledge boundary could turn GRAIT into an online detector of what the model knows, beyond the current one-shot split.
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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 GRAIT, a refusal-aware instruction tuning framework with two components: (1) gradient-based selection of 'I don't know' (idk) samples using a Refusal Influence score, and (2) adaptive weighting of idk samples during SFT using a Stable Influence score intended to reduce over-refusal. The method is motivated by two theoretical observations O1 and O2, derived from first-order Taylor expansions of the loss, and is evaluated on MMLU/ARC-c and TriviaQA/NQ with LLaMA2-7B-Chat and LLaMA3-8B-Instruct, comparing against several baselines including R-Tuning and CRaFT. The paper includes ablations, sensitivity analyses, and a correlation analysis between the two influence terms.

Significance. If the empirical results hold, GRAIT is a useful and practical method for data distillation and reweighting in refusal-aware instruction tuning, and the attempt to ground sample selection in gradient influence is a worthwhile direction. The paper provides ablations, sensitivity studies, and a clear three-stage workflow, and it commits to releasing code and data. However, the main theoretical derivation for the over-refusal component (O2) rests on an invalid assumption about the loss function, and the experiments are single-run with no measures of uncertainty. The significance of the paper is therefore contingent on either repairing the derivation or reframing the weighting mechanism as an empirically motivated heuristic.

major comments (5)
  1. [Appendix A.1.2, Eq. (14)] The symmetric-loss assumption Delta L(x_ik; y_ik) approximately equals -Delta L(x_ik; y_idk) is not valid for the next-token cross-entropy loss used in Eq. (11). For a single token, Delta L(y) = log p0(y) - log p(y), so the assumption requires p(y_ik)p(y_idk) approximately equals p0(y_ik)p0(y_idk). Nothing in cross-entropy guarantees this, and simple counterexamples (e.g., p0=(0.5,0.5), p=(0.1,0.9)) show that the two loss changes are not opposite in sign. Since Eq. (14) is the basis for Stable Influence (Eq. 9) and the weights in Eqs. (10)-(11), the claimed C2 mechanism is not actually derived. The paper provides no empirical check of this assumption; Figure 5 reports a correlation between I_ref and an undefined I_over, not a check of the loss symmetry.
  2. [Algorithm 1, lines 4 and 7] The implementation of Stable Influence appears inconsistent with Eq. (9). The definition in Eq. (9) requires the gradient E_{xo in D_ik}[nabla L(xo_ik, y_idk; theta)], i.e., the gradient of the refusal label on correct inputs. In Algorithm 1, line 4 computes gidk(Dik) as the average of x.gidk over Dik, but the paper does not specify whether x.gidk for Dik samples is the gradient with their correct label y_ik or with the refusal label y_idk. If it is the former, the implemented weight does not correspond to the derived Ista; if it is the latter, this must be stated explicitly because it is not the standard forward pass for Dik samples. This ambiguity is load-bearing for the O2 contribution.
  3. [Section 6.2, Table 2] All results are single runs with no standard errors, confidence intervals, or significance tests. The text repeatedly claims that GRAIT 'significantly' outperforms baselines (e.g., Section 6.2.1), but with one run per cell there is no statistical basis for this claim. This is particularly problematic where the differences are small (e.g., MMLU THS 20.1 vs. 20.0 for w/o O2 on LLaMA2-7B-Chat; TriviaQA Pw 18.3 vs. 18.3 for full GRAIT and w/o O2 on LLaMA3-8B-Instruct). The authors should report multiple seeds and error bars, or at least temper the word 'significantly'.
  4. [Section 6.2.1, Table 2, NQ row] The claim that GRAIT 'consistently demonstrates superior performance on OOD datasets' is not supported by the NQ results for LLaMA2-7B-Chat: GRAIT achieves THS 0.0, while CRaFT achieves 1.5. Additionally, the statement that 'GRAIT surpasses existing methods in THS score with an average of 3.66' is not defined; it is unclear which average or comparison this number refers to, and it cannot be directly derived from the table.
  5. [Eq. (14), second-to-last line] Even setting aside the symmetric-loss assumption, the derivation of Eq. (14) contains an unjustified approximation step. After replacing E_{ik}[Delta L(xu_ik, yu_ik)] with -E_{ik}[Delta L(xu_ik, yu_idk)], the combined expression is expanded as an inner product between the difference (E_idk[g_idk] - E_ik[g_ik_idk]) and the sum (E_idk[g_idk] + E_ik[g_ik]). The final line keeps only the E_idk[g_idk] part of the second factor. Dropping the E_ik[g_ik] cross-terms is not justified by Assumption 2, which only asserts orthogonality between E_idk[g_idk] and E_ik[g_ik]; the needed orthogonality between E_ik[g_ik_idk] and either E_idk[g_idk] or E_ik[g_ik] is neither stated nor empirically verified.
minor comments (5)
  1. [Eq. (12)] The THS definition is under-specified: the point U in the denominator is not defined, and the sign convention for claiming that a point is 'above' or 'below' the line OS1 is not formalized. Please clarify the geometric construction and the range of THS.
  2. [Appendix A.1.2, Eq. (14)] There is an apparent typo in the intermediate line: the first factor changes from E_ik[nabla L(xu_ik, yu_ik)] to E_ik[nabla L(xu_ik, yu_idk)] without comment. The derivation should be corrected for readability.
  3. [Section 3, Definition 1] The notation in Definition 1 has a typo: 'xik is the unknown question' should presumably read 'xidk is the unknown question'. Please correct.
  4. [Section 6.3, Figure 5] The variable I_over is referenced in the figure caption and in the text but is never formally defined. Please define it explicitly or remove the reference.
  5. [Section 6.1, Appendix A.6] The sensitivity experiments in Tables 10 and 11 report only THS values. Since the weighting mechanism is specifically designed to control over-refusal, reporting Pc and Pw (or at least the refusal rate) for these sensitivity runs would be more informative.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: GRAIT's gradient influence scores are derived from a first-order Taylor model and validated on held-out external benchmarks; the only self-citation (CRaFT baseline, THS metric) is evaluative, not a premise.

full rationale

Walking the derivation chain: Eq. (1) defines influence as η⟨∇L(x_o),∇L(x_u)⟩ from a first-order Taylor/SGD update; Eq. (4) and App. A.1.1 express the expected idk test-loss change as negative expected influence, giving the Refusal Influence score I_ref = ⟨∇L(x), E_{D_idk}∇L⟩ used in Eqs. (6)-(7). Eq. (5) and App. A.1.2 split the total objective into an idk self-influence term and a cross idk→ik influence term, motivating Stable Influence I_sta in Eq. (9) and the softmax weights in Eq. (10). These are mathematical approximations of the same loss being optimized, not fitted parameters renamed as predictions. The reported claims are benchmarked on distinct held-out splits (MMLU-val, ARC-c, TriviaQA-dev, NQ) against external baselines; no target-metric value is used to construct I_ref or I_sta. The only self-referential elements are the CRaFT baseline and THS metric from Zhu et al. (2024), whose authors overlap with the present paper; these are used as evaluative tools, not as load-bearing premises of the derivation. The symmetric-loss assumption in App. A.1.2 is a stated approximation and is a correctness/validity risk rather than a circular step. Accordingly, no circular step is identified; score 2 reflects only the mild, non-load-bearing self-citation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method rests on two explicit statistical assumptions about gradient distributions, a first-order Taylor approximation of training influence, and a loss-symmetry assumption introduced specifically to make the over-refusal derivation work. The main free hyperparameters TC and tau are selected using the same MMLU split that is later reported as the in-domain test set.

free parameters (3)
  • Correctness threshold TC = 0.5
    Threshold used to split samples into ik and idk; chosen after sensitivity runs on MMLU (Table 11), where TC=0.3 gives the best THS, so the selected value is not the optimum of that sweep.
  • Temperature tau = 0.05
    Temperature in the softmax over Stable Influence weights; sensitivity on MMLU (Table 10) shows tau=0.01 gives slightly higher THS, so 0.05 is a hand-picked value evaluated on the reported in-domain test set.
  • Dataset subset sizes Nik and Nidk = exact values not reported
    The algorithm takes Nik and Nidk as inputs, and the text says a 1:4 ik:idk ratio is used with 5000 training samples, but exact counts and the method for subsampling the original datasets are not reported.
assumptions (4)
  • domain assumption Train and test ik/idk distributions are identically distributed (Assumption 1, Section 4).
    Needed for the expectation identities in O1 and O2 to transfer from the constructed dataset to the test set; unverified beyond dataset splits.
  • domain assumption The mean gradient of idk is orthogonal to the mean gradient of ik (Assumption 2, Equation 3).
    Verified empirically for Llama2-7B-Chat on MMLU only (Appendix A.3); if it fails on other models or tasks, the O1 proof step that drops the ik-gradient term breaks.
  • domain assumption Loss change is approximated by a first-order Taylor expansion with a single SGD step (Definition 2, Equation 1).
    Actual training uses LoRA, batches, and multiple epochs; higher-order and trajectory effects are discarded with O(eta squared) terms.
  • ad hoc to paper For ik inputs, Delta L(xik; yik) approximately equals -Delta L(xik; yidk) under correct versus refusal labels (Appendix A.1.2).
    Invoked to convert the over-refusal loss into a gradient inner product; not generally true for cross-entropy loss, and no empirical check is provided.

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Cite this review

Pith. "Pith review of GRAIT: Gradient-Driven Refusal-Aware Instruction Tuning for Effective Hallucination Mitigation." pith.science (2026). https://pith.science/paper/TBEAAFIA

@misc{pith2026250205911,
  author       = {Pith},
  title        = {Pith review of: GRAIT: Gradient-Driven Refusal-Aware Instruction Tuning for Effective Hallucination Mitigation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TBEAAFIA}},
  note         = {Machine review of arXiv:2502.05911}
}
read the original abstract

Refusal-Aware Instruction Tuning (RAIT) aims to enhance Large Language Models (LLMs) by improving their ability to refuse responses to questions beyond their knowledge, thereby reducing hallucinations and improving reliability. Effective RAIT must address two key challenges: firstly, effectively reject unknown questions to minimize hallucinations; secondly, avoid over-refusal to ensure questions that can be correctly answered are not rejected, thereby maintain the helpfulness of LLM outputs. In this paper, we address the two challenges by deriving insightful observations from the gradient-based perspective, and proposing the Gradient-driven Refusal Aware Instruction Tuning Framework GRAIT: (1) employs gradient-driven sample selection to effectively minimize hallucinations and (2) introduces an adaptive weighting mechanism during fine-tuning to reduce the risk of over-refusal, achieving the balance between accurate refusals and maintaining useful responses. Experimental evaluations on open-ended and multiple-choice question answering tasks demonstrate that GRAIT significantly outperforms existing RAIT methods in the overall performance. The source code and data will be available at https://github.com/opendatalab/GRAIT .

Figures

Figures reproduced from arXiv: 2502.05911 by the authors.

Figure 1
Figure 1. Descriptions of C1 & C2. After RAIT, the initial LLM model will largely reject unknown questions to avoid errors. However, the overly conservative nature of RAIT also led to a decrease in accuracy. 2024; Kang et al., 2024), which ultimately limits the reliability and usefulness of LLMs. Ideally, the responsible LLM should decline to answer questions beyond its knowledge to mini￾mize hallucinations (Wen et al.; Li et… view at source ↗
Figure 2
Figure 2. Case of mitigating hallucination and avoiding [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Overview of our framework. GRAIT contains three stages: (1) Constructing datasets Dik and Didk by querying the internal state of LLMs. (2) Distilling the datasets to select idk samples based on the first observation O1. (3) Performing Influence-directed Refusal-aware Instruction Tuning using the second observation O2. (4) and define Refusal Influence of each training sample on the model’s loss as: I ref(x) = D ∇L(x;… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Illustration of Truthful Helpfulness Score. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Relationship between I ref and I over in MMLU performance on LLaMA2-7B-Chat and LLaMA3-8B￾Instruct. Influence helps reduce over-refusal while maintain￾ing a stable hallucination rate, effectively address￾ing the challenges posed by C2. In addition, we conducted sensiti…
Figure 6
Figure 6. Figure 6: The overview of our proposed GRAIT. • Clear answers: Existing chat LLMs often have a certain level of self-awareness and may choose not to answer or give vague responses like “I’m not sure” or “for reference only” when facing uncertain questions. However, we expect the…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.